Coherence and Ultrashort Pulse Laser Emission Part 2 pdf

32 Coherence and Ultrashort Pulse Laser Emission Here σI and σμ are the standard deviations of the spectral density and spectral degree of coherence at the source plane, respectively The coordinates r1 and r2 are located in the plane of the source and A is the normalization constant The analysis shows that six transverse modes are contributing to the total radiation field of FLASH From Fig 8a one can easily see that the contribution of the modes falls exponentially with the mode number j Thereby the contribution of the first mode is about 59% and the contribution of the second mode is 24% of the total radiation power The contribution of the sixth mode is more than two orders of magnitude smaller From Fig 8b a transverse coherence length of ξx = 715 μm can be obtained Thus the experimentally measured values were considerably lower than those calculated in terms of the GSM The apparent source size corresponding to the measured values for the coherence length was calculated making use of the GSM The resulting value of σI = 180 µm was in good agreement with the source size observed in wave front measurements (Kuhlmann et al., 2006), but 2.5 times larger than considered in the theoretical modeling Fig (a) Contribution of individual modes in the GSM to the cross spectral density (b) Absolute value of the spectral degree of coherence taken along a line through the middle of the beam profile In the inset the spectral density S(x) is shown Calculations for the FEL operating in saturation are performed in the frame of a Gaussian-Schell model 20 m downstream from the source at a wavelength λ = 13.7 nm; after reference (Singer et al., 2008) Recently Vartanyants & Singer employed the GSM to evaluate the transverse coherence properties of the proposed (Altarelli et al., 2006) SASE undulator of the European XFEL, scheduled to begin operation in 2014 Simulations were made for a GSM source with an rms source size σs = 27.9 µm and a transverse coherence length ξs = 48.3 µm at the source for a wavelength of λ = 0.1 nm (corresponding to h·ν = 12 keV), taken from the XFEL technical design report (Altarelli et al., 2006) Figure shows the evolution of the beam size Σ(z) and the transverse coherence length Ξ(z) with the distance of propagation z At a distance z = 500 m from the source a transverse coherence length of Ξ(z) = 348 μm and a beam size of Σ(z) = 214 μm is obtained for the XFEL Thus the coherence decreases less rapid than the spatial intensity of the beam At present this prediction differs significantly from the experimental results for both TTF and FLASH Distinct from a synchrotron source the coherence properties of the radiation field from the XFEL is of the same order of magnitude both for the vertical and the horizontal direction Coherence of XUV Laser Sources 33 Fig Beam size Σ(z) (dashed line) and the transverse coherence length Ξ(z) (solid line) at different distances z from the SASE undulator of the European XFEL, from (Vartanyants & Singer, 2010) Earlier, results of numerical time dependent simulations for the coherence properties of LCLS XFEL at SLAC in Stanford have been reported (Reiche, 2006) For a wavelength of λ = 0.15 nm (corresponding to h·ν = 8.27 keV) the effective coherence area within which the field amplitude and phase have a significant correlation to each other amounts to 0.32 mm² That is about five times larger than the spot size with a value of 0.044 mm² when evaluated at the first experimental location 115 m downstream from the undulator 5.2 Temporal coherence For an experimental measurement of the temporal coherence ideally time-delayed amplitude replicas of the FEL pulses should be brought to interference However, the lack of amplitude splitting optical elements in the x-ray regime permits only the use of wavefront splitting mirrors in grazing incidence These elements can then, however, be applied in a broad spectral region Such a beam splitter and delay unit is shown schematically in Fig 10(a) Fig 10 (a) Schematic drawing of the layout of the autocorrelator Grazing angles of 3° and 6°for the fixed and variable delay arms, respectively, are employed to ensure a high reflectivity of the soft x-ray radiation (b) Calculated reflectivity for amorphous carbon coated silicon mirrors for hν = 30 to 200 eV The full green line shows the reflectivity of a single mirror for a grazing angle of 6° 34 Coherence and Ultrashort Pulse Laser Emission Based on geometrical wave front beam splitting by a sharp