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KrF laser picosecond pulse source by stimulated scattering processes
Optics Communications 215 (2003) 163–167 www.elsevier.com/locate/optcom
KrF laser picosecond pulse source by stimulated scattering processes Eiichi Takahashi a,*, Leonid L. Losev b, Yuji Matsumoto a, Isao Okuda a, Isao Matsushima a, Susumu Kato a, Hirotaka Nakamura c, Kenji Kuwahara d, Yoshiro Owadano a a
National Institute of Advanced Industrial Science and Technology (AIST) Central 2, Umezono, 1-1-4 Tsukuba, Ibaraki 305-8568, Japan b Division of Quantum Radiophysics, P.N. Lebedev Physical Institute, Keninsky prospekt, 53 117924 Moscow, Russia c Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan d SUMITOMO 3M Limited, 3-8-8, Minami-Hashimoto, Sagamihara-shi, Kanagawa 229-1185, Japan Received 18 July 2002; received in revised form 5 November 2002; accepted 22 November 2002
Abstract A new short-pulse KrF laser source was developed by combining stimulated scattering processes, namely, Raman, Brillouin, and four-wave-mixing (FWM). Short pulses of 1.1 ps were obtained from 4 ns oscillator output. Only two commercial discharge KrF lasers are required for this system. This method is very simple and could be extended to an ArF laser wavelength in principle. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 42.55.L; 42.55.Y; 42.65.E; 42.65.H Keywords: Excimer lasers; SRS; SBS; FWM
1. Introduction Excimer lasers are widely used in material processing and analysis, because of their short wavelength and large photon energy. In such fields of research, a short-pulse source is needed to improve accuracy and achieve high intensity inter-
*
Corresponding author. Tel.: +81-298-615-705; fax: +81-298615-717. E-mail address: [email protected] (E. Takahashi).
actions [1]. Additional short-pulse lasers, for example Ti:sapphire or dye lasers, and successive wavelength conversions are usually used to generate the excimer wavelength (KrF:248 nm, ArF:193 nm) short seed pulses [2,3] because modelocking is difficult for excimer lasers itself. However, these seed lasers are very complex. The wavelength conversion to excimer wavelength, especially for ArF, is difficult. Stimulated Brillouin scattering (SBS) can compress the nanosecond output of excimer laser pulses. The wavelength shift through the SBS is so
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 2 ) 0 2 2 3 2 - 0
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E. Takahashi et al. / Optics Communications 215 (2003) 163–167
small (104 –103 nm) that it is possible for the excimer laser amplifier to amplify the compressed pulse again and thus achieve a large amount of energy. The pulse width of the compressed Stokes pulses is around Tphonon 100 ps or less in the ultraviolet wavelength region. In previous papers, we showed that the heavily saturated amplification in KrF lasers can shorten the Stokes pulses [4,5] because excimer lasers have 2 a small saturation fluence, Es 2 mJ=cm , and is capable of the direct short-pulse saturated amplification without damage to the laser medium. We achieved the formation of 7 ps short pulses by the electron beam pumped KrF laser system. However, the pulse width achieved by the commercial discharge KrF laser amplifier was 50 ps [4]. Multipass amplification would shorten the pulse width, but the suppression of amplified spontaneous emission would be crucial. In addition, since these picosecond short pulses, which are shortened by saturated amplification, accompany a nanosecond tail, they have practical application problems. Stimulated Raman scattering (SRS) pulse compression can generate a shorter pulse because of its short transverse dephasing time, T2 (27 ps for methane gas). However, the wavelength shift is so large (20 nm) that it is impossible for the excimer amplifier to amplify the output Stokes pulses again. Grasyuk et al. [6] uses anti-Stokes pulse generation through a four-wave-mixing (FWM) process to recover the Raman-shifted wavelength for Nd:Glass laser output. In this paper, we report on the development of a new short-pulse excimer source by the combination of SBS, SRS, and FWM. Backward SRS compressed Stokes pulses were recovered in wavelength by successive FWM. This FWM process also works to form very steep leading-edge Stokes pulses [7]. This is because this process is in a transient regime and the leading-edge growth rate can be faster than T2 [8]. The steep leading-edge pulses can be shortened by heavily saturated amplification.
