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Short pulse amplification in the ultraviolet using stimulated Raman scattering
1 May 1991
OPTICS COMMUNICATIONS
Volume 82, number 56
Short pulse amplification in the ultraviolet using stimulated Raman scattering C.J. Hooker,
J.M.D.
Lister
and P.A. Rodgers
SERC Central Laser Facility, RutherfordAppleton Laboratory, Chilton, Didcot, Oxon OX11 OQX. UK
Received 18 October 1990; revised manuscript received 10 December 1990
Experimental results are presented for high gain high conversion amplification of short ultraviolet laser pulses in a methane filled Raman amplifier. The results are found to be in good agreement with a numerical solution of the equations for transient plane wave stimulated Raman scattering, using an experimental estimate of the Raman gain coefficient, for a range of input intensities and three pulse lengths.
1. Introduction
2. Theory and numerical model
The high performance excimer laser system at the Rutherford Appleton Laboratory [ I-61 is based upon the large electron-beam pumped krypton fluoride modules GOBLIN and SPRITE [ 7,8], whose output is used to pump a chain of three methane tilled Raman amplifiers which deliver a high-quality prepulse-free beam for target experiments [ 9 1. The use of “beam-combining” in Raman amplifiers to produce a single high quality Stokes pulse from seven pump beams with efficiencies in excess of 50% has also been demonstrated [ 11. The Raman amplifiers require input pulses at 249 nm, the KrF wavelength, and 268 nm, the Stokes shifted KrF wavelength in methane (a shift of 29 17 cm- ’ ). The Raman linewidth, Av,, at the pressures employed in this study (2-3 atm) is approximately 0.35 cm-’ (AYE= 0.32+0.012P, AU, is the fwhm in cm-’ and Pis the methane pressure in atmospheres) and so the dephasing time, T, = 1/ ( XAZJR ), is approximately 30 ps [ lo]. In this paper we report experimental and theoretical results on high gain high efficiency short pulse amplification of 4 ps, 8 ps and 40 ps pulses. For these pulse lengths the Raman gain is in the transient regime.
Raman amplification occurs in gases via stimulated Raman scattering (SRS). This is a nonlinear process by which two laser beams - at the pump and Stokes frequencies (w, and 0s) - are coupled through a material excitation, or optical phonon, Q (oo=orws). The equations describing SRS can be derived by treating the molecules as damped harmonic oscillators and expanding their polarizability in a Taylor series as a function of inter-nuclear separation [ 111 or by using a three-level system model and the Rabi frequency techniques of quantum optics [ 121. In both cases we must solve the Maxwell equations and make the slowly varying envelope approximation. For single mode plane waves the equations are a&(&
t)/az=
- (WP/WS) Q(z, t) -&(Z, t)
aw,
o/a=
Q*k
aQ(z, l)lat+Q(z,
f) h(Z, t) ,
,
(1) (2)
t)lT,
= c, c, Ep(Z, t) &(z, t) .
(3)
Ep(z, t) and E,(z,
t) are the pump and Stokes electric field pulse envelopes; z is the distance travelled along the amplifier; t = t’ -z/u is the retarded time where u is the pulse velocity and t’ the laboratory time; Q( z, t) is the phonon; T, is the dephasing time
003O-4018/9 l/%03.50 0 199 1 - Elsevier Science Publishers B.V. ( North-Holland )
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OPTICS COMMUNICATIONS
of the media which sets the timescales for the interaction; and C, and C, are proportional to the polarizability of the medium and determine, with T,, the strength of the interaction (and hence the amplification). We have written an iterative and fully implicit finite difference computer code to solve the coupled equations ( 1 )-( 3) in the high conversion transient regime where analytic solutions are not known. We have tested the code in the steady state limit (aQ/at=O) against the exact solution for the intensity
h(z)
=zol+
Y=~C,
ZRewWOz)
(~d~dZ~expW0z)
C2T2lm3,
’
(4) (5)
whereZ(z)=~eovlE(z)12,ZR=Zs(0)/ZP(O) andIe= Zp(0) + (wp/ws)Zs(0) (eO is permittivity). In the non-depletion limit (Zr (z) = Zp(0) ) the gain is exponential Zs(Z)=Zs(O)
exp(yZ&) ,
(6)
yZJ.is usually called the steady state small signal gain. We have also checked the code in the transient nondepletion limit against the approximation of Duncan et al. [ 131 to the exact solution of Carmen et al. [141?
u2=
8C,
C2zb !z UC0
+z,z. 2
Here & is the pump pulse energy per square centimeter and rp the pulse length. For gaussian pulses &= 1.06rpZp where rp is the fwhm and Zp is the peak intensity (therefore u2=(2.12r,/T2)yZrL). We have made a number of approximations in the derivation of eqs. (1 )-( 3): ( i ) We have assumed transform limited pulses and neglected self phase modulation and any other phase structure of the pulses. (ii) We have assumed the pulses travel with the same velocity, (i.e. there is no dispersion). (iii ) We have neglected the transverse structure of the fields (see ref. [ 15 ] for 2-D SRS calculations). (iv) We have used plane wave single mode fields 498
1 May 1991
(see ref. [ 16 ] for details of focussed SRS ). (v) We have neglected higher order processes (second Stokes, anti-stokes, backward scattering, etc). There are several important differences between steady state and transient SRS. As the fwhm of the pulse becomes shorter (i.e. comparable to T2) the pulse shape becomes less important; the relative timing of the pulses affects the amplification (optimum gain is achieved when the Stokes pulse leads the pump); and the pulse energy influences amplification more than the peak intensity. For each pulse length the code was run for a range of pump-Stokes delays to find the optimum time delay between the pulses and the energy gain (amplification) and conversion efficiency (defined as & (L ) / 8s ( 0 ) and 100 x [~s(L)-&(0)]/~p(O)) werecalculatedtocompare with the experimental results.
