- Email: [email protected]
Study of high-power diode-end-pumped Nd:YVO4 laser at 1.34 μm: influence of Auger upconversion
15 May 1999
Optics Communications 163 Ž1999. 198–202
Study of high-power diode-end-pumped Nd:YVO4 laser at 1.34 mm: influence of Auger upconversion Y.F. Chen ) , L.J. Lee, T.M. Huang, C.L. Wang Precision Instrument DeÕelopment Center, National Science Council, 20 R & D Road VI, Hsinchu Science-Based Industrial Park, Hsinchu, Taiwan Received 5 January 1999; received in revised form 2 March 1999; accepted 4 March 1999
Abstract We demonstrated an experimental study of the influence of the Nd 3q concentration on scaling diode-pumped Nd:YVO4 1.34-mm lasers to higher power. An output power of 5.1 W at 1.34 mm was obtained with a 0.5-at.% Nd-doped YVO4 at 13.5 W of incident pump power. The strong dependence of the slope efficiency on the dopant concentration is attributed to an Auger upconversion process. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.55.y f; 42.60 Keywords: Neodymium; Diode-pumped; Solid-state laser; Auger upconversion
1. Introduction Yttrium orthovanadate ŽYVO4 . doped with Nd 3q is one of the efficient laser host materials currently used for diode-pumped solid-state lasers w1x. Most research on this material concerns the 1.06-mm transition. There is widespread need for a source operating near 1.3 mm to coincide with the transmission window of silica optical fibers w2x. Recently, a diode-pumped 1.34-mm Nd:YVO4 microchip laser was investigated by several groups w3–6x. However, the maximum pump power was less than 1 W in these investigations. In this paper, we investigated the performance in scaling diode-end-pumped 1.34-mm Nd:YVO4 lasers to higher power. With the 0.5-at.% Nddoped YVO4 , we obtained the highest slope efficiency of 44%. An analytical model for upconversion effect was developed to study the influence of Nd 3q concentrations on the performance of the diode-pumped 1.34 mm.
)
Corresponding author. E-mail: [email protected]
2. Experiments A concave–flat cavity shown in Fig. 1 was adopted to perform the laser experiments for 1.06 mm and 1.34 mm. Nd:YVO4 crystals with different Nd 3q concentrations and high optical quality were supplied by Fujian Castech Crystals. The lengths of Nd:YVO4 crystals are 6, 3, 2, and 2 mm for 0.5, 1.0, 2.0, and 3.0 at.% Nd 3q concentrations, respectively. For a lower Nd 3q concentration, a longer crystal was chosen to increase the absorption efficiency. All crystals were a-cut to obtain the high-gain p transition. In addition, Nd:YVO4 crystals were wrapped with indium foil and was press fitted into a water-cooled copper housing. The water temperature was held at 178C. Laser crystals were singly end-pumped by a fiber-coupled laser diode through a concave high-reflection mirror with a radius of 1 m. The output coupler was a flat mirror. The reflectivity of output couplers covered the range 90–99%. For 1.34-mm operation, both mirrors have a transmission of 95% at 1.06 mm to suppress the 1.06-mm laser line. Cavity length was fixed to as short as 50 mm to prevent thermal focusing from affecting the laser performance in
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 1 3 2 - 7
Y.F. Chen et al.r Optics Communications 163 (1999) 198–202
199
Fig. 1. Structure of diode-pumped Nd:YVO4 lasers for 1.06-mm and 1.34-mm operations.
