Pump-Induced Temporal Contrast Degradation in Optical Parametric Chirped-Pulse Amplification. Analysis and Experiment

Pump-Induced Temporal Contrast Degradation in Optical Parametric Chirped-Pulse Ampliication: Analysis and Experiment Introduction Laser matter interactions in new regimes have occurred due to the generation o high-intensity optical pulses using largescale laser systems. 1 The interaction regime o a laser pulse with a target is basically set by the peak intensity o the pulse, which is undamentally proportional to the ratio o the pulse energy to the duration o the pulse and surace o the ocal spot. Intensities o the order o 1 W/cm have been claimed, and acilities delivering high-energy, high-intensity laser pulses are under operation or construction. 3 The interaction can be detrimentally impacted by light present beore the main pulse since absorbed light can lead to physical modiication o the target. 4 The temporal contrast o a laser pulse is the ratio o the peak power o the main pulse to the power o the light in some predetermined temporal range beore the main pulse. The contrast can be reduced signiicantly during the generation and ampliication o laser pulses, and contrast degradation maniests itsel as isolated prepulses or as a slowly varying pedestal. Incoherent laser and parametric luorescence can signiicantly impact the contrast o laser pulses and can lead to a long-range pedestal on the recompressed pulse. 4,5 This contrast degradation is undamental since luorescence is always present or classical optical ampliiers. The contrast o optical parametric chirped-pulse ampliiers, however, is also detrimentally impacted by temporal variations o the intensity o the pump pulse that induce spectral variations on the stretched ampliied signal via the instantaneous parametric gain. This is a practical limitation that can be eliminated or reduced by proper design o the pump pulse and the optical parametric chirped-pulse ampliication (OPCPA) system. The parametric gain induced by a pump pulse in a nonlinear crystal is an eicient process or large-bandwidth, high-energy ampliication o chirped optical pulses. 6 8 It is used in stand-alone systems 9 16 or as the ront end o largescale laser acilities. 17 The impact o temporal luctuations on the contrast o the recompressed signal in an OPCPA system was irst identiied by Forget et al. 18 Simulations o the eect o pump-pulse ampliied spontaneous emission (ASE) on an OPCPA system have linked the ASE coherence time to the temporal extent o the induced pedestal. 19 These publications oer a physical explanation o pump-induced contrast degradation, but an analytical treatment is necessary to quantiy the impact o this phenomenon, improve the contrast o existing systems, and design new high-contrast OPCPA systems. This article quantiies the impact o incoherent pump-pulse ASE using an analytic ormalism or pump-induced temporal contrast degradation in OPCPA systems and presents an experimental solution to reduce this impact. The impact o incoherent pump ASE is analytically quantiied as a unction o the operating regime o the OPCPA system. The ollowing sections (1) present the necessary ormalism and derive general equations describing the pump-induced contrast degradation in OPCPA systems; () compare these analytical derivations with simulations, bringing to light the magnitude o these eects in a typical OPCPA system; and (3) describe an LLE experiment that demonstrates the reduction o pump-induced temporal contrast degradation by iltering the pump pulse with a volume Bragg grating (VBG) in a regenerative ampliier. Analysis o Pump-Induced Contrast Degradation in an OPCPA System 1. General Approach The derivations presented in this section assume a onedimensional representation o the electric ield o the signal and pump as a unction o time (and equivalently optical requency), without spatial resolution. Such a model is suicient to introduce the various aspects o contrast degradation in OPCPA systems. Some o these systems use lattop pumps and signals, in which case the temporal contrast is mostly limited by the contrast obtained in the constant-intensity portion o the beam. For high energy extraction, eicient phase matching, and optimal beam quality, OPCPA systems are usually run in conigurations where spatial walk-o and diraction are not signiicant. An instantaneous transer unction between the intensity o the pump, the intensity o the input and the intensity o the output signal is used to describe the parametric ampliier. This applies to an ampliier where temporal walk-o and dispersion-induced changes in the intensity o the interacting waves are small compared to the time scales o the LLE Review, Volume 111 135