3. Experiment The Raman amplifier consists of a 3 m long stainless steel pressure cell with calcium fluoride windows. The system for generating the short KrF pump pulses is described in detail elsewhere [ 11. Briefly, pulses are originally generated at 746 nm in a syncpumped dye laser and the pulse duration is varied by inserting etalons into the dye laser cavity. After amplification and frequency tripling to 248 nm the beam is spatially filtered and amplified in double pass in a KrF discharge laser ( Lambda-Physik EMG 103 ). The first pass is used to pump the Raman generator and part of the second pass pumps the Raman amplifier as shown in fig. 1. A dichroic beamsplitter couples the pump beam into the amplifier, while transmitting 70% of the Stokes beam; the pump energy is about 5 mJ at the input window to the cell. The layout of the system ensures that the two pulses can be synchronised by fine adjustment of the pump beam timing, made with a sliding mirror. The collimated pump and Stokes beams travel at a small angle to one another along the amplifier, and are separated by dispersion in a prism at the output. The energy is the amplified Stokes beam is typically 1 mJ per pulse. The angle between the pump and Stokes beams must be chosen with care, as it is essential to avoid
OPTICS COMMUNICATIONS
Volume 82, number 5,6
Raman KrF
generator
input
IA
JU
WI
Raman
amplifier
(RAO)
I Power
\
Dlchroic
meter (2)
Pump
beamsplitter
beam
Power meter (1)
Fig. 1. Experimental arrangement for gain measurements on the Raman amplifier.
the phase-matching angle for the four-wave mixing process which generates second Stokes radiation. This angle is close to 2 mrad (the exact value depending on the pressure in the amplifier) and is extremely sharply defined. When the pump beam is offset to the correct angle we observe strong depletion of the output first Stokes beam and the simultaneous appearance of a second Stokes beam after the dispersing prism. Alternatively, if the pump and Stokes beams are exactly collinear, the fringes present on the pump imprint themselves on the amplified Stokes. These fringes arise from diffraction at the rectangular exit aperture of the EMG 103 and at the spatial split. The pump beam is therefore given a shear of about 1 mrad along a diagonal with respect to the Stokes so that the effect of intensity averaging along the Stokes path cleans up both horizontal and vertical fringes. To investigate the performance of the Raman amplifier, we measured the gain and pump-to-Stokes conversion efficiency at pulse lengths of 4 ps, 8 ps and 40 ps, with variable Stokes inputs and constant pump intensity. The pump beam timing relative to the Stokes was adjusted before each set of measurements to obtain maximum output for the pulse length being used; this is necessary because the optimum timing varies with the pulse length. The methane pressure in the amplifier was adjusted to the highest level consistent with there being no self-generation of Stokes light by the pump beam. Self-generated Stokes would compete with the input Stokes and distort the measurements. Pressures of between 2 and
1 May 1991
3 atm of methane were used, again depending on pulse length. The energies of the input and output Stokes pulses were obtained from average-power measurements made with a power meter. Pump energies were obtained using a second power meter, which was previously cross-calibrated against the first power meter. Both detectors have slow time constants, of order 10 s, while the pulse repetition frequency was 8 Hz, so the effects of shot-to-shot variations in pulse energies were averaged out. Before taking each set of data the pump power was measured with the second power meter, which was then placed in a spatially split-off part of the KrF beam as a check that the pump power remained constant. After the dispersion prism at the output of the amplifier, the Stokes beam was directed onto the first power meter through an aperture of known area, to restrict the measured part to a region of good uniformity. The Stokes input was varied by attenuating the beam with metallised quartz neutral density filters, which had previously been calibrated at 268 nm with a spectrophotometer. Calculated adjustments of the pump timing were made to compensate the extra optical path introduced by the filters. The amplified Stokes power was measured over as wide a range of inputs as the power meter sensitivity would permit, attenuation factors of up to lo4 being used. The meter had sufficient sensitivity to measure the unattenuated input Stokes power, and this was monitored at intervals during the data-taking to allow slow variations due to timing drifts in the lasers to be corrected. The transmission of the amplifier and other optics at 268 nm was measured separately. The intensity of the Stokes beam was assumed uniform across the area measured, and was calculated from the energy per pulse (the measured power divided by the repetition frequency of 8 Hz) and the pulse duration. The actual input intensity was determined from the power of the unamplified beam by applying the attenuation factors of the filters and the system optics. The extraction efficiency was calculated as the ratio of output Stokes energy to input pump energy, both corrected. for Fresnel losses in the amplifier windows to give a true internal efficiency. Measurements were made of the pulse length and spectrum of the 249 nm output of the EMG 103, since 499
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OPTICS COMMUNICATIONS
