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Stimulated Brillouin scattering of Q-switched laser pulses in large-core optical fibres
Optics & Laser Technology 33 (2001) 617–622
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Stimulated Brillouin scattering of Q-switched laser pulses in large-core optical (bres V. Pashinina , V. Sturmb; ∗ , V. Tumorina , R. Nollb a General
Physics Institute, 38 Vavilov Street, 117942 Moscow, Russia f"ur Lasertechnik (ILT), Steinbachstr. 15, 52074 Aachen, Germany
b Fraunhofer-Institut
Received 29 January 2001; accepted 11 September 2001
Abstract Q-switched Nd : glass laser pulses of 60 ns duration are transmitted through multimode fused-silica (bres of 0.4 –1 mm core diam and lengths of up to 20 m. For laser radiation with narrow spectral width, stimulated Brillouin scattering (SBS) is observed for energies well below the threshold energy of (bre damage. The SBS threshold is shifted beyond the threshold of (bre damage through increasing the spectral width of the laser radiation. The SBS threshold energies of step-index and gradient-index (bres are measured for various (bre c 2001 Elsevier Science Ltd. All rights reserved. and laser parameters. Keywords: Fibre; Stimulated Brillouin scattering; Laser
1. Introduction Q-switched laser pulses with energies of up to several 100 mJ are used, e.g. for holographic interferometry [1], laser spectroscopy [2], or velocimetry [3]. Optical (bre transmission of the laser radiation would signi(cantly facilitate such laser applications in metrology. In holography, the object beam can be transmitted through multimode (bres since, in any case, the scattering at the object destroys the transversal mode structure of the laser beam. Damage of the fused-silica (bre core or core-cladding interface is often regarded as the only limiting process in high-energy nanosecond pulse transmission through (bres with large core diameters of 0.4 –1 mm [4,5]. Stimulated Brillouin scattering (SBS) in (bres has been the subject of numerous investigations, which mainly focused on single-mode (bres (core diam of ∼10 m) or small-core multimode (bres (core diam of ¡ 50 m), for communication purposes, with lengths in the km-range and use of continuous-wave radiation [6 –15]. In [16,17], SBS thresholds are measured for (bres of 0.1 and 0:2 mm diam with respect to using the (bres for phase conjugators. However, for (bres of diam ¿ 0:4 mm there are only a few reports ∗
Corresponding author. Tel.: +49-241-8906-0; fax: +49-241-806-121. E-mail address: [email protected] (V. Sturm).
about stimulated scattering of ruby [18] or Nd : YAG [19] laser pulses. In [18,19], the peak power of the Q-switched laser pulses is reduced, e.g. by pulse stretching [18] or by distributing the energy to microsecond-spaced multiple pulses of a burst [19], in order to avoid (bre damage, but stimulated scattering is observed as the limiting process for (bre transmission. The scattering mechanism is assumed to be SBS in [18,19], but it has not been revealed by measurement. In this study, Nd : glass laser pulses are employed in the determination of the scattering mechanism through spectral analysis. The Nd : glass laser with its large gain bandwidth allows to vary the spectral width of the laser radiation over a wide range. Stimulated scattering thresholds are measured in dependence of diFerent (bre parameters, in order to (nd appropriate conditions for stimulated scattering suppression. The gain coeGcient of SBS, gB , in fused silica at 1 m, is ∼1–5 × 10−9 cm=W and is, therefore, a factor of approximately 500 times larger than the gain coeGcient for stimulated Raman scattering (SRS) [15]. The Brillouin linewidth, IB , of (bres is much larger than that expected for bulk silica (∼35 MHz at 1:06 m [15]). Most of the increase in the linewidth is due to inhomogeneities in the cross section along the (bre length. Depending on each speci(c (bre, the Brillouin linewidth can be as large as ∼210 MHz at 1:06 m [15, p. 267]. Since the Brillouin linewidth, IB , is proportional to 1=p2 , the SBS gain coeGcient, gB ˙ 1=(p2 IB ), is
c 2001 Elsevier Science Ltd. All rights reserved. 0030-3992/01/$ - see front matter PII: S 0 0 3 0 - 3 9 9 2 ( 0 1 ) 0 0 0 8 6 - X
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V. Pashinin et al. / Optics & Laser Technology 33 (2001) 617–622
almost independent of the wavelength of the incident pump wave, p [15], which is the laser wavelength in our experiments. SBS is suppressed in favour of SRS if the spectral width of the laser, Ip , exceeds IB by a multiple of the ratio of SBS gain to SRS gain [8, p. 230], i.e. if Ip is a multiple of 500 × IB ≈ 105 GHz = 3:5 cm−1 . We used a maximum spectral width of 0:65 cm−1 . Therefore, the occurrence of SRS is not expected. For narrow-band pumping conditions, Ip IB , the SBS threshold irradiation for a single-mode (bre, under steady-state conditions and linear polarization, is independent of the spectral width of the laser [7,20]: Ip; th ≈ 21=(gB LeF ):
(1)
The eFective interaction length LeF is given in [16] by 1=LeF = 1=Lcoh + 1=L (Lcoh coherence length of the SBS pump radiation). For broad-band pumping [21], Ip IB , and if Lcoh LeF , the SBS threshold irradiation increases almost linearly with Ip [10,15, p. 267]: Ip; th ≈ [21=(gB LeF )](1 + Ip =IB ):
(2)
In case of multimode (bres, the laser energy is distributed over many modes and over a larger volume, compared to single-mode (bres. In addition, the actual intensity distribution over the guided modes can be important with respect to the threshold pump irradiance. Therefore, Eqs. (1) and (2) represent a lower limit for the threshold pump irradiance of multimode (bres. 2. Experimental setup The 1054-nm Nd : doped phosphate glass laser with a resonator length of 1 m consists of a H4 mm × 100 mm Nd : glass rod, a LiF : F2− crystal for passive Q-switching, an intracavity telescope L1, L2 (f1 = 200 mm; f2 = − 70 mm), a 25%-reQective output mirror with a radius of curvature of 5 m and a plane high-reQecting rear mirror. Within a single Qashlamp pulse (max. repetition rate of ∼1 Hz), optionally up to six Q-switched pulses of ∼60 ns duration can be generated with interpulse separations of 10 –30 s (determined by passive Q-switching and resonator parameters). Three laser resonators have been con(gured to obtain spectral widths of 0:65 cm−1 (broad-band con(guration, denoted as BB laser in the following), 0:1 cm−1 (intermediate-band con(guration, IB), and ¡ 0:0016 cm−1 (narrow-band con(guration, NB). For the IB and BB laser, broadband pumping conditions of Eq. (2) are given, while the spectral width of the NB laser is probably smaller, but not very small, compared to the Brillouin linewidth IB ≈ 35–210 MHz = 0:0012–0:007 cm−1 . Hence, the conditions of Eq. (1) are not ful(lled strictly in this intermediate range, but Eq. (1) should be helpful for approximate calculations. The IB con(guration uses a 0.25-mm-thin plane–parallel glass plate as a spectrally selective output mirror. The NB
Table 1 List of (bre types and measured SBS threshold energies, Ep; th , for NB laser radiationa ◦
◦
◦
◦
No.