temporal variations o the signal and pump. This also applies to a sequence o ampliiers where scaled versions o the same pump are used in each ampliier with an identical relative delay between the signal being ampliied and the pump. Figure 111.1 presents a schematic o an OPCPA system. The short input signal is stretched by a stretcher, ampliied by the pump pulse in an optical parametric ampliier (one or several nonlinear crystals properly phase matched), and recompressed. As identiied in Res. 18 and 19, the variations o the parametric gain due to variations in the pump intensity lead to modulations o the temporal intensity o the ampliied stretched pulse, which are equivalent to modulations o the spectrum o this pulse. These modulations lead to contrast-reducing temporal eatures ater recompression. Input signal E E1587JR Chirped signal E 1 Pump I pump Stretcher ({) Ampliied signal E 3 Compressor ( {) OPA Ampliied chirped signal E Figure 111.1 Schematic o an OPCPA system. Pump-intensity modulation gets transerred onto the spectrum o the chirped signal in an optical parametric ampliier (OPA). The modulation o the spectrum o the recompressed signal induces contrast-reducing temporal eatures on the recompressed signal.. Contrast Degradation o an OPCPA System in the Presence o Pump Noise In this article, E and Eu relate to the temporal and spectral representations o the analytic signal o an electric ield, and I and Iu relate to the corresponding intensities. The initial signal is described by the spectral ield E u signal,( ~ ). Ater stretching with second-order dispersion {, the stretched pulse is described in the time domain by E 1( t) = ` 1 { jeu _ t { iexp a- it { k up to some multiplicative constants. The quadratic phase describes the one-to-one correspondence between time and optical requency in the highly stretched pulse, which is symbolically written as t = {~. The temporal intensity o the signal ater parametric ampliication is a unction o the temporal intensity o the stretched signal I 1( t) = _ 1 { iiu _ t { i and the temporal intensity o the pump I pump (t), which can be written as I ] tg = 8I 1( t), Ipump( t) B. (1) The unction depends on the parametric ampliier length and nonlinear coeicient. Figure 111. displays two examples o behavior o the unction or a given input signal intensity, namely the relation between the output signal intensity and the pump intensity. In Fig. 111.(a), the ampliier is unsaturated, and there is a linear relation between variations o the pump intensity and variations o the ampliied signal intensity around point A. In Fig. 111.(b), the ampliier is saturated. The output signal intensity reaches a local maximum, and there is a quadratic relation between variations o the pump intensity and variations o the ampliied signal intensity around point B. Assuming that the intensity modulation o the pump does not signiicantly modiy the instantaneous requency o the chirped the intensity o a spectral component o the ampliied signal at the optical requency ~ is 8I 1^ {~ h, Ipump^ {~ hb = 9Iu ( ~ ) {, Ipump^ {~ hc. The pump-intensity noise di pump (t) is introduced by writing ] the intensity as I ( t) I g pump = pump( t) + dipump( t). Assuming the ampliier is not saturated [Fig. 111.(a)], the unction is developed to irst order around the operating point set by Ipump g ] as 9Iu ( ~ ) {, Ipump^{~ hc = : Iu ( ~ ) {, Ipump ^{~ hd + d Ipump^{~ h : Iu ( ), I I ~ { pump ^{~ hd. () pump The spectral intensity o the ampliied recompressed signal is Iu 3( ~ ) = { 9 Iu ( ~ ) {, Ipump( {~ ) C. 136 LLE Review, Volume 111

(a) (b) I signal A I signal B Figure 111. Representation o the transer unction between output signal intensity and pump intensity around the operating point o a parametric ampliier in the (a) unsaturated and (b) saturated regimes. At point A, there is a linear relation between pump-intensity modulation and ampliied-signal-intensity modulation. At point B, there is a quadratic relation between pump-intensity modulation and ampliied-signal-intensity modulation. I pump I pump E15871JR and one can deine One can deine u] g I 3( ~ ) = { : Iu ( ~ ) {, Ipump ^{~ hd Eu ] g 3( ~ ) = ui 3( ~ ) exp 7i{ residual( ~ ) A as the spectral intensity o the signal ampliied by a noiseless pump. The partial derivative o with respect to the pump intensity is assumed to be independent o the signal intensity, and one deines the constant 1 = Iu : ( ), I I ~ { pump ^{~ hd. pump For a compressor matched to the stretcher up to a residual spectral phase { residual (~), the electric ield o the recompressed signal is simply Eu 3( ~ ) = u] g I 3( ~ ) + { ] 1gd Ipump^{~ h # exp 7i{ residual( ~ ) A. (3) as the electric ield o the recompressed signal in the absence o noise. In the OPCPA process, the spectral density o the ampliied signal is usually approximately constant (or slowly varying) because o saturation eects, so that I u ] g signal,3( ~ ) is replaced by {I in the denominator o Eq. (4). This leads to I 1 d pump {~ Eu 3( ~ ) = Eu ^ h 3( ~ ) > 1 + H. (5) I The Fourier transorm o Eq. (5) gives the electric ield in the temporal domain: ] 1g E = E + I { A irst-order development o Eq. (3) gives a spectral representation o the signal: Eu 3( ~ ) = u] g I 3( ~ ) exp 7i{ residual( ~ ) A # E 7 d Iu t { i. Further simpliication stems rom deining ] I g ^ 1, Nh = ] 1g pump I, (6) { ] 1gd Ipump^{~ h # > 1 +. u H (4) I 3( ~ ) which is the change in intensity o the ampliied signal normalized to the intensity o the ampliied signal or a change in the pump intensity normalized to the pump intensity. The ield o LLE Review, Volume 111 137

