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Analysis of Raman and thermal effects in kilowatt fiber lasers
Optics Communications 242 (2004) 487–502 www.elsevier.com/locate/optcom
Analysis of Raman and thermal effects in kilowatt fiber lasers Yong Wang a
a,*
, Chang-Qing Xu a, Hong Po
b
Department of Engineering Physics, McMaster University, 1280 Main Street, JHE-A317, Hamilton, ON, Canada L8S 4L7 b Lasersharp Corporation, 86 South Street, Hopkinton, MA 01748, USA Received 16 April 2004; received in revised form 1 September 2004; accepted 2 September 2004
Abstract A theoretical analysis of Raman and thermal effects in kilowatt ytterbium-doped double-clad (YDDC) fiber lasers is presented. Solutions to suppress these detrimental effects in the YDDC fiber lasers under bidirectional end pump and distributed pump are discussed. The quantitative analysis shows that the Raman effects can be suppressed by using large-mode-area fibers, shortening the cavity length, adopting a longer lasing wavelength, and reducing reflections at the Raman–Stokes wavelengths; and the thermal effects can be effectively eliminated by utilizing the distributed pump and optimizing the arrangement of pump powers, pump absorption coefficients, and fiber lengths. 2004 Elsevier B.V. All rights reserved. Keywords: Thermal effects; Stimulated Raman scattering; Fiber lasers; Ytterbium; Double clad
1. Introduction Rare-earth-doped single-transverse-mode fiber lasers pumped by low-cost laser diodes have attracted considerable attention recently in commercial and military applications due to their high brightness, eminent efficiency, good compactness, excellent beam quality, efficient heat dissipation, etc., compared to traditional gas and solid-state la-
*
Corresponding author. Tel.: +1 905 5259140; fax: +1 905 5298406. E-mail address: [email protected] (Y. Wang).
sers [1–4]. With the availability of high-power laser diode bars and clad-pumping techniques, the output power of double-clad fiber lasers is able to reach hundreds of watts even a kilowatt in continuous-wave (CW) regime [4–11]. In particular, a ytterbium (Yb)-doped single-mode fiber laser with an output power of 400 W and M2 < 1.05 [7], a Yb and neodymium (Nd) codoped fiber laser with an output power of 500 W and M2 < 1.5 [8], a Ybdoped large-core fiber laser with an output power of 610 W and M2 = 2.7 [9], a 1-kW Yb-doped fiber laser with M2 = 3.4 [10], and a 1.3-kW Yb-doped fiber laser with M2 < 3 [11] have been reported recently. The Raman and thermal effects are known
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.09.008
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as major restrictions to laser performance in a kilowatt power domain [2,4,12–15]. The stimulated Raman scattering (SRS) in fibers can convert part of the signal into the undesirable Raman–Stokes waves at longer wavelengths [16], and hence degrades the laser efficiency. The Raman effects caused by the SRS take place mainly in those long-cavity fiber lasers with small-core fibers. The critical signal power to reach a threshold of stimulated Brillouin scattering (SBS), as defined in [16], is about 3 kW for a double-clad fiber with a 20-lm core, a 100-m length, and a 1-nm signal bandwidth. Since this SBS threshold is much higher than the power to reach an SRS threshold as shown in this paper, we can neglect the SBS effects. The pump-induced heating can cause a number of serious problems [2,4], such as formation of thermal cracks due to internal thermal stress and expansion, shortening of fiber lifetime due to damage of fiber coatings, even melting of the glass, degradation of laser beam quality due to thermal lensing, deterioration of optical coupling efficiency due to undesirable temperature-induced motion of mechanical parts, and decrease of laser quantum efficiency. Generally speaking, the SRS can be effectively suppressed by increasing the fiber core area and shortening the fiber length, and the dissipated heat can be greatly diminished by reducing the dopant concentration (or pump absorption coefficient) together with properly lengthening the fiber. Therefore, the design of a kilowatt fiber laser is based on the following two steps. The first step is to remove the harmful Raman effects by selecting suitable double-clad fibers and cavity parameters. The other is to lower the thermal effects by controlling the operating temperature of the lasers. Of course, once an appropriate operating temperature distribution is established in the fiber, other issues like thermal-optic effects, mechanical stability, system reliability, etc., are easily solved. During the above two steps, the laser conversion efficiency must be considered. Air cooling is a good candidate for many applications because of compact structures and moderate dissipating efficiency, hence is adopted in our modeling. In this paper, by solving a set of laser rate equations in combination with the SRS, the threshold
conditions for the detrimental Raman effects are obtained under different fiber conditions. Some solutions to facilitate heat dissipation in CW kilowatt Yb-doped double-clad (YDDC) fiber lasers were proposed previously [14,15]. However, only a brief description rather than a systematic analysis was given in the previous Letter [15]. Here, we detail the related analysis on both the Raman and thermal effects, and illustrate the selection of parameters and optimization procedures. The theoretical model and simulation results are important to the design and development of kilowatt fiber lasers. The contents of this paper are arranged as follows. In Section 2, a conventional end-pumped laser scheme as well as the distributed schemes is introduced, and the related theories, including the laser rate equations in combination with the SRS and the thermal conduction equations under air cooling, are also given. To find out some critical fiber and cavity parameters, the end-pumped scheme is first analyzed in Section 5.1, regardless of the Raman and thermal effects. In Section 5.2, the SRS and its influence on the lasers are studied. Temperature distributions in fibers are then obtained for different laser schemes in Section 5.3. To reduce the operating temperature, these schemes are compared, and the related optimization procedures are described.
2. Laser configurations and theoretical modeling The configuration of a typical YDDC fiber laser under CW end pump (PpF and PpB) is schematically shown in Fig. 1(a) (namely scheme A). The YDDC fiber has a length of L and a uniform dopant concentration in the fiber core. In practice, one cannot have such a YDDC fiber straight over its length like what is shown in Fig. 1(a). However, based on a mode filtering technique [17,18], this YDDC fiber can be appropriately coiled to realize a single-mode operation without a significant bending loss. The laser has a highreflectivity (HR) mirror at z = 0 and an output coupler (OC) at z = L. This HR mirror, which can be either a dichroic mirror or a fiber grating, has a peak reflectivity of 99% at the wavelength
Y. Wang et al. / Optics Communications 242 (2004) 487–502 HR
L, N PpB
PpF
(a) z = 0 HR
(b)
(c)
z
L1, N1
z=L
Lj, Nj
L1, N
PpF1
PpB1, PpF2
LJ, ΝJ
OC
PpB
PpF
HR
OC
Lj, N
PpBj-1, PpFj
PpBj, PpFj+1
LJ, Ν OC PpBJ-1, PpFJ
PpBJ
Fig. 1. Schematic configurations of YDDC fiber laser under (a) end pump and a uniform dopant concentration, (b) end pump and nonuniform dopant concentrations, (c) distributed pump and a uniform dopant concentration.
ks. The OC can be either a cleaved fiber facet or a fiber grating. In order to compare the laser performance easily under different dopant concentrations (N) and fiber core diameters (Dc), we assume in this paper that these YDDC fibers have fixed inner and outer cladding diameters of 250 lm (2r2) and 400 lm (2r3). The proposed laser schemes with nonuniform dopant concentrations (namely scheme B) and distributed pump (namely scheme C), as shown in Figs. 1(b) and 1(c), respectively, are discussed in the following section. The steady-state rate equations to describe the pump, signal and Stokes waves in these CW lasers are given by N ¼ N 1 þ N 2;
ð1Þ
N2 Cp kp ¼ ra ðkp ÞN 1 re ðkp ÞN 2 ðP þ p þ Pp Þ s hcA Cs ks ½ra ðks ÞN 1 re ðks ÞN 2 ðP þ þ s þ Ps Þ hcA CR kR ½ra ðkR ÞN 1 re ðkR ÞN 2 ðP þ þ R þ P R Þ; hcA ð2Þ dP p ¼ Cp ra ðkp ÞN 1 re ðkp ÞN 2 P p aðkp ÞP p ; dz ð3Þ
dP s ¼ Cs ½re ðks ÞN 2 ra ðks ÞN 1 P s dz 2 hc aðks ÞP s 2re ðks ÞN 2 3 Dks ks kR g R þ ðP þ P R ÞP s ; ks Aeff R dP R ¼ CR ½re ðkR ÞN 2 ra ðkR ÞN 1 P R dz 2 hc aðkR ÞP R 2re ðkR ÞN 2 3 DkR kR gR þ ðP þ P s ÞP R ; Aeff s
489
ð4Þ
ð5Þ
where P p is the pump power, P s is the signal power, and P R is the first-order Raman–Stokes power (± correspond to forward and backward propagations, respectively). Since the threshold conditions of the first-order Stokes wave are concerned in this work, the higher-order Stokes waves together with the spontaneous Raman scattering can hence be neglected. N is the Yb ion concentration, N1 and N2 are the population densities of the ground and upper levels, respectively. ra and re are the absorption and emission cross-sections of Yb ions, respectively [3]. The pump wavelength kp is 915 nm, which is selected with respect to a relative high and flat absorption peak of Yb-doped silica fibers around 915 nm [3,4]. Although the absorption cross-section at 976 nm is nearly three times as high as that at 915 nm and the laser quantum efficiency is also higher, a narrow absorption bandwidth (5-nm FWHM) renders wavelength-unlocked pump diodes unusable in practice. A typical signal wavelength (ks) is 1065 nm, and the Stokes wavelength (kR) is correspondingly 1117 nm, based on a 440 cm1 frequency shift in germanosilicate fibers. The second term in the right-hand side of Eqs. (3)–(5) represents the transmission loss, and a(k) is the fiber attenuation coefficient. The third term in the right-hand side of Eqs. (4) and (5) corresponds to the spontaneous emission, where the signal and Stokes bandwidths (Dks and DkR) are 2 and 5 nm, and the out-of-signal-band amplified-spontaneous-emission (ASE) power is neglected. c is the light velocity in the vacuum, h is the PlanckÕs constant, s is the
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spontaneous lifetime (1.3 ms), and A is the doped area of the YDDC fiber. Aeff is the effective core area associated with the signal and Stokes waves, and calculated through the method described in [19] with a fiber numerical aperture of 0.1. Cp(Cs, CR) is the overlapping factor between the pump (signal, Stokes wave) and the doped area, and easily calculated with assumptions of Gaussian distributions for the signal and Stokes waves in the core and a uniform distribution for the pump in the inner cladding. Therefore, the radial intensities of the pump, signal and Stokes waves can be obtained when the longitudinal power distributions are solved from the above Eqs. (1)–(5). Furthermore, we take gR = 0.92 · 1013 m/W for the interaction between the 1065-nm signal and the 1117-nm Stokes wave. For other wavelengths, gR can be obtained by using the inverse dependence of gR on wavelength [16]. For the laser configuration in Fig. 1(a), twopoint boundary conditions associated with the above ordinary differential equations are given by Pþ p ð0Þ ¼ g1 P pF þ RHR ðkp Þ P p ð0Þ; þ P p ðLÞ ¼ g1 P pB þ ROC ðkp Þ P p ðLÞ; Pþ s ð0Þ ¼ RHR ðks Þ P s ð0Þ; þ P s ðLÞ ¼ ROC ðks Þ P s ðLÞ; Pþ R ð0Þ ¼ RHR ðkR Þ P R ð0Þ; þ P R ðLÞ ¼ ROC ðkR Þ P R ðLÞ;
ð6Þ
where g1 is the pump coupling efficiency, and RHR is the equivalent reflectivity of the HR mirror, which may be different at the pump, signal and Stokes wavelengths. ROC is the OC reflectivity and assumed to be the same for the pump, signal and Stokes waves for a cleaved fiber facet, and wavelength-dependent for a fiber grating. We take g1 = 0.90, RHR(ks) = 0.99, RHR(kp) = 0 and ROC (ks) = ROC(kp) = 0.035 in the following simulations. RHR(kR) and ROC(kR) are discussed in the next section. When this boundary-value problem is solved [20], the output signal and Stokes powers are given by P out ¼ ½1 ROC ðks Þ P þ s s ðLÞ;
ð7Þ
þ P out R ¼ ½1 ROC ðkR Þ P R ðLÞ:
ð8Þ
A simple air-cooling model [2] is considered to facilitate the heat dissipation in this laser. The heat dissipation as well as transverse and longitudinal temperature distributions in the fiber under air cooling is governed by the following thermal conduction equations in symmetric cylindrical coordinates (r, z) [2,15]: 1 o oT ðr; zÞ o2 T ðr; zÞ qðr; zÞ r ¼ ; ð9Þ þ r or or oz2 jF oT ðr; zÞ H ¼ ½T h T ðr ¼ a3 ; zÞ; ð10Þ or r¼a3 jF H ¼ 0:5Nu jA a1 3 ;
ð11Þ
Nu expð2=NuÞ ¼ 0:16ðGr PrÞ1=3 ;
ð12Þ
2 Gr ¼ 8g d 2A a33 ½T ðr ¼ a3 ; zÞT 1 h 1lA ;
ð13Þ
where T is the temperature in the fiber, and Th is the heat sink temperature. q(r, z) is the heat dissipated in unit volume, which can be calculated by considering all input and output lights into and out of a unit volume at (r, z) in the fiber. Since most of the pump power is absorbed in the fiber core, the maximum temperature is hence expected to occur at the fiber axis. jF is the fiber thermal conductivity, and H is the convective coefficient. Nu, Gr and Pr are the Nusselt, Grashof and Prandtl numbers [2], respectively. dA, lA and jA are the density, viscosity and thermal conductivity of air. The air convection is controlled to keep the heat sink temperature constant (300 K). Furthermore, the following parameters are used: g = 9.8 m/s2, Pr = 0.71, dA = 1.2 kg/m3, lA = 1.85 · 105 kg m1 s1, jF = 1.38 W m1 K1, jA = 0.026 W m1 K1.