high pumping power region. Under this cavity length, the beam waist ranges from 240 mm at 5 W of pump power, down to 205 mm at 14 W. Laser crystals were antireflection-coated for 0.808, 1.06, and 1.34 mm on both end surfaces. The fibers were drawn into round bundles of 1.15 mm diameter and a numerical aperture of 0.11. The focus pump-spot radius was around 0.29 mm. An aperture was inserted in the cavity to control the laser mode in TEMoo. The experimental results show that the optimum reflectivity of output couplers are 90% and 96% for 1.06-mm and 1.34-mm operations, respectively. The output powers of 1.06-mm and 1.34-mm lasers in Nd:YVO4 crystals with different concentrations were obtained with the optimum output couplers and are shown in Fig. 2Ža. and Žb.. Fig. 2Žb. shows that 5.1 W of 1.34-mm laser output power was obtained with a 0.5-at.% Nd-doped YVO4 at 13.5 W of incident pump power. To our knowledge, this is the highest CW 1.34-mm output power achieved to date. Fig. 2Ža. and Žb. reveals that the 3.0-at.% Nd-doped material is not appropriate for high power operations of both 1.06 mm and 1.34 mm because of thermally-induced fracture w7x, although for special applications like single-frequency operation of microchip lasers, the rather high absorption coefficient will be useful. It is important to note that the threshold pump power and the slope efficiency in the 1.06-mm operation are almost identical for the Nd 3q concentrations in the range of 0.5–2.0 at.%; however, the slope efficiency of 0.5-at.% Nd-doped crystal in the 1.34mm operation is certainly higher than that of 1.0–2.0-at.% Nd:YVO4 . As discussed below, we believe that this result is due to Auger upconversion losses.
3. Auger upconversion effects
Fig. 2. Ža. A plot of the output powers of 1.06-mm laser obtained with the optimum output couplers, T s90%, in Nd:YVO4 with different concentrations. Žb. A plot of the output powers of 1.34-mm laser obtained with the optimum output couplers, T s 96%, in Nd:YVO4 with different concentrations.
Excited-state absorption ŽESA. and Auger energy transfer upconversion are the two possible processes that negatively influence laser operation at high population inversion densities. An ESA effect could occur either at the pump or at the laser emission. Guyot et al. w8x developed an analytical model to investigate the influence of ESA, in the pumping as well as in the emission domains, on the laser performance of a four-level laser system. This analytical model shows that ESA has a significant effect only for p l . larger than 0.5, rŽ sem y s ESA the value of the ratio s ESA
Y.F. Chen et al.r Optics Communications 163 (1999) 198–202
200
p l where s ESA and s ESA are the ESA cross-sections at the pump and laser wavelengths and sem is the stimulated emission cross-section. A number of publications w8,9x show that ESA in the infrared metastable level 4F3r2 of Nd 3q in most laser crystals at the main laser wavelengths is negligible. These papers also show that ESA in the laser diode-pumping domain around 800 nm could occur but with much weaker cross-sections. Therefore, it is concluded that ESA in the diode-pumped Nd-doped laser-related materials should not influence the laser performance significantly. The Auger upconversion process involves two nearby ions in the metastable level 4F3r2 . One ion returns to the ground state by transferring its energy to the other which is, in turn, brought into a higher excited state from which the excited ion relaxes down to the 4F3r2 level mostly via multiphonon emission. Consequently, upconversion processes not only reduce the population inversion but also increase the thermal loading in the laser material. The Auger upconversion rate depends on the number density of excited ions and is the main energy-transfer process at high excitations. Several recent works w10–14x show that Auger upconversion is a detrimental process in many practically important Nd-doped laser crystals, especially in high small-signal amplifiers and Q-switched lasers. In comparison with 1.06-mm, the higher laser threshold at 1.34 mm gives rise to a greater clamped inversion, thereby leading to higher Auger upconversion losses. The similar claim has also been proposed in the recent study of luminescence quenching and energy transfer upconversion in Nd-doped LaSc 3ŽBO 3 .4 ŽLSB. and GdVO4 ŽGVO. laser crystals w14x. To study the upconversion effect, we use the kinetic equation w14x:
dn dt
sRŽ r , z . y
n
t
y g n2 ,
Ž1.
where n is the population density, RŽ r, z . is the rate of the pump intensity at any radial location r or axial location z, t is the emission lifetime, and g is the upconversion rate. Here we neglect the self-quenching effect which is roughly one order of magnitude smaller than the upconversion effect w12x. The population density of the laser level under CW excitation is obtained by setting d nrdt s 0; therefore: nŽ r , z . s
(1 q 4t g R Ž r , z . y 1 2
2tg .