the recompressed signal is ^1, Nh E = E + { Ipump # E 7 d Iu t { i, and the intensity o the compressed signal is (7) I d pump {~ Eu 3( ~ ) = Eu ^ h 3( ~ ) 1 +. 4I > H (1) The Fourier transorm o Eq. (1) gives the temporal ield o the recompressed signal: ^, Nh E = E + E, ( t) signal 3 4: { IpumpD ^1, Nh I = I + 4: { IpumpD 7 d Iu t { i 7 d Iu t { i, (11) # E 7 d Iu t { i, using the act that the irst term in the right-hand side o Eq. (7) is a short pulse while the second term describes the contrast reduction over a large temporal range. When the ampliier is saturated [Fig. 111.(b)], (1) = and Eq. () must be replaced by the second-order decomposition o, which is 9Iu ( ~ ) {, Ipump^{~ hc = Iu : ( ~ ) {, Ipump ^{~ hd 1 + d I 8 pump^{~ hb (8) # Iu :, ( ), I signal ~ { pump ^{~ hd. (9) I pump Assuming that the second-order derivative o with respect to the pump intensity does not depend on the signal intensity, one deines = I Iu pump : ( ~ ) {, Ipump ^{~ hd. ] where = I ^, Nh 9 g pumpc I is the normalized change in the ampliied signal intensity or a normalized change in the pump intensity. Finally, the intensity o the recompressed signal is ^, Nh I = I + 4 16: { IpumpD # E 7 d Iu t { i 7 d Iu t { i. (1) Equations (8) and (1) are general expressions linking the variations in pump intensity to the intensity o the recompressed pulse in the two practically relevant cases: (1)! describes the linear modulation regime, with a linear relation between the pump intensity and the ampliied stretched signal intensity around the operating point; (1) =, ()! describe the quadratic modulation regime, with a quadratic relation between the pump intensity and the ampliied stretched signal intensity around the operating point. In the next two subsections these general expressions are evaluated when ASE is present on the pump pulse. 3. Contrast Degradation o an OPCPA System in the Linear- Modulation Regime due to the Pump-Pulse ASE The pump-pulse ASE is described as an additive stationary process E ASE, and the ield o the pump pulse is Replacing Iu signal ] g,3( ~ ) by {I, one obtains ] E ( t) E g pump = pump( t) + EASE( t). (13) 138 LLE Review, Volume 111

One has at irst order Ipump( t) = Ipump( t) + E ( t) E* pump ASE( t) * + Epump( t) EASE( t), which allows one to identiy * * d Ipump( t) = Epump( t) EASE( t) + Epump( t) EASE( t). One can use the simpliication * Epump( t) = Epump( t) = Ipump ] 1, N g ^ h signal I = I + 4{pump # 8Iu T _ t { i + Iu T _- t { ib. (16) The pedestal due to the ASE present on the pump pulse is thereore directly given by a symmetrized version o the spectrum o the ASE present on the pump pulse. The symmetrized spectrum o the ASE is spread in time proportionally to the second-order dispersion o the chirped pulse. Integration o Eq. (15) gives g signal = signal ] 91 + ^1, Nh T pumpc, which allows the energy in the pedestal pedestal normalized to the energy o the signal signal to be expressed as over the interval [,T ], where the pump has signiicant intensity, and set the ASE electric ield to outside the interval [,T ]. The electric ield o one realization o the ASE restricted to the interval [,T ] and its Fourier transorm are noted E T and E u T, respectively. One obtains pedestal ^1, Nh T =. pump signal The ratio o the pedestal energy to the signal energy, ^h pedestal signal, (17) * d Iu pump( ~ ) = Ipump ; Eu T ( ~ ) + Eu T (- ~ ) E. (14) In the linear modulation regime, the calculation o the intensity o the recompressed pulse using this expression and Eq. (8) leads to ^ 1, Nh I = I + # I t 4 3 ^ - { ~ lh pump # 8Iu T ] ~ lg + Iu T ]- ~ lg Bd~ l, (15) where pump is the energy o the pump pulse. The pumpinduced pedestal is thereore given by a convolution o the symmetrized spectrum o the ASE present on the pump pulse with the recompressed pulse intensity. The intensity o the pedestal is proportional to ^1,Nh. Proper spectral iltering o the pump pulse reduces the temporal extent o the induced pedestal. In the usual case where the recompressed pulse is signiicantly shorter than the temporal variations o the induced pedestal, Eq. (15) can be simpliied as is directly proportional to the ratio o the energy o the ASE in the temporal range deined by the pump to the energy o the pump. The ratio T pump is called ractional ASE energy in the remainder o this article. 4. Contrast Degradation o an OPCPA System in the Quadratic-Modulation Regime due to the Pump ASE The intensity o the recompressed pulse or an OPCPA system in the quadratic-modulation regime with ASE present on the pump can be calculated using Eqs. (1) and (14): ^, Nh I = I + I 8`{pumpj 7 8Iu T _ t { i + Iu T _- t { ib 7 8Iu T _ t { i + Iu T _- t { ib. (18) Equation (18) shows that the pedestal is given by the double convolution o the symmetrized spectrum o the pump ASE LLE Review, Volume 111 139