3. General consideration The critical parameters of the fiber laser shown in Fig. 1(a) comprise fiber core diameter (Dc), dopant concentration (N) and fiber length (L). Of course, large-mode-area (LMA) fibers should be used in these high-power fiber lasers to effectively suppress detrimental nonlinear effects. Three typi-
Y. Wang et al. / Optics Communications 242 (2004) 487–502
cal core diameters of 10, 20 and 30 lm are first considered in this section, which are based on the commercial double-clad fibers. To analyze the laser shown in Fig. 1(a), we first neglect the Raman and thermal effects. This can be done by setting P R ¼ 0 and solving Eqs. (1)–(4). Under given pump conditions, the optimal fiber length Lopt corresponding to a maximal output signal power, is relative to fiber core diameter (Dc) and dopant concentration (N). Generally speaking, the pump absorption coefficient of a YDDC fiber exhibits some longitudinal dependence although the distribution of N is uniform in the fiber core. In order to compare laser performance under different core diameters and concentrations, we define an average pump absorption coefficient, in dB/m for a bi-directionally pumped YDDC fiber with a length of l, as " # Pþ P 1 p ð0Þ p ðlÞ ap ¼ log10 þ þ log10 10: ð14Þ 2l P p ðlÞ P p ð0Þ For core diameters of 10, 20 and 30 lm, the optimal fiber length Lopt for the above scheme is shown as a function of ap in Fig. 2(a). The output signal power under equal pump powers of 500 W 80 1 m / Div
Lopt (m)
60 40 20
0.05 dB/m / Div
(a) 0
2 W / Div
700
Ps
out
(W)
750
650
600
(b) 0.0
0.05 dB/m / Div
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m)
Fig. 2. (a) Optimal fiber length versus pump absorption coefficient, (b) laser output power at the optimal fiber length. The insets detail the difference among three fiber core diameters of 10 (solid), 20 (dashed) and 30 lm (dotted) around ap = 1.0 dB/m.
491
at both fiber ends is depicted in Fig. 2(b). The insets show the detailed difference among three core diameters around ap = 1.0 dB/m, from which we can see that both Lopt and P out are nearly indes pendent of Dc. It is also found that Lopt is nearly independent of pump power in the range of 500– 3000 W. Therefore, it is implied that ap is a robust parameter to describe the YDDC fibers. One can see in Fig. 2 that in the absence of the Raman and thermal effects the laser has better conversion efficiency at a higher ap and a shorter Lopt. In particular, with ap = 1.0 dB/m, the optimal fiber length is 20 m, and the output power is 725 W. And with ap = 0.25 dB/m, the optimal fiber length is 60 m, and the output power is 630 W. However, no apparent improvement of efficiency occurs for ap > 1.5 dB/m; meanwhile, if ap is too high, the laser may suffer other serious problems, such as the ion quenching [4] and thermal effects as described in Section 5.
4. Raman effects From Fig. 2, we know that in the absence of the Raman and thermal effects, the laser performance depends on the pump absorption coefficient and fiber length. However, when the SRS is taken into account, the optimization turns to a different scenario. To find out the Raman threshold conditions, in this section we first neglect the thermal effects, and assume that the laser can work normally under any pump power. Two fiber core diameters of 20 and 30 lm are compared in this section, and a 10-lm core is unsuitable for kilowatt fiber lasers. The ion concentrations are adjusted to meet the required pump absorption coefficient for different core diameters. For two typical ap of 0.25 and 1.0 dB/m, the fiber lengths of 60 and 20 m are selected with respect to the optimal fiber lengths shown in Fig. 2. The effective reflectivities of the HR mirror and OC at the Stokes wavelength are related to a practical system. We first assume that both RHR(kR) and ROC(kR) are equal to 3.5%. With these assumptions, the laser output powers under different fiber conditions are depicted in Fig. 3. The left and right columns correspond to L = 20 and 60 m (ap = 1.0
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Y. Wang et al. / Optics Communications 242 (2004) 487–502 800 (a) Dc= 20 µm, L = 20 m
Power (W)
600
400
400
1 300 2 3 200
200
100
(b) Dc= 20 µm, L = 60 m
1 2 3
4 4 0 800 0 100 200 300 400 1200 (d) 2400 (c) Dc= 30 µm, L = 20 m Dc= 30 µm, L = 60 m 0
0
200
400
600
1 900 2 3 600
Power (W)
1800
1200
1 2 3
300
600
0
4 0
600
1200
1800
Pump Power (W)
2400
4 0
0
300
600
900
1200
Pump Power (W)
Fig. 3. Signal and Stokes powers for RHR(kR) = ROC(kR) = 3.5% and for different fiber core diameters and lengths. 1: Ideal signal power without consideration of SRS, 2: total output power, 3: signal power and 4: Stokes power.
and 0.25 dB/m), while two rows refer to different core diameters. In each figure, there are four curves. Curve 1 (solid) is the ideal output power without consideration of the SRS; curve 2 (dashed) out is the total output power, i.e., P out s þ P R ; curve 3 out (dotted) is the output signal power P s ; curve 4 (dash-dotted) is the output Stokes power P out R . In each figure, curve 2 is lower than curve 1 in the presence of the SRS, which results from two aspects. On the one hand, part of optical power turns into heat in the fiber when the signal is converted to the Stokes wave; on the other hand, most of the backward Stokes power leaves the fiber at z = 0, which is approximately equal to the forward output power P out due to RHR(kR) = ROC(kR). R Then it is absorbed in some optical components, and converted into heat finally. From the trends of curves 3 and 4, one can see that in the presence of the SRS, P out drops with an increase of pump s power. As expected, the Stokes power can be reduced effectively in a YDDC fiber with either a larger core diameter or a shorter fiber length. The threshold pump powers for the generation of SRS (denoted by P th p ) and the corresponding sig-
nal powers (namely critical signal power and denoted by P cr s ) under different core diameters and fiber lengths are detailed in Table 1. We can see 2 that P cr s obeys neither a Dc dependence on fiber core diameter nor a proportional dependence on fiber length in this case, which can be understood by considering that both the laser stimulated transitions of Yb ions and the SRS in fibers have significant contributions to P out R . Near the SRS threshold, the slope efficiency of the output Stokes power with respect to the total pump power is only dependent on fiber length, and nearly independent of core diameter. It is 42% for a 20-m long fiber, and 39% for a 60-m long fiber. Moreover, only under Dc = 30 lm and L < 30 m, can the laser ideally have a clean signal power of more than 1000 W. To avoid the detrimental Raman effects, the pump power should not exceed P th p hence the maximum output signal power is P cr . s When both RHR(kR) and ROC(kR) can be reduced by using narrow-band mirrors, such as fiber gratings, the Stokes power is expected to be suppressed. The calculated threshold powers for RHR(kR) = ROC(kR) = 0.1%, also given in Table
Y. Wang et al. / Optics Communications 242 (2004) 487–502
493
Table 1 cr Threshold pump power ðP th p Þ and critical signal power ðP s Þ at ks = 1065 nm and under different reflectivities [RHR(kR) and ROC (kR)], fiber core diameters (Dc), and fiber lengths (L) RHR(kR), ROC(kR)
Power (W)
Dc = 20 lm L = 20 m
Dc = 30 lm L = 60 m
L = 20 m
L = 60 m
3.5%
P th p P cr s
686.3 497.0
321.1 201.8
2079.0 1509.2
865.4 546.6
0.1%
P th p P cr s
2211.4 1603.6
899.2 566.6
5510.1 4002.3
2164.0 1368.6
1, are at least two and a half times as high as the corresponding powers for RHR(kR) = ROC(kR) = 3.5%. The Stokes slope efficiency is correspondingly 40% for a 20-m long fiber, and 38% for a 60-m long fiber. Compared to the previous case with RHR(kR) = ROC(kR) = 3.5%, the ranges of the fiber parameters required to generate a desired clean signal power are advantageously enlarged. For instance, a clean signal power of more than 1000 W can be generated under Dc = 30 lm and L > 60 m, as well as Dc = 20 lm and L < 30 m. It is worth nothing that in this case P cr s approximately obeys a D2c dependence on core diameter and a proportional dependence on fiber length. This is because with an increase of signal power, the contribution from the Raman gain is enlarged by a few times, compared to the contribution from the stimulated transitions of Yb ions. From Eq. (5), we know that the Stokes wave at the wavelength kR is also amplified by the stimulated transition of Yb ions like the signal at ks. To suppress this gain, it is reasonable to consider shifting ks to a longer wavelength, and consequently kR is located in a lower-gain range of Yb-doped fibers. When taking ks = 1085 nm, we
have kR = 1140 nm. Both the emission and absorption cross-sections of Yb ions, as given in [3], drop by 50% when kR shifts from 1117 to 1140 nm. By following the same procedure as that for ks = 1065 nm, the threshold pump power ðP th p Þ and critical signal power (Pscr) are calculated and given in Table 2 under two reflectivities of 3.5% and 0.1%. As 2 expected, P cr s apparently obeys a Dc dependence on core diameter and a proportional dependence on fiber length. We can see from Tables 1 and 2 that when ks shifts from 1065 to 1085 nm, the increases th in P cr s and P p are more significant for a smaller core diameter, a shorter fiber length, and a higher reflectivity. For example, P cr s increases by 70% for Dc = 20 lm, L = 20 m, and RHR(kR) = ROC(kR) = 3.5%, and by 10% for Dc = 30 lm, L = 60 m, and RHR(kR) = ROC(kR) = 0.1%, respectively. Though the SRS effects can be further suppressed with a further increase of ks, the reduction of laser quantum efficiency and the increase of the incurred heat should be taken into account. This is discussed in the next section. With these quantitative results above, one can estimate the practical Raman thresholds ðP cr s Þ in the previous experiments by properly scaling the
Table 2 cr Threshold pump power ðP th p Þ and critical signal power ðP s Þ at ks = 1085 nm and under different reflectivities [RHR(kR) and ROC(kR)], fiber core diameters (Dc), and fiber lengths (L) RHR(kR), ROC(kR)
Power (W)
Dc = 20 lm L = 20 m
Dc = 30 lm L = 60 m
L = 20 m
L = 60 m
3.5%
P th p P cr s
1214.5 863.9
477.8 295.4
2756.8 1963.8
1080.9 670.1
0.1%
P th p P cr s
2769.7 1971.2
1067.0 660.4
6256.5 4458.2
2405.6 1492.8
Y. Wang et al. / Optics Communications 242 (2004) 487–502
discussion, with appropriate selection of two reflectors, and under a 1000-W pump and a 30lm core, the SRS effects are assumed to be suppressed completely. 5.1. Scheme A First, we consider the end-pumped scheme (scheme A) with equal pump powers of 500 W at the both ends. Fig. 4(a) shows the calculated temperature distributions at the fiber axis (r = 0) and the inner/outer claddings boundary (r = 125 lm). The selection of L = 20 m is based on the optimal fiber length for ap = 1.0 dB/m, as shown in Fig. 2(a). It can be seen that the temperature distribution is apparently uneven along the fiber, and the temperature difference in the radial direction is smaller than that in the axial direction. A maximum temperature of 340 C is reached at the fiber output side, while a minimum one of 94 C is located near the mid span of the cavity. Therefore, for such an end-pumped scheme, more care must be taken in practice to prevent thermal damage at both fiber ends than that in the middle [4]. Fig. 4(b) shows the pump and signal power
400
Temperature (˚C)
fiber parameters. For example in [6], for a singlemode fiber laser resonator with given parameters Dc = 9 lm, L = 60 m, ks = 1086 nm, RHR e ðks Þ ¼ HR 99:9%, ROC ðk Þ ¼ 5%, we take R s e e ðkR Þ ¼ ROC ðk Þ ¼ 0:1% for the laser cavity composed of R e two fiber Bragg gratings. Simply read from Table 2, the critical signal power is 660.4 W for Dc = 20 lm, L = 60 m, ks = 1085 nm, and Re(kR) = 0.1%. Taking D2c dependence in power scaling and neglecting a small difference in ks leads to P cr s ¼ 133:7 W. This is in good agreement with the measured one (135 W). One can conclude from the above results that when the pump power exceeds a certain threshold, the laser conversion efficiency starts to drop due to the presence of the bi-directional Stokes waves, which can cause detrimental effects in many applications. To suppress the SRS effects in kilowatt fiber lasers, an LMA fiber with at least a 20-lm core for a 20-m long cavity, and a 30-lm core for a 60m long cavity is indispensable; the shorter the fiber length, the lower the Stokes power, which is also consistent with the requirement of the laser conversion efficiency as discussed in the previous section. Selecting a longer lasing wavelength is proved to be able to suppress the SRS to some extent. However, it may cause a reduction of laser efficiency and an increase of heat dissipation. This tradeoff should be considered in the laser design. Under any conditions, the reflectivities RHR(kR) and ROC(kR) should be well suppressed, and wavelength-selective reflectors are obviously helpful. Since it may be difficult in practice to reduce these reflectivities to a level of lower than 0.1%, an alternative solution for relatively small core-diameter fibers is to use the so-called master oscillator and power amplifier (MOPA), where the reflections at the fiber ends of the power amplifier can be effectively removed.