Using a fiber-coupled laser diode in an end-pumping configuration, the pump rate can be expressed as a top-hat distribution w7x: RŽ r , z . s
Pin
a eya z
hnp pv p2 w 1 y ey a l x
Q Ž v p2 y r 2 . ,
Ž3.
where Pin is the incident pump power, np is the pump frequency, a is the absorption coefficient at the pump
wavelength, v p is the pump size, l is the length of the active medium, and Q Ž. is the Heaviside step function. The average population number is given by: Ns
l
vp
H0 d zH0
n Ž r , z . 2p rd r
Ž4.
It can be found that if g s 0, the average population number at threshold is given by N 0 s t Pthrhn P . Therefore, the fractional reduction of the population inversion due to upconversion can be expressed as: Fuc s Ž N 0 y N . rN 0 .
Ž5.
Substituting Eqs. Ž2. – Ž4. into Eq. Ž5., and integrating over the medium length and transverse dimensions, the fractional reduction can be found to be: Fuc Ž r . s1y
2
r Ž 1y ey a l .
½ Ž'
'
1q r y 1q r eya l
2
eya l 2q r y2 1q r
'
Ž
qln
ya l
2q r e
'
.
ya l
y2 1q r e
5
yal ,
. Ž6.
where:
rs
4gt 2a Pin
pv p2 hn P
.
Ž7.
To take upconversion effects into account, the quantum efficiency, which is defined as the number of photons contributing to laser emission divided by the number of pump photons, is then given by:
hQ Ž r . s hQ0 w 1 y Fuc Ž r . x ,
Ž8.
where hQ0 is the quantum efficiency in the absence of upconversion processes. If concentration quenching and ESA are not significant, the quantum efficiency, hQ0 , is almost equal to unity. According to Eq. Ž7., the parameter is proportional to the factor gt and the population inversion density. Therefore, the upconversion effects strongly increase with the increase of the population inversion density. Even so, for a CW laser above threshold, the inversion density is pinned to the critical inversion at the threshold condition. Consequently, the upconversion effect remains constant for pump power above threshold and the effective quantum efficiency for a CW laser above threshold should be determined by hQŽ rth ., where:
rth s
4gt 2a Pth
pv p2 hn P
Ž9.
and Pth is the threshold pump power. Eqs. Ž6. – Ž9. represent the dependence of upconversion effects on the emission lifetime, the absorption coefficient, the threshold power, and the upconversion rate. The pa-
Y.F. Chen et al.r Optics Communications 163 (1999) 198–202
201
rameters such as the emission lifetime, the absorption coefficient and the threshold power, are all related to the dopant concentration. In other words, Eqs. Ž6. – Ž9. reveal the dependence of upconversion effects on the dopant concentration. Experimental results show that the absorption coefficient of Nd:YVO4 crystals for a typical fibercoupled laser diode with the center wavelength of 808 nm is given by:
a s 20 Nd Ž cmy1 .
Ž 10.
where Nd is the Nd dopant concentration in units of at.%. On the other hand, the emission lifetime of Nd:YVO4 crystals can be fitted to the relation w15x: 100
ts 1q
Nd
2
Ž ms . ,
Ž 11.
ž / Ndo
where Ndo s 2.2 at.%. To estimate the influence of upconversion on laser performance, the value for the rate of the Auger upconversion process was measured by using the method in Ref. w14x. The estimated value of g is Ž2.0 " 1. = 10 15 cm3rs. This value is close to that in Nd:GdVO4 crystal, Ž1.2–1.4. = 10 15 cm3rs w14x. Applying g s 2 = 10 15 cm3rs and the experimental threshold powers into Eqs. Ž6. – Ž9., the effective quantum efficiency was calculated as a function of the dopant concentration for 1.06-mm and 1.34-mm laser operations. Here we assume hQ0 s 1. The calculation results were shown in Fig. 3. As expected, the influence of the upconversion on 1.34-mm laser operation is more significant than that on 1.06-mm laser operation because of high threshold powers. In addition, the dependence of the up-
Fig. 3. A plot of the effective quantum efficiency as a function of dopant concentration for 1.06-mm and 1.34-mm laser operations.