with the recompressed signal in the absence o pump ASE. The convolution o the symmetrized spectrum o ASE with itsel is broader than the spectrum o ASE (e.g., by a actor or a Gaussian spectrum). Thereore, the temporal extent o the pedestal is larger than in the linear-modulation regime. In the case where the intensity o the recompressed signal is short compared to the temporal variations o the pedestal, Eq. (18) can be simpliied into, N ^ h signal I = I + 8{ pump # 8Iu T _ t { i + Iu T _- t { ib 7 8Iu T _ t { i + Iu T _- t { ib. (19) Finally, integrating Eq. (18) leads to the energy in the pedestal, pedestal ^, Nh T =. signal pump () In the quadratic-modulation regime, the ratio o the energy o the pedestal to the energy o the signal is proportional to the square o the ractional ASE energy. Comparing Eq. () with Eq. (17) leads to the conclusion that i T pump < 8 ^1, Nh ^, NhB, there is less energy in the pedestal when the ampliier is run in the quadratic-modulation regime. Operating the OPCPA in the saturation regime locally decreases the modulation o the output intensity and reduces the total energy o the associated temporal pedestal, provided that the previous inequality is veriied. Simulations o Pump-Induced Contrast Degradation 1. Model Description Simulations o an OPCPA system with parameters similar to those o the OPCPA preampliier o LLE s Multi-Terawatt laser 1 and the ront end o the OMEGA EP Laser Facility 17 have been perormed. The signal has a central wavelength equal to 153 nm. The case o a lat spectral density has been simulated since it corresponds closely to the derivations perormed in the previous section. The case o a Gaussian spectral density with a ull width at hal maximum (FWHM) equal to 6 nm has also been simulated since it is closer to the actual experimental conditions. The stretcher introduces a dispersion equal to 3 ps/nm, i.e., { = 1.76 # 1 s. The preampliier has two lithium triborate (LBO) crystals cut or type-i phase matching at 153 nm and 56.5 nm in collinear interaction, i.e., { LBO = 11.8 and i LBO = 9, with a total length o 59.5 mm. The OPCPA pump at 56.5 nm is obtained by doubling a pump pulse at 153 nm in an 11-mm LBO crystal. The pump at 153 nm is a th-order super-gaussian, with a FWHM equal to.6 ns. The intensity o the up-converted pump has been obtained using a Runge Kutta resolution o the corresponding nonlinear equations. Figure 111.3 displays the normalized intensity o the pump and stretched signal in the OPCPA crystal. The operation o the preampliier was simulated by solving the system o three equations describing the parametric interaction o the electric ield o the idler, and pump using the Runge Kutta method. No spatial resolution or temporal eects have been introduced, or the reasons expressed at the beginning o the previous section. It is straightorward (although computationally more intensive) to introduce these eects. The phase mismatch between the interacting waves was chosen equal to zero. Figure 111.4 displays the ampliied stretched signal intensity as a unction o the pump intensity or an input stretched signal intensity o.1 W/cm, i.e., the unction I = 7I 1, IpumpA used in the previous section or I 1 =.1 W/cm. Points A and B correspond to the linear- and quadratic-modulation regimes, respectively. A it o the curve plotted in Fig. 111.4 around these two points leads to the values (1,N) = 8 and (,N) = 66. The next two subsections present the contrast degradation results or a pump with ASE and a signal with constant spectral density ollowed by results or a pump with ASE and a signal with a Gaussian spectral density. For the sake o clarity, the intensity o the recompressed signal is plotted only at negative times (i.e., beore the peak o the signal), bearing in mind that the pump-induced contrast degradation is symmetric. Normalized intensity 1..8.6.4. E1587JR. 1.5 1..5..5 1. 1.5 Time (ns) Figure 111.3 Normalized intensity o the chirped Gaussian signal (solid curve) and pump (dashed curve) in the OPCPA system. 14 LLE Review, Volume 111

Signal intensity (GW/cm ).5.4.3..1 E15873JR...5 1. 1.5 A B Pump intensity (GW/cm ) Figure 111.4 Transer unction o the OPCPA preampliier or a signal intensity equal to.1 W/cm. Points A and B identiy the linear and quadratic regimes o operation, respectively.. Pump with ASE and Signal with Flat Spectral Density In this section, the stretched signal has a lat spectral density and an intensity o.1 W/cm. The pump ASE spectrum is assumed Gaussian and centered at the wavelength o the pump pulse. The FWHM o the spectrum is chosen equal to either.14 nm (which was experimentally measured on the Nd:YLF regenerative ampliier used to generate the pump pulse) or.3 nm (which corresponds to a hypothetical pump spectral bandpass iltering). Figure 111.5 displays close-ups o the simulated intensity o the pump or an ASE bandwidth o.14 nm and.3 nm at various ractional ASE energies T pump. The homodyne beating o the electric ield o the ASE with the electric ield o the pump leads to signiicant pump intensity modulation even at low ASE energy levels. Figure 111.6 displays a comparison o the results o the simulation with the analytical results or the.14-nm bandwidth. The OPCPA is run either in the linear modulation regime [Figs. 111.6(a) 111.6(c)] or in the quadratic-modulation regime [Figs. 111.6(d) 111.6()]. The ractional ASE energy is speciied as 1 5, 1 4, and 1 3. Signiicant pedestal levels are observed, even or relatively low pump intensity modulation, indicating that such contrast degradation can severely limit OPCPA systems, or laser systems that include an OPCPA as one o their ampliiers. Good agreement o the simulations with the