(a)
300
r=0 r = 125 µm
200 100 0 800
Power (W)
494
(b)
600
Forward Pump Backward Pump Forward Signal Backward Signal
400 200
5. Thermal effects 0
To compare the laser efficiency and operating temperature among different schemes shown in Fig. 1, in this section we assume that the total pump power is 1000 W, and the YDDC fiber has a core diameter of 30 lm. Based on the previous
0
5
10
15
20
Position (m) Fig. 4. Temperature and power distributions in 20-m YDDC fiber under end pump and with uniform pump absorption coefficient of 1.0 dB/m.
Y. Wang et al. / Optics Communications 242 (2004) 487–502
T ave ¼
1 L
Z
L
T ðr ¼ 0; zÞdz:
ð15Þ
0
Based on the optimal fiber lengths shown in Fig. 2(a), Tmax and Tave versus ap are plotted in Fig. 5. We can see that both Tmax and Tave rise with an increase of ap, and the highest pump absorption coefficient can hence be restricted under a certain operating temperature. For example, when we reduce ap from 1.0 (Lopt = 20 m) to 0.25 dB/m (Lopt = 60 m), the maximum operating temperature drops from 340 to 137 C; whereas the laser output power drops from 725 to 630 W. Hence, lowering pump absorption together with lengthening the fiber to suppress the thermal effects is not a good solution to some extent. It is interesting to compare these analyses with the previous experimental results [10,11]. As reported in [10], with high pump absorption (1.5–3.0 dB/m) and a short cavity (8 m), the slope efficiency as high as 80% was obtained. However, the thermal effect seems to be a major factor to degrade the laser beam quality and system reliability. In contrast, when a
600
Tmax Tave
500
Temperature (oC)
distributions along the cavity. The laser output power is 725 W. One can see that the uneven temperature distribution results from nonuniform pump absorption in the fiber, and most of the heat is generated near the fiber ends due to the higher pump absorption. In general, the laser operation under this temperature (hundreds of degrees) is impractical. On the one hand, the strong thermal-optic effect can degrade the output beam quality; on the other hand, such a high operating temperature will severely deteriorate the system stability and reliability. In particular, for most commercial double-clad fibers, the fiber polymer coatings cannot bear such a high temperature in long-term applications. As a result, we can use a lower pump absorption coefficient and a longer fiber to reduce the operating temperature for this scheme. Since the highest temperature occurs at the fiber axis, we need to pay more attention to the temperature distribution along the fiber axis. We thus define Tmax as the maximum temperature, and Tave as the longitudinally averaged temperature along the fiber axis. The latter is given by
495
400 300 200 100 0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m)
Fig. 5. Maximum and average temperatures versus pump absorption coefficient.
50-m lower-absorption LMA fiber was adopted in [11], the thermal effect was eliminated, but the slope efficiency dropped to 65%. It has been shown in the previous section that an increase of ks can help suppress the SRS to some extent. Fig. 6 shows the output power and temperatures varying with ks for typical 20- and 60-m fiber lengths. Since the maximum gain is located in the range 1030–1040 nm under the current pump and fiber conditions, a wavelength shift toward the longer wavelength side can lead to a lower output power, and increases in Tmax and Tave. For example, when ks shifts from 1065 to 1085 nm, the output signal power drops by 14 and 11 W for 20- and 60-m cavities, and Tmax increases by about 6 C for both 20- and 60-m lengths. For these two lengths, the variation slope of output power is 0.7 and 0.55 W/nm, while the corresponding temperature variation slope is 0.3 and 0.35 C/nm. Of course, for some fiber lasers approaching the Raman threshold conditions, selecting a longer lasing wavelength is favorable if the power decrease and the temperature increase are acceptable. Fiber attenuation coefficients at the pump and signal waves, including the background and bending losses, are important to the laser performance. For the commercial YDDC fibers, the background loss is usually less than 10 dB/km. The bending loss is dependent on the YDDC fiber structure
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Y. Wang et al. / Optics Communications 242 (2004) 487–502
Power (W)
730
(a)
L = 20 m
640
out
Ps
720
630
710
620
700
610
Temperature (˚C)
350
300
(c)
150
Tmax
(b) T and T max ave
(d)
L = 60 m out
Ps
Tmax and Tave Tmax
125 250 100 200
150 1060
Tave
Tave 1070
1080
1090
Wavelength (nm)
75 1060
1070
1080
1090
Wavelength (nm)
Fig. 6. Output power, maximum and average temperatures versus signal wavelength for fiber lengths of 20 and 60 m.
and the diameter of the spool, onto which the fiber is coiled. A theoretical analysis on bending losses was detailed in [21]. Due to a high numerical aperture (NA) for the pump light in the inner cladding, its bending loss is less sensitive to the bending curvature than that of the signal. For pump absorption coefficients of 0.25 and 1.0 dB/m, the optimal fiber length, the corresponding output power and temperatures versus fiber attenuation coefficients are shown in Fig. 7, where the solid and dashed lines refer to pump losses of 13 and 26 dB/km, respectively. We can see that with an increase in fiber loss, both the optimal fiber length and the output power decrease, and the fiber temperature increases. Due to a longer fiber length, the influence of the signal attenuation on the laser is more severe for a lower ap than a higher ap. For example, when a(ks) increases from 10 to 100 dB/ km, for ap = 0.25 and 1.0 dB/m, the output signal power drops by 38% and 18%, the optimal fiber length is shortened by 32 and 8 m, and the maximum temperature increases by 156 and 100 C, respectively. Due to a significant increase in temperature and a considerable decrease in laser efficiency, the bending losses must be greatly suppressed.
5.2. Scheme B One can see in scheme A that on the one hand, most of the pump power is absorbed near the two fiber ends, which causes a lot of heat; on the other hand, the adoption of a relatively low ap for the whole fiber deteriorates the laser efficiency. Therefore for an end-pumped scheme, an uneven distribution of ap, e.g., a lower ap arranged near the pump launching points, as shown in Fig. 1(b) (scheme B), is expected to compromise heat dissipation and laser efficiency. The calculated results for a five-segment scheme are depicted in Fig. 8, where pump absorption coefficients of 0.33, 0.57, 0.81, 0.38, 0.24 dB/m and fiber lengths of 6.0, 2.7, 15.0, 6.8, 5.5 m are arranged for segments 1, 2, 3, 4 and 5, respectively, and the total fiber length is 36 m. These pump absorption coefficients and fiber lengths are obtained with respect to the following two criteria: (1) The maximum temperature in each fiber segment is the same. (2) A higher pump absorption coefficient and a shorter fiber length are preferred for each segment. Meanwhile, it is assumed that these fiber segments are well spliced together, with a typical splicing loss of 0.05 dB for both the signal and the pump.
Y. Wang et al. / Optics Communications 242 (2004) 487–502 80
Lopt (m)
(a)
(W) out
Ps
o
25
(d)
α(λp) = 13 dB/km α (λp) = 26 dB/km
60
15
20
10 750
(b)
600
700
500
650
400
600
300
550
(c)
300
αp= 1.0 dB/m (αp) = 13 dB/km (αp) = 26 dB/km
20
40
700
Tmax & Tave ( C)
αp= 0.25 dB/m
(e)
Tmax
(f)
400
Tmax
497
300
200
Tave
Tave
200
100 0
20
40
60
80
100
100
0
20
40
60
80
100
α (λ s) (dB/km)
α (λ s) (dB/km)
Fig. 7. Optimal fiber length, output power, maximum and average temperatures versus fiber attenuation coefficients for pump absorption coefficients of 0.25 and 1.0 dB/m.
It is shown in Fig. 8 that the fiber temperature ranges between 84 and 137 C, and the output power is 665 W. Compared to scheme A with
Temperature (oC)
150
(a)
125 100 75
r=0 r = 125 µm
50
Power (W)
800
(b)
600
Forward Pump Backward Pump Forward Signal Backward Signal
400 200
ap = 0.25 dB/m and L = 60 m, the maximum temperature in the fiber is the same, whereas the output power increases by 35 W, and the fiber length is advantageously shortened by 24 m. Therefore, scheme B is better than scheme A. By following the similar procedure, more results under different Tmax are obtained and given in Table 3. In contrast to Tmax = 137 C (case 3, shown in Fig. 8), if Tmax = 179 C is allowed (case 1), the output power will increase 20 W. On the contrary, if Tmax < 100 C is required (case 5), the laser suffers a rather low output power (608 W). It is also found that further flattening the temperature distribution by using more segments can degrade the laser efficiency significantly, which is due to more splicing losses introduced into the cavity. 5.3. Scheme C
0 0
10
20
30
40
Position (m) Fig. 8. Temperature and power distributions in 36-m YDDC fiber under end pump and with nonuniform pump absorption coefficients in five segments.
To further reduce the fiber temperature and flatten its distribution, more uniform distribution of pump power is indispensable. Compared to the previous schemes A and B, a distributed
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Table 3 Calculated results with distributed ap in five segments No.