wavelength recovery were adopted. The generated short pulses could then be amplified and shortened by excimer laser amplifier. Methane gas is a Raman medium with a large gain and dephasing time T2 of 27 ps [9]. Since the optimum pulse compression factor of stimulated scattering is around 20 [10], sub-nanosecond or shorter pump pulses are basically necessary to have efficient backward SRS compression. In addition, the pump spectral bandwidth should be comparable to the width of the methane gas media, Dm ðcm1 Þ ¼ 0:32 þ 0:012p (atm), so that a large SRS gain can be achieved. The experimental setup is shown in Fig. 1. The detailed parameters are also noted in the figure. The pulse width of the KrF oscillator was 4 ns; we precompressed the output by SBS pulse leadingedge steepening and short-pulse formation by saturated amplification of the SBS Stokes pulses. To have efficient and stable stimulated scattering, the pump pulse should have a narrow spectral bandwidth and good beam focusability [11]. The directional property of the oscillator output was improved by the spatial filter (SF). The beam diameter after the SF was 7 mm. The beam focusability of the output pulses was close to diffraction limited. The energy of the oscillator output was 3 mJ, and only 8% of the energy passed through the SF. Etalon (F.S.R. ¼ 50 cm1 , Finesse ¼ 15) was inserted into the beam path to reduce its bandwidth. The spectrum before and after the etalon is shown in Fig. 2. The peak position was always adjusted to locate at the maximum. The energy transmission through the etalon was 40%. The improved output pulses of 100 lJ were amplified by the discharge pump KrF laser amplifier (Lambda Physics, Compex102). The amplified pump pulses were injected into the Brillouin
2. Experiment To generate picosecond short pulses, backward SRS pulse compression and transient FWM
Fig. 1. Experimental setup.
E. Takahashi et al. / Optics Communications 215 (2003) 163–167
165
two-photon absorption in BaF2 crystal [14]. In addition, spectrum and energy were measured.
3. Results and discussion
Fig. 2. The spectrum before and after pass through the etalon.
cell filled with Fluorinate FC-72 by using a convex lens. This SBS liquid is an ideal medium because it has a high breakdown threshold for UV radiation and high optical transmittance up to 90% at 190 nm [4,12]. The generated SBS Stokes pulses were amplified again going back on the same optical path. The Stokes pulses were separated by the polarizer and injected into a Raman cell filled with methane gas (0.75 MPa) to create backward SRS compressed Stokes pulses. A dichroic mirror was used to separate the pump and Raman Stokes pulses (k ¼ 268 nm). The Raman Stokes pulses were introduced into an FWM cell filled with methane gas (0.75 MPa). The usual phase matching angle of the FWM process is finite to the incident laser beam propagation axis because the media has dispersion [13]. In order to avoid a ring shape anti-Stokes pulse generation, the focused intensity was increased by using the lens of a short focal length to satisfy the condition; the wave number mismatch was smaller than the Raman gain focused intensity product, Dk gI. The output light consisted of first anti-Stokes light and higher order Stokes light components. Only the anti-Stokes component of the pulses was amplified by the final amplifier pass. The waveforms of the pulses at each compression stage were measured with an oscilloscope, a streak camera, and an autocorrelator by using
The waveforms measured with the oscilloscope are shown in Fig. 3. The width of the pulses decreases with each process. The following overshooting in the Raman Stokes pulse is due to the short-pulse width. The pulse energy of the amplified SBS Stokes and the backward SRS Stokes pulse were 13 and 1 mJ, respectively. The pulse width after the backward SRS pulse compression stage was shorter than the temporal resolution of the oscilloscope (0.75 GHz); a streak camera was used to measure the waveform in detail (Fig. 4). The FWHM of the amplified SBS Stokes pulse and the backward SRS Stokes pulse were 700 and 60 ps, respectively. The amplified SBS Stokes pulse has a tail, but the successive Raman Stokes pulse has no tail. The pulse compression ratio at the SRS stage was 12. The spectrum of the backward SRS Stokes pulse and the output of FWM were measured by a grating spectrometer (Fig. 5). There was no measurable KrF laser wavelength component for a backward SRS Stokes pulse. The creation of an
Fig. 3. Waveforms measured by an oscilloscope: (a) PSX100 KrF laser oscillator output pulse; (b) amplified SBS Stokes pulse; (c) backward SRS Stokes pulse.