analytical predictions is obtained. Discrepancy in the quadratic modulation regime at low ractional ASE energies is attributed to the leading and the alling edge o the pump, or which the ampliication process is in the linear regime. The pedestal due to the pump ASE extends at longer times in the case o quadratic modulation, as expected rom the double convolution o Eq. (18). The pedestal is typically more intense at short times in the linear regime, and it can also be seen that the total energy in the Intensity (arbitrary units) Intensity (arbitrary units) 1.1 1..9 1.1 1..9 E15875JR (a) (b) 1..5..5 1. Time (ns) (c) (d) 1..5..5 1. Time (ns) Figure 111.5 Close-ups o the temporal intensity o the pump or ASE with a Gaussian spectrum with a FWHM equal to.14 nm and a ractional energy equal to (a) 1 5, (b) 1 4, and (c) 1 3, and (d) or ASE with a Gaussian spectrum with a FWHM equal to.3 nm and a ractional energy equal to 1 3. pedestal is smaller in the quadratic modulation regime than in the linear modulation regime {in agreement with the relation ASE, T pump < 8 ^1, Nh ^, NhB, with 8 ^1, Nh ^, NhB =. 14}. It should be noted, however, that the two modulation regimes lead to similar pedestal levels around 1 ps. Figures 111.7(a) and 111.7(d) display the intensity o the recompressed signal or an ASE bandwidth o.3 nm and a ractional ASE energy equal to 1 3, which can be compared to the intensity plotted in Figs. 111.6(c) and 111.6(). Reduction o the bandwidth o the pump ASE leads to a drastic improvement o the signal temporal contrast. This result shows that a signiicant increase in the contrast o OPCPA systems can be obtained via proper spectral iltering o the pump pulse, as is discussed in Experimental Demonstration o Temporal Contrast Improvement o an OPCPA System by Pump Spectral Filtering (p. 144). While this was expressed previously in terms o the coherence time o the pump 19 the temporal contrast away rom the peak o the signal is inluenced mostly by the spectral density o the ASE at optical requencies signiicantly dierent rom the central requency o the pump. A non-zero spectral density at these optical requencies leads to a inite extinction ratio or the pulse. The coherence time o the ASE describes the variations o the temporal electric ield o the ASE due to intererence between dierent optical requencies in the ASE spectrum. LLE Review, Volume 111 141

Normalized intensity (db) Normalized intensity (db) E15876JR 4 6 8 1 4 6 8 (a) (b) (c) (d) (e) () 1 1 1 5 1 5 Figure 111.6 Intensity o the recompressed signal or an input signal with a lat spectral density and an ASE Gaussian spectrum with a FWHM equal to.14 nm. (a) (c) correspond to an ampliier run in the linear-modulation regime when the ractional ASE energy is equal to (a) 1 5, (b) 1 4, and (c) 1 3. (d) () correspond to an ampliier run in the quadratic-modulation regime when the ractional ASE energy is equal to (d) 1 5, (e) 1 4, and () 1 3. In each case, the simulated intensity is plotted with a continuous line, and the intensity predicted analytically is plotted with solid circles. Normalized intensity (db) Normalized intensity (db) E15877JR 4 6 8 1 4 6 8 (a) (b) (c) (d) (e) () 1 1 5 1 5 1 5 Figure 111.7 Intensity o the recompressed signal or an input signal with a lat spectral density, ASE with various Gaussian spectra, and ractional ASE energy equal to 1 3. (a) and (d) correspond to a FWHM equal to.3 nm in the linear and quadratic modulation regimes, respectively. (b) and (e) correspond to a FWHM equal to.14 nm iltered by a.-nm FWHM, th-order super-gaussian ilter in the linear and quadratic modulation regimes, respectively. (c) and () correspond to a FWHM equal to.14 nm centered.7 nm away rom the central wavelength o the pump in the linear and quadratic modulation regimes. In each case, the simulated intensity is plotted with a continuous line, and the intensity predicted analytically is plotted with solid circles. 14 LLE Review, Volume 111

However, the modulations o pump intensity are mostly due to the intererence between optical requencies o the noiseless pump pulse and optical requencies o the pump ASE. Figure 111.7 presents simulations and analytic predictions or two dierent ASE spectra that have a FWHM equal to.14 nm, i.e., the same coherence time, or a ractional ASE energy equal to 1 3. In the irst case [Figs. 111.7(b) and 111.7(e)], a th-order super-gaussian ilter with.-nm FWHM has been used to ilter the ASE. A large decrease in the level o the pedestal is observed away rom the peak o the pulse, although the pedestal conserved its value closer to the peak, as expected rom the dependence o the pedestal to the spectrum o the ASE. In the second case [Figs. 111.7(c) and 111.7()], the ASE has a Gaussian spectrum with.14-nm FWHM centered.7 nm away rom the central wavelength o the pump. The contrast is signiicantly degraded compared to Figs. 111.6(c) and 111.6(), and an increase o the pedestal intensity by approximately db is observed. Optimization o the contrast can be perormed by proper spectral iltering o the pump. A narrow ilter on the pump pulse increases the contrast o the recompressed signal and is not detrimental to the operation o the OPCPA system as long as the pump pulse is not temporally distorted by the spectral ilter. Generally speaking, the pedestal shape, extent, and intensity vary signiicantly with the energy o the its spectrum, and the regime o operation o the ampliier. 