Type
d (mm)
Ep; th (0 ) (mJ)
Ep; th (6 ) (mJ)
p; th (0 ) (J=cm2 )
p; th (6 ) (J=cm2 )
1 2 3 4 5 6 7 8 9
S,UV S,WF S,UV S,WF S,UV G G G G
0.4 0.6 0.6 0.8 1.0 0.4 0.6 0.8 1.0
1.4 5.8 3.4 10.0 9.0 0.27 0.75 1.8 5.0
3.7 7.8 6.2 13.3 20.0 1.7 3.0 7.4 11.0
1.1 2.1 1.2 2.0 1.1 0.21 0.26 0.36 0.64
2.9 2.8 2.2 2.7 2.5 1.4 1.1 1.5 1.4
a Fibre
NA 0.22, length 5 m, input NA ∼0:07, (bre bending 800 × ◦ core diam. Ep; th for perpendicular (∼0 ) and non-perpendicular cou◦ pling (∼6 ), p; th threshold energy density, d (bre core diameter, S step-index (bre, G gradient-index (bre; UV (bre glass with enhanced short wavelength transmission; WF Water-free, (bre glass with enhanced near-infrared transmission. All (bres are PCVD manufactured by CeramOptec (Bonn, Germany).
resonator selects a single longitudinal mode by an inserted etalon and a rear mirror, consisting of several adjusted plane–parallel plates having a peak reQection of 60% and a free spectral range of ∼10 cm−1 . The maximum output energy is 0:13 J (single pulse) and 0:8 J (six-pulse burst) for the BB and IB con(guration, and 0:08 J (single pulse) and 0:5 J (six-pulse burst) for the NB con(guration. The temporal pro(les of the laser pulses are smooth since the mode beating modulation depth is very small due to the large number of modes for the broad-band con(guration, whereas for the narrow-band case, only a single mode exists. Table 1 lists the various (bre types used in the experiments. The end faces of the (bres were prepared by cleaving and optically inspected using a microscope. A (bre damage threshold of 60 J=cm2 is measured for a step-index (bre ((bre No. 1 in Table 1) and 6 J=cm2 for a gradient-index (bre (No. 6), if the laser output is coupled to the (bre by a single lens with f = 150 mm. For these measurements, the (bre lengths are 0:5 m and the beam waist diameter of ∼0:1 mm is located ∼20 mm in front of the (bre end. The lower damage threshold of the gradient-index (bre is due, most probably, to the small numerical aperture of the laser radiation at the (bre input (input NA) which results in the focusing of the radiation inside the (bre. To increase the divergence, a capillary tube is used, as depicted in Fig. 1(a). The damage threshold of the gradient-index (bre is increased to 16 J=cm2 , whereas the damage threshold of the step-index (bre is not inQuenced signi(cantly. Therefore, this coupling con(guration with linearly polarized (bre input radiation is used for all measurements presented in the (gures in this paper. The typical (bre output energy was 80% of the input energy from the capillary tube. The beam waist diameter at the focus of the coupling lens is 0:27 mm, for this coupling con(guration. To measure the inQuence of the polarization, the laser radiation is depolarized by means of a KDP
V. Pashinin et al. / Optics & Laser Technology 33 (2001) 617–622
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Fig. 1. Set-up for the (bre coupling of the polarized laser radiation (a) and the depolarized laser radiation (b). KDP crystal 10 × 10 × 8 mm3 , CT capillary tube 0:8 mm i.d. ×50 mm long. To vary the numerical aperture of the (bre coupling, lens L8 (positive or negative) can be inserted optionally.
crystal (see Fig. 1(b)). The laser energies were varied by (lters with a minimum step of 10%.
Fig. 3. Determination of the spectral shift of the backscattered radiation for step-index (bre No. 3. Spectrum of the reQected laser radiation with (bre input power below the threshold of stimulated backscattering (a), and spectrum of the backward radiation with (bre input power above threshold (b).
3. Spectral analysis To determine the spectral shift and the spectral width of the backscattered radiation, the Nd : glass laser radiation is coupled into the (bre, whilst the backward radiation is spectrally analysed by recording the fringe pattern of a Fabry– Perot interferometer (FPI) with a CCD linear array (Fig. 2). The spectral analysis is carried out with step-index and gradient-index (bres of 0.6-mm core diam, 5-m length, and an input NA of 0.05, unless otherwise noted. The NB laser is used because of the higher accuracy of measurement due to the narrow spectral width. The spectral shift is measured using a 5-mm air-gap FPI (free spectral range 1 cm−1 , spectral resolution of 0:15 cm−1 ). Few orders of the FPI circular fringe pattern are registered by the CCD linear array at the focal plane of lens L (focal length 400 mm).
Fig. 2. Set-up for spectral analysis of backscattered radiation and the measurement of incident, transmitted and backscattered laser radiation. Detector D1 (fast photomultiplier tube, rise time 3 ns, 500-MHz oscilloscope) registers the temporal pro(le of the backscattered laser pulse; D2, D3 time-integrating photodetectors (1 ms, 100-MHz storage oscilloscope) for input and transmitted energy; L lens; FCO (bre coupling optics as depicted in Fig. 1; BS wedge-shaped beam splitters; M1, M2 mirrors; M2 optionally inserted.