both affect the behaviour of the Raman amplifier. Two techniques were used to determine pulse lengths; a streak camera was used for the longer pulses and a cross-correlator for the shortest. Streaks were recorded on film at the output of the camera image intensifier and densitometered; the measured pulse length was 40 ps fwhm, and the shape was asymmetric (with the fall time approximately twice the rise time). The cross-correlation measurement [ 171 was performed by mixing the 249 nm and residual 746 nm light in a KDP crystal to yield a difference frequency signal at -373 nm. The 249 nm wavefront was sheared by diffraction from a grating (in first order) before mixing. The 373 nm signal was detected with a 1D array, and its spatial extent gives a measure of the pulse length. The pulse length determined in this way was 4 ps, which is identical to that from’ the dye oscillator within the limits of error. No measurements were possible of the intermediate pulse length at 249 nm; we assume it was close to the 8 ps found from the autocorrelation measurement at 746 nm. The spectrum of the 249 nm amplified beam was examined using a grating spectrometer with a 1D reticon readout. This instrument has a resolution of approximately 0.8 cm-‘. The bandwidth of the 40 ps pulses was less than the instrumental limit, but the 4 ps pulses exhibited a spectrum with multiple peaks and marked shot-to-shot variation. These fluctuations originate in the sync-pumped oscillator, and are a consequence of the leading edge of the pulse picking up cavity noise as it circulates [ 18 1. The average width of the spectrum was 10 cm-‘, which for a 4 ps pulse is about three times the transform limit. The spectrum of the 40 ps pulses was measured using an etalon with a free spectral range of 1.1 cm-’ and was found to be 0.3 cm-‘, which corresponds to the transform limited spectral width.
lMay1991
theoretical predictions (solid line) are explained below. In tables 1 and 2 we compare the experimentally measured maximum energy gains and peak conversion efficiencies for 4 ps, 8 ps and 40 ps pulses with numerical solutions of eqs. ( 1 )-( 3). The code used the experimentally measured pulse lengths and in-
l+----i
Input
Stokes
Intensity
(W/cm21
Fig. 2. Comparison of measured gain (crosses) for 4 ps pulses with code prediction (solid line) using yE= 0.60 y. Pressure = 2.5 atm, peak pump intensity= 1.5 GW/cm-2 and z= 300 cm.
4. Results and discussion The measured gain for approximately constant pump intensities ( 1.5 GWcm-’ for 4 ps pulses, 1.361.44 GWcm-’ for 8 ps pulses, and 0.19-0.23 GWcm-2 for 40 ps pulses) is plotted against the input Stokes intensity (crosses) in figs. 2,3 and 4. The 500
1022 WY
103
D‘ 105 lo6 Input Stokes Intensity (W/cm2)
107
Fig. 3. Comparison of measured gain (crosses) for 8 ps pulses with code prediction (solid line) using y,=O.68 y. Pre.ssure.=2.2 atm, peak pump intensity= 1.36-1.44 GW/cmmZ and z=300 cm.
Volume 82, number 5,6
E “a”-”
lo2
OPTICS COMMUNICATIONS
3
“““‘1
“.,,&I’
Input
Stokes
’
.
‘,.I*
106
105
loL
103
Intensity (W/cm21
Fig. 4. Comparison of measured gain (crosses) for 40 ps pulses with code prediction (solid line) using ya=O.SO y. Pressure= 3.0 atm, peak pump intensity=0.19-0.23 GW/cm-* and z=300 cm. Table 1. Comparison of predicted and observed maximum gains for 4, 8 and 40 ps pulses. Pulse length (ps)
4 8 40
Input intensity (Wcm-s)
Maximum gain
pump
Stokes
predicted
observed
1.5x 109 1.4x lo9 1.9x108
1.2x 103 2.6x lo* 3.1x102
1.4x 10” 1.7x 106 1.8x lo5
4.5x 10’ 2.6x IO5 4.4x 104
Table 2. Comparison of predicted and observed peak efftciencies for 4, 8 and 40 ps pulses. Pulse length (ps)
4 8 40
Input intensity (Wcm-*)
Peak efficiency %
pump
Stokes
predicted
observed
1.5x IO9 1.4x 109 2.3x 10s
2.9~10~ 1.9~10~ 6.8x10’
62 69 79
54 66 73
tensities, and calculated values of T2 from ref. [ lo]. y=O.24 cm/GW at 1 atm and is linearly dependent on the pressure of methane in the amplifier [ 4,19 1. The maximum energy gain occurs for low Stokes inputs (table 1) and the peak efficiencies occur for
1 May 1991
high Stokes inputs (table 2). The theory agrees well with experiment at high Stokes input intensities, but diverges significantly in the small signal regime. Here the predicted gain is very sensitive to the pump energy (eqs. ( 7 ) and ( 8 ) ) and small errors in the measured power or pulse length could thus account for some of the discrepancy. The discrepancy is largest for 4 ps pulses, which are known to be non-transform-limited. It is likely that the inclusion of bandwidth effects in the code model will lead to reduced gains and more accurate predictions of amplifier behaviour. Inclusion of multi-mode random phase noise [20] is being investigated. The combination of non-transform-limited pulses and non-collinear pumping will also reduce the effective length over which amplification can occur [ 1,111 and further reduce the gain. To take account of these effects it is possible to derive an experimental estimate of the ‘effective’ Raman gain coefficient, YE.This can be done approximately by setting &(z)/&(O) in eq. (7) equal to the measured gain in the small signal regime and using eq. (8) to find YE.However the true small signal gain regime was only reached for 4 ps pulses. Instead we ran the code for the lowest Stokes input at each pulse length and found YEby setting yEI& equal to the yZ,L which gave the experimentally measured gain. The results are summarised in table 3. The reduction of y required increases as the pulses become shorter. The code predictions using YEover a range of input Stokes intensities are shown by the solid lines in figs. 2, 3 and 4, and are in good agreement with the experimental data. A ye/y of approximately 90% was used by MacPherson et al. to model 18 ns pulses at 532 nm being amplified in 10 atm of hydrogen (T,x2 ns) [ 161.