Tmax (C)
Tave (C)
L (m)
P out (W) s
1 2 3 4 5
179 157 137 117 99
140 122 113 100 86
26.6 32.0 36.0 45.0 63.5
685 675 665 646 608
pumping scheme (scheme C) shown in Fig. 1(c), can hence be the best solution, where the pump light is separately launched into a few fiber segments through the side-coupling techniques using prisms [22] or V-grooves [23]. This scheme can effectively reduce the requirements for high brightness of pump laser diodes in the end-pumped schemes. For the jth segment with a length of Lj, j = 1, . . . , J, PpFj and PpBj stand for forward and backward pump powers. The total fiber length is L. Multipoint boundary conditions associated with Eqs. (3)–(5) are considered for this case. In particular, the boundary conditions for the jth segment at z = zj and zj + 1 are given by þ Pþ pj ðzj Þ ¼ g2 P pFj þ g3 P pj1 ðzj Þ; P pj ðzjþ1 Þ ¼ g2 P pBj þ g3 P pjþ1 ðzjþ1 Þ;
ser efficiency. In principle, their optimal values can be searched out by calculating the laser efficient at each point of the meshed parameter space. Technically speaking, some relations among these parameters can be obtained prior to a complete search, which are helpful to facilitate the optimization process. We take g1 = g2 = 0.9, g4 = g5 = 1, a = 13 dB/km for all segments in the following simulations. Fig. 9 shows the output power, maximum and average temperatures varying with ap for different J. The pump powers are arranged to obtain the same local maximum temperature in each fiber segment. Unlike the previous end-pumped scheme, the total fiber length in this scheme is relatively long to ensure effective pump absorption. The pump transmission coefficient g3 is 0.9. The total fiber length L is 50 m, and equally divided into J segments. As expected, with either a decrease in ap or an increase in J, both the output power and fiber temperature decrease. An increase of J results in a more uniform temperature distribution in the fiber, whereas the laser suffers more pump losses. However, the decrease of P out is less signifs icant at a higher ap. This is because most of the pump power is absorbed in each fiber segment,
þ Pþ sj ðzj Þ ¼ g4 P sj1 ðzj Þ; P sj ðzjþ1 Þ ¼ g4 P sjþ1 ðzjþ1 Þ; o
Tmax ( C)
150 100 50
(a)
90 o
where and are the pump, signal and Stokes powers, respectively, in the jth segment (±correspond to forward and backward propagations, respectively). g2 is the side-pump coupling efficient, while g3, g4 and g5 are the pump, signal and Stokes transmission coefficients between neighboring two segments. The boundary conditions at the two fiber ends take Eqs. (6). Only a uniform pump absorption coefficient is considered, and the lengths of those side-coupling components are neglected. Based on a certain maximal operating temperature and a total pump power of 1000 W, the fiber parameters and pump powers, i.e., ap, J, Lj, PpFj, PpBj, j = 1, . . . , J, can be optimized for a highest la-
Tave ( C)
P Rj ðzÞ
80
J=5~9
70 60
(b)
J = 5, J = 7, J=9
J=6 J=8
J = 5, J = 7, J=9
J=6 J=8
700
(W)
P sj ðzÞ
ð16Þ
out
P pj ðzÞ;
J= 5 6 7 8 9
200
Ps
þ Pþ Rj ðzj Þ ¼ g5 P Rj1 ðzj Þ; P Rj ðzjþ1 Þ ¼ g5 P Rjþ1 ðzjþ1 Þ;
600
J=5~9
500 400 300
(c) 0.0
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m)
Fig. 9. Maximum and average temperatures, and output power versus pump absorption coefficient for different segment numbers.
Y. Wang et al. / Optics Communications 242 (2004) 487–502 5 m, 8 m,
(a)
6 m, 9 m,
7m 10 m
150
o
Tmax ( C)
200
100
Lj = 5 ~ 10 m
50
out
(W)
700 (b)
Ps
and the losses of the transmitted pump powers at those launching points are trivial. For ap = 1.2 dB/m, Tmax and P out versus J are detailed in Fig. s 10, where the impacts of two pump transmission coefficients (g3) of 0.8 and 0.9 are compared. We can see that the decrease of Tmax is not apparent after J exceeds 6; whereas, the degradation of P out is significant after J exceeds 8, especially for s a lower g3 Similar results are also obtained for other ap, which implies that J = 6 or 7 is optimal if Tmax = 100 C is required. Based on the above information, Tmax and P out s varying with ap under different fiber lengths are plotted in Figs. 11 and 12 for J = 6 and 7, respectively. These fiber segments have the same Lj and ap. g3 is equal to 0.9. We can see in Figs. 11 and 12 that for any ap, Tmax drops with an increase of Lj, but no apparent decrease is found when Lj > 10 m. Therefore, a longer Lj is better for ap < 1.0 dB/m, and a shorter Lj is better for ap > 1.5 dB/m. In the range 1.0–1.5 dB/m, the relations among these curves are complicated, which hence implies the existence of the optimal parameters. The fiber parameters can be selected according to the following procedure. Under a certain maximum temperature required by the compo-
499
Lj = 5 ~ 10 m Lj = 5 ~ 10 m
600 500
5 m, 8 m,
400
6 m, 9 m,
7m 10 m
300 0.0
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m)
Fig. 11. Maximum temperature and output power versus pump absorption coefficient with six fiber segments.
nents (usually about 85–150 C for most commercial double-clad fibers), the ranges of ap can be obtained in Figs. 11(a) and 12(a) for J = 6 and 7, respectively. For instance, when we take Tmax = 98 C, the maximum ap is 0.45 and 1.2 dB/m for Lj = 5 and 10 m from Fig. 11(a), and 0.7 and 1.45 dB/m
η3 = 0.9 η3 = 0.8
300
200
5 m, 8 m,
(a)
6 m, 9 m,
7m 10 m
Tmax ( C)
o
Tmax ( C)
400
150
o
200 100
(a)
100
Lj = 5 ~ 10 m
0 50
700
(b)
out
Ps
Ps
600
(W)
η3 = 0.9 η3 = 0.8
out
(W)
700
650
(b)
Lj = 5 ~ 10 m Lj = 5 ~ 10 m
600 500
5 m, 8 m,
400
550 0
2
4
6
8
10
12
J Fig. 10. Maximum temperature and output power versus the number of segments for different pump transmission coefficients of 0.8 and 0.9.
6 m, 9 m,
7m 10 m
300 0.0
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m) Fig. 12. Maximum temperature and output power versus pump absorption coefficient with seven fiber segments.
100
(a)
90 80
r=0 r = 125 µm
70 60 100
Power (W)
for Lj = 5 and 10 m from Fig. 12(a), respectively. Then in these ranges of ap, we can find out the maximum output power together with an optimal fiber length. In addition, it is found that appropriately lengthening the first and the last segments can reduce the incomplete pump absorption, hence improve the laser efficiency to some extent. With a maximal temperature of 98 C, the optimal solution with seven segments is given blow. The first and last segments are 10 m long, the others are identically 7 m long, and the total fiber length is 55 m. The pump absorption coefficient is 1.2 dB/m. The pump powers, totalling 1000 W, are 100, 85, 85, 75, 75, 70, 70, 65, 65, 61, 61, 61, 61, 66 W for segments 1, 2, 3, 4, 5, 6 and 7, respectively. The temperature and power distributions in the laser cavity are depicted in Fig. 13. We can see that the maximum and minimum temperatures at the fiber axis are 98 and 66 C, and the output power is 670 W. Compared to the previous results of scheme B, this scheme offers both better temperature uniformity and a higher output power. Moreover, under a maximum temperature of 128 C, an output power of more than 690 W can be obtained with ap = 2 dB/m and Lj = 6 m (j = 1– 7). It is hence concluded that an increase of J can reduce the pump power required for each segment, decrease the operating temperature in the fiber, and improve the uniformity of the axial temperature distribution. However, the output power is lower due to more pump transmission losses. Meanwhile, the laser suffers a higher manufacturing cost. As discussed in the previous section, the selection of a longer ks can suppress the Raman effects. For the laser configuration shown in Fig. 13, if ks shifts from 1065 to 1085 nm, the output power and the maximum temperature will be 659 W and 103 C, compared to 670 W and 98 C at ks = 1065 nm. This tradeoff as well as the requirements for system volume, component availability, operating conditions, etc., should be comprehensively considered in the practical design and optimization of kilowatt fiber lasers. It is worth noting that though water cooling is proved to be more efficient to dissipate heat than air cooling, it cannot be directly applied to the fiber surfaces. This is because water or moisture can degrade the performance and reliability of the com-
Temperature (oC)
Y. Wang et al. / Optics Communications 242 (2004) 487–502
Forward Backward
(b) Pump
80 60 40 20 0 800
Power (W)
500
(c) Signal 600 400
Forward Backward
200 0 0
10
20
30
40
50
60
Position (m) Fig. 13. Temperature and power distributions in 55-m YDDC fiber under distributed pump and with a uniform pump absorption coefficient of 1.2 dB/m.
mercial YDDC fibers. However, the YDDC fibers usually have to be packaged in some casing. To maintain a certain environmental temperature of the fiber, an external cooling for the fiber casing or heat sink is indispensable in kilowatt applications. Of course in this case, the water cooling is more efficient, while the air cooling is more compact.
6. Conclusion By solving laser rate equations in combination with thermal conduction equations, we have obtained the power and temperature distributions in the YDDC fibers, with which we can quantitatively analyze the Raman and thermal effects in different laser schemes. In the presence of the SRS, the laser efficiency decreases, and the considerable backward Stokes power may cause detrimental effects. To suppress the Raman effects in these kilowatt fiber lasers, an LMA fiber with at least a 20-lm core for a 20-m long cavity, and a
Y. Wang et al. / Optics Communications 242 (2004) 487–502
30-lm core for a 60-m long cavity is indispensable; the reflection at the Stokes wavelength in the laser cavity should be greatly eliminated; and selection of a longer lasing wavelength is also effective. From the viewpoint of output power, the traditional end-pumped scheme with a higher pump absorption coefficient and a shorter cavity length offers the best laser efficiency and is free of the detrimental Raman effects. However, the strong thermal effects can definitely deteriorate the beam quality and system reliability due to a high operating temperature, and render this scheme currently impractical for long-term applications. To lower fiber operating temperature for the end-pumped scheme, one can simply reduce pump absorption and lengthen the cavity. However, the laser suffers relatively low efficiency. As a better solution, the arrangement of uneven pump absorption coefficients along the cavity, e.g., smaller ones near the pump ends, can reduce fiber temperature and improve laser efficiency to some extent. The best solution is to adopt the distributed pumping scheme, with which the acceptable laser efficiency and temperature distribution can be achieved by optimizing the arrangement of pump powers, pump absorption coefficients, and fiber lengths. Acknowledgment The authors acknowledge support from the Ontario Photonics Consortium of Canada.
References [1] H. Po, J. Cao, B.M. Laliberte, R.A. Minns, R.F. Robinson, B.H. Rockney, R.R. Tricca, Y.H. Zhang, High power neodymium-doped single transverse mode fibre laser, Eletron. Lett. 29 (1993) 1500. [2] L. Zenteno, High-power double-clad fiber lasers, J. Lightwave Technol. 11 (1993) 1435. [3] H.M. Pask, R.J. Carman, D.C. Hanna, A.C. Tropper, C.J. Mackechnie, P.R. Barber, J.M. Dawes, Ytterbiumdoped silica fiber lasers: versatile sources for the 1–1.2 lm region, IEEE J. Select. Top. Quantum Electron. 1 (1995) 2. [4] M.J.F. Digonnet, Rare-earth-doped Fiber Lasers and Amplifiers, second ed., Marcel Dekker, New York, 2001.