Fig. 3(a) shows the spectrum of the backward radiation with the (bre input power below the threshold of stimulated backscattering. The spectrum coincides with that of the incoming laser radiation; this is due to Fresnel reQection at the (bre end surface. If the (bre input energy exceeds the threshold of the stimulated backscattering, then the characteristic pulse is observed with detector D1 at that moment when the Stokes component appears in the spectrum (Fig. 3(b)). The measured spectral shift of 0:52 ± 0:02 cm−1 , coincides with the known spectral shift of Brillouin scattering at 1:06 m (0:54 cm−1 , [22]), within measuring uncertainties. The same has been observed for other step-index and gradient-index (bres and also for the IB laser. Thus, we conclude that the observed stimulated backscattering is due to SBS. The spectral width is determined using an 800-mm long-base FPI and an imaging lens L of 2300 mm focal length. The broadening of the spectral width of the backscattered radiation, with respect to the spectral width of the incoming radiation does not exceed 0:0005 cm−1 , which is smaller than the spectral width of spontaneous Brillouin scattering of 0:0011 cm−1 [22]. Similar results were obtained for gradient-index (bres and also when the ◦ step-index (bre was inclined at some angle (∼6 ) to the propagation direction of the input laser beam (denoted as non-perpendicular coupling in the following). We explain the absence of an additional spectral broadening of the backscattered radiation, in the case of non-perpendicular coupling into the (bre, by the initiation of phase conjugation [14]. Kuzin et al. [14] used a 30-m diam (bre. We measured that ∼80% of the energy backscattered from the (bres was transmitted through the capillary tube. This is similar to the transmission of the incident laser radiation through the capillary tube. Thus, we conclude that almost 100% of backscattered radiation is phase-conjugated.
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4. Threshold energy of SBS 4.1. In9uence of :bre parameters and radiation coupling All SBS threshold energies are measured with an uncertainty of approx. ±10% at the (bre output, linearly polarized input radiation, and uniform bending of the (bres with 48 cm diam, unless otherwise noted. The SBS threshold energy is that laser pulse energy for which the backscattered pulse power is equal to the (bre end reQected pulse power, both being registered by detector D1 (see Fig. 2). The thresholds for non-perpendicular (bre coupling are higher than those for perpendicular coupling, ranging from factors of ∼1:3–2.6 for step-index (bres, and factors of ∼2:2– 6.3 for gradient-index (bres (see Table 1). The average energy densities (pulse energy)=((bre core area), are given for comparison, but particularly for gradient-index (bres, the energy densities are only a lower limit estimation, due to the focusing of the radiation inside the (bre. The SBS threshold energies of the gradient-index (bres are smaller, by a factor of ∼2–8, in comparison to the thresholds of step-index (bres. There is a great variation in the threshold energy density from sample to sample, since for the small input NA, the unavoidable (bre surface and core diameter non-uniformities, as well as the (bre bending, can vary the divergence of radiation passing through the (bre and, hence, the SBS threshold (see below). A signi(cant enhancement of the threshold energy density by a factor of ∼3, with increasing core diameter, was observed for the gradient-index (bres and perpendicular coupling. However, the threshold energy density is always lower than that of step-index (bres. For non-perpendicular coupling, there is less variation in the threshold energy density, and it remains almost constant for step-index and gradient-index (bres. In particular, for small (bre diameters, the ratio of the threshold energy density for step-index (bres with respect to gradient-index (bres is also smaller than that for perpendicular coupling (only a factor of ∼2 instead of a factor of up to 5; see Table 1). For the NB laser, Fig. 4 shows the increase of the SBS threshold energy by a factor of 2.1 (5-m long (bre) or 1.9 (20-m long (bre) when the input NA varies by a factor of 6.7 up to approximately the full (bre NA. For the IB laser, the SBS threshold energies are much higher due to the higher spectral width (see below), but the increase of the SBS threshold energy due to the input NA is only a factor of ∼1:4 (Fig. 5). The uniform bending of the (bre does not signi(cantly inQuence the SBS threshold (Fig. 6(a)). A more important factor is the variation of the bending radius, for example, when a non-uniform bending is applied. For an elliptical bending and the IB laser, the SBS threshold increases from 26 to 32 mJ, for an input NA of ∼0:07. For the NB laser, the SBS threshold increases by a factor of ∼1:9. The combination of increasing the input beam divergence and non-uniform elliptical bending (input NA ∼0:16, axes of ellipse 30 and 10 cm, see Fig. 6) yields an SBS threshold of 18 mJ for (bre
Fig. 4. Dependence of the SBS threshold energy on the input NA for (bre length (a) 5 m, and (b) 20 m. Step-index (bre No. 2, NB laser.
Fig. 5. Dependence of the SBS threshold energy on the input NA. Step-index (bre No. 3 of 5 m length, IB laser.
Fig. 6. Dependence of the SBS threshold energy on the (bre bending for (a) uniform bending and (b) non-uniform bending. Step-index (bre No. 2 of 5 m length, NB laser, (bre input NA ∼0:07.
No. 2, i.e. an increase by a factor of approximately three. For the other (bres, the following increased threshold energies have been observed for NB laser radiation: 6 mJ ((bre No. 1), 14 mJ (No. 3), and 24 mJ (No. 4). Hence, the SBS
V. Pashinin et al. / Optics & Laser Technology 33 (2001) 617–622
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Table 2 SBS threshold energies Ep; th (in mJ) dependent on the spectral width Ip of the laser radiationa No.
Type
Ip ¡ 0:002 cm−1
Ip = 0:1 cm−1
Ip = 0:65 cm−1
2 3 8
S,WF S,UV G
5.8 3.4 0.75
45 26 8
¿ 90 (SP) ¿ 90 (SP), 300 (FFB) ¿ 30 (SP)
a For
the broad spectral width, the (bre damage thresholds are given as a lower limit estimation of the actually higher SBS thresholds. Fibre-core diam 0:6 mm, (bre length 5 m, input NA ∼0:07. SP is single laser pulse, FPB is (ve-pulse burst with 10 s interpulse separations (further abbreviations, see Table 1).