mirror edge and grazing incident angles the autocorrelator covers the fundamental energy range of FLASH (20 - 200 eV) with an efficiency of better than 50%, see Fig 10 (b) Grazing angles of 3° and 6° for the fixed and variable delay arms, respectively, are employed to ensure a high reflectivity of the soft x-ray radiation Looking in the propagation direction the beam splitter with a sharp edge reflects the left part of the incoming FEL pulse horizontally into a fixed beam path The other part of the beam passes this beam splitting mirror unaffected and is then reflected vertically by the second mirror into a variable delay line A variable time delay between -5 ps and +20 ps with respect to the fixed beam path can be achieved with a nominal step size of 40 as The seventh and eighth mirror reflect the partial beams into their original direction Alternatively, small angles can be introduced to achieve and vary a spatial overlap of the partial beams Mitzner et al investigated the temporal coherence properties of soft x-ray pulses at FLASH at λ = 23.9 nm by interfering two time-delayed partial beams directly on a CCD camera (Mitzner et al., 2008) Fig 11 shows two interferograms at zero and 50 fs delay, respectively The overlap of the two partial beams is Δx ≈ 1.2 mm which corresponds ~ 44% of the beam diameter in this case where an mm aperture is set 65 m in front of the detector near the center of the beam profile In these particular cases the contrast of the interference fringes yields via equation (4) a visibility of V = 0.82 and V = 0.07, respectively Fig 11 Single exposure interference fringes at λ = 24 nm (a) at zero and (b) at 55 fs delay between both partial beams The crossing angle of the partial beams is α = 60 µrad Scanning now the delay between the two pulses and calculating at each time step the visibility of the interference fringes (applying Equation 4) the temporal coherence properties of FLASH pulses are investigated Figure 12 shows the time delay dependence of the average visibility observed for two different wavelengths, λ = 23.9 nm and λ = nm Each data point (red dots) is the average of the visibility of ten single exposure interference pictures In Fig 12(a) the (averaged) visibility of V = 0.63 at zero time delay rapidly decreases as the time delay is increased The central maximum of the correlation can be described by a Gaussian function (green line) with a width of 12 fs (FWHM) Then a coherence time corresponding to half of the full width of τcoh = fs is obtained Remarkably, the visibility, i.e the mutual coherence, is not a monotonic function of the delay time between both partial beams Instead, a minimum at about 7.4 fs after the main maximum and a secondary maximum at about 12.3 fs appear, symmetrically on both sides of the main maximum In addition, a small but discernible increase of the visibility occurs at a delay around 40 fs Coherence of XUV Laser Sources 35 Fig 12 Observed visibility (experimental data points: red dots) as a function of time delay for (a) λ = 24 nm and (b) λ = nm The green line depicts a Gaussian function with a coherence time of (a) τcoh = fs and (b) τcoh = fs, representing a single Fourier transform limited pulses Since the interferences were measured for independent single pulses of the FEL and then their visibilities averaged, this behavior of the temporal coherence function reflects an intrinsic feature of the FEL pulses at the time of the measurements The radiation of SASE FELs consists of independently radiating transverse and longitudinal modes In the time domain the radiation is emitted in short bursts with random phase relationship between the bursts Time domain and spectral domain are related to each other via a Fourier transformation which leads to narrow spikes within the bandwidth of the undulator in the spectral domain, see also the calculated spectrum of a SASE FEL shown in Fig In the linear autocorrelation experiments shown in Fig 12a (Mitzner et al., 2008) these independent modes can interact at longer time delays as a cross correlation This behavior was found to be accountable for the nonmonotonous decay of the visibility A second sub-pulse at Δt = 12 fs and a weak third one at Δt = 40 fs can be stated as a reason for this behavior Figure 12 (b) shows the result from an analogous measurement at λ = nm From a Gaussian fit with a FWHM of fs a coherence time of τc = fs is obtained The non-monotonous decay that was discussed before for the 24 nm measurement is not apparent here Recently, a similar measurement