3. Pump with ASE and Signal with Gaussian Spectral Density In this section, the spectral density o the signal is assumed Gaussian, and the intensity o the stretched signal varies signiicantly as a unction o time, taking its maximal value o.1 W/cm at the peak o the pulse. The condition that the irst-order derivative or second-order derivative o the unction as a unction o the intensity o the signal is independent o the signal intensity is not strictly veriied. Some temporal components (i.e., spectral components) o the signal have an optical intensity placing them in the quadratic-modulation regime or the OPCPA process, but other components have an optical intensity placing them in the linear-modulation regime. The contrast o the recompressed signal is generally linked in a nontrivial manner to the noise o the pump pulse. Figure 111.8 displays the transer unction between pump intensity and output signal intensity or a signal input intensity equal to.1 W/cm and.5 W/cm. While the pump intensity corresponding to point B ensures that the output signal intensity is approximately the same or these two input signal intensities (i.e., the spectral density o the ampliied pulse does not depend on the wavelength at irst order), it allows operation only in the quadratic-modulation regime or the highest signal intensity. Figure 111.9 presents the intensities simulated with ASE parameters identical to those o Fig. 111.6. The analytical results plotted on this igure correspond to the stretched signal pulse with a constant intensity o.1 W/cm. For the linear- and quadraticmodulation regimes, no signiicant dierence between the two sets o simulations is observed, and the analytical derivation is still in good agreement with the simulations. In the linear regime or the peak intensity o the stretched pulse, all o the optical requencies in the pulse are in a similar linear regime, and the resulting contrast is equivalent to the contrast obtained or a constant spectral density. The discrepancy observed or low ASE energy in the quadratic regime is more prevalent in this case, which indicates that additional contribution to the Signal intensity (GW/cm ) E15878JR.6.5 B (a).4.3 A..1...5 1. 1.5 Pump intensity (GW/cm ).55 (b).5 B.45.4.9.95 1. 1.5 1.1 Pump intensity (GW/cm ) Figure 111.8 Transer unction o the parametric preampliier or a signal intensity equal to.1 W/cm (solid curve) and.5 W/cm (dashed curve). Points A and B represent the linear- and quadratic-modulation regimes or the OPCPA system or a stretched signal intensity o.1 W/cm. (a) Full transer unction; (b) close-up around point B. LLE Review, Volume 111 143

Normalized intensity (db) Normalized intensity (db) Normalized intensity (db) 4 6 8 1 1 1 5 E15879JR 4 6 8 1 4 6 8 (a) (b) (c) 1 5 Figure 111.9 Intensity o the recompressed signal or an input signal with a Gaussian spectral density and ASE with a Gaussian spectrum with a FWHM equal to.14 nm. (a) (c) correspond to an ampliier run in the linear-modulation regime when the ractional ASE energy is equal to (a) 1 5, (b) 1 4, and (c) 1 3. (d) () correspond to an ampliier run in the quadratic-modulation regime when the ractional ASE energy is equal to (d) 1 5, (e) 1 4, and () 1 3. In each case, the simulated intensity is plotted with a continuous line, and the intensity predicted analytically is plotted with solid circles. pedestal is present due to some components o the signal in the linear-modulation regime. The coupling between pump intensity and ampliied signal intensity or these wavelengths is smaller than at point A o Fig. 111.4. A it o the dashed curve o Fig. 111.8 at its intersection with the vertical dashed line representing the pump intensity or these simulations leads to (1,N) = 4, which implies a smaller impact o the pump intensity modulation. These results demonstrate that, in the general case, both linear- and quadratic-modulation regimes inluence the induced pedestal on an OPCPA system. (d) (e) () Experimental Demonstration o Temporal Contrast Improvement o an OPCPA System by Pump Spectral Filtering 1. Experimental Setup A general approach to signiicantly improve the contrast o OPCPA systems by spectrally iltering the pump pulse has been experimentally demonstrated. Simple and eicient iltering o the pump pulse is perormed in a regenerative ampliier using a VBG, and the bandwidth o the iltering is narrowed signiicantly by the large number o round-trips in the cavity. Contrast improvement by regenerative spectral iltering was perormed on the prototype ront end o the OMEGA EP Laser Facility (Fig. 111.1). 1,17 The pump pulse is generated by a iber integrated ront-end source (IFES), where a.4-ns pulse around 153 nm is temporally shaped to precompensate the square-pulse distortion during ampliication. This pulse is ampliied at 5 Hz rom 1 pj to 4 mj in a diode-pumped regenerative ampliier (DPRA). One o the lat end-cavity mirrors o the DPRA is replaced by the VBG and a lat mirror, so that the mirror acts as the DPRA end-cavity mirror and the beam is relected twice per round-trip on the VBG. The incidence angle on the VBG, designed or high relection at 157.5 nm at normal incidence, is approximately 7 to provide maximum relection at 153 nm. The VBG is a bulk piece o photothermoreractive glass, where a grating is permanently written by UV illumination ollowed by thermal development. 