Fig. 7. InQuence of the (bre length on the SBS threshold energy. Fibre diam 0:6 mm, IB laser, input NA ∼0:07.
threshold energy density is approximately ∼5 J=cm2 for all step-index (bre samples. For (bre lengths of 1–20 m, the SBS threshold is almost independent of the (bre length (Fig. 7), when the IB laser is used. We assume that this results from the short coherence length, Lcoh , of this laser which is Lcoh = c=Ip ≈ 10 cm. From Eq. (1), a decrease of a factor 1.09 is expected which agrees with the measured factor of 1.07 for the step-index (bre. For the NB laser (Lcoh ¿ 5 m), a signi(cant decrease of the threshold is observed when the (bre length is increased from 5 to 20 m (see curve (a) and (b) of Fig. 4). In this case, the coherence length is of the same order of magnitude as the (bre length. The measured decrease of a factor ∼1:5 is also in agreement with the factor 1.6 from Eq. (1). For the IB laser, the inQuence of the polarization of the laser radiation is smaller than the factor of two usually observed, with narrow-band laser radiation and (bres which are short, when compared with the depolarization and coherence lengths of the radiation. The threshold increases by only a factor of ∼1:5 (from 26 to 40 mJ) for step-index (bre No. 3 and a factor of ∼1:4 (from 8 to 11 mJ) for gradient-index (bre No. 7. No inQuence on the SBS threshold is observed when the polarization of the input laser beam is changed from linear to circular polarization. 4.2. In9uence of the spectral width of the laser For narrow-band pumping conditions, the SBS threshold is independent of the spectral width of the laser, Ip (Eq. (1)), while for broad-band pumping conditions it should vary almost linearly with Ip according to Eq. (2). Table 2 summarizes the SBS threshold energies measured for the diFerent spectral widths of the laser radiation. The threshold increases by a factor of ∼7:5 for the step-index (bres and ∼10 for the gradient-index (bre, respectively, when the spectral width is changed from the NB laser to the IB laser (i.e. by at least a factor of ∼50). For the BB laser,
the SBS thresholds exceed the damage thresholds of the (bre input surface for all samples when single laser pulses are used. Hence, the SBS threshold cannot be determined for the broad spectral width. The (bre damage occurs, without stimulated backscattering, at the same energy, independent of the (bre length. If we apply Eq. (2)—although the conditions are not ful(lled for the NB laser—then we calculate an increase by a factor of ∼12 between NB and IB laser, and a factor of ∼6:5 between the IB and BB laser, respectively. In the (rst case, the calculated factor is approximately in the range of the measured value, and in the second case, at least, it is not in contradiction with the measurement. 5. Conclusions For large-core (bres of 0.4 –1 mm, SBS thresholds of step-index and graded-index (bres are measured for various (bre and laser parameters. Spectral analysis of the backscattered radiation revealed SBS as the scattering mechanism even for large-core (bres. Almost 100% of the backscattered radiation is phase conjugated. From all parameters investigated, the major inQuence on the SBS threshold is given by the spectral width of the laser radiation. For narrow-band laser radiation, which is required in holography for suGcient coherence length, we observed SBS as the limiting factor for (bre transmission of Q-switched laser pulses of 60 ns duration. The SBS threshold energy of ∼6 mJ for a 0.6-mm diam (bre of 5-m length is increased up to ∼18 mJ by non-uniform elliptical (bre bending and aperture (lling (spectral width ¡ 0:002 cm−1 , coherence length of the laser ¿ 5 m). Taking into account that the SBS threshold is inversely proportional to the (bre length, the threshold of ∼6 mJ is in good agreement with the threshold energy of 300 mJ measured for 50 times shorter (bre pieces of 10 cm length and stretched pulses of a ruby laser [18]. Thus, for holography, the spectral width of the laser should be well adapted to the requirements, which means that it should be narrowest for large coherence length and broadest for high SBS threshold. However, as a result, the beam guidance through the (bres restricts the dimensions of the measuring
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object due to the energy available at the (bre output. For other applications, which do not require narrow-band laser radiation, the SBS threshold can be shifted beyond the damage threshold of the (bre by increasing the spectral width of the laser radiation. Energies of ¿ 90 mJ for single pulses, and 300 mJ for (ve-pulse bursts, are transmitted through 0.6-mm diam (bres of up to 20-m length, when a broad-band laser with a spectral width of 0:65 cm−1 is used. Acknowledgements This work was supported by the Bundesministerium fUur Bildung, Wissenschaft, Forschung und Technologie, Germany, under reference No. 13N5908=7. Major parts of the experimental work have been conducted in cooperation with CeramOptec Systems in Moscow. References [1] Jones R, Wykes C. Holographic and speckle interferometry, 2nd ed. Cambridge: Cambridge University Press, 1989. p. 254 [Chapter 6]. [2] Sattmann R, Sturm V, Noll R. Laser-induced breakdown spectroscopy of steel samples using multiple Q-switch Nd : YAG laser pulses. J Phys D 1995;28:2181–7. [3] Anderson DJ, et al. An optical (bre delivery system for pulsed laser particle image velocimetry illumination. Meas Sci Technol 1995;6:809–14. [4] Trott WM, Meeks KD. High-power Nd : glass laser transmission through optical (bers and its use in acceleration of thin foil targets. J Appl Phys 1990;67(7):3297–301. [5] Setchell RE, et al. High-power transmission through step-index, multimode (bers. In: Bennett HE, et al. editors. Laser-induced damage in optical materials. Washington DC: SPIE — The International Society for Optical Engineering 1990. Proceedings of SPIE, vol. 1441, 1991, p. 61–70.