Fig. 4. A plot of the variations of the slope efficiency at 1.06-mm and 1.34-mm lasers with the dopant concentration: experimental results Žsymbol. and theoretical results Žsolid lines..
conversion effect on the dopant concentration at 1.34-mm laser is stronger than that at 1.06-mm laser in the range of 0.5–2.0 at.%. From the space-dependent rate equation analysis, the slope efficiency is given by w16x: Se s
T TqL
hQ Ž rth .
lp ll
h0 ,
Ž 12.
where T is the power transmission of the output coupler, Isat is the saturation intensity, l is the length of the active medium, l l is the laser wavelength, l p is the pump wavelength, ho is the overlapping efficiency, and L denotes the round-trip cavity excess losses which include thermally-induced diffraction losses, nondiffraction roundtrip losses such as scattering at interfaces, imperfect reflection, and excited-state absorption. For quantitative comparison, the dependence of the slope efficiency on the dopant concentration was evaluated by substituting the cavity parameters and the calculated quantum efficiency into Eq. Ž12.. Note that h f 0.95 and the values of L were obtained by adjusting the theoretical results for the best fit to the experimental slope efficiency at the region of T ™ 0. The values of L were found to be around 0.009–0.011 for different crystals. Fig. 4 shows the variations of the slope efficiency at 1.06-mm and 1.34-mm lasers with the dopant concentration. The theoretical result is consistent with the experimental result that the slope efficiency at 1.34-mm laser is more sensitive than that at 1.06-mm laser to the dopant concentration. The good agreement obtained between experimental results and theoretical predictions confirms our physical analysis and validates the present model.
202
Y.F. Chen et al.r Optics Communications 163 (1999) 198–202
4. Summary In summary, we have investigated the influence of Nd 3q concentrations on the diode-pumped Nd:YVO4 operating in 1.34-mm laser. The concentration-dependent slope efficiencies have been discussed from the Auger upconversion. The results showed that the upconversioninduced population reduction in 1.34-mm laser is a strong increasing function of the Nd 3q concentration in the range of 0.5 to 2.0 at.%, whereas the fractional reduction in the 1.06-mm laser is not sensitive to the Nd 3q concentration in the range of 0.5 to 2.0 at.%. Special care is necessary to minimize the negative influence of upconversion, especially at high threshold values typical for weak 1.3–1.4-mm Nd transitions.
References w1x R.A. Fields, M. Birnbaum, C.L. Fincher, Appl. Phys. Lett. 51 Ž1986. 1885. w2x A.W. Tucker, M. Birnaum, C.L. Fincher, L.G. DeShazer, J. Appl. Phys. 47 Ž1976. 232. w3x R. Fluck, B. Braun, E. Gini, H. Melchior, U. Keller, Opt. Lett. 22 Ž1997. 991.