Table 3. Stokes pulse lead, amplifier pressure and derived values of y used in tigs. 2,3 and 4. Pulse length
Stokes lead
Pressure
(PSI
h)
(atm)
4 8 40
2 5 28
2.5 2.2 3.0
YE/Y
60% 68% 80%
501
Volume 82, number 56
OPTICS COMMUNICATIONS
5. Conclusion
We have obtained conversion efficiencies of 73% for short pulse amplification using stimulated Raman scattering in the transient regime. For pulses of poor spectral quality (three times transform-limited) in the very transient regime (4 ps pulses in a medium with a 30 ps relaxation time) we achieved conversion efficiencies of 54%. These results are in good agreement with numerical predictions. In the high-gain low-depletion limit we have used an experimentally determined value of the Raman gain coefficient yE to model deviations from the straightforward 1D transform limited computations. . Ackr;owledgement
The, authors wish to acknowledge ‘useful discussions with Dr. M.J. Shaw.
References
~
[ 1] I.N. Ross, M.J. Shaw, C.J. Hooker, M.H. Key, EC. Harvey, J.M.D. Lister, J.E. Andrew, G,J. Hirst and P.A. Rodgers, Optics Comm. 78 (1990) 263. [2]M.H. Key, M.J. Shaw, I.N. Ross, P.R. Rodgers and M.C. Gower, Rutherford Appleton Laboratory Report RAL890133 (1989). [ 3 ] M.J. Shaw, J.P. Partanen, Y. Owadano, LN. Ross,. E. Hodgson, C.B. Edwards and F. O’Neill, J. Opt. SocAm. B3 (1986) 1466. ’
502
1 May 1991
[4]N.J. Everall, J.P. Partanen, J.R.M. Barr and M.J. Shaw, Optics Comm. 64 (1987) 393. [5] J.R.M. Barr, N.J. Everall, C.J. Hooker, M.J. Shaw and W.T. Toner, Optics Comm. 66 ( 1988) 127. [6] J.R.M. Barr, N.J. Everall, C.J. Hooker, J.P. Partanen and M.J. Shaw, Proc. SPIE 874 (1988) 60. [ 71 F. Kannari, M.J. Shaw and F. O’Neill, J. Appl. Phys. 61 (1987) 476. [ 81 C.B. Edwards, F. O’Neill, M.J. Shaw, D. Baker and D. Craddock, in: Excimer laser-1983, AIP Conf. Proc. No 100, eds. C.K. Rhodes, H. Egger and H. Plummer (American Institute of Physics, New York, 1983) p. 59. [9] 0. Willi, G. Kiehn, J. Edwards, V. Barrow, R.A. Smith, J. Wark and E. Turcu, Europhys. Lett. 10 ( 1989) 141. [lo] Y. Taira, K. Ide and H. Takuma, Chem. Phys. Lett. 91 (1982) 299. [ 111 J.P. Partanen and M.J. Shaw, J. Opt. Sot. Am. B3 (1986) 1374. [ 121 M.G. Raymer, J. Mostowski and J.L. Carlsten, Phys. Rev. Al9 (1979) 2304. [ 131 M.D. Duncan, R. Mahon, L.L. Tankersley and J. Reintjes, J. Opt. Sot. Am. BS:( 1988) 37. [ 141 R.L. Carmen, F. Shimizu, C.S. Wang and N. Bloembergen, Phys. Rev. A2 ( 1970) 60. [ 151 J.W. Haus and M. Scalora, Phys. Rev. A42 (1990) 3149. [ 161 D.C. MacPherson, R.C. Swanson and J.L. Carlsten, IEEE J.Quantum Electron. QE-25 (1989) 1741. [ 171 I.N. Ross, D. Karadia and J.R.M. Barr, Appl. Optics 28 (1989) 4054. [ 181 J.M. Catherall and G.H.C. New, IEEE J. Quantum Electron QE-25 (1986) 1593. [ 191 W.K. Bischel and G. Black, in: Excimer laser-1983, AIP Conf. Proc. No 100, eds C.K. Rhodes, H. Egger and H. Plummer (American Institute of Physics, New York, 1983) p. 181. [ 201 D.J. Bradley and G.H.C. New, Proc. IEEE62 ( 1974) 3 13.