[6] Ippen EP, Stolen RH. Stimulated Brillouin scattering in optical (bers. Appl Phys Lett 1972;21:539–41. [7] Smith RG. Optical power handling capacity of low loss optical (bers as determined by stimulated Raman and Brillouin scattering. Appl Opt 1972;11(11):2489–94. [8] Ippen EP. In: Jacobs S, et al., editors. Laser applications to optics and spectroscopy. Reading, MA: Addison-Wesley, 1975. p. 213– 44. [9] Stolen RH. In: Miller SE, Chynoweth AG, editors. Optical (ber telecommunications. New York: Academic Press, 1979. p. 125 –50. [10] Lichtman E, Friesem AA. Stimulated Brillouin scattering excited by a multimode laser in single-mode optical (bers. Opt Commun 1987;64(6):544–8. [11] Lichtman E, et al. Stimulated Brillouin scattering excited by two pump waves in single-mode (bers. J Opt Soc Am 1987;B4(9):1397– 403. [12] Basiev TT, et al. Stimulated Mandel’shtam–Brillouin scattering in a multimode glass (ber lightguide. JETP Lett 1982;36(3):104–7. [13] Edge C, Goodwin MJ, Bennion I. Investigation of nonlinear power transmission limits in optical-(bre devices. IEE Proc 1987;134(3):180–2. [14] Kuzin EA, Petrov MP, Davydenko BE. Opt Quantum Electronics 1985;17:393. [15] Agrawal GP. Nonlinear (ber optics. San Diego: Academic Press, 1989. p. 263–87. [16] Eichler HJ, Kunde J, Liu B. Quartz (bre phase conjugators with high (delity and reQectivity. Opt Commun 1997;139:327–34. [17] Eichler HJ, Kunde J, Liu B. Fiber phase conjugators at 1064-nm, 532-nm, and 355-nm wavelengths. Opt Lett 1997;22(8):495–7. [18] PQUuger S, Sellhorst M, Sturm V, Noll R. Fiber-optic transmission of stretched pulses from a Q-switched ruby laser. Appl Opt 1996;35:5165–9. [19] Sturm V, Sattmann R, Noll R. Optical (ber transmission of multiple Q-switch Nd : YAG laser pulses with microsecond interpulse separations. Appl Phys B 1996;63:363–70. [20] Zel’dovich BY, Pilipetsky NF, Shkunov VV. Principles of phase conjugation. Berlin: Springer, 1985. p. 50. [21] Valley GC. A review of stimulated Brillouin scattering excited with a broad-band pump laser. IEEE J Quantum Electronics 1986;QE-22(5):704–12. [22] Stolen RG. Proc. IEEE 1980;68:1232.
www.elsevier.com/locate/optlastec
Stimulated Brillouin scattering of Q-switched laser pulses in large-core optical (bres V. Pashinina , V. Sturmb; ∗ , V. Tumorina , R. Nollb a General
Physics Institute, 38 Vavilov Street, 117942 Moscow, Russia f"ur Lasertechnik (ILT), Steinbachstr. 15, 52074 Aachen, Germany
b Fraunhofer-Institut
Received 29 January 2001; accepted 11 September 2001
Abstract Q-switched Nd : glass laser pulses of 60 ns duration are transmitted through multimode fused-silica (bres of 0.4 –1 mm core diam and lengths of up to 20 m. For laser radiation with narrow spectral width, stimulated Brillouin scattering (SBS) is observed for energies well below the threshold energy of (bre damage. The SBS threshold is shifted beyond the threshold of (bre damage through increasing the spectral width of the laser radiation. The SBS threshold energies of step-index and gradient-index (bres are measured for various (bre c 2001 Elsevier Science Ltd. All rights reserved. and laser parameters. Keywords: Fibre; Stimulated Brillouin scattering; Laser
1. Introduction Q-switched laser pulses with energies of up to several 100 mJ are used, e.g. for holographic interferometry [1], laser spectroscopy [2], or velocimetry [3]. Optical (bre transmission of the laser radiation would signi(cantly facilitate such laser applications in metrology. In holography, the object beam can be transmitted through multimode (bres since, in any case, the scattering at the object destroys the transversal mode structure of the laser beam. Damage of the fused-silica (bre core or core-cladding interface is often regarded as the only limiting process in high-energy nanosecond pulse transmission through (bres with large core diameters of 0.4 –1 mm [4,5]. Stimulated Brillouin scattering (SBS) in (bres has been the subject of numerous investigations, which mainly focused on single-mode (bres (core diam of ∼10 m) or small-core multimode (bres (core diam of ¡ 50 m), for communication purposes, with lengths in the km-range and use of continuous-wave radiation [6 –15]. In [16,17], SBS thresholds are measured for (bres of 0.1 and 0:2 mm diam with respect to using the (bres for phase conjugators. However, for (bres of diam ¿ 0:4 mm there are only a few reports ∗
Corresponding author. Tel.: +49-241-8906-0; fax: +49-241-806-121. E-mail address: [email protected] (V. Sturm).
about stimulated scattering of ruby [18] or Nd : YAG [19] laser pulses. In [18,19], the peak power of the Q-switched laser pulses is reduced, e.g. by pulse stretching [18] or by distributing the energy to microsecond-spaced multiple pulses of a burst [19], in order to avoid (bre damage, but stimulated scattering is observed as the limiting process for (bre transmission. The scattering mechanism is assumed to be SBS in [18,19], but it has not been revealed by measurement. In this study, Nd : glass laser pulses are employed in the determination of the scattering mechanism through spectral analysis. The Nd : glass laser with its large gain bandwidth allows to vary the spectral width of the laser radiation over a wide range. Stimulated scattering thresholds are measured in dependence of diFerent (bre parameters, in order to (nd appropriate conditions for stimulated scattering suppression. The gain coeGcient of SBS, gB , in fused silica at 1 m, is ∼1–5 × 10−9 cm=W and is, therefore, a factor of approximately 500 times larger than the gain coeGcient for stimulated Raman scattering (SRS) [15]. The Brillouin linewidth, IB , of (bres is much larger than that expected for bulk silica (∼35 MHz at 1:06 m [15]). Most of the increase in the linewidth is due to inhomogeneities in the cross section along the (bre length. Depending on each speci(c (bre, the Brillouin linewidth can be as large as ∼210 MHz at 1:06 m [15, p. 267]. Since the Brillouin linewidth, IB , is proportional to 1=p2 , the SBS gain coeGcient, gB ˙ 1=(p2 IB ), is
c 2001 Elsevier Science Ltd. All rights reserved. 0030-3992/01/$ - see front matter PII: S 0 0 3 0 - 3 9 9 2 ( 0 1 ) 0 0 0 8 6 - X