also utilizing an autocorrelator that employs wave front beam splitters was performed for FLASH radiating at λ = 9.1 nm and λ = 33.2 nm (Schlotter et al, 2010) These data were compared to Fourier transformed spectral bandwidth measurements obtained in the frequency domain by single-shot spectra A good agreement with the measurements in the time domain was found In addition to single shot exposures the temporal coherence was measured in the 15-pulse-per-train mode Figure 13 shows the time delay dependence of the average visibility observed for two different wavelengths, λ = 33.2 nm (single shot: black triangles; 15 bunches: red triangles) and λ = 9.6 nm (single shot: black squares; 15 bunches: red dots) In order to plot the data of both wavelengths into one graph the abscissa is given in cτ/λ which represents the number of periods of the lightwave For the 15 bunch per train data a clearly lower coherence at longer timescales is observed than for the single shot data To explain this behavior we should take a look at a single point in the interference pattern If a maximum of the intensity appears at this point for zero delay and for a path length n differences  n ⋅ λ , minima will appear for ⋅ λ The wavelength of the FEL radiation shows 36 Coherence and Ultrashort Pulse Laser Emission Fig 13 The normalized degree of coherence |γ| plotted versus the delay given in units of the wavelength The dashed curve was calculated from spectral measurements at 33.2 nm Taken from reference (Schlotter et al., 2010) small shot-to-shot fluctuations Therefore for longer path length differences (n ~ 50) a π phase difference occurs for different wavelengths λk At the same point of the detector the interference pattern corresponding to a wavelength λ1 may now show a maximum while the interference pattern corresponding to a wavelength λ2 shows a minimum Thus, the visibility appears blurred, when k = 15 bunches with slightly different wavelengths form interference patterns before the read-out of the detector 5.3 Coherence enhancement through seeding An essential drawback of SASE FEL starting from shot noise is the limited temporal coherence Therefore, the improvement of the temporal coherence is of great practical importance One idea to overcome this problem was presented by Feldhaus et al (Feldhaus et al., 1997) The FEL described consists of two undulators and an X-ray monochromator located between them (see Fig 14) The first undulator operates in the linear regime of amplification and starts from noise The radiation output has the usual SASE properties with significant shot-to-shot fluctuations After the first undulator the electron beam is guided through a by-pass, where it is demodulated The light pulse on the other hand is monochromatized by a grating At the entrance of the second undulator the monochromatic X-ray beam is recombined with the demodulated electron beam, thereby acting as a seed for the second undulator For this purpose, the electron micro-bunching induced in the first undulator must be destroyed, because this electron micro-bunching from the first undulator corresponds to shot noise that was amplified The degree of micro-bunching can thus be characterized by the power of shot noise which has the same order of magnitude as the output power of the FEL When the radiation now passes the monochromator only a narrow bandwidth and thus only a small amount of the energy is transmitted Thus at the entrance of the second undulator a radiation-signal to shot-noise ratio much larger than unity has to be provided This can be achieved because of the finite value of the natural energy spread in the beam and by applying a special design of the electron by-pass At the entrance of the second undulator the radiation power from the monochromator then dominates over the shot noise and the residual electron bunching, such that the second stage of the FEL amplifier will operate in the steady-state regime when the input signal Coherence of XUV Laser Sources 37 Fig 14 Principal scheme of a single-pass two-stage SASE X-ray FEL with internal monochromator; after (Saldin et al., 2000a) bandwidth is small with respect to the FEL amplifier bandwidth The second undulator will thus amplify the seed radiation The additional benefits derived from this configuration are superior stability, control of the central wavelength, narrower bandwidth, and much smaller energy fluctuations than SASE Further, it is tunable over a wide photon energy range, determined only by the FEL and the grating An