OPTICS COMMUNICATIONS
Volume 82, number 56
Short pulse amplification in the ultraviolet using stimulated Raman scattering C.J. Hooker,
J.M.D.
Lister
and P.A. Rodgers
SERC Central Laser Facility, RutherfordAppleton Laboratory, Chilton, Didcot, Oxon OX11 OQX. UK
Received 18 October 1990; revised manuscript received 10 December 1990
Experimental results are presented for high gain high conversion amplification of short ultraviolet laser pulses in a methane filled Raman amplifier. The results are found to be in good agreement with a numerical solution of the equations for transient plane wave stimulated Raman scattering, using an experimental estimate of the Raman gain coefficient, for a range of input intensities and three pulse lengths.
1. Introduction
2. Theory and numerical model
The high performance excimer laser system at the Rutherford Appleton Laboratory [ I-61 is based upon the large electron-beam pumped krypton fluoride modules GOBLIN and SPRITE [ 7,8], whose output is used to pump a chain of three methane tilled Raman amplifiers which deliver a high-quality prepulse-free beam for target experiments [ 9 1. The use of “beam-combining” in Raman amplifiers to produce a single high quality Stokes pulse from seven pump beams with efficiencies in excess of 50% has also been demonstrated [ 11. The Raman amplifiers require input pulses at 249 nm, the KrF wavelength, and 268 nm, the Stokes shifted KrF wavelength in methane (a shift of 29 17 cm- ’ ). The Raman linewidth, Av,, at the pressures employed in this study (2-3 atm) is approximately 0.35 cm-’ (AYE= 0.32+0.012P, AU, is the fwhm in cm-’ and Pis the methane pressure in atmospheres) and so the dephasing time, T, = 1/ ( XAZJR ), is approximately 30 ps [ lo]. In this paper we report experimental and theoretical results on high gain high efficiency short pulse amplification of 4 ps, 8 ps and 40 ps pulses. For these pulse lengths the Raman gain is in the transient regime.
Raman amplification occurs in gases via stimulated Raman scattering (SRS). This is a nonlinear process by which two laser beams - at the pump and Stokes frequencies (w, and 0s) - are coupled through a material excitation, or optical phonon, Q (oo=orws). The equations describing SRS can be derived by treating the molecules as damped harmonic oscillators and expanding their polarizability in a Taylor series as a function of inter-nuclear separation [ 111 or by using a three-level system model and the Rabi frequency techniques of quantum optics [ 121. In both cases we must solve the Maxwell equations and make the slowly varying envelope approximation. For single mode plane waves the equations are a&(&
t)/az=
- (WP/WS) Q(z, t) -&(Z, t)
aw,
o/a=
Q*k
aQ(z, l)lat+Q(z,
f) h(Z, t) ,
,
(1) (2)
t)lT,
= c, c, Ep(Z, t) &(z, t) .
(3)
Ep(z, t) and E,(z,
t) are the pump and Stokes electric field pulse envelopes; z is the distance travelled along the amplifier; t = t’ -z/u is the retarded time where u is the pulse velocity and t’ the laboratory time; Q( z, t) is the phonon; T, is the dephasing time
003O-4018/9 l/%03.50 0 199 1 - Elsevier Science Publishers B.V. ( North-Holland )
497
Volume 82, number 5,6
OPTICS COMMUNICATIONS
of the media which sets the timescales for the interaction; and C, and C, are proportional to the polarizability of the medium and determine, with T,, the strength of the interaction (and hence the amplification). We have written an iterative and fully implicit finite difference computer code to solve the coupled equations ( 1 )-( 3) in the high conversion transient regime where analytic solutions are not known. We have tested the code in the steady state limit (aQ/at=O) against the exact solution for the intensity
h(z)
=zol+
Y=~C,
ZRewWOz)
(~d~dZ~expW0z)
C2T2lm3,
’
(4) (5)
whereZ(z)=~eovlE(z)12,ZR=Zs(0)/ZP(O) andIe= Zp(0) + (wp/ws)Zs(0) (eO is permittivity). In the non-depletion limit (Zr (z) = Zp(0) ) the gain is exponential Zs(Z)=Zs(O)
exp(yZ&) ,
(6)
yZJ.is usually called the steady state small signal gain. We have also checked the code in the transient nondepletion limit against the approximation of Duncan et al. [ 131 to the exact solution of Carmen et al. [141?
u2=
8C,
C2zb !z UC0
+z,z. 2
Here & is the pump pulse energy per square centimeter and rp the pulse length. For gaussian pulses &= 1.06rpZp where rp is the fwhm and Zp is the peak intensity (therefore u2=(2.12r,/T2)yZrL). We have made a number of approximations in the derivation of eqs. (1 )-( 3): ( i ) We have assumed transform limited pulses and neglected self phase modulation and any other phase structure of the pulses. (ii) We have assumed the pulses travel with the same velocity, (i.e. there is no dispersion). (iii ) We have neglected the transverse structure of the fields (see ref. [ 15 ] for 2-D SRS calculations). (iv) We have used plane wave single mode fields 498
1 May 1991
(see ref. [ 16 ] for details of focussed SRS ). (v) We have neglected higher order processes (second Stokes, anti-stokes, backward scattering, etc). There are several important differences between steady state and transient SRS. As the fwhm of the pulse becomes shorter (i.e. comparable to T2) the pulse shape becomes less important; the relative timing of the pulses affects the amplification (optimum gain is achieved when the Stokes pulse leads the pump); and the pulse energy influences amplification more than the peak intensity. For each pulse length the code was run for a range of pump-Stokes delays to find the optimum time delay between the pulses and the energy gain (amplification) and conversion efficiency (defined as & (L ) / 8s ( 0 ) and 100 x [~s(L)-&(0)]/~p(O)) werecalculatedtocompare with the experimental results.