w4x R. Fluck, G. Zhang, U. Keller, K.J. Weingarten, M. Moser, Opt. Lett. 21 Ž1996. 1378. w5x G.C. Bowkett, G.W. Baxter, D.J. Booth, T. Taira, H. Teranishi, T. Kobayashi, Opt. Lett. 19 Ž1994. 957. w6x R.S. Conroy, A.J. Kemp, G.J. Friel, B.D. Sinclair, Opt. Lett. 22 Ž1997. 1781. w7x Y.F. Chen, T.M. Huang, C.F. Kao, C.L. Wang, S.C. Wang, IEEE J. Quantum Electron. 35 Ž1999. 234. w8x Y. Guyot, H. Manan, J.Y. Rivoire, R. Moncorg, N. Garnier, E. Descroix, M. Bon, P. Laporte, Phys. Rev. B 51 Ž1995. 784. w9x Y. Guyot, R. Moncorg, J. Appl. Phys. 73 Ž1993. 8526. w10x J.D. Zuegel, W. Seka, in: IEEE Lasers and Electro-Optics Society Annual Meeting, 8th Annual Meeting Conference Proceedings, Vol. 2, 1995, p. 204. w11x T. Chuang, H.R. Verdum, IEEE J. Quantum Electron. 32 Ž1996. 79. w12x S. Guy, C.L. Bonner, D.P. Shepherd, D.C. Hanna, A.C. Tropper, B. Ferrand, IEEE J. Quantum Electron. 34 Ž1998. 900. w13x M. Pollnau, P.J. Hardman, W.A. Clarkson, D.C. Hanna, Opt. Commun. 147 Ž1998. 203. w14x V. Ostroumov, T. Jensen, J.P. Meyen, G. Huber, M.A. Noginov, J. Opt. Soc. Am. B 15 Ž1998. 1052. w15x H. Nagamoto, M. Nakatsuka, K. Naito, M. Yamanaka, K. Yoshida, T. Sasaki, T. Kanabe, S. Saito, Y. Kuwano, Laser Res. 18 Ž1990. 639. w16x P. Laporta, M. Brussard, IEEE J. Quantum Electron. 27 Ž1991. 2319.
Optics Communications 163 Ž1999. 198–202
Study of high-power diode-end-pumped Nd:YVO4 laser at 1.34 mm: influence of Auger upconversion Y.F. Chen ) , L.J. Lee, T.M. Huang, C.L. Wang Precision Instrument DeÕelopment Center, National Science Council, 20 R & D Road VI, Hsinchu Science-Based Industrial Park, Hsinchu, Taiwan Received 5 January 1999; received in revised form 2 March 1999; accepted 4 March 1999
Abstract We demonstrated an experimental study of the influence of the Nd 3q concentration on scaling diode-pumped Nd:YVO4 1.34-mm lasers to higher power. An output power of 5.1 W at 1.34 mm was obtained with a 0.5-at.% Nd-doped YVO4 at 13.5 W of incident pump power. The strong dependence of the slope efficiency on the dopant concentration is attributed to an Auger upconversion process. q 1999 Elsevier Science B.V. All rights reserved. PACS: 42.55.y f; 42.60 Keywords: Neodymium; Diode-pumped; Solid-state laser; Auger upconversion
1. Introduction Yttrium orthovanadate ŽYVO4 . doped with Nd 3q is one of the efficient laser host materials currently used for diode-pumped solid-state lasers w1x. Most research on this material concerns the 1.06-mm transition. There is widespread need for a source operating near 1.3 mm to coincide with the transmission window of silica optical fibers w2x. Recently, a diode-pumped 1.34-mm Nd:YVO4 microchip laser was investigated by several groups w3–6x. However, the maximum pump power was less than 1 W in these investigations. In this paper, we investigated the performance in scaling diode-end-pumped 1.34-mm Nd:YVO4 lasers to higher power. With the 0.5-at.% Nddoped YVO4 , we obtained the highest slope efficiency of 44%. An analytical model for upconversion effect was developed to study the influence of Nd 3q concentrations on the performance of the diode-pumped 1.34 mm.