alternative approach is based on seeding with a laser, see ref (Yu et al., 1991, 2000) Such a scheme has been applied at the Deep Ultraviolet FEL (DUV FEL) at the National Synchrotron Light Source (NSLS) of Brookhaven National Laboratory (BNL) (Yu et al., 2003) The set-up is shown in Fig 15 In high-gain harmonic generation (HGHG) a small energy modulation is imposed on the electron beam by its interaction with a seed laser (1) in a short undulator (8) (the modulator) tuned to the seed wavelength λ The laser seed introduces an energy modulation to the electron bunch In a dispersive three-dipole magnetic chicane (9) this energy modulation is then converted into a coherent longitudinal density modulation In a second long undulator (10) (the radiator), which is tuned to the nth odd harmonic of the seed frequency, the microbunched electron beam emits coherent radiation at the harmonic frequency nλ, which is then amplified in the radiator until saturation is reached The modulator (resonant at λ = 800 nm) of the DUV FEL is seeded by an 800 nm CPA Ti:sapphire laser (pulse duration: ps) This laser drives also the rf gun of the photocathode producing an electron bunch of ps duration In this way an inherent synchronization between the electron bunches and the seeding pulses is achieved The output properties of the HGHG FEL directly maps those of the seed laser which can show a high degree of temporal coherence In the present case the output HGHG radiation shows a bandwidth of 0.23 nm FWHM (corresponding to ~0.1%), an energy fluctuation of only 7% and a pulse length of ps (equal to the electron bunch length) when the undulator is seeded with an input seed power of Pin = 30 MW The bandwidth within a ps slice of the chirped seed is 0.8 nm (corresponding to 0.1% bandwidth) and the chirp in the HGHG output is expected to be the same, i.e., 0.1% · 266 nm = 0.26 nm This is consistent with a bandwidth of Δλ = 0.23 nm [FWHM] experimentally observed A Fourier-transform limited flat-top ps pulse would have a bandwidth of Δλ = 0.23 nm and a ps (FWHM) Gaussian pulse would have a bandwidth of Δλ = 0.1 nm Besides the high degree of temporal coherence a further advantage compared to a SASE FEL is the reduced shot-to-shot fluctuations of the output radiation if the second undulator operates in 38 Coherence and Ultrashort Pulse Laser Emission saturation A similar scheme will also be applied at the FERMI FEL at Elettra that will start operation in 2011 providing wavelengths down to λ = nm for the fundamental and λ = nm for the third harmonic (Allaria et al., 2010) Fig 15 The NSLS DUV FEL layout 1: gun and seed laser system; 2: rf gun; 3: linac tanks; 4: focusing triplets; 5: magnetic chicane; 6: spectrometer dipoles; 7: seed laser mirror; 8: modulator; 9: dispersive section; 10: radiator; 11: beam dumps; 12: FEL radiation measurements area After reference (Yu et al., 2003) Another possibility to generate coherent radiation from an FEL amplifier is seeding with high harmonics (HH) generated by an ultrafast laser source whose beam properties are simple to manipulate, see reference (Sheehy et al., 2006; Lambert et al., 2008) In this way extremely short XUV pulses are obtained, down to a few femtoseconds Such a scheme was applied at the Spring-8 compact SASE source (Lambert et al., 2008) and is depicted schematically in Fig 16 Fig 16 Experimental setup for HHG seeding of the Spring-8 Compact SASE source, after (Lambert et al., 2008) A Ti:sapphire laser (800 nm, 20 mJ, 100 fs FWHM, 10 Hz) that is locked to the highly stable 476 MHz clock of the accelerator passes a delay line that is necessary to synchronize the HHG seed with the electron bunches For this purpose a streak camera observes the 800 nm laser light and the electron bunch signal from an optical transition radiation (OTR) screen The beam is then focused into a xenon gas cell in order to produce high harmonics Using a telescope and periscope optics the HHG seed beam is spectrally selected, refocused and spatially and temporally overlapped with the electron bunch (150 MeV, ps FWHM, 10 Hz) in the two consecutive undulator sections and Both undulators are tuned to λ = 160 nm, corresponding to the fifth harmonic of the laser The beam position is monitored on optical transition radiation (OTR) screens The output radiation is characterized with an imaging spectrometer for different seeding pulse energies between 0.53 nJ and 4.3 nJ per pulse Coherence of XUV Laser Sources 39 Figure 17 shows the spectra of the unseeded undulator emission (purple, enlarged 