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almost independent of the wavelength of the incident pump wave, p [15], which is the laser wavelength in our experiments. SBS is suppressed in favour of SRS if the spectral width of the laser, Ip , exceeds IB by a multiple of the ratio of SBS gain to SRS gain [8, p. 230], i.e. if Ip is a multiple of 500 × IB ≈ 105 GHz = 3:5 cm−1 . We used a maximum spectral width of 0:65 cm−1 . Therefore, the occurrence of SRS is not expected. For narrow-band pumping conditions, Ip IB , the SBS threshold irradiation for a single-mode (bre, under steady-state conditions and linear polarization, is independent of the spectral width of the laser [7,20]: Ip; th ≈ 21=(gB LeF ):
(1)
The eFective interaction length LeF is given in [16] by 1=LeF = 1=Lcoh + 1=L (Lcoh coherence length of the SBS pump radiation). For broad-band pumping [21], Ip IB , and if Lcoh LeF , the SBS threshold irradiation increases almost linearly with Ip [10,15, p. 267]: Ip; th ≈ [21=(gB LeF )](1 + Ip =IB ):
(2)
In case of multimode (bres, the laser energy is distributed over many modes and over a larger volume, compared to single-mode (bres. In addition, the actual intensity distribution over the guided modes can be important with respect to the threshold pump irradiance. Therefore, Eqs. (1) and (2) represent a lower limit for the threshold pump irradiance of multimode (bres. 2. Experimental setup The 1054-nm Nd : doped phosphate glass laser with a resonator length of 1 m consists of a H4 mm × 100 mm Nd : glass rod, a LiF : F2− crystal for passive Q-switching, an intracavity telescope L1, L2 (f1 = 200 mm; f2 = − 70 mm), a 25%-reQective output mirror with a radius of curvature of 5 m and a plane high-reQecting rear mirror. Within a single Qashlamp pulse (max. repetition rate of ∼1 Hz), optionally up to six Q-switched pulses of ∼60 ns duration can be generated with interpulse separations of 10 –30 s (determined by passive Q-switching and resonator parameters). Three laser resonators have been con(gured to obtain spectral widths of 0:65 cm−1 (broad-band con(guration, denoted as BB laser in the following), 0:1 cm−1 (intermediate-band con(guration, IB), and ¡ 0:0016 cm−1 (narrow-band con(guration, NB). For the IB and BB laser, broadband pumping conditions of Eq. (2) are given, while the spectral width of the NB laser is probably smaller, but not very small, compared to the Brillouin linewidth IB ≈ 35–210 MHz = 0:0012–0:007 cm−1 . Hence, the conditions of Eq. (1) are not ful(lled strictly in this intermediate range, but Eq. (1) should be helpful for approximate calculations. The IB con(guration uses a 0.25-mm-thin plane–parallel glass plate as a spectrally selective output mirror. The NB
Table 1 List of (bre types and measured SBS threshold energies, Ep; th , for NB laser radiationa ◦
◦
◦
◦
No.
Type
d (mm)
Ep; th (0 ) (mJ)
Ep; th (6 ) (mJ)
p; th (0 ) (J=cm2 )
p; th (6 ) (J=cm2 )
1 2 3 4 5 6 7 8 9
S,UV S,WF S,UV S,WF S,UV G G G G
0.4 0.6 0.6 0.8 1.0 0.4 0.6 0.8 1.0
1.4 5.8 3.4 10.0 9.0 0.27 0.75 1.8 5.0
3.7 7.8 6.2 13.3 20.0 1.7 3.0 7.4 11.0
1.1 2.1 1.2 2.0 1.1 0.21 0.26 0.36 0.64
2.9 2.8 2.2 2.7 2.5 1.4 1.1 1.5 1.4
a Fibre
NA 0.22, length 5 m, input NA ∼0:07, (bre bending 800 × ◦ core diam. Ep; th for perpendicular (∼0 ) and non-perpendicular cou◦ pling (∼6 ), p; th threshold energy density, d (bre core diameter, S step-index (bre, G gradient-index (bre; UV (bre glass with enhanced short wavelength transmission; WF Water-free, (bre glass with enhanced near-infrared transmission. All (bres are PCVD manufactured by CeramOptec (Bonn, Germany).
resonator selects a single longitudinal mode by an inserted etalon and a rear mirror, consisting of several adjusted plane–parallel plates having a peak reQection of 60% and a free spectral range of ∼10 cm−1 . The maximum output energy is 0:13 J (single pulse) and 0:8 J (six-pulse burst) for the BB and IB con(guration, and 0:08 J (single pulse) and 0:5 J (six-pulse burst) for the NB con(guration. The temporal pro(les of the laser pulses are smooth since the mode beating modulation depth is very small due to the large number of modes for the broad-band con(guration, whereas for the narrow-band case, only a single mode exists. Table 1 lists the various (bre types used in the experiments. The end faces of the (bres were prepared by cleaving and optically inspected using a microscope. A (bre damage threshold of 60 J=cm2 is measured for a step-index (bre ((bre No. 1 in Table 1) and 6 J=cm2 for a gradient-index (bre (No. 6), if the laser output is coupled to the (bre by a single lens with f = 150 mm. For these measurements, the (bre lengths are 0:5 m and the beam waist diameter of ∼0:1 mm is located ∼20 mm in front of the (bre end. The lower damage threshold of the gradient-index (bre is due, most probably, to the small numerical aperture of the laser radiation at the (bre input (input NA) which results in the focusing of the radiation inside the (bre. To increase the divergence, a capillary tube is used, as depicted in Fig. 1(a). The damage threshold of the gradient-index (bre is increased to 16 J=cm2 , whereas the damage threshold of the step-index (bre is not inQuenced signi(cantly. Therefore, this coupling con(guration with linearly polarized (bre input radiation is used for all measurements presented in the (gures in this paper. The typical (bre output energy was 80% of the input energy from the capillary tube. The beam waist diameter at the focus of the coupling lens is 0:27 mm, for this coupling con(guration. To measure the inQuence of the polarization, the laser radiation is depolarized by means of a KDP
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Fig. 1. Set-up for the (bre coupling of the polarized laser radiation (a) and the depolarized laser radiation (b). KDP crystal 10 × 10 × 8 mm3 , CT capillary tube 0:8 mm i.d. ×50 mm long. To vary the numerical aperture of the (bre coupling, lens L8 (positive or negative) can be inserted optionally.
crystal (see Fig. 1(b)). The laser energies were varied by (lters with a minimum step of 10%.
Fig. 3. Determination of the spectral shift of the backscattered radiation for step-index (bre No. 3. Spectrum of the reQected laser radiation with (bre input power below the threshold of stimulated backscattering (a), and spectrum of the backward radiation with (bre input power above threshold (b).