3. Experiment The Raman amplifier consists of a 3 m long stainless steel pressure cell with calcium fluoride windows. The system for generating the short KrF pump pulses is described in detail elsewhere [ 11. Briefly, pulses are originally generated at 746 nm in a syncpumped dye laser and the pulse duration is varied by inserting etalons into the dye laser cavity. After amplification and frequency tripling to 248 nm the beam is spatially filtered and amplified in double pass in a KrF discharge laser ( Lambda-Physik EMG 103 ). The first pass is used to pump the Raman generator and part of the second pass pumps the Raman amplifier as shown in fig. 1. A dichroic beamsplitter couples the pump beam into the amplifier, while transmitting 70% of the Stokes beam; the pump energy is about 5 mJ at the input window to the cell. The layout of the system ensures that the two pulses can be synchronised by fine adjustment of the pump beam timing, made with a sliding mirror. The collimated pump and Stokes beams travel at a small angle to one another along the amplifier, and are separated by dispersion in a prism at the output. The energy is the amplified Stokes beam is typically 1 mJ per pulse. The angle between the pump and Stokes beams must be chosen with care, as it is essential to avoid
OPTICS COMMUNICATIONS
Volume 82, number 5,6
Raman KrF
generator
input
IA
JU
WI
Raman
amplifier
(RAO)
I Power
\
Dlchroic
meter (2)
Pump
beamsplitter
beam
Power meter (1)
Fig. 1. Experimental arrangement for gain measurements on the Raman amplifier.
the phase-matching angle for the four-wave mixing process which generates second Stokes radiation. This angle is close to 2 mrad (the exact value depending on the pressure in the amplifier) and is extremely sharply defined. When the pump beam is offset to the correct angle we observe strong depletion of the output first Stokes beam and the simultaneous appearance of a second Stokes beam after the dispersing prism. Alternatively, if the pump and Stokes beams are exactly collinear, the fringes present on the pump imprint themselves on the amplified Stokes. These fringes arise from diffraction at the rectangular exit aperture of the EMG 103 and at the spatial split. The pump beam is therefore given a shear of about 1 mrad along a diagonal with respect to the Stokes so that the effect of intensity averaging along the Stokes path cleans up both horizontal and vertical fringes. To investigate the performance of the Raman amplifier, we measured the gain and pump-to-Stokes conversion efficiency at pulse lengths of 4 ps, 8 ps and 40 ps, with variable Stokes inputs and constant pump intensity. The pump beam timing relative to the Stokes was adjusted before each set of measurements to obtain maximum output for the pulse length being used; this is necessary because the optimum timing varies with the pulse length. The methane pressure in the amplifier was adjusted to the highest level consistent with there being no self-generation of Stokes light by the pump beam. Self-generated Stokes would compete with the input Stokes and distort the measurements. Pressures of between 2 and
1 May 1991
3 atm of methane were used, again depending on pulse length. The energies of the input and output Stokes pulses were obtained from average-power measurements made with a power meter. Pump energies were obtained using a second power meter, which was previously cross-calibrated against the first power meter. Both detectors have slow time constants, of order 10 s, while the pulse repetition frequency was 8 Hz, so the effects of shot-to-shot variations in pulse energies were averaged out. Before taking each set of data the pump power was measured with the second power meter, which was then placed in a spatially split-off part of the KrF beam as a check that the pump power remained constant. After the dispersion prism at the output of the amplifier, the Stokes beam was directed onto the first power meter through an aperture of known area, to restrict the measured part to a region of good uniformity. The Stokes input was varied by attenuating the beam with metallised quartz neutral density filters, which had previously been calibrated at 268 nm with a spectrophotometer. Calculated adjustments of the pump timing were made to compensate the extra optical path introduced by the filters. The amplified Stokes power was measured over as wide a range of inputs as the power meter sensitivity would permit, attenuation factors of up to lo4 being used. The meter had sufficient sensitivity to measure the unattenuated input Stokes power, and this was monitored at intervals during the data-taking to allow slow variations due to timing drifts in the lasers to be corrected. The transmission of the amplifier and other optics at 268 nm was measured separately. The intensity of the Stokes beam was assumed uniform across the area measured, and was calculated from the energy per pulse (the measured power divided by the repetition frequency of 8 Hz) and the pulse duration. The actual input intensity was determined from the power of the unamplified beam by applying the attenuation factors of the filters and the system optics. The extraction efficiency was calculated as the ratio of output Stokes energy to input pump energy, both corrected. for Fresnel losses in the amplifier windows to give a true internal efficiency. Measurements were made of the pulse length and spectrum of the 249 nm output of the EMG 103, since 499