1 The damage threshold o similar VBG s has been ound to be higher than 1 J/cm in the nanosecond regime. With sol-gel antirelection coating, the VBG has a single-pass relectivity o 99.4% at 153 nm, and the slight increase in the DPRA build-up time due to the additional losses was compensated by increasing the diode-pump current. No change in the output beam spatial proile was observed. Without active temperature control o the VBG, the DPRA operated or several days in a temperature-controlled room with no variation in perormance. (Additional characterization can be ound in Re..) The bandwidth o the VBG relectivity around 157.5 nm is 3 pm, which, assuming a Gaussian shape, should provide a 3-pm bandwidth ater 5 round-trips in the DPRA, with two relections on the VBG per round-trip. With the intracavity VBG, the unseeded DPRA output spectrum shows a reduction o the bandwidth o the DPRA rom 146 pm to 41 pm, but is broad enough to ampliy the pump pulse without distortion (Fig. 111.11). Subsequent ampliication to J is perormed by our passes in a crystal large-aperture ring ampliier containing two lash-lamp pumped Nd:YLF rods, ater apodization o the DPRA beam. 3 Frequency conversion to 56.5 nm occurs in an 11-mm LBO crystal with an eiciency o 7%. Filtering in the DPRA decreases the amount o ASE rom the IFES and 144 LLE Review, Volume 111

IFES DPRA CLARA SHG Cross-correlator Mode-locked laser Stretcher OPCPA preampliier OPCPA power ampliier Compressor E15778JR Figure 111.1 Schematic o the laser system. IFES: integrated ront-end source; DPRA: diode-pumped regenerative ampliier; CLARA: crystal large-aperture ring ampliier; SHG: sum-harmonic generation. Filtering o the pump pulse is perormed in the DPRA (shown above in bold). Spectral density (db) E15779JR 1 3 4 153. 153.3 153.6 Wavelength (nm) Figure 111.11 Optical spectrum o the unseeded DPRA measured with a mirror in the cavity (thin solid curve with open circles) and with the VBG in the cavity (solid curve with solid squares). The optical spectrum o the signal ampliied by the DPRA (dashed curve) is limited by the resolution o the optical spectrum analyzer and is signiicantly narrower than the unseeded DPRA with the intracavity VBG. rom the DPRA itsel (these two high-gain stages having the largest contribution to the pump ASE) and beneits rom the large number o relections on the ilter. The OPCPA system is composed o a mode-locked laser operating at 153 nm, an Öner-triplet stretcher providing a dispersion o 3 ps/nm, a preampliier with two 9.75-mm LBO crystals in a walk-o compensating geometry, a power ampliier with one 16.5-mm LBO crystal, and a two-grating compressor in a double-pass coniguration. The pump pulse is split to pump the preampliier and power ampliier. Ampliication o the signal to 5 mj is achieved, and a portion o the ampliied pulse is sent to the diagnostic compressor.. Experimental Results The temporal contrast was measured using a scanning thirdorder cross-correlator (Sequoia, Amplitude Technologies). The dynamic range o the diagnostics is 1 11 but is limited to 1 8 by the parametric luorescence rom the OPCPA system. Postpulses are due to multiple relections in the cross-correlator and are o no practical concern. Figure 111.1 displays the cross-correlations measured (a) when the preampliier and power ampliier are operated at ull energy, (b) when only the preampliier is operated at saturation, and (c) when only the preampliier is operated at hal its nominal output power. The prepulse contrast is consistently improved with the intracavity VBG. The pump-induced contrast degradation is particularly important in the preampliier, even when it is run at saturation, and a contrast improvement o the order o db is observed. When the preampliier is run at hal output power, a larger coupling between the pump intensity and the ampliied signal intensity magniies the impact o the pump noise on the contrast. These two operating points correspond to the linear- and quadratic-modulation regimes or the preampliier, as identiied by points A and B in Fig. 111.4. The choice o the crystals and pump intensities in this system reduces the spatial-intensity modulations in the ampliied signal. This decreases the temporal-intensity modulations in the ampliied signal and reduces the impact o the pump-intensity variations on the contrast o the recompressed pulse. Most OPCPA systems are not designed with these considerations in mind, and the contrast improvement is expected to be signiicant or these systems. The optical signal-to-noise ratio (OSNR) o the OPCPA pump pulse was reduced by decreasing the average power o the monochromatic source in the IFES rom its nominal value o 1 mw to mw,.4 mw, and.1 mw, and compensating the reduced output energy by increasing the DPRA diode pump current. The reduced OSNR is due to the reduced seed level in both the IFES iber ampliier and the DPRA. Figure 111.13 displays the cross-correlations measured when the preampliier and power ampliier are operated in nominal conditions [the cross-correlations measured or the nominal value o 1 mw can be seen in Fig. 111.1(a)]. Without spectral iltering, a large increase in the temporal pedestal is observed, and the contrast LLE Review, Volume 111 145