)
Corresponding author. E-mail: [email protected]
2. Experiments A concave–flat cavity shown in Fig. 1 was adopted to perform the laser experiments for 1.06 mm and 1.34 mm. Nd:YVO4 crystals with different Nd 3q concentrations and high optical quality were supplied by Fujian Castech Crystals. The lengths of Nd:YVO4 crystals are 6, 3, 2, and 2 mm for 0.5, 1.0, 2.0, and 3.0 at.% Nd 3q concentrations, respectively. For a lower Nd 3q concentration, a longer crystal was chosen to increase the absorption efficiency. All crystals were a-cut to obtain the high-gain p transition. In addition, Nd:YVO4 crystals were wrapped with indium foil and was press fitted into a water-cooled copper housing. The water temperature was held at 178C. Laser crystals were singly end-pumped by a fiber-coupled laser diode through a concave high-reflection mirror with a radius of 1 m. The output coupler was a flat mirror. The reflectivity of output couplers covered the range 90–99%. For 1.34-mm operation, both mirrors have a transmission of 95% at 1.06 mm to suppress the 1.06-mm laser line. Cavity length was fixed to as short as 50 mm to prevent thermal focusing from affecting the laser performance in
0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 9 9 . 0 0 1 3 2 - 7
Y.F. Chen et al.r Optics Communications 163 (1999) 198–202
199
Fig. 1. Structure of diode-pumped Nd:YVO4 lasers for 1.06-mm and 1.34-mm operations.
high pumping power region. Under this cavity length, the beam waist ranges from 240 mm at 5 W of pump power, down to 205 mm at 14 W. Laser crystals were antireflection-coated for 0.808, 1.06, and 1.34 mm on both end surfaces. The fibers were drawn into round bundles of 1.15 mm diameter and a numerical aperture of 0.11. The focus pump-spot radius was around 0.29 mm. An aperture was inserted in the cavity to control the laser mode in TEMoo. The experimental results show that the optimum reflectivity of output couplers are 90% and 96% for 1.06-mm and 1.34-mm operations, respectively. The output powers of 1.06-mm and 1.34-mm lasers in Nd:YVO4 crystals with different concentrations were obtained with the optimum output couplers and are shown in Fig. 2Ža. and Žb.. Fig. 2Žb. shows that 5.1 W of 1.34-mm laser output power was obtained with a 0.5-at.% Nd-doped YVO4 at 13.5 W of incident pump power. To our knowledge, this is the highest CW 1.34-mm output power achieved to date. Fig. 2Ža. and Žb. reveals that the 3.0-at.% Nd-doped material is not appropriate for high power operations of both 1.06 mm and 1.34 mm because of thermally-induced fracture w7x, although for special applications like single-frequency operation of microchip lasers, the rather high absorption coefficient will be useful. It is important to note that the threshold pump power and the slope efficiency in the 1.06-mm operation are almost identical for the Nd 3q concentrations in the range of 0.5–2.0 at.%; however, the slope efficiency of 0.5-at.% Nd-doped crystal in the 1.34mm operation is certainly higher than that of 1.0–2.0-at.% Nd:YVO4 . As discussed below, we believe that this result is due to Auger upconversion losses.
3. Auger upconversion effects
Fig. 2. Ža. A plot of the output powers of 1.06-mm laser obtained with the optimum output couplers, T s90%, in Nd:YVO4 with different concentrations. Žb. A plot of the output powers of 1.34-mm laser obtained with the optimum output couplers, T s 96%, in Nd:YVO4 with different concentrations.
Excited-state absorption ŽESA. and Auger energy transfer upconversion are the two possible processes that negatively influence laser operation at high population inversion densities. An ESA effect could occur either at the pump or at the laser emission. Guyot et al. w8x developed an analytical model to investigate the influence of ESA, in the pumping as well as in the emission domains, on the laser performance of a four-level laser system. This analytical model shows that ESA has a significant effect only for p l . larger than 0.5, rŽ sem y s ESA the value of the ratio s ESA
Y.F. Chen et al.r Optics Communications 163 (1999) 198–202
200
p l where s ESA and s ESA are the ESA cross-sections at the pump and laser wavelengths and sem is the stimulated emission cross-section. A number of publications w8,9x show that ESA in the infrared metastable level 4F3r2 of Nd 3q in most laser crystals at the main laser wavelengths is negligible. These papers also show that ESA in the laser diode-pumping domain around 800 nm could occur but with much weaker cross-sections. Therefore, it is concluded that ESA in the diode-pumped Nd-doped laser-related materials should not influence the laser performance significantly. The Auger upconversion process involves two nearby ions in the metastable level 4F3r2 . One ion returns to the ground state by transferring its energy to the other which is, in turn, brought into a higher excited state from which the excited ion relaxes down to the 4F3r2 level mostly via multiphonon emission. Consequently, upconversion processes not only reduce the population inversion but also increase the thermal loading in the laser material. The Auger upconversion rate depends on the number density of excited ions and is the main energy-transfer process at high excitations. Several recent works w10–14x show that Auger upconversion is a detrimental process in many practically important Nd-doped laser crystals, especially in high small-signal amplifiers and Q-switched lasers. In comparison with 1.06-mm, the higher laser threshold at 1.34 mm gives rise to a greater clamped inversion, thereby leading to higher Auger upconversion losses. The similar claim has also been proposed in the recent study of luminescence quenching and energy transfer upconversion in Nd-doped LaSc 3ŽBO 3 .4 ŽLSB. and GdVO4 ŽGVO. laser crystals w14x. To study the upconversion effect, we use the kinetic equation w14x:
dn dt
sRŽ r , z . y
n
t
y g n2 ,
Ž1.