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both affect the behaviour of the Raman amplifier. Two techniques were used to determine pulse lengths; a streak camera was used for the longer pulses and a cross-correlator for the shortest. Streaks were recorded on film at the output of the camera image intensifier and densitometered; the measured pulse length was 40 ps fwhm, and the shape was asymmetric (with the fall time approximately twice the rise time). The cross-correlation measurement [ 171 was performed by mixing the 249 nm and residual 746 nm light in a KDP crystal to yield a difference frequency signal at -373 nm. The 249 nm wavefront was sheared by diffraction from a grating (in first order) before mixing. The 373 nm signal was detected with a 1D array, and its spatial extent gives a measure of the pulse length. The pulse length determined in this way was 4 ps, which is identical to that from’ the dye oscillator within the limits of error. No measurements were possible of the intermediate pulse length at 249 nm; we assume it was close to the 8 ps found from the autocorrelation measurement at 746 nm. The spectrum of the 249 nm amplified beam was examined using a grating spectrometer with a 1D reticon readout. This instrument has a resolution of approximately 0.8 cm-‘. The bandwidth of the 40 ps pulses was less than the instrumental limit, but the 4 ps pulses exhibited a spectrum with multiple peaks and marked shot-to-shot variation. These fluctuations originate in the sync-pumped oscillator, and are a consequence of the leading edge of the pulse picking up cavity noise as it circulates [ 18 1. The average width of the spectrum was 10 cm-‘, which for a 4 ps pulse is about three times the transform limit. The spectrum of the 40 ps pulses was measured using an etalon with a free spectral range of 1.1 cm-’ and was found to be 0.3 cm-‘, which corresponds to the transform limited spectral width.
lMay1991
theoretical predictions (solid line) are explained below. In tables 1 and 2 we compare the experimentally measured maximum energy gains and peak conversion efficiencies for 4 ps, 8 ps and 40 ps pulses with numerical solutions of eqs. ( 1 )-( 3). The code used the experimentally measured pulse lengths and in-
l+----i
Input
Stokes
Intensity
(W/cm21
Fig. 2. Comparison of measured gain (crosses) for 4 ps pulses with code prediction (solid line) using yE= 0.60 y. Pressure = 2.5 atm, peak pump intensity= 1.5 GW/cm-2 and z= 300 cm.
4. Results and discussion The measured gain for approximately constant pump intensities ( 1.5 GWcm-’ for 4 ps pulses, 1.361.44 GWcm-’ for 8 ps pulses, and 0.19-0.23 GWcm-2 for 40 ps pulses) is plotted against the input Stokes intensity (crosses) in figs. 2,3 and 4. The 500
1022 WY
103
D‘ 105 lo6 Input Stokes Intensity (W/cm2)
107
Fig. 3. Comparison of measured gain (crosses) for 8 ps pulses with code prediction (solid line) using y,=O.68 y. Pre.ssure.=2.2 atm, peak pump intensity= 1.36-1.44 GW/cmmZ and z=300 cm.
Volume 82, number 5,6
E “a”-”
lo2
OPTICS COMMUNICATIONS
3
“““‘1
“.,,&I’
Input
Stokes
’
.
‘,.I*
106
105
loL
103
Intensity (W/cm21
Fig. 4. Comparison of measured gain (crosses) for 40 ps pulses with code prediction (solid line) using ya=O.SO y. Pressure= 3.0 atm, peak pump intensity=0.19-0.23 GW/cm-* and z=300 cm. Table 1. Comparison of predicted and observed maximum gains for 4, 8 and 40 ps pulses. Pulse length (ps)
4 8 40
Input intensity (Wcm-s)
Maximum gain
pump
Stokes
predicted
observed
1.5x 109 1.4x lo9 1.9x108
1.2x 103 2.6x lo* 3.1x102
1.4x 10” 1.7x 106 1.8x lo5
4.5x 10’ 2.6x IO5 4.4x 104
Table 2. Comparison of predicted and observed peak efftciencies for 4, 8 and 40 ps pulses. Pulse length (ps)
4 8 40
Input intensity (Wcm-*)
Peak efficiency %
pump
Stokes
predicted
observed
1.5x IO9 1.4x 109 2.3x 10s
2.9~10~ 1.9~10~ 6.8x10’
62 69 79
54 66 73
tensities, and calculated values of T2 from ref. [ lo]. y=O.24 cm/GW at 1 atm and is linearly dependent on the pressure of methane in the amplifier [ 4,19 1. The maximum energy gain occurs for low Stokes inputs (table 1) and the peak efficiencies occur for
1 May 1991
high Stokes inputs (table 2). The theory agrees well with experiment at high Stokes input intensities, but diverges significantly in the small signal regime. Here the predicted gain is very sensitive to the pump energy (eqs. ( 7 ) and ( 8 ) ) and small errors in the measured power or pulse length could thus account for some of the discrepancy. The discrepancy is largest for 4 ps pulses, which are known to be non-transform-limited. It is likely that the inclusion of bandwidth effects in the code model will lead to reduced gains and more accurate predictions of amplifier behaviour. Inclusion of multi-mode random phase noise [20] is being investigated. The combination of non-transform-limited pulses and non-collinear pumping will also reduce the effective length over which amplification can occur [ 1,111 and further reduce the gain. To take account of these effects it is possible to derive an experimental estimate of the ‘effective’ Raman gain coefficient, YE.This can be done approximately by setting &(z)/&(O) in eq. (7) equal to the measured gain in the small signal regime and using eq. (8) to find YE.However the true small signal gain regime was only reached for 4 ps pulses. Instead we ran the code for the lowest Stokes input at each pulse length and found YEby setting yEI& equal to the yZ,L which gave the experimentally measured gain. The results are summarised in table 3. The reduction of y required increases as the pulses become shorter. The code predictions using YEover a range of input Stokes intensities are shown by the solid lines in figs. 2, 3 and 4, and are in good agreement with the experimental data. A ye/y of approximately 90% was used by MacPherson et al. to model 18 ns pulses at 532 nm being amplified in 10 atm of hydrogen (T,x2 ns) [ 161.