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[5] L. Zenteno, Design of a device for pumping a double-clad fiber laser with a laser-diode bar, Appl. Opt. 33 (1994) 7282. [6] N.S. Platonov, D.V. Gapontsev, V.P. Gapontsev, V. Shumilin, 135 W CW fiber laser with perfect single mode output, in: Proc. of Conference on Lasers and ElectroOptics (CLEO) 2002, Long Beach, USA, 19–24 May 2002 (postdeadline paper CPDC3). [7] V.P. Gapontsev, N.S. Platonov, O. Shkurihin, I. Zaitsev, 400 W low-noise single-mode CW ytterbium fiber laser with an integrated fiber delivery, in: Proc. of the Conference on Lasers and Electro-Optics 2003, Baltimore, MD, USA, June 1–6, 2003 (postdeadline paper CThPDB9). [8] J. Limpert, A. Liem, H. Zellmer, A. Tu¨nnermann, 500 W continuous-wave fibre laser with excellent beam quality, Electron. Lett. 39 (2003) 645. [9] Y. Jeong, J.K. Sahu, S. Baek, C. Alegria, D.B.S. Soh, C. Codemard, J. Nilsson, Cladding-pumped ytterbium-doped large-core fiber laser with 610 W of output power, Opt. Commun. 234 (2004) 315. [10] Y. Jeong, J.K. Sahu, D.N. Payne, J. Nilsson, Ytterbiumdoped large-core fiber laser with 1 kW continuous-wave output power, in: Presented at the Conference on Advanced Solid-State Photonics 2004, Santa Fe, NM, USA, Feb. 1–4, 2004 (postdeadline paper PD1). [11] A. Liem, J. Limpert, H. Zellmer, A. Tu¨nnermann, V. Reichel, K. Mo¨rl, S. Jetschke, S. Unger, H.-R Mu¨ller, J. Kirchhof, T. Sandrock, A. Harschak, 1.3 kW Yb-doped fiber laser with excellent beam quality, in: Proc. of Conference on Lasers and Electro-Optics (CLEO) 2004, san Francisco, CA, USA, 16–21 May 2004 (postdeadline paper CPDD2). [12] M.K. Davis, M.J.F. Digonnet, R.H. Pantell, Thermal effects in doped fibers, J. Lightwave Technol. 16 (1998) 1013. [13] D.C. Brown, H.J. Hoffman, Thermal, stress, and thermaloptic effects in high average power double-clad silica fiber lasers, IEEE J. Quantum Electron. 37 (2001) 207. [14] Y. Wang, C.-Q. Xu, H. Po, Pump arrangement for kilowatt fiber lasers, in: Proc. of IEEE LEOS Annual Meeting 2003, vol. 1, Tucson, AZ, USA, Oct. 26–30, 2003, p. 71. [15] Y. Wang, C.-Q. Xu, H. Po, Thermal effects in kilowatt fiber lasers, IEEE Photon. Technol. Lett. 16 (2004) 63. [16] G.P. Agrawal, Nonlinear Fiber Optics, second ed., Academic Press, San Diego, 1995. [17] J.P. Koplow, D.A.V. Kliner, L. Goldberg, Single-mode operation of a coiled multimode fiber amplifier, Opt. Lett. 25 (2000) 442. [18] F.D. Teodoro, J.P. Koplow, S.W. Moore, D.A.V. Kliner, Diffraction-limited, 300-kW peak-power pulses from a coiled multimode fiber amplifier, Opt. Lett. 27 (2002) 518. [19] W.P. Urquhart, P.J. Laybourn, Effective core area for stimulated Raman scattering in single-mode optical fibres, IEE Proc. 132 (1985) 201.
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[20] L. Fox, D.F. Mayers, Numerical Solution of Ordinary Differential Equations, Chapman & Hall, New York, 1987. [21] D. Marcuse, Curvature loss formula for optical fibers, J. Opt. Soc. Am. 66 (1976) 216. [22] T. Weber, W. Lu¨thy, H.P. Weber, V. Neuman, H. Berthou, G. Kotrotsios, A longitudinal and side-
pumped single transverse mode double-clad fiber laser with a special silicone coating, Opt. Commun. 115 (1995) 99. [23] D.J. Ripin, L. Goldberg, High efficiency side-coupling of light into optical fibres using imbedded V-grooves, Electron. Lett. 31 (1995) 2204.
Analysis of Raman and thermal effects in kilowatt fiber lasers Yong Wang a
a,*
, Chang-Qing Xu a, Hong Po
b
Department of Engineering Physics, McMaster University, 1280 Main Street, JHE-A317, Hamilton, ON, Canada L8S 4L7 b Lasersharp Corporation, 86 South Street, Hopkinton, MA 01748, USA Received 16 April 2004; received in revised form 1 September 2004; accepted 2 September 2004
Abstract A theoretical analysis of Raman and thermal effects in kilowatt ytterbium-doped double-clad (YDDC) fiber lasers is presented. Solutions to suppress these detrimental effects in the YDDC fiber lasers under bidirectional end pump and distributed pump are discussed. The quantitative analysis shows that the Raman effects can be suppressed by using large-mode-area fibers, shortening the cavity length, adopting a longer lasing wavelength, and reducing reflections at the Raman–Stokes wavelengths; and the thermal effects can be effectively eliminated by utilizing the distributed pump and optimizing the arrangement of pump powers, pump absorption coefficients, and fiber lengths. 2004 Elsevier B.V. All rights reserved. Keywords: Thermal effects; Stimulated Raman scattering; Fiber lasers; Ytterbium; Double clad
1. Introduction Rare-earth-doped single-transverse-mode fiber lasers pumped by low-cost laser diodes have attracted considerable attention recently in commercial and military applications due to their high brightness, eminent efficiency, good compactness, excellent beam quality, efficient heat dissipation, etc., compared to traditional gas and solid-state la-
*
Corresponding author. Tel.: +1 905 5259140; fax: +1 905 5298406. E-mail address: [email protected] (Y. Wang).
sers [1–4]. With the availability of high-power laser diode bars and clad-pumping techniques, the output power of double-clad fiber lasers is able to reach hundreds of watts even a kilowatt in continuous-wave (CW) regime [4–11]. In particular, a ytterbium (Yb)-doped single-mode fiber laser with an output power of 400 W and M2 < 1.05 [7], a Yb and neodymium (Nd) codoped fiber laser with an output power of 500 W and M2 < 1.5 [8], a Ybdoped large-core fiber laser with an output power of 610 W and M2 = 2.7 [9], a 1-kW Yb-doped fiber laser with M2 = 3.4 [10], and a 1.3-kW Yb-doped fiber laser with M2 < 3 [11] have been reported recently. The Raman and thermal effects are known
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.09.008
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Y. Wang et al. / Optics Communications 242 (2004) 487–502
as major restrictions to laser performance in a kilowatt power domain [2,4,12–15]. The stimulated Raman scattering (SRS) in fibers can convert part of the signal into the undesirable Raman–Stokes waves at longer wavelengths [16], and hence degrades the laser efficiency. The Raman effects caused by the SRS take place mainly in those long-cavity fiber lasers with small-core fibers. The critical signal power to reach a threshold of stimulated Brillouin scattering (SBS), as defined in [16], is about 3 kW for a double-clad fiber with a 20-lm core, a 100-m length, and a 1-nm signal bandwidth. Since this SBS threshold is much higher than the power to reach an SRS threshold as shown in this paper, we can neglect the SBS effects. The pump-induced heating can cause a number of serious problems [2,4], such as formation of thermal cracks due to internal thermal stress and expansion, shortening of fiber lifetime due to damage of fiber coatings, even melting of the glass, degradation of laser beam quality due to thermal lensing, deterioration of optical coupling efficiency due to undesirable temperature-induced motion of mechanical parts, and decrease of laser quantum efficiency. Generally speaking, the SRS can be effectively suppressed by increasing the fiber core area and shortening the fiber length, and the dissipated heat can be greatly diminished by reducing the dopant concentration (or pump absorption coefficient) together with properly lengthening the fiber. Therefore, the design of a kilowatt fiber laser is based on the following two steps. The first step is to remove the harmful Raman effects by selecting suitable double-clad fibers and cavity parameters. The other is to lower the thermal effects by controlling the operating temperature of the lasers. Of course, once an appropriate operating temperature distribution is established in the fiber, other issues like thermal-optic effects, mechanical stability, system reliability, etc., are easily solved. During the above two steps, the laser conversion efficiency must be considered. Air cooling is a good candidate for many applications because of compact structures and moderate dissipating efficiency, hence is adopted in our modeling. In this paper, by solving a set of laser rate equations in combination with the SRS, the threshold
conditions for the detrimental Raman effects are obtained under different fiber conditions. Some solutions to facilitate heat dissipation in CW kilowatt Yb-doped double-clad (YDDC) fiber lasers were proposed previously [14,15]. However, only a brief description rather than a systematic analysis was given in the previous Letter [15]. Here, we detail the related analysis on both the Raman and thermal effects, and illustrate the selection of parameters and optimization procedures. The theoretical model and simulation results are important to the design and development of kilowatt fiber lasers. The contents of this paper are arranged as follows. In Section 2, a conventional end-pumped laser scheme as well as the distributed schemes is introduced, and the related theories, including the laser rate equations in combination with the SRS and the thermal conduction equations under air cooling, are also given. To find out some critical fiber and cavity parameters, the end-pumped scheme is first analyzed in Section 5.1, regardless of the Raman and thermal effects. In Section 5.2, the SRS and its influence on the lasers are studied. Temperature distributions in fibers are then obtained for different laser schemes in Section 5.3. To reduce the operating temperature, these schemes are compared, and the related optimization procedures are described.
2. Laser configurations and theoretical modeling The configuration of a typical YDDC fiber laser under CW end pump (PpF and PpB) is schematically shown in Fig. 1(a) (namely scheme A). The YDDC fiber has a length of L and a uniform dopant concentration in the fiber core. In practice, one cannot have such a YDDC fiber straight over its length like what is shown in Fig. 1(a). However, based on a mode filtering technique [17,18], this YDDC fiber can be appropriately coiled to realize a single-mode operation without a significant bending loss. The laser has a highreflectivity (HR) mirror at z = 0 and an output coupler (OC) at z = L. This HR mirror, which can be either a dichroic mirror or a fiber grating, has a peak reflectivity of 99% at the wavelength
Y. Wang et al. / Optics Communications 242 (2004) 487–502 HR
L, N PpB
PpF
(a) z = 0 HR
(b)
(c)
z
L1, N1
z=L
Lj, Nj
L1, N
PpF1
PpB1, PpF2
LJ, ΝJ
OC
PpB
PpF
HR
OC
Lj, N
PpBj-1, PpFj
PpBj, PpFj+1
LJ, Ν OC PpBJ-1, PpFJ
PpBJ
Fig. 1. Schematic configurations of YDDC fiber laser under (a) end pump and a uniform dopant concentration, (b) end pump and nonuniform dopant concentrations, (c) distributed pump and a uniform dopant concentration.