where n is the population density, RŽ r, z . is the rate of the pump intensity at any radial location r or axial location z, t is the emission lifetime, and g is the upconversion rate. Here we neglect the self-quenching effect which is roughly one order of magnitude smaller than the upconversion effect w12x. The population density of the laser level under CW excitation is obtained by setting d nrdt s 0; therefore: nŽ r , z . s
(1 q 4t g R Ž r , z . y 1 2
2tg .
Using a fiber-coupled laser diode in an end-pumping configuration, the pump rate can be expressed as a top-hat distribution w7x: RŽ r , z . s
Pin
a eya z
hnp pv p2 w 1 y ey a l x
Q Ž v p2 y r 2 . ,
Ž3.
where Pin is the incident pump power, np is the pump frequency, a is the absorption coefficient at the pump
wavelength, v p is the pump size, l is the length of the active medium, and Q Ž. is the Heaviside step function. The average population number is given by: Ns
l
vp
H0 d zH0
n Ž r , z . 2p rd r
Ž4.
It can be found that if g s 0, the average population number at threshold is given by N 0 s t Pthrhn P . Therefore, the fractional reduction of the population inversion due to upconversion can be expressed as: Fuc s Ž N 0 y N . rN 0 .
Ž5.
Substituting Eqs. Ž2. – Ž4. into Eq. Ž5., and integrating over the medium length and transverse dimensions, the fractional reduction can be found to be: Fuc Ž r . s1y
2
r Ž 1y ey a l .
½ Ž'
'
1q r y 1q r eya l
2
eya l 2q r y2 1q r
'
Ž
qln
ya l
2q r e
'
.
ya l
y2 1q r e
5
yal ,
. Ž6.
where:
rs
4gt 2a Pin
pv p2 hn P
.
Ž7.
To take upconversion effects into account, the quantum efficiency, which is defined as the number of photons contributing to laser emission divided by the number of pump photons, is then given by:
hQ Ž r . s hQ0 w 1 y Fuc Ž r . x ,
Ž8.
where hQ0 is the quantum efficiency in the absence of upconversion processes. If concentration quenching and ESA are not significant, the quantum efficiency, hQ0 , is almost equal to unity. According to Eq. Ž7., the parameter is proportional to the factor gt and the population inversion density. Therefore, the upconversion effects strongly increase with the increase of the population inversion density. Even so, for a CW laser above threshold, the inversion density is pinned to the critical inversion at the threshold condition. Consequently, the upconversion effect remains constant for pump power above threshold and the effective quantum efficiency for a CW laser above threshold should be determined by hQŽ rth ., where:
rth s
4gt 2a Pth
pv p2 hn P
Ž9.
and Pth is the threshold pump power. Eqs. Ž6. – Ž9. represent the dependence of upconversion effects on the emission lifetime, the absorption coefficient, the threshold power, and the upconversion rate. The pa-
Y.F. Chen et al.r Optics Communications 163 (1999) 198–202
201
rameters such as the emission lifetime, the absorption coefficient and the threshold power, are all related to the dopant concentration. In other words, Eqs. Ž6. – Ž9. reveal the dependence of upconversion effects on the dopant concentration. Experimental results show that the absorption coefficient of Nd:YVO4 crystals for a typical fibercoupled laser diode with the center wavelength of 808 nm is given by:
a s 20 Nd Ž cmy1 .