Table 3. Stokes pulse lead, amplifier pressure and derived values of y used in tigs. 2,3 and 4. Pulse length
Stokes lead
Pressure
(PSI
h)
(atm)
4 8 40
2 5 28
2.5 2.2 3.0
YE/Y
60% 68% 80%
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5. Conclusion
We have obtained conversion efficiencies of 73% for short pulse amplification using stimulated Raman scattering in the transient regime. For pulses of poor spectral quality (three times transform-limited) in the very transient regime (4 ps pulses in a medium with a 30 ps relaxation time) we achieved conversion efficiencies of 54%. These results are in good agreement with numerical predictions. In the high-gain low-depletion limit we have used an experimentally determined value of the Raman gain coefficient yE to model deviations from the straightforward 1D transform limited computations. . Ackr;owledgement
The, authors wish to acknowledge ‘useful discussions with Dr. M.J. Shaw.
References
~
[ 1] I.N. Ross, M.J. Shaw, C.J. Hooker, M.H. Key, EC. Harvey, J.M.D. Lister, J.E. Andrew, G,J. Hirst and P.A. Rodgers, Optics Comm. 78 (1990) 263. [2]M.H. Key, M.J. Shaw, I.N. Ross, P.R. Rodgers and M.C. Gower, Rutherford Appleton Laboratory Report RAL890133 (1989). [ 3 ] M.J. Shaw, J.P. Partanen, Y. Owadano, LN. Ross,. E. Hodgson, C.B. Edwards and F. O’Neill, J. Opt. SocAm. B3 (1986) 1466. ’
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[4]N.J. Everall, J.P. Partanen, J.R.M. Barr and M.J. Shaw, Optics Comm. 64 (1987) 393. [5] J.R.M. Barr, N.J. Everall, C.J. Hooker, M.J. Shaw and W.T. Toner, Optics Comm. 66 ( 1988) 127. [6] J.R.M. Barr, N.J. Everall, C.J. Hooker, J.P. Partanen and M.J. Shaw, Proc. SPIE 874 (1988) 60. [ 71 F. Kannari, M.J. Shaw and F. O’Neill, J. Appl. Phys. 61 (1987) 476. [ 81 C.B. Edwards, F. O’Neill, M.J. Shaw, D. Baker and D. Craddock, in: Excimer laser-1983, AIP Conf. Proc. No 100, eds. C.K. Rhodes, H. Egger and H. Plummer (American Institute of Physics, New York, 1983) p. 59. [9] 0. Willi, G. Kiehn, J. Edwards, V. Barrow, R.A. Smith, J. Wark and E. Turcu, Europhys. Lett. 10 ( 1989) 141. [lo] Y. Taira, K. Ide and H. Takuma, Chem. Phys. Lett. 91 (1982) 299. [ 111 J.P. Partanen and M.J. Shaw, J. Opt. Sot. Am. B3 (1986) 1374. [ 121 M.G. Raymer, J. Mostowski and J.L. Carlsten, Phys. Rev. Al9 (1979) 2304. [ 131 M.D. Duncan, R. Mahon, L.L. Tankersley and J. Reintjes, J. Opt. Sot. Am. BS:( 1988) 37. [ 141 R.L. Carmen, F. Shimizu, C.S. Wang and N. Bloembergen, Phys. Rev. A2 ( 1970) 60. [ 151 J.W. Haus and M. Scalora, Phys. Rev. A42 (1990) 3149. [ 161 D.C. MacPherson, R.C. Swanson and J.L. Carlsten, IEEE J.Quantum Electron. QE-25 (1989) 1741. [ 171 I.N. Ross, D. Karadia and J.R.M. Barr, Appl. Optics 28 (1989) 4054. [ 181 J.M. Catherall and G.H.C. New, IEEE J. Quantum Electron QE-25 (1986) 1593. [ 191 W.K. Bischel and G. Black, in: Excimer laser-1983, AIP Conf. Proc. No 100, eds C.K. Rhodes, H. Egger and H. Plummer (American Institute of Physics, New York, 1983) p. 181. [ 201 D.J. Bradley and G.H.C. New, Proc. IEEE62 ( 1974) 3 13.