35 times), the HHG seed (yellow, enlarged 72 times) and the seeded radiation output (green) for a seed pulse energy of 4.3 nJ A spectral narrowing for the seeded output radiation and a significant shift to longer wavelengths compared with the seed radiation is obvious The measured relative spectral widths of the seeded FEL are reduced compared to the unseeded one from 0.54% to 0.46 % (0.53 nJ seed) and from 0.88% to 0.44% (4.3 nJ seed) A similar narrowing is observed for the spectra of the third (λ = 53.55 nm) and fifth harmonic (λ = 32.1 nm) Fig 17 Experimentally obtained spectra of the FEL fundamental emission (λ = 160 nm): SASE (red), seed radiation (green) and seeded output (blue), after (Lambert et al., 2008) For a fully coherent seed pulse the seeded FEL should also show a high temporal coherence which, however, is not yet experimentally confirmed The pulse should then also show a duration close to the Fourier transform limit From the measured spectral width of Δλ = 0.74 nm (for 0.53 nJ seed) one might conclude a Fourier transform limited duration of 57 fs Currently several facilities using HHG as a seed source are proposed or under construction e.g references (McNeil et al., 2007; Miltchev et al., 2009) Temporal coherence of high-order harmonic generation sources The generation of high-order harmonics of a short laser pulse in a gas jet has attracted a lot of attention since the first discovery in the late 1980s (McPherson et al., 1987; Ferray et al., 1988; Li et al., 1989) High harmonic radiation has become a useful short-pulse coherent light source in the XUV spectral regime (Haarlammert & Zacharias, 2009; Nisoli & Sansone, 2009) By focussing an intense femtosecond laser pulse into rare gases odd order high harmonics of the original laser frequency can be generated This can be explained in terms of the three step model (Corkum, 1993; Kulander et al., 1993; Lewenstein et al., 1994) The focused pumping laser beam typically has intensities of more than 1013 W/cm2, which is in the order of the atomic potential This leads to a disturbance of the atomic potential of the target atoms allowing the electron to tunnel through the remaining barrier, see Fig 18a Figure 18b shows how the electron is then accelerated away from the atom core by the electric field of the driving laser lightwave After half an optical cycle the direction of the driving laser field reverses and the electron is forced to turn back to the core There, a small fraction of the electrons recombine with the ion, and the energy that was gained in the accelerating processes before plus the ionization energy IP is emitted as light, see Fig 18c When the electrons turn back to the core they can basically follow two 40 Coherence and Ultrashort Pulse Laser Emission Fig 18 Illustration of the three step model for high harmonic generation (a) deformation of the atomic potential and tunnel ionization of the target atoms (b) acceleration of the free electrons in the laser electric field (c) recombination and photon emission different trajectories, a short one and a long one, respectively The short trajectory shows an excursion time close to half an optical cycle, whereas the long trajectory takes slightly less than the whole optical period Both of them show different phase properties with respect to the dipole moment of the particular harmonic The phase of the short trajectory does not significantly vary with the laser intensity as opposed to the phase of the long trajectory that varies rapidly with the laser intensity (Lewenstein et al., 1995; Mairesse et al., 2003) The energy acquired by the electron in the light field corresponds to the ponderomotive energy Up U p = e Eo / 4meω (12) Here E0 denotes the electric field strength, e the elementary charge, me the electron mass and ω the angular frequency The maximum photon energy emitted, the cut-off energy, is given by Ecutoff = 3.17 ⋅ U pon +  I p , (13) where Ip denotes the ionization potential of the atom A theoretical study of the coherence properties of high order harmonics generated by an intense short-pulse low-frequency laser is presented particularly for the 45th harmonic of a 825 nm wavelength laser (Salières, L’Huillier & Lewenstein, 1995) First, the generation of the radiation by a single atom is calculated by means of a semi-classical model (Lewenstein et al., 1994) Phase and amplitude of each harmonic frequency are evaluated and then in a second step propagated in terms of the slowly varying amplitude approximation (L’Huillier et al., 