ks. The OC can be either a cleaved fiber facet or a fiber grating. In order to compare the laser performance easily under different dopant concentrations (N) and fiber core diameters (Dc), we assume in this paper that these YDDC fibers have fixed inner and outer cladding diameters of 250 lm (2r2) and 400 lm (2r3). The proposed laser schemes with nonuniform dopant concentrations (namely scheme B) and distributed pump (namely scheme C), as shown in Figs. 1(b) and 1(c), respectively, are discussed in the following section. The steady-state rate equations to describe the pump, signal and Stokes waves in these CW lasers are given by N ¼ N 1 þ N 2;
ð1Þ
N2 Cp kp ¼ ra ðkp ÞN 1 re ðkp ÞN 2 ðP þ p þ Pp Þ s hcA Cs ks ½ra ðks ÞN 1 re ðks ÞN 2 ðP þ þ s þ Ps Þ hcA CR kR ½ra ðkR ÞN 1 re ðkR ÞN 2 ðP þ þ R þ P R Þ; hcA ð2Þ dP p ¼ Cp ra ðkp ÞN 1 re ðkp ÞN 2 P p aðkp ÞP p ; dz ð3Þ
dP s ¼ Cs ½re ðks ÞN 2 ra ðks ÞN 1 P s dz 2 hc aðks ÞP s 2re ðks ÞN 2 3 Dks ks kR g R þ ðP þ P R ÞP s ; ks Aeff R dP R ¼ CR ½re ðkR ÞN 2 ra ðkR ÞN 1 P R dz 2 hc aðkR ÞP R 2re ðkR ÞN 2 3 DkR kR gR þ ðP þ P s ÞP R ; Aeff s
489
ð4Þ
ð5Þ
where P p is the pump power, P s is the signal power, and P R is the first-order Raman–Stokes power (± correspond to forward and backward propagations, respectively). Since the threshold conditions of the first-order Stokes wave are concerned in this work, the higher-order Stokes waves together with the spontaneous Raman scattering can hence be neglected. N is the Yb ion concentration, N1 and N2 are the population densities of the ground and upper levels, respectively. ra and re are the absorption and emission cross-sections of Yb ions, respectively [3]. The pump wavelength kp is 915 nm, which is selected with respect to a relative high and flat absorption peak of Yb-doped silica fibers around 915 nm [3,4]. Although the absorption cross-section at 976 nm is nearly three times as high as that at 915 nm and the laser quantum efficiency is also higher, a narrow absorption bandwidth (5-nm FWHM) renders wavelength-unlocked pump diodes unusable in practice. A typical signal wavelength (ks) is 1065 nm, and the Stokes wavelength (kR) is correspondingly 1117 nm, based on a 440 cm1 frequency shift in germanosilicate fibers. The second term in the right-hand side of Eqs. (3)–(5) represents the transmission loss, and a(k) is the fiber attenuation coefficient. The third term in the right-hand side of Eqs. (4) and (5) corresponds to the spontaneous emission, where the signal and Stokes bandwidths (Dks and DkR) are 2 and 5 nm, and the out-of-signal-band amplified-spontaneous-emission (ASE) power is neglected. c is the light velocity in the vacuum, h is the PlanckÕs constant, s is the
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Y. Wang et al. / Optics Communications 242 (2004) 487–502
spontaneous lifetime (1.3 ms), and A is the doped area of the YDDC fiber. Aeff is the effective core area associated with the signal and Stokes waves, and calculated through the method described in [19] with a fiber numerical aperture of 0.1. Cp(Cs, CR) is the overlapping factor between the pump (signal, Stokes wave) and the doped area, and easily calculated with assumptions of Gaussian distributions for the signal and Stokes waves in the core and a uniform distribution for the pump in the inner cladding. Therefore, the radial intensities of the pump, signal and Stokes waves can be obtained when the longitudinal power distributions are solved from the above Eqs. (1)–(5). Furthermore, we take gR = 0.92 · 1013 m/W for the interaction between the 1065-nm signal and the 1117-nm Stokes wave. For other wavelengths, gR can be obtained by using the inverse dependence of gR on wavelength [16]. For the laser configuration in Fig. 1(a), twopoint boundary conditions associated with the above ordinary differential equations are given by Pþ p ð0Þ ¼ g1 P pF þ RHR ðkp Þ P p ð0Þ; þ P p ðLÞ ¼ g1 P pB þ ROC ðkp Þ P p ðLÞ; Pþ s ð0Þ ¼ RHR ðks Þ P s ð0Þ; þ P s ðLÞ ¼ ROC ðks Þ P s ðLÞ; Pþ R ð0Þ ¼ RHR ðkR Þ P R ð0Þ; þ P R ðLÞ ¼ ROC ðkR Þ P R ðLÞ;
ð6Þ
where g1 is the pump coupling efficiency, and RHR is the equivalent reflectivity of the HR mirror, which may be different at the pump, signal and Stokes wavelengths. ROC is the OC reflectivity and assumed to be the same for the pump, signal and Stokes waves for a cleaved fiber facet, and wavelength-dependent for a fiber grating. We take g1 = 0.90, RHR(ks) = 0.99, RHR(kp) = 0 and ROC (ks) = ROC(kp) = 0.035 in the following simulations. RHR(kR) and ROC(kR) are discussed in the next section. When this boundary-value problem is solved [20], the output signal and Stokes powers are given by P out ¼ ½1 ROC ðks Þ P þ s s ðLÞ;
ð7Þ
þ P out R ¼ ½1 ROC ðkR Þ P R ðLÞ:
ð8Þ
A simple air-cooling model [2] is considered to facilitate the heat dissipation in this laser. The heat dissipation as well as transverse and longitudinal temperature distributions in the fiber under air cooling is governed by the following thermal conduction equations in symmetric cylindrical coordinates (r, z) [2,15]: 1 o oT ðr; zÞ o2 T ðr; zÞ qðr; zÞ r ¼ ; ð9Þ þ r or or oz2 jF oT ðr; zÞ H ¼ ½T h T ðr ¼ a3 ; zÞ; ð10Þ or r¼a3 jF H ¼ 0:5Nu jA a1 3 ;
ð11Þ
Nu expð2=NuÞ ¼ 0:16ðGr PrÞ1=3 ;
ð12Þ
2 Gr ¼ 8g d 2A a33 ½T ðr ¼ a3 ; zÞT 1 h 1lA ;
ð13Þ
where T is the temperature in the fiber, and Th is the heat sink temperature. q(r, z) is the heat dissipated in unit volume, which can be calculated by considering all input and output lights into and out of a unit volume at (r, z) in the fiber. Since most of the pump power is absorbed in the fiber core, the maximum temperature is hence expected to occur at the fiber axis. jF is the fiber thermal conductivity, and H is the convective coefficient. Nu, Gr and Pr are the Nusselt, Grashof and Prandtl numbers [2], respectively. dA, lA and jA are the density, viscosity and thermal conductivity of air. The air convection is controlled to keep the heat sink temperature constant (300 K). Furthermore, the following parameters are used: g = 9.8 m/s2, Pr = 0.71, dA = 1.2 kg/m3, lA = 1.85 · 105 kg m1 s1, jF = 1.38 W m1 K1, jA = 0.026 W m1 K1.
3. General consideration The critical parameters of the fiber laser shown in Fig. 1(a) comprise fiber core diameter (Dc), dopant concentration (N) and fiber length (L). Of course, large-mode-area (LMA) fibers should be used in these high-power fiber lasers to effectively suppress detrimental nonlinear effects. Three typi-
Y. Wang et al. / Optics Communications 242 (2004) 487–502
cal core diameters of 10, 20 and 30 lm are first considered in this section, which are based on the commercial double-clad fibers. To analyze the laser shown in Fig. 1(a), we first neglect the Raman and thermal effects. This can be done by setting P R ¼ 0 and solving Eqs. (1)–(4). Under given pump conditions, the optimal fiber length Lopt corresponding to a maximal output signal power, is relative to fiber core diameter (Dc) and dopant concentration (N). Generally speaking, the pump absorption coefficient of a YDDC fiber exhibits some longitudinal dependence although the distribution of N is uniform in the fiber core. In order to compare laser performance under different core diameters and concentrations, we define an average pump absorption coefficient, in dB/m for a bi-directionally pumped YDDC fiber with a length of l, as " # Pþ P 1 p ð0Þ p ðlÞ ap ¼ log10 þ þ log10 10: ð14Þ 2l P p ðlÞ P p ð0Þ For core diameters of 10, 20 and 30 lm, the optimal fiber length Lopt for the above scheme is shown as a function of ap in Fig. 2(a). The output signal power under equal pump powers of 500 W 80 1 m / Div
Lopt (m)
60 40 20
0.05 dB/m / Div
(a) 0
2 W / Div
700
Ps
out
(W)
750
650
600
(b) 0.0
0.05 dB/m / Div
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m)
Fig. 2. (a) Optimal fiber length versus pump absorption coefficient, (b) laser output power at the optimal fiber length. The insets detail the difference among three fiber core diameters of 10 (solid), 20 (dashed) and 30 lm (dotted) around ap = 1.0 dB/m.
491
at both fiber ends is depicted in Fig. 2(b). The insets show the detailed difference among three core diameters around ap = 1.0 dB/m, from which we can see that both Lopt and P out are nearly indes pendent of Dc. It is also found that Lopt is nearly independent of pump power in the range of 500– 3000 W. Therefore, it is implied that ap is a robust parameter to describe the YDDC fibers. One can see in Fig. 2 that in the absence of the Raman and thermal effects the laser has better conversion efficiency at a higher ap and a shorter Lopt. In particular, with ap = 1.0 dB/m, the optimal fiber length is 20 m, and the output power is 725 W. And with ap = 0.25 dB/m, the optimal fiber length is 60 m, and the output power is 630 W. However, no apparent improvement of efficiency occurs for ap > 1.5 dB/m; meanwhile, if ap is too high, the laser may suffer other serious problems, such as the ion quenching [4] and thermal effects as described in Section 5.
4. Raman effects From Fig. 2, we know that in the absence of the Raman and thermal effects, the laser performance depends on the pump absorption coefficient and fiber length. However, when the SRS is taken into account, the optimization turns to a different scenario. To find out the Raman threshold conditions, in this section we first neglect the thermal effects, and assume that the laser can work normally under any pump power. Two fiber core diameters of 20 and 30 lm are compared in this section, and a 10-lm core is unsuitable for kilowatt fiber lasers. The ion concentrations are adjusted to meet the required pump absorption coefficient for different core diameters. For two typical ap of 0.25 and 1.0 dB/m, the fiber lengths of 60 and 20 m are selected with respect to the optimal fiber lengths shown in Fig. 2. The effective reflectivities of the HR mirror and OC at the Stokes wavelength are related to a practical system. We first assume that both RHR(kR) and ROC(kR) are equal to 3.5%. With these assumptions, the laser output powers under different fiber conditions are depicted in Fig. 3. The left and right columns correspond to L = 20 and 60 m (ap = 1.0
492
Y. Wang et al. / Optics Communications 242 (2004) 487–502 800 (a) Dc= 20 µm, L = 20 m
Power (W)
600
400
400
1 300 2 3 200
200
100
(b) Dc= 20 µm, L = 60 m
1 2 3
4 4 0 800 0 100 200 300 400 1200 (d) 2400 (c) Dc= 30 µm, L = 20 m Dc= 30 µm, L = 60 m 0
0
200
400
600
1 900 2 3 600
Power (W)
1800
1200
1 2 3
300
600
0
4 0
600
1200
1800
Pump Power (W)
2400
4 0
0
300
600
900
1200
Pump Power (W)
Fig. 3. Signal and Stokes powers for RHR(kR) = ROC(kR) = 3.5% and for different fiber core diameters and lengths. 1: Ideal signal power without consideration of SRS, 2: total output power, 3: signal power and 4: Stokes power.