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Fig. 4. The waveforms of amplified SBS Stokes pulse, backward SRS compressed Stokes pulse measured by streak camera.
original KrF laser wavelength component and higher order Stokes lights by the FWM process was clearly observed. The conversion efficiency to the KrF laser wavelength was around 5%. The phase matching angle is usually finite to the incident beam direction because the methane gas has spectral dispersion. In this case, the wave number mismatch Dk ¼ 0:2 cm1 is smaller than the gain intensity product (gI). The output of the KrF laser and the higher order Stokes light component also appear on the axis of incident Stokes pulses. These SRS and FWM processes completely eliminate the foot pulse as well. The pulse width of amplified anti-Stokes pulses was measured by an autocorrelator using two-
Fig. 6. Autocorrelation trace of amplified anti-Stokes pulse by using two-photon absorption in BaF2 crystal.
photon absorption in BaF2 crystal (Fig. 6). The FWHM of the trace was 1.1 ps. This was shorter than the SRS Stokes pulse width. We suppose that the anti-Stokes pulse had a steep leading-edge [7], which was generated by a transient Raman process, formed the short peak. The additional peaks in the autocorrelation trace suggest that the pulses have a picosecond scale tail. The energy of this amplified anti-Stokes output was 1.8 mJ. This picosecond range pulse width in UV region is very attractive. Only two commercial discharge KrF lasers are required for this short-pulse source. A stimulated scattering process has phase conjugate behavior, and the whole system is mechanically stable. In principle, not only the window material but also the Brillouin medium is transparent for the ArF wavelength (193 nm). This short-pulse source can be operate at an ArF wavelength.
4. Conclusion
Fig. 5. The spectrum of backward SRS Stokes pulse (dashed) and the output of FWM (solid).
The new short-pulse excimer source was developed by using the combination of stimulated scattering processes. The output pulse width was 1.1 ps. We demonstrated this short-pulse source at a KrF laser wavelength, but this technique could be extended to an ArF laser wavelength.
E. Takahashi et al. / Optics Communications 215 (2003) 163–167
Acknowledgements A part of this study was financially supported by the Budget for Nuclear Research of the Ministry of Education, Culture, Sports, Science and Technology, based on the screening and counseling by the Atomic Energy Commission.
References [1] N. Saito, K. Koyama, M. Tanimoto, J. Mass Spectrom. Soc. Jpn. 48 (4) (2000) 241. [2] J.R.M. Barr, N.J. Everall, C.J. Hooker, I.N. Ross, M.J. Shaw, W.T. Toner, Opt. Commun. 68 (3) (1988) 196. [3] F.P. Schafer, L. Wenchong, S. Szatmari, Appl. Phys. B 32 (3) (1983) 123.
167
[4] K. Kuwahara, E. Takahashi, Y. Matsumoto, S. Kato, Y. Owadano, J. Opt. Soc. Am. B 17 (11) (2000) 1943. [5] E. Takahashi, K. Kuwahara, Y. Matsumoto, I. Okuda, I. Matsushima, S. Kato, Y. Owadano, Opt. Commun. 185 (2000) 431. [6] A.Z. Grasyuk, L.L. Losev, A.P. Lutsenko, S.N. Sazonov, Sov. J. Quantum Electron. 19 (8) (1989) 1045. [7] L.L. Losev, V.I. Soskov, Opt. Commun. 135 (1997) 71. [8] S.A. Akhmanov, K.N. Drabovich, A.P. Sukhorukov, A.S. Chirkin, Sov. Phys. JETP 32 (2) (1971) 266. [9] Y. Taira, K. Ide, H. Takuma, Chem. Phys. Lett. 91 (4) (1982) 299. [10] V.A. Gorbunov, S.B. Papernyi, V.F. Petrov, V.R. Startsev, Sov. J. Quantum Electron. 13 (7) (1983) 900. [11] Yu.E. DÕyakov, JETP Lett. 11 (7) (1970) 243. [12] V. Kmetik, T. Kanabe, H. Fujita, M. Nakatsuka, T. Yamanaka, Rev. Laser Eng. 26 (4) (1998) 322. [13] J.P. Partanen, M.J. Shaw, J. Opt. Soc. Am. B 3 (10) (1986) 1374. [14] Y.M. Li, R. Fedosejevs, Appl. Opt. 35 (15) (1996) 2583.