3. Spectral analysis To determine the spectral shift and the spectral width of the backscattered radiation, the Nd : glass laser radiation is coupled into the (bre, whilst the backward radiation is spectrally analysed by recording the fringe pattern of a Fabry– Perot interferometer (FPI) with a CCD linear array (Fig. 2). The spectral analysis is carried out with step-index and gradient-index (bres of 0.6-mm core diam, 5-m length, and an input NA of 0.05, unless otherwise noted. The NB laser is used because of the higher accuracy of measurement due to the narrow spectral width. The spectral shift is measured using a 5-mm air-gap FPI (free spectral range 1 cm−1 , spectral resolution of 0:15 cm−1 ). Few orders of the FPI circular fringe pattern are registered by the CCD linear array at the focal plane of lens L (focal length 400 mm).
Fig. 2. Set-up for spectral analysis of backscattered radiation and the measurement of incident, transmitted and backscattered laser radiation. Detector D1 (fast photomultiplier tube, rise time 3 ns, 500-MHz oscilloscope) registers the temporal pro(le of the backscattered laser pulse; D2, D3 time-integrating photodetectors (1 ms, 100-MHz storage oscilloscope) for input and transmitted energy; L lens; FCO (bre coupling optics as depicted in Fig. 1; BS wedge-shaped beam splitters; M1, M2 mirrors; M2 optionally inserted.
Fig. 3(a) shows the spectrum of the backward radiation with the (bre input power below the threshold of stimulated backscattering. The spectrum coincides with that of the incoming laser radiation; this is due to Fresnel reQection at the (bre end surface. If the (bre input energy exceeds the threshold of the stimulated backscattering, then the characteristic pulse is observed with detector D1 at that moment when the Stokes component appears in the spectrum (Fig. 3(b)). The measured spectral shift of 0:52 ± 0:02 cm−1 , coincides with the known spectral shift of Brillouin scattering at 1:06 m (0:54 cm−1 , [22]), within measuring uncertainties. The same has been observed for other step-index and gradient-index (bres and also for the IB laser. Thus, we conclude that the observed stimulated backscattering is due to SBS. The spectral width is determined using an 800-mm long-base FPI and an imaging lens L of 2300 mm focal length. The broadening of the spectral width of the backscattered radiation, with respect to the spectral width of the incoming radiation does not exceed 0:0005 cm−1 , which is smaller than the spectral width of spontaneous Brillouin scattering of 0:0011 cm−1 [22]. Similar results were obtained for gradient-index (bres and also when the ◦ step-index (bre was inclined at some angle (∼6 ) to the propagation direction of the input laser beam (denoted as non-perpendicular coupling in the following). We explain the absence of an additional spectral broadening of the backscattered radiation, in the case of non-perpendicular coupling into the (bre, by the initiation of phase conjugation [14]. Kuzin et al. [14] used a 30-m diam (bre. We measured that ∼80% of the energy backscattered from the (bres was transmitted through the capillary tube. This is similar to the transmission of the incident laser radiation through the capillary tube. Thus, we conclude that almost 100% of backscattered radiation is phase-conjugated.
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4. Threshold energy of SBS 4.1. In9uence of :bre parameters and radiation coupling All SBS threshold energies are measured with an uncertainty of approx. ±10% at the (bre output, linearly polarized input radiation, and uniform bending of the (bres with 48 cm diam, unless otherwise noted. The SBS threshold energy is that laser pulse energy for which the backscattered pulse power is equal to the (bre end reQected pulse power, both being registered by detector D1 (see Fig. 2). The thresholds for non-perpendicular (bre coupling are higher than those for perpendicular coupling, ranging from factors of ∼1:3–2.6 for step-index (bres, and factors of ∼2:2– 6.3 for gradient-index (bres (see Table 1). The average energy densities (pulse energy)=((bre core area), are given for comparison, but particularly for gradient-index (bres, the energy densities are only a lower limit estimation, due to the focusing of the radiation inside the (bre. The SBS threshold energies of the gradient-index (bres are smaller, by a factor of ∼2–8, in comparison to the thresholds of step-index (bres. There is a great variation in the threshold energy density from sample to sample, since for the small input NA, the unavoidable (bre surface and core diameter non-uniformities, as well as the (bre bending, can vary the divergence of radiation passing through the (bre and, hence, the SBS threshold (see below). A signi(cant enhancement of the threshold energy density by a factor of ∼3, with increasing core diameter, was observed for the gradient-index (bres and perpendicular coupling. However, the threshold energy density is always lower than that of step-index (bres. For non-perpendicular coupling, there is less variation in the threshold energy density, and it remains almost constant for step-index and gradient-index (bres. In particular, for small (bre diameters, the ratio of the threshold energy density for step-index (bres with respect to gradient-index (bres is also smaller than that for perpendicular coupling (only a factor of ∼2 instead of a factor of up to 5; see Table 1). For the NB laser, Fig. 4 shows the increase of the SBS threshold energy by a factor of 2.1 (5-m long (bre) or 1.9 (20-m long (bre) when the input NA varies by a factor of 6.7 up to approximately the full (bre NA. For the IB laser, the SBS threshold energies are much higher due to the higher spectral width (see below), but the increase of the SBS threshold energy due to the input NA is only a factor of ∼1:4 (Fig. 5). The uniform bending of the (bre does not signi(cantly inQuence the SBS threshold (Fig. 6(a)). A more important factor is the variation of the bending radius, for example, when a non-uniform bending is applied. For an elliptical bending and the IB laser, the SBS threshold increases from 26 to 32 mJ, for an input NA of ∼0:07. For the NB laser, the SBS threshold increases by a factor of ∼1:9. The combination of increasing the input beam divergence and non-uniform elliptical bending (input NA ∼0:16, axes of ellipse 30 and 10 cm, see Fig. 6) yields an SBS threshold of 18 mJ for (bre
Fig. 4. Dependence of the SBS threshold energy on the input NA for (bre length (a) 5 m, and (b) 20 m. Step-index (bre No. 2, NB laser.
Fig. 5. Dependence of the SBS threshold energy on the input NA. Step-index (bre No. 3 of 5 m length, IB laser.
Fig. 6. Dependence of the SBS threshold energy on the (bre bending for (a) uniform bending and (b) non-uniform bending. Step-index (bre No. 2 of 5 m length, NB laser, (bre input NA ∼0:07.
No. 2, i.e. an increase by a factor of approximately three. For the other (bres, the following increased threshold energies have been observed for NB laser radiation: 6 mJ ((bre No. 1), 14 mJ (No. 3), and 24 mJ (No. 4). Hence, the SBS
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Table 2 SBS threshold energies Ep; th (in mJ) dependent on the spectral width Ip of the laser radiationa No.