and 0.25 dB/m), while two rows refer to different core diameters. In each figure, there are four curves. Curve 1 (solid) is the ideal output power without consideration of the SRS; curve 2 (dashed) out is the total output power, i.e., P out s þ P R ; curve 3 out (dotted) is the output signal power P s ; curve 4 (dash-dotted) is the output Stokes power P out R . In each figure, curve 2 is lower than curve 1 in the presence of the SRS, which results from two aspects. On the one hand, part of optical power turns into heat in the fiber when the signal is converted to the Stokes wave; on the other hand, most of the backward Stokes power leaves the fiber at z = 0, which is approximately equal to the forward output power P out due to RHR(kR) = ROC(kR). R Then it is absorbed in some optical components, and converted into heat finally. From the trends of curves 3 and 4, one can see that in the presence of the SRS, P out drops with an increase of pump s power. As expected, the Stokes power can be reduced effectively in a YDDC fiber with either a larger core diameter or a shorter fiber length. The threshold pump powers for the generation of SRS (denoted by P th p ) and the corresponding sig-
nal powers (namely critical signal power and denoted by P cr s ) under different core diameters and fiber lengths are detailed in Table 1. We can see 2 that P cr s obeys neither a Dc dependence on fiber core diameter nor a proportional dependence on fiber length in this case, which can be understood by considering that both the laser stimulated transitions of Yb ions and the SRS in fibers have significant contributions to P out R . Near the SRS threshold, the slope efficiency of the output Stokes power with respect to the total pump power is only dependent on fiber length, and nearly independent of core diameter. It is 42% for a 20-m long fiber, and 39% for a 60-m long fiber. Moreover, only under Dc = 30 lm and L < 30 m, can the laser ideally have a clean signal power of more than 1000 W. To avoid the detrimental Raman effects, the pump power should not exceed P th p hence the maximum output signal power is P cr . s When both RHR(kR) and ROC(kR) can be reduced by using narrow-band mirrors, such as fiber gratings, the Stokes power is expected to be suppressed. The calculated threshold powers for RHR(kR) = ROC(kR) = 0.1%, also given in Table
Y. Wang et al. / Optics Communications 242 (2004) 487–502
493
Table 1 cr Threshold pump power ðP th p Þ and critical signal power ðP s Þ at ks = 1065 nm and under different reflectivities [RHR(kR) and ROC (kR)], fiber core diameters (Dc), and fiber lengths (L) RHR(kR), ROC(kR)
Power (W)
Dc = 20 lm L = 20 m
Dc = 30 lm L = 60 m
L = 20 m
L = 60 m
3.5%
P th p P cr s
686.3 497.0
321.1 201.8
2079.0 1509.2
865.4 546.6
0.1%
P th p P cr s
2211.4 1603.6
899.2 566.6
5510.1 4002.3
2164.0 1368.6
1, are at least two and a half times as high as the corresponding powers for RHR(kR) = ROC(kR) = 3.5%. The Stokes slope efficiency is correspondingly 40% for a 20-m long fiber, and 38% for a 60-m long fiber. Compared to the previous case with RHR(kR) = ROC(kR) = 3.5%, the ranges of the fiber parameters required to generate a desired clean signal power are advantageously enlarged. For instance, a clean signal power of more than 1000 W can be generated under Dc = 30 lm and L > 60 m, as well as Dc = 20 lm and L < 30 m. It is worth nothing that in this case P cr s approximately obeys a D2c dependence on core diameter and a proportional dependence on fiber length. This is because with an increase of signal power, the contribution from the Raman gain is enlarged by a few times, compared to the contribution from the stimulated transitions of Yb ions. From Eq. (5), we know that the Stokes wave at the wavelength kR is also amplified by the stimulated transition of Yb ions like the signal at ks. To suppress this gain, it is reasonable to consider shifting ks to a longer wavelength, and consequently kR is located in a lower-gain range of Yb-doped fibers. When taking ks = 1085 nm, we
have kR = 1140 nm. Both the emission and absorption cross-sections of Yb ions, as given in [3], drop by 50% when kR shifts from 1117 to 1140 nm. By following the same procedure as that for ks = 1065 nm, the threshold pump power ðP th p Þ and critical signal power (Pscr) are calculated and given in Table 2 under two reflectivities of 3.5% and 0.1%. As 2 expected, P cr s apparently obeys a Dc dependence on core diameter and a proportional dependence on fiber length. We can see from Tables 1 and 2 that when ks shifts from 1065 to 1085 nm, the increases th in P cr s and P p are more significant for a smaller core diameter, a shorter fiber length, and a higher reflectivity. For example, P cr s increases by 70% for Dc = 20 lm, L = 20 m, and RHR(kR) = ROC(kR) = 3.5%, and by 10% for Dc = 30 lm, L = 60 m, and RHR(kR) = ROC(kR) = 0.1%, respectively. Though the SRS effects can be further suppressed with a further increase of ks, the reduction of laser quantum efficiency and the increase of the incurred heat should be taken into account. This is discussed in the next section. With these quantitative results above, one can estimate the practical Raman thresholds ðP cr s Þ in the previous experiments by properly scaling the
Table 2 cr Threshold pump power ðP th p Þ and critical signal power ðP s Þ at ks = 1085 nm and under different reflectivities [RHR(kR) and ROC(kR)], fiber core diameters (Dc), and fiber lengths (L) RHR(kR), ROC(kR)
Power (W)
Dc = 20 lm L = 20 m
Dc = 30 lm L = 60 m
L = 20 m
L = 60 m
3.5%
P th p P cr s
1214.5 863.9
477.8 295.4
2756.8 1963.8
1080.9 670.1
0.1%
P th p P cr s
2769.7 1971.2
1067.0 660.4
6256.5 4458.2
2405.6 1492.8
Y. Wang et al. / Optics Communications 242 (2004) 487–502
discussion, with appropriate selection of two reflectors, and under a 1000-W pump and a 30lm core, the SRS effects are assumed to be suppressed completely. 5.1. Scheme A First, we consider the end-pumped scheme (scheme A) with equal pump powers of 500 W at the both ends. Fig. 4(a) shows the calculated temperature distributions at the fiber axis (r = 0) and the inner/outer claddings boundary (r = 125 lm). The selection of L = 20 m is based on the optimal fiber length for ap = 1.0 dB/m, as shown in Fig. 2(a). It can be seen that the temperature distribution is apparently uneven along the fiber, and the temperature difference in the radial direction is smaller than that in the axial direction. A maximum temperature of 340 C is reached at the fiber output side, while a minimum one of 94 C is located near the mid span of the cavity. Therefore, for such an end-pumped scheme, more care must be taken in practice to prevent thermal damage at both fiber ends than that in the middle [4]. Fig. 4(b) shows the pump and signal power
400
Temperature (˚C)
fiber parameters. For example in [6], for a singlemode fiber laser resonator with given parameters Dc = 9 lm, L = 60 m, ks = 1086 nm, RHR e ðks Þ ¼ HR 99:9%, ROC ðk Þ ¼ 5%, we take R s e e ðkR Þ ¼ ROC ðk Þ ¼ 0:1% for the laser cavity composed of R e two fiber Bragg gratings. Simply read from Table 2, the critical signal power is 660.4 W for Dc = 20 lm, L = 60 m, ks = 1085 nm, and Re(kR) = 0.1%. Taking D2c dependence in power scaling and neglecting a small difference in ks leads to P cr s ¼ 133:7 W. This is in good agreement with the measured one (135 W). One can conclude from the above results that when the pump power exceeds a certain threshold, the laser conversion efficiency starts to drop due to the presence of the bi-directional Stokes waves, which can cause detrimental effects in many applications. To suppress the SRS effects in kilowatt fiber lasers, an LMA fiber with at least a 20-lm core for a 20-m long cavity, and a 30-lm core for a 60m long cavity is indispensable; the shorter the fiber length, the lower the Stokes power, which is also consistent with the requirement of the laser conversion efficiency as discussed in the previous section. Selecting a longer lasing wavelength is proved to be able to suppress the SRS to some extent. However, it may cause a reduction of laser efficiency and an increase of heat dissipation. This tradeoff should be considered in the laser design. Under any conditions, the reflectivities RHR(kR) and ROC(kR) should be well suppressed, and wavelength-selective reflectors are obviously helpful. Since it may be difficult in practice to reduce these reflectivities to a level of lower than 0.1%, an alternative solution for relatively small core-diameter fibers is to use the so-called master oscillator and power amplifier (MOPA), where the reflections at the fiber ends of the power amplifier can be effectively removed.
(a)
300
r=0 r = 125 µm
200 100 0 800
Power (W)
494
(b)
600
Forward Pump Backward Pump Forward Signal Backward Signal
400 200
5. Thermal effects 0
To compare the laser efficiency and operating temperature among different schemes shown in Fig. 1, in this section we assume that the total pump power is 1000 W, and the YDDC fiber has a core diameter of 30 lm. Based on the previous
0
5
10
15
20
Position (m) Fig. 4. Temperature and power distributions in 20-m YDDC fiber under end pump and with uniform pump absorption coefficient of 1.0 dB/m.
Y. Wang et al. / Optics Communications 242 (2004) 487–502
T ave ¼
1 L
Z
L
T ðr ¼ 0; zÞdz:
ð15Þ
0
Based on the optimal fiber lengths shown in Fig. 2(a), Tmax and Tave versus ap are plotted in Fig. 5. We can see that both Tmax and Tave rise with an increase of ap, and the highest pump absorption coefficient can hence be restricted under a certain operating temperature. For example, when we reduce ap from 1.0 (Lopt = 20 m) to 0.25 dB/m (Lopt = 60 m), the maximum operating temperature drops from 340 to 137 C; whereas the laser output power drops from 725 to 630 W. Hence, lowering pump absorption together with lengthening the fiber to suppress the thermal effects is not a good solution to some extent. It is interesting to compare these analyses with the previous experimental results [10,11]. As reported in [10], with high pump absorption (1.5–3.0 dB/m) and a short cavity (8 m), the slope efficiency as high as 80% was obtained. However, the thermal effect seems to be a major factor to degrade the laser beam quality and system reliability. In contrast, when a
600
Tmax Tave
500
Temperature (oC)
distributions along the cavity. The laser output power is 725 W. One can see that the uneven temperature distribution results from nonuniform pump absorption in the fiber, and most of the heat is generated near the fiber ends due to the higher pump absorption. In general, the laser operation under this temperature (hundreds of degrees) is impractical. On the one hand, the strong thermal-optic effect can degrade the output beam quality; on the other hand, such a high operating temperature will severely deteriorate the system stability and reliability. In particular, for most commercial double-clad fibers, the fiber polymer coatings cannot bear such a high temperature in long-term applications. As a result, we can use a lower pump absorption coefficient and a longer fiber to reduce the operating temperature for this scheme. Since the highest temperature occurs at the fiber axis, we need to pay more attention to the temperature distribution along the fiber axis. We thus define Tmax as the maximum temperature, and Tave as the longitudinally averaged temperature along the fiber axis. The latter is given by
495
400 300 200 100 0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m)
Fig. 5. Maximum and average temperatures versus pump absorption coefficient.
50-m lower-absorption LMA fiber was adopted in [11], the thermal effect was eliminated, but the slope efficiency dropped to 65%. It has been shown in the previous section that an increase of ks can help suppress the SRS to some extent. Fig. 6 shows the output power and temperatures varying with ks for typical 20- and 60-m fiber lengths. Since the maximum gain is located in the range 1030–1040 nm under the current pump and fiber conditions, a wavelength shift toward the longer wavelength side can lead to a lower output power, and increases in Tmax and Tave. For example, when ks shifts from 1065 to 1085 nm, the output signal power drops by 14 and 11 W for 20- and 60-m cavities, and Tmax increases by about 6 C for both 20- and 60-m lengths. For these two lengths, the variation slope of output power is 0.7 and 0.55 W/nm, while the corresponding temperature variation slope is 0.3 and 0.35 C/nm. Of course, for some fiber lasers approaching the Raman threshold conditions, selecting a longer lasing wavelength is favorable if the power decrease and the temperature increase are acceptable. Fiber attenuation coefficients at the pump and signal waves, including the background and bending losses, are important to the laser performance. For the commercial YDDC fibers, the background loss is usually less than 10 dB/km. The bending loss is dependent on the YDDC fiber structure
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Y. Wang et al. / Optics Communications 242 (2004) 487–502
Power (W)
730
(a)
L = 20 m
640
out
Ps
720
630
710
620
700
610
Temperature (˚C)
350
300
(c)
150
Tmax
(b) T and T max ave
(d)
L = 60 m out
Ps
Tmax and Tave Tmax
125 250 100 200
150 1060
Tave
Tave 1070
1080
1090
Wavelength (nm)
75 1060
1070
1080
1090
Wavelength (nm)
Fig. 6. Output power, maximum and average temperatures versus signal wavelength for fiber lengths of 20 and 60 m.
and the diameter of the spool, onto which the fiber is coiled. A theoretical analysis on bending losses was detailed in [21]. Due to a high numerical aperture (NA) for the pump light in the inner cladding, its bending loss is less sensitive to the bending curvature than that of the signal. For pump absorption coefficients of 0.25 and 1.0 dB/m, the optimal fiber length, the corresponding output power and temperatures versus fiber attenuation coefficients are shown in Fig. 7, where the solid and dashed lines refer to pump losses of 13 and 26 dB/km, respectively. We can see that with an increase in fiber loss, both the optimal fiber length and the output power decrease, and the fiber temperature increases. Due to a longer fiber length, the influence of the signal attenuation on the laser is more severe for a lower ap than a higher ap. For example, when a(ks) increases from 10 to 100 dB/ km, for ap = 0.25 and 1.0 dB/m, the output signal power drops by 38% and 18%, the optimal fiber length is shortened by 32 and 8 m, and the maximum temperature increases by 156 and 100 C, respectively. Due to a significant increase in temperature and a considerable decrease in laser efficiency, the bending losses must be greatly suppressed.
5.2. Scheme B One can see in scheme A that on the one hand, most of the pump power is absorbed near the two fiber ends, which causes a lot of heat; on the other hand, the adoption of a relatively low ap for the whole fiber deteriorates the laser efficiency. Therefore for an end-pumped scheme, an uneven distribution of ap, e.g., a lower ap arranged near the pump launching points, as shown in Fig. 1(b) (scheme B), is expected to compromise heat dissipation and laser efficiency. The calculated results for a five-segment scheme are depicted in Fig. 8, where pump absorption coefficients of 0.33, 0.57, 0.81, 0.38, 0.24 dB/m and fiber lengths of 6.0, 2.7, 15.0, 6.8, 5.5 m are arranged for segments 1, 2, 3, 4 and 5, respectively, and the total fiber length is 36 m. These pump absorption coefficients and fiber lengths are obtained with respect to the following two criteria: (1) The maximum temperature in each fiber segment is the same. (2) A higher pump absorption coefficient and a shorter fiber length are preferred for each segment. Meanwhile, it is assumed that these fiber segments are well spliced together, with a typical splicing loss of 0.05 dB for both the signal and the pump.
Y. Wang et al. / Optics Communications 242 (2004) 487–502 80
Lopt (m)
(a)
(W) out
Ps
o
25
(d)
α(λp) = 13 dB/km α (λp) = 26 dB/km
60
15
20
10 750
(b)
600
700
500
650
400
600
300
550
(c)
300
αp= 1.0 dB/m (αp) = 13 dB/km (αp) = 26 dB/km
20
40
700
Tmax & Tave ( C)
αp= 0.25 dB/m
(e)
Tmax
(f)
400
Tmax
497
300
200
Tave
Tave
200
100 0
20
40
60
80
100
100
0
20
40
60
80
100
α (λ s) (dB/km)
α (λ s) (dB/km)
Fig. 7. Optimal fiber length, output power, maximum and average temperatures versus fiber attenuation coefficients for pump absorption coefficients of 0.25 and 1.0 dB/m.