KrF laser picosecond pulse source by stimulated scattering processes Eiichi Takahashi a,*, Leonid L. Losev b, Yuji Matsumoto a, Isao Okuda a, Isao Matsushima a, Susumu Kato a, Hirotaka Nakamura c, Kenji Kuwahara d, Yoshiro Owadano a a
National Institute of Advanced Industrial Science and Technology (AIST) Central 2, Umezono, 1-1-4 Tsukuba, Ibaraki 305-8568, Japan b Division of Quantum Radiophysics, P.N. Lebedev Physical Institute, Keninsky prospekt, 53 117924 Moscow, Russia c Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan d SUMITOMO 3M Limited, 3-8-8, Minami-Hashimoto, Sagamihara-shi, Kanagawa 229-1185, Japan Received 18 July 2002; received in revised form 5 November 2002; accepted 22 November 2002
Abstract A new short-pulse KrF laser source was developed by combining stimulated scattering processes, namely, Raman, Brillouin, and four-wave-mixing (FWM). Short pulses of 1.1 ps were obtained from 4 ns oscillator output. Only two commercial discharge KrF lasers are required for this system. This method is very simple and could be extended to an ArF laser wavelength in principle. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 42.55.L; 42.55.Y; 42.65.E; 42.65.H Keywords: Excimer lasers; SRS; SBS; FWM
1. Introduction Excimer lasers are widely used in material processing and analysis, because of their short wavelength and large photon energy. In such fields of research, a short-pulse source is needed to improve accuracy and achieve high intensity inter-
*
Corresponding author. Tel.: +81-298-615-705; fax: +81-298615-717. E-mail address: [email protected] (E. Takahashi).
actions [1]. Additional short-pulse lasers, for example Ti:sapphire or dye lasers, and successive wavelength conversions are usually used to generate the excimer wavelength (KrF:248 nm, ArF:193 nm) short seed pulses [2,3] because modelocking is difficult for excimer lasers itself. However, these seed lasers are very complex. The wavelength conversion to excimer wavelength, especially for ArF, is difficult. Stimulated Brillouin scattering (SBS) can compress the nanosecond output of excimer laser pulses. The wavelength shift through the SBS is so
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 2 ) 0 2 2 3 2 - 0
164
E. Takahashi et al. / Optics Communications 215 (2003) 163–167
small (104 –103 nm) that it is possible for the excimer laser amplifier to amplify the compressed pulse again and thus achieve a large amount of energy. The pulse width of the compressed Stokes pulses is around Tphonon 100 ps or less in the ultraviolet wavelength region. In previous papers, we showed that the heavily saturated amplification in KrF lasers can shorten the Stokes pulses [4,5] because excimer lasers have 2 a small saturation fluence, Es 2 mJ=cm , and is capable of the direct short-pulse saturated amplification without damage to the laser medium. We achieved the formation of 7 ps short pulses by the electron beam pumped KrF laser system. However, the pulse width achieved by the commercial discharge KrF laser amplifier was 50 ps [4]. Multipass amplification would shorten the pulse width, but the suppression of amplified spontaneous emission would be crucial. In addition, since these picosecond short pulses, which are shortened by saturated amplification, accompany a nanosecond tail, they have practical application problems. Stimulated Raman scattering (SRS) pulse compression can generate a shorter pulse because of its short transverse dephasing time, T2 (27 ps for methane gas). However, the wavelength shift is so large (20 nm) that it is impossible for the excimer amplifier to amplify the output Stokes pulses again. Grasyuk et al. [6] uses anti-Stokes pulse generation through a four-wave-mixing (FWM) process to recover the Raman-shifted wavelength for Nd:Glass laser output. In this paper, we report on the development of a new short-pulse excimer source by the combination of SBS, SRS, and FWM. Backward SRS compressed Stokes pulses were recovered in wavelength by successive FWM. This FWM process also works to form very steep leading-edge Stokes pulses [7]. This is because this process is in a transient regime and the leading-edge growth rate can be faster than T2 [8]. The steep leading-edge pulses can be shortened by heavily saturated amplification.