Type
Ip ¡ 0:002 cm−1
Ip = 0:1 cm−1
Ip = 0:65 cm−1
2 3 8
S,WF S,UV G
5.8 3.4 0.75
45 26 8
¿ 90 (SP) ¿ 90 (SP), 300 (FFB) ¿ 30 (SP)
a For
the broad spectral width, the (bre damage thresholds are given as a lower limit estimation of the actually higher SBS thresholds. Fibre-core diam 0:6 mm, (bre length 5 m, input NA ∼0:07. SP is single laser pulse, FPB is (ve-pulse burst with 10 s interpulse separations (further abbreviations, see Table 1).
Fig. 7. InQuence of the (bre length on the SBS threshold energy. Fibre diam 0:6 mm, IB laser, input NA ∼0:07.
threshold energy density is approximately ∼5 J=cm2 for all step-index (bre samples. For (bre lengths of 1–20 m, the SBS threshold is almost independent of the (bre length (Fig. 7), when the IB laser is used. We assume that this results from the short coherence length, Lcoh , of this laser which is Lcoh = c=Ip ≈ 10 cm. From Eq. (1), a decrease of a factor 1.09 is expected which agrees with the measured factor of 1.07 for the step-index (bre. For the NB laser (Lcoh ¿ 5 m), a signi(cant decrease of the threshold is observed when the (bre length is increased from 5 to 20 m (see curve (a) and (b) of Fig. 4). In this case, the coherence length is of the same order of magnitude as the (bre length. The measured decrease of a factor ∼1:5 is also in agreement with the factor 1.6 from Eq. (1). For the IB laser, the inQuence of the polarization of the laser radiation is smaller than the factor of two usually observed, with narrow-band laser radiation and (bres which are short, when compared with the depolarization and coherence lengths of the radiation. The threshold increases by only a factor of ∼1:5 (from 26 to 40 mJ) for step-index (bre No. 3 and a factor of ∼1:4 (from 8 to 11 mJ) for gradient-index (bre No. 7. No inQuence on the SBS threshold is observed when the polarization of the input laser beam is changed from linear to circular polarization. 4.2. In9uence of the spectral width of the laser For narrow-band pumping conditions, the SBS threshold is independent of the spectral width of the laser, Ip (Eq. (1)), while for broad-band pumping conditions it should vary almost linearly with Ip according to Eq. (2). Table 2 summarizes the SBS threshold energies measured for the diFerent spectral widths of the laser radiation. The threshold increases by a factor of ∼7:5 for the step-index (bres and ∼10 for the gradient-index (bre, respectively, when the spectral width is changed from the NB laser to the IB laser (i.e. by at least a factor of ∼50). For the BB laser,
the SBS thresholds exceed the damage thresholds of the (bre input surface for all samples when single laser pulses are used. Hence, the SBS threshold cannot be determined for the broad spectral width. The (bre damage occurs, without stimulated backscattering, at the same energy, independent of the (bre length. If we apply Eq. (2)—although the conditions are not ful(lled for the NB laser—then we calculate an increase by a factor of ∼12 between NB and IB laser, and a factor of ∼6:5 between the IB and BB laser, respectively. In the (rst case, the calculated factor is approximately in the range of the measured value, and in the second case, at least, it is not in contradiction with the measurement. 5. Conclusions For large-core (bres of 0.4 –1 mm, SBS thresholds of step-index and graded-index (bres are measured for various (bre and laser parameters. Spectral analysis of the backscattered radiation revealed SBS as the scattering mechanism even for large-core (bres. Almost 100% of the backscattered radiation is phase conjugated. From all parameters investigated, the major inQuence on the SBS threshold is given by the spectral width of the laser radiation. For narrow-band laser radiation, which is required in holography for suGcient coherence length, we observed SBS as the limiting factor for (bre transmission of Q-switched laser pulses of 60 ns duration. The SBS threshold energy of ∼6 mJ for a 0.6-mm diam (bre of 5-m length is increased up to ∼18 mJ by non-uniform elliptical (bre bending and aperture (lling (spectral width ¡ 0:002 cm−1 , coherence length of the laser ¿ 5 m). Taking into account that the SBS threshold is inversely proportional to the (bre length, the threshold of ∼6 mJ is in good agreement with the threshold energy of 300 mJ measured for 50 times shorter (bre pieces of 10 cm length and stretched pulses of a ruby laser [18]. Thus, for holography, the spectral width of the laser should be well adapted to the requirements, which means that it should be narrowest for large coherence length and broadest for high SBS threshold. However, as a result, the beam guidance through the (bres restricts the dimensions of the measuring
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object due to the energy available at the (bre output. For other applications, which do not require narrow-band laser radiation, the SBS threshold can be shifted beyond the damage threshold of the (bre by increasing the spectral width of the laser radiation. Energies of ¿ 90 mJ for single pulses, and 300 mJ for (ve-pulse bursts, are transmitted through 0.6-mm diam (bres of up to 20-m length, when a broad-band laser with a spectral width of 0:65 cm−1 is used. Acknowledgements This work was supported by the Bundesministerium fUur Bildung, Wissenschaft, Forschung und Technologie, Germany, under reference No. 13N5908=7. Major parts of the experimental work have been conducted in cooperation with CeramOptec Systems in Moscow. References [1] Jones R, Wykes C. Holographic and speckle interferometry, 2nd ed. Cambridge: Cambridge University Press, 1989. p. 254 [Chapter 6]. [2] Sattmann R, Sturm V, Noll R. Laser-induced breakdown spectroscopy of steel samples using multiple Q-switch Nd : YAG laser pulses. J Phys D 1995;28:2181–7. [3] Anderson DJ, et al. An optical (bre delivery system for pulsed laser particle image velocimetry illumination. Meas Sci Technol 1995;6:809–14. [4] Trott WM, Meeks KD. High-power Nd : glass laser transmission through optical (bers and its use in acceleration of thin foil targets. J Appl Phys 1990;67(7):3297–301. [5] Setchell RE, et al. High-power transmission through step-index, multimode (bers. In: Bennett HE, et al. editors. Laser-induced damage in optical materials. Washington DC: SPIE — The International Society for Optical Engineering 1990. Proceedings of SPIE, vol. 1441, 1991, p. 61–70.
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