Ž 10.
where Nd is the Nd dopant concentration in units of at.%. On the other hand, the emission lifetime of Nd:YVO4 crystals can be fitted to the relation w15x: 100
ts 1q
Nd
2
Ž ms . ,
Ž 11.
ž / Ndo
where Ndo s 2.2 at.%. To estimate the influence of upconversion on laser performance, the value for the rate of the Auger upconversion process was measured by using the method in Ref. w14x. The estimated value of g is Ž2.0 " 1. = 10 15 cm3rs. This value is close to that in Nd:GdVO4 crystal, Ž1.2–1.4. = 10 15 cm3rs w14x. Applying g s 2 = 10 15 cm3rs and the experimental threshold powers into Eqs. Ž6. – Ž9., the effective quantum efficiency was calculated as a function of the dopant concentration for 1.06-mm and 1.34-mm laser operations. Here we assume hQ0 s 1. The calculation results were shown in Fig. 3. As expected, the influence of the upconversion on 1.34-mm laser operation is more significant than that on 1.06-mm laser operation because of high threshold powers. In addition, the dependence of the up-
Fig. 3. A plot of the effective quantum efficiency as a function of dopant concentration for 1.06-mm and 1.34-mm laser operations.
Fig. 4. A plot of the variations of the slope efficiency at 1.06-mm and 1.34-mm lasers with the dopant concentration: experimental results Žsymbol. and theoretical results Žsolid lines..
conversion effect on the dopant concentration at 1.34-mm laser is stronger than that at 1.06-mm laser in the range of 0.5–2.0 at.%. From the space-dependent rate equation analysis, the slope efficiency is given by w16x: Se s
T TqL
hQ Ž rth .
lp ll
h0 ,
Ž 12.
where T is the power transmission of the output coupler, Isat is the saturation intensity, l is the length of the active medium, l l is the laser wavelength, l p is the pump wavelength, ho is the overlapping efficiency, and L denotes the round-trip cavity excess losses which include thermally-induced diffraction losses, nondiffraction roundtrip losses such as scattering at interfaces, imperfect reflection, and excited-state absorption. For quantitative comparison, the dependence of the slope efficiency on the dopant concentration was evaluated by substituting the cavity parameters and the calculated quantum efficiency into Eq. Ž12.. Note that h f 0.95 and the values of L were obtained by adjusting the theoretical results for the best fit to the experimental slope efficiency at the region of T ™ 0. The values of L were found to be around 0.009–0.011 for different crystals. Fig. 4 shows the variations of the slope efficiency at 1.06-mm and 1.34-mm lasers with the dopant concentration. The theoretical result is consistent with the experimental result that the slope efficiency at 1.34-mm laser is more sensitive than that at 1.06-mm laser to the dopant concentration. The good agreement obtained between experimental results and theoretical predictions confirms our physical analysis and validates the present model.
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4. Summary In summary, we have investigated the influence of Nd 3q concentrations on the diode-pumped Nd:YVO4 operating in 1.34-mm laser. The concentration-dependent slope efficiencies have been discussed from the Auger upconversion. The results showed that the upconversioninduced population reduction in 1.34-mm laser is a strong increasing function of the Nd 3q concentration in the range of 0.5 to 2.0 at.%, whereas the fractional reduction in the 1.06-mm laser is not sensitive to the Nd 3q concentration in the range of 0.5 to 2.0 at.%. Special care is necessary to minimize the negative influence of upconversion, especially at high threshold values typical for weak 1.3–1.4-mm Nd transitions.
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