wavelength recovery were adopted. The generated short pulses could then be amplified and shortened by excimer laser amplifier. Methane gas is a Raman medium with a large gain and dephasing time T2 of 27 ps [9]. Since the optimum pulse compression factor of stimulated scattering is around 20 [10], sub-nanosecond or shorter pump pulses are basically necessary to have efficient backward SRS compression. In addition, the pump spectral bandwidth should be comparable to the width of the methane gas media, Dm ðcm1 Þ ¼ 0:32 þ 0:012p (atm), so that a large SRS gain can be achieved. The experimental setup is shown in Fig. 1. The detailed parameters are also noted in the figure. The pulse width of the KrF oscillator was 4 ns; we precompressed the output by SBS pulse leadingedge steepening and short-pulse formation by saturated amplification of the SBS Stokes pulses. To have efficient and stable stimulated scattering, the pump pulse should have a narrow spectral bandwidth and good beam focusability [11]. The directional property of the oscillator output was improved by the spatial filter (SF). The beam diameter after the SF was 7 mm. The beam focusability of the output pulses was close to diffraction limited. The energy of the oscillator output was 3 mJ, and only 8% of the energy passed through the SF. Etalon (F.S.R. ¼ 50 cm1 , Finesse ¼ 15) was inserted into the beam path to reduce its bandwidth. The spectrum before and after the etalon is shown in Fig. 2. The peak position was always adjusted to locate at the maximum. The energy transmission through the etalon was 40%. The improved output pulses of 100 lJ were amplified by the discharge pump KrF laser amplifier (Lambda Physics, Compex102). The amplified pump pulses were injected into the Brillouin
2. Experiment To generate picosecond short pulses, backward SRS pulse compression and transient FWM
Fig. 1. Experimental setup.
E. Takahashi et al. / Optics Communications 215 (2003) 163–167
165
two-photon absorption in BaF2 crystal [14]. In addition, spectrum and energy were measured.
3. Results and discussion
Fig. 2. The spectrum before and after pass through the etalon.
cell filled with Fluorinate FC-72 by using a convex lens. This SBS liquid is an ideal medium because it has a high breakdown threshold for UV radiation and high optical transmittance up to 90% at 190 nm [4,12]. The generated SBS Stokes pulses were amplified again going back on the same optical path. The Stokes pulses were separated by the polarizer and injected into a Raman cell filled with methane gas (0.75 MPa) to create backward SRS compressed Stokes pulses. A dichroic mirror was used to separate the pump and Raman Stokes pulses (k ¼ 268 nm). The Raman Stokes pulses were introduced into an FWM cell filled with methane gas (0.75 MPa). The usual phase matching angle of the FWM process is finite to the incident laser beam propagation axis because the media has dispersion [13]. In order to avoid a ring shape anti-Stokes pulse generation, the focused intensity was increased by using the lens of a short focal length to satisfy the condition; the wave number mismatch was smaller than the Raman gain focused intensity product, Dk gI. The output light consisted of first anti-Stokes light and higher order Stokes light components. Only the anti-Stokes component of the pulses was amplified by the final amplifier pass. The waveforms of the pulses at each compression stage were measured with an oscilloscope, a streak camera, and an autocorrelator by using
The waveforms measured with the oscilloscope are shown in Fig. 3. The width of the pulses decreases with each process. The following overshooting in the Raman Stokes pulse is due to the short-pulse width. The pulse energy of the amplified SBS Stokes and the backward SRS Stokes pulse were 13 and 1 mJ, respectively. The pulse width after the backward SRS pulse compression stage was shorter than the temporal resolution of the oscilloscope (0.75 GHz); a streak camera was used to measure the waveform in detail (Fig. 4). The FWHM of the amplified SBS Stokes pulse and the backward SRS Stokes pulse were 700 and 60 ps, respectively. The amplified SBS Stokes pulse has a tail, but the successive Raman Stokes pulse has no tail. The pulse compression ratio at the SRS stage was 12. The spectrum of the backward SRS Stokes pulse and the output of FWM were measured by a grating spectrometer (Fig. 5). There was no measurable KrF laser wavelength component for a backward SRS Stokes pulse. The creation of an
Fig. 3. Waveforms measured by an oscilloscope: (a) PSX100 KrF laser oscillator output pulse; (b) amplified SBS Stokes pulse; (c) backward SRS Stokes pulse.