It is shown in Fig. 8 that the fiber temperature ranges between 84 and 137 C, and the output power is 665 W. Compared to scheme A with
Temperature (oC)
150
(a)
125 100 75
r=0 r = 125 µm
50
Power (W)
800
(b)
600
Forward Pump Backward Pump Forward Signal Backward Signal
400 200
ap = 0.25 dB/m and L = 60 m, the maximum temperature in the fiber is the same, whereas the output power increases by 35 W, and the fiber length is advantageously shortened by 24 m. Therefore, scheme B is better than scheme A. By following the similar procedure, more results under different Tmax are obtained and given in Table 3. In contrast to Tmax = 137 C (case 3, shown in Fig. 8), if Tmax = 179 C is allowed (case 1), the output power will increase 20 W. On the contrary, if Tmax < 100 C is required (case 5), the laser suffers a rather low output power (608 W). It is also found that further flattening the temperature distribution by using more segments can degrade the laser efficiency significantly, which is due to more splicing losses introduced into the cavity. 5.3. Scheme C
0 0
10
20
30
40
Position (m) Fig. 8. Temperature and power distributions in 36-m YDDC fiber under end pump and with nonuniform pump absorption coefficients in five segments.
To further reduce the fiber temperature and flatten its distribution, more uniform distribution of pump power is indispensable. Compared to the previous schemes A and B, a distributed
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Y. Wang et al. / Optics Communications 242 (2004) 487–502
Table 3 Calculated results with distributed ap in five segments No.
Tmax (C)
Tave (C)
L (m)
P out (W) s
1 2 3 4 5
179 157 137 117 99
140 122 113 100 86
26.6 32.0 36.0 45.0 63.5
685 675 665 646 608
pumping scheme (scheme C) shown in Fig. 1(c), can hence be the best solution, where the pump light is separately launched into a few fiber segments through the side-coupling techniques using prisms [22] or V-grooves [23]. This scheme can effectively reduce the requirements for high brightness of pump laser diodes in the end-pumped schemes. For the jth segment with a length of Lj, j = 1, . . . , J, PpFj and PpBj stand for forward and backward pump powers. The total fiber length is L. Multipoint boundary conditions associated with Eqs. (3)–(5) are considered for this case. In particular, the boundary conditions for the jth segment at z = zj and zj + 1 are given by þ Pþ pj ðzj Þ ¼ g2 P pFj þ g3 P pj1 ðzj Þ; P pj ðzjþ1 Þ ¼ g2 P pBj þ g3 P pjþ1 ðzjþ1 Þ;
ser efficiency. In principle, their optimal values can be searched out by calculating the laser efficient at each point of the meshed parameter space. Technically speaking, some relations among these parameters can be obtained prior to a complete search, which are helpful to facilitate the optimization process. We take g1 = g2 = 0.9, g4 = g5 = 1, a = 13 dB/km for all segments in the following simulations. Fig. 9 shows the output power, maximum and average temperatures varying with ap for different J. The pump powers are arranged to obtain the same local maximum temperature in each fiber segment. Unlike the previous end-pumped scheme, the total fiber length in this scheme is relatively long to ensure effective pump absorption. The pump transmission coefficient g3 is 0.9. The total fiber length L is 50 m, and equally divided into J segments. As expected, with either a decrease in ap or an increase in J, both the output power and fiber temperature decrease. An increase of J results in a more uniform temperature distribution in the fiber, whereas the laser suffers more pump losses. However, the decrease of P out is less signifs icant at a higher ap. This is because most of the pump power is absorbed in each fiber segment,
þ Pþ sj ðzj Þ ¼ g4 P sj1 ðzj Þ; P sj ðzjþ1 Þ ¼ g4 P sjþ1 ðzjþ1 Þ; o
Tmax ( C)
150 100 50
(a)
90 o
where and are the pump, signal and Stokes powers, respectively, in the jth segment (±correspond to forward and backward propagations, respectively). g2 is the side-pump coupling efficient, while g3, g4 and g5 are the pump, signal and Stokes transmission coefficients between neighboring two segments. The boundary conditions at the two fiber ends take Eqs. (6). Only a uniform pump absorption coefficient is considered, and the lengths of those side-coupling components are neglected. Based on a certain maximal operating temperature and a total pump power of 1000 W, the fiber parameters and pump powers, i.e., ap, J, Lj, PpFj, PpBj, j = 1, . . . , J, can be optimized for a highest la-
Tave ( C)
P Rj ðzÞ
80
J=5~9
70 60
(b)
J = 5, J = 7, J=9
J=6 J=8
J = 5, J = 7, J=9
J=6 J=8
700
(W)
P sj ðzÞ
ð16Þ
out
P pj ðzÞ;
J= 5 6 7 8 9
200
Ps
þ Pþ Rj ðzj Þ ¼ g5 P Rj1 ðzj Þ; P Rj ðzjþ1 Þ ¼ g5 P Rjþ1 ðzjþ1 Þ;
600
J=5~9
500 400 300
(c) 0.0
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m)
Fig. 9. Maximum and average temperatures, and output power versus pump absorption coefficient for different segment numbers.
Y. Wang et al. / Optics Communications 242 (2004) 487–502 5 m, 8 m,
(a)
6 m, 9 m,
7m 10 m
150
o
Tmax ( C)
200
100
Lj = 5 ~ 10 m
50
out
(W)
700 (b)
Ps
and the losses of the transmitted pump powers at those launching points are trivial. For ap = 1.2 dB/m, Tmax and P out versus J are detailed in Fig. s 10, where the impacts of two pump transmission coefficients (g3) of 0.8 and 0.9 are compared. We can see that the decrease of Tmax is not apparent after J exceeds 6; whereas, the degradation of P out is significant after J exceeds 8, especially for s a lower g3 Similar results are also obtained for other ap, which implies that J = 6 or 7 is optimal if Tmax = 100 C is required. Based on the above information, Tmax and P out s varying with ap under different fiber lengths are plotted in Figs. 11 and 12 for J = 6 and 7, respectively. These fiber segments have the same Lj and ap. g3 is equal to 0.9. We can see in Figs. 11 and 12 that for any ap, Tmax drops with an increase of Lj, but no apparent decrease is found when Lj > 10 m. Therefore, a longer Lj is better for ap < 1.0 dB/m, and a shorter Lj is better for ap > 1.5 dB/m. In the range 1.0–1.5 dB/m, the relations among these curves are complicated, which hence implies the existence of the optimal parameters. The fiber parameters can be selected according to the following procedure. Under a certain maximum temperature required by the compo-
499
Lj = 5 ~ 10 m Lj = 5 ~ 10 m
600 500
5 m, 8 m,
400
6 m, 9 m,
7m 10 m
300 0.0
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m)
Fig. 11. Maximum temperature and output power versus pump absorption coefficient with six fiber segments.
nents (usually about 85–150 C for most commercial double-clad fibers), the ranges of ap can be obtained in Figs. 11(a) and 12(a) for J = 6 and 7, respectively. For instance, when we take Tmax = 98 C, the maximum ap is 0.45 and 1.2 dB/m for Lj = 5 and 10 m from Fig. 11(a), and 0.7 and 1.45 dB/m
η3 = 0.9 η3 = 0.8
300
200
5 m, 8 m,
(a)
6 m, 9 m,
7m 10 m
Tmax ( C)
o
Tmax ( C)
400
150
o
200 100
(a)
100
Lj = 5 ~ 10 m
0 50
700
(b)
out
Ps
Ps
600
(W)
η3 = 0.9 η3 = 0.8
out
(W)
700
650
(b)
Lj = 5 ~ 10 m Lj = 5 ~ 10 m
600 500
5 m, 8 m,
400
550 0
2
4
6
8
10
12
J Fig. 10. Maximum temperature and output power versus the number of segments for different pump transmission coefficients of 0.8 and 0.9.
6 m, 9 m,
7m 10 m
300 0.0
0.5
1.0
1.5
2.0
2.5
3.0
αp (dB/m) Fig. 12. Maximum temperature and output power versus pump absorption coefficient with seven fiber segments.
100
(a)
90 80
r=0 r = 125 µm
70 60 100
Power (W)
for Lj = 5 and 10 m from Fig. 12(a), respectively. Then in these ranges of ap, we can find out the maximum output power together with an optimal fiber length. In addition, it is found that appropriately lengthening the first and the last segments can reduce the incomplete pump absorption, hence improve the laser efficiency to some extent. With a maximal temperature of 98 C, the optimal solution with seven segments is given blow. The first and last segments are 10 m long, the others are identically 7 m long, and the total fiber length is 55 m. The pump absorption coefficient is 1.2 dB/m. The pump powers, totalling 1000 W, are 100, 85, 85, 75, 75, 70, 70, 65, 65, 61, 61, 61, 61, 66 W for segments 1, 2, 3, 4, 5, 6 and 7, respectively. The temperature and power distributions in the laser cavity are depicted in Fig. 13. We can see that the maximum and minimum temperatures at the fiber axis are 98 and 66 C, and the output power is 670 W. Compared to the previous results of scheme B, this scheme offers both better temperature uniformity and a higher output power. Moreover, under a maximum temperature of 128 C, an output power of more than 690 W can be obtained with ap = 2 dB/m and Lj = 6 m (j = 1– 7). It is hence concluded that an increase of J can reduce the pump power required for each segment, decrease the operating temperature in the fiber, and improve the uniformity of the axial temperature distribution. However, the output power is lower due to more pump transmission losses. Meanwhile, the laser suffers a higher manufacturing cost. As discussed in the previous section, the selection of a longer ks can suppress the Raman effects. For the laser configuration shown in Fig. 13, if ks shifts from 1065 to 1085 nm, the output power and the maximum temperature will be 659 W and 103 C, compared to 670 W and 98 C at ks = 1065 nm. This tradeoff as well as the requirements for system volume, component availability, operating conditions, etc., should be comprehensively considered in the practical design and optimization of kilowatt fiber lasers. It is worth noting that though water cooling is proved to be more efficient to dissipate heat than air cooling, it cannot be directly applied to the fiber surfaces. This is because water or moisture can degrade the performance and reliability of the com-
Temperature (oC)
Y. Wang et al. / Optics Communications 242 (2004) 487–502
Forward Backward
(b) Pump
80 60 40 20 0 800
Power (W)
500
(c) Signal 600 400
Forward Backward
200 0 0
10
20
30
40
50
60
Position (m) Fig. 13. Temperature and power distributions in 55-m YDDC fiber under distributed pump and with a uniform pump absorption coefficient of 1.2 dB/m.
mercial YDDC fibers. However, the YDDC fibers usually have to be packaged in some casing. To maintain a certain environmental temperature of the fiber, an external cooling for the fiber casing or heat sink is indispensable in kilowatt applications. Of course in this case, the water cooling is more efficient, while the air cooling is more compact.
6. Conclusion By solving laser rate equations in combination with thermal conduction equations, we have obtained the power and temperature distributions in the YDDC fibers, with which we can quantitatively analyze the Raman and thermal effects in different laser schemes. In the presence of the SRS, the laser efficiency decreases, and the considerable backward Stokes power may cause detrimental effects. To suppress the Raman effects in these kilowatt fiber lasers, an LMA fiber with at least a 20-lm core for a 20-m long cavity, and a
Y. Wang et al. / Optics Communications 242 (2004) 487–502
30-lm core for a 60-m long cavity is indispensable; the reflection at the Stokes wavelength in the laser cavity should be greatly eliminated; and selection of a longer lasing wavelength is also effective. From the viewpoint of output power, the traditional end-pumped scheme with a higher pump absorption coefficient and a shorter cavity length offers the best laser efficiency and is free of the detrimental Raman effects. However, the strong thermal effects can definitely deteriorate the beam quality and system reliability due to a high operating temperature, and render this scheme currently impractical for long-term applications. To lower fiber operating temperature for the end-pumped scheme, one can simply reduce pump absorption and lengthen the cavity. However, the laser suffers relatively low efficiency. As a better solution, the arrangement of uneven pump absorption coefficients along the cavity, e.g., smaller ones near the pump ends, can reduce fiber temperature and improve laser efficiency to some extent. The best solution is to adopt the distributed pumping scheme, with which the acceptable laser efficiency and temperature distribution can be achieved by optimizing the arrangement of pump powers, pump absorption coefficients, and fiber lengths. Acknowledgment The authors acknowledge support from the Ontario Photonics Consortium of Canada.
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