Normalized intensity (db) E1578JR 4 6 8 (a) (b) (c) 1 5 5 1 Mirror in DPRA VBG in DPRA 1 5 5 1 1 5 5 1 Figure 111.1 Third-order scanning cross-correlation o the OPCPA output pulse (a) when the preampliier and power ampliier are operated at ull energy, (b) when only the preampliier is operated at saturation, and (c) when only the preampliier is operated at hal its nominal output power. In each case, the cross-correlation measured with the mirror in the DPRA is plotted with a solid line, and the cross-correlation measured with the VBG in the DPRA is plotted with a dashed line. 5 ps beore the peak o the pulse is 54 db, 46 db, and 35 db, respectively, or a -mw,.4-mw, and.1-mw average power. No contrast degradation is observed with the iltered DPRA, and the contrast 5 ps beore the peak o the pulse is consistently equal to 68 db. Normalized intensity (db) Normalized intensity (db) E15781JR 146 4 6 8 4 6 (a) (c) 8 1 5 5 1 Figure 111.13 Third-order scanning cross-correlation o the OPCPA output pulse when the average power o the monochromatic laser o IFES is reduced rom 1 mw to (a) mw, (b).4 mw, and (c).1 mw. In each case, the cross-correlation measured with the mirror in the DPRA is plotted with a solid line, and the cross-correlation measured with the VBG in the DPRA is plotted with a dashed line. (b) 1 5 5 1 Mirror in DPRA VBG in DPRA Conclusions An analysis o pump-induced contrast degradation in an OPCPA system has been perormed. The general link between pump modulation and the contrast o the recompressed pulse has been derived in the two cases o practical interest, or which pump-intensity modulation couples either linearly or quadratically to the ampliied signal intensity during the parametric process. Analytical expressions linking the spectrum o the ASE present on the pump pulse to the temporal pedestal o the signal ampliied in the OPCPA system have been derived and compared to simulations. Signiicant reduction o the induced temporal pedestal was experimentally demonstrated in an OPCPA system by iltering the pump pulse during its ampliication in a regenerative ampliier. The general expressions o the contrast degradation should prove useul or understanding the contrast limitation o current OPCPA systems and predicting the perormance o uture systems. The demonstrated solution is simple to implement and is applicable to most OPCPA systems. Acknowledgment This work was supported by the U.S. Department o Energy Oice o Inertial Coninement Fusion under Cooperative Agreement No. DE-FC5-9SF1946, the University o Rochester, and the New York State Energy Research and Development Authority. The support o DOE does not constitute an endorsement by DOE o the views expressed in this article. Reerences 1. D. Umstadter, Phys. Plasmas 8, 1774 (1).. S.-W. Bahk et al., Opt. Lett. 9, 837 (4). 3. J. D. Zuegel, S. Borneis, C. Barty, B. LeGarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. LeBlanc, T. J. Kessler, A. W. Schmid, LLE Review, Volume 111

L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, Fusion Sci. Technol. 49, 453 (6). 4. M. Nantel et al., IEEE J. Sel. Top. Quantum Electron. 4, 449 (1998). 5. V. Bagnoud, J. D. Zuegel, N. Forget, and C. Le Blanc, Opt. Express 15, 554 (7). 6. A. Dubietis, G. Jonusauskas, and A. Piskarskas, Opt. Commun. 88, 437 (199). 7. I. N. Ross et al., Opt. Commun. 144, 15 (1997). 8. A. Dubietis, R. Butkus, and A. P. Piskarskas, IEEE J. Sel. Top. Quantum Electron. 1, 163 (6). 9. H. Yoshida et al., Opt. Lett. 8, 57 (3). 1. V. Bagnoud, I. A. Begishev, M. J. Guardalben, J. Puth, and J. D. Zuegel, Opt. Lett. 3, 1843 (5). 11. N. Ishii et al., Opt. Lett. 3, 567 (5). 1. I. Jovanovic et al., Opt. Lett. 3, 136 (5). 13. S. Witte et al., Opt. Express 13, 493 (5). 15. O. V. Chekhlov et al., Opt. Lett. 31, 3665 (6). 16. D. Kraemer et al., J. Opt. Soc. Am. B 4, 813 (7). 17. J. H. Kelly, L. J. Waxer, V. Bagnoud, I. A. Begishev, J. Bromage, B. E. Kruschwitz, T. J. Kessler, S. J. Loucks, D. N. Maywar, R. L. McCrory, D. D. Meyerhoer, S. F. B. Morse, J. B. Oliver, A. L. Rigatti, A. W. Schmid, C. Stoeckl, S. Dalton, L. Folnsbee, M. J. Guardalben, R. Jungquist, J. Puth, M. J. Shoup III, D. Weiner, and J. D. Zuegel, J. Phys. IV France 133, 75 (6). 18. N. Forget et al., Opt. Lett. 3, 91 (5). 19. I. N. Ross, G. H. C. New, and P. K. Bates, Opt. Commun. 73, 51 (7).. A. V. Okishev and J. D. Zuegel, Appl. Opt. 43, 618 (4). 1. L. B. Glebov et al., in Laser Weapons Technology III, edited by W. E. Thompson and P. H. Merritt (SPIE, Bellingham, WA, ), Vol. 474, pp. 11 19.. A. V. Okishev, C. Dorrer, V. I. Smirnov, L. B. Glebov, and J. D. Zuegel, Opt. Express 15, 8197 (7). 3. V. Bagnoud, M. J. Guardalben, J. Puth, J. D. Zuegel, T. Mooney, and P. Dumas, Appl. Opt. 44, 8 (5). 14. V. V. Lozhkarev et al., Opt. Express 14, 446 (6). LLE Review, Volume 111 147