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Fig. 4. The waveforms of amplified SBS Stokes pulse, backward SRS compressed Stokes pulse measured by streak camera.
original KrF laser wavelength component and higher order Stokes lights by the FWM process was clearly observed. The conversion efficiency to the KrF laser wavelength was around 5%. The phase matching angle is usually finite to the incident beam direction because the methane gas has spectral dispersion. In this case, the wave number mismatch Dk ¼ 0:2 cm1 is smaller than the gain intensity product (gI). The output of the KrF laser and the higher order Stokes light component also appear on the axis of incident Stokes pulses. These SRS and FWM processes completely eliminate the foot pulse as well. The pulse width of amplified anti-Stokes pulses was measured by an autocorrelator using two-
Fig. 6. Autocorrelation trace of amplified anti-Stokes pulse by using two-photon absorption in BaF2 crystal.
photon absorption in BaF2 crystal (Fig. 6). The FWHM of the trace was 1.1 ps. This was shorter than the SRS Stokes pulse width. We suppose that the anti-Stokes pulse had a steep leading-edge [7], which was generated by a transient Raman process, formed the short peak. The additional peaks in the autocorrelation trace suggest that the pulses have a picosecond scale tail. The energy of this amplified anti-Stokes output was 1.8 mJ. This picosecond range pulse width in UV region is very attractive. Only two commercial discharge KrF lasers are required for this short-pulse source. A stimulated scattering process has phase conjugate behavior, and the whole system is mechanically stable. In principle, not only the window material but also the Brillouin medium is transparent for the ArF wavelength (193 nm). This short-pulse source can be operate at an ArF wavelength.
4. Conclusion
Fig. 5. The spectrum of backward SRS Stokes pulse (dashed) and the output of FWM (solid).
The new short-pulse excimer source was developed by using the combination of stimulated scattering processes. The output pulse width was 1.1 ps. We demonstrated this short-pulse source at a KrF laser wavelength, but this technique could be extended to an ArF laser wavelength.
E. Takahashi et al. / Optics Communications 215 (2003) 163–167
Acknowledgements A part of this study was financially supported by the Budget for Nuclear Research of the Ministry of Education, Culture, Sports, Science and Technology, based on the screening and counseling by the Atomic Energy Commission.
References [1] N. Saito, K. Koyama, M. Tanimoto, J. Mass Spectrom. Soc. Jpn. 48 (4) (2000) 241. [2] J.R.M. Barr, N.J. Everall, C.J. Hooker, I.N. Ross, M.J. Shaw, W.T. Toner, Opt. Commun. 68 (3) (1988) 196. [3] F.P. Schafer, L. Wenchong, S. Szatmari, Appl. Phys. B 32 (3) (1983) 123.
167
[4] K. Kuwahara, E. Takahashi, Y. Matsumoto, S. Kato, Y. Owadano, J. Opt. Soc. Am. B 17 (11) (2000) 1943. [5] E. Takahashi, K. Kuwahara, Y. Matsumoto, I. Okuda, I. Matsushima, S. Kato, Y. Owadano, Opt. Commun. 185 (2000) 431. [6] A.Z. Grasyuk, L.L. Losev, A.P. Lutsenko, S.N. Sazonov, Sov. J. Quantum Electron. 19 (8) (1989) 1045. [7] L.L. Losev, V.I. Soskov, Opt. Commun. 135 (1997) 71. [8] S.A. Akhmanov, K.N. Drabovich, A.P. Sukhorukov, A.S. Chirkin, Sov. Phys. JETP 32 (2) (1971) 266. [9] Y. Taira, K. Ide, H. Takuma, Chem. Phys. Lett. 91 (4) (1982) 299. [10] V.A. Gorbunov, S.B. Papernyi, V.F. Petrov, V.R. Startsev, Sov. J. Quantum Electron. 13 (7) (1983) 900. [11] Yu.E. DÕyakov, JETP Lett. 11 (7) (1970) 243. [12] V. Kmetik, T. Kanabe, H. Fujita, M. Nakatsuka, T. Yamanaka, Rev. Laser Eng. 26 (4) (1998) 322. [13] J.P. Partanen, M.J. Shaw, J. Opt. Soc. Am. B 3 (10) (1986) 1374. [14] Y.M. Li, R. Fedosejevs, Appl. Opt. 35 (15) (1996) 2583.