1992) Harmonic generation is optimized when the phase-difference between the electromagnetic field of the driving laser and the electromagnetic field of the output radiation is minimized over the length of the medium At this point phase-matching is achieved It is shown that the coherence properties and consequently the output of the harmonics can be controlled and optimized by adjusting the position of the laser focus relative to the nonlinear medium Bellini et al investigated experimentally the temporal coherence of high-order harmonics up to the 15th order produced by focusing 100 fs laser pulses into an argon gas jet (Bellini et al., 1998; Lyngå et al., 1999) The visibility of the interference fringes produced when two spatially separated harmonic sources interfere in the far-field was measured as a function of time delay between the two sources The possibility to create two phase-locked HHG sources that are able to form an interference pattern in the far-field had been demonstrated earlier (Zerne et al., 1997) A high transverse coherence that is necessary for two beams to interfere under an angle had been proven by a Youngs double-slit set-up (Ditmire et al., 1996) The experimental set-up used for the coherence measurements is shown in Fig 19 56 Laser Pulses Coherence and Ultrashort Pulse Laser Emission We need to dispersion balance the CPA chain, to recompress the pulse to its transform limit The total group delay, GDtotal vs wavelength for the system must be constant at the output, or GDtotal (λ) = GDstretcher (λ) + GDcompressor (λ) + GD f iber (λ) + GDoscillator (λ) + GDampli f ier (λ) + GDmaterial (λ) = C1 , where C1 is an arbitrary constant From Eq (5), φ(ω ) = ∞ −∞ GD ( ω ) dω Any frequency dependence in the total group delay will degrade pulse fidelity Several approaches to achieving dispersion balance exist In the Taylor’s expansion (Eq (5)) of the phase of a well behaved dispersive element, when n < m the contribution of a term n to the total phase is much larger than of a term m, or |φ(n) (0)Δω n /n!| |φ(m) (0)Δω m /m!|, where Δω is the pulse bandwidth One approach to achieve dispersion balance is to calculate the total GDD, TOD, and higher order terms for the system and attempt to zero them For example, when terms up to the 4th order are zero, the system is quintic limited This term-by-term cancellation approach can become problematic when successive terms in the Taylor’s expansion not decrease rapidly It is often preferable to minimize the residual group delay, GDRMS , over the pulse bandwidth (Eq 8) GDRMS = ∞ ¯ −∞ ( GD ( ω ) − GD ) |E ( ω )| dω ∞ ∞ |E ( ω )| dω ¯ ¯ where GD is the mean group delay, GD ≡ ∞ −∞ GD ( ω )|E ( ω )| dω ∞ |E (ω )|2 dω −∞ (8) A sample pulse stretcher is shown in Fig The stretcher consists of a single grating, a lens of focal length f , a retro-reflecting folding mirror placed f away from the lens and a vertical roof mirror The folding mirror simplifies stretcher configuration and alignment by eliminating a second grating and lens pair A vertical roof mirror double passes the beam through the stretcher and takes out the spatial chirp The total dispersion of the stretcher is determined by the distance from the grating to the lens, L f When L f = f , the path lengths at all wavelengths are equal and the net dispersion is zero When L f > f , the chirp becomes negative, same as in the compressor In a stretcher, L f < f producing a positive chirp We can calculate the dispersion, or GD (ω ) = nω L(ω )/c, where L(ω ) is the frequency dependent propagation distance and nω is the frequency dependent refractive index, using various techniques Here, we give a compact equation for GDD (ω ) = ∂GD (ω )/∂ω, from which all other dispersion terms can be determined Assuming an aberration free stretcher in the thin lens approximate, GDD (ω ) is then given by Eq Vert roof mirror Grating Lens, f Lf Folding mirror red blue f Fig Grating and lens based stretcher is folded with a flat mirror The distance from the grating to the focal length of the lens determine the sign and magnitude of the chirp λ [sin (φ) + sin (ψ)]2 (9) πc2 cos2 (φ) where the diffraction angle, φ is a function of ω The aberration free approximation is important, because a real lens introduces both chromatic and geometric beam aberrations which modify higher order dispersion terms from those derived from Eq GDD (ω ) = 2( f − L f ) 57 Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources A compressor, which is typically a final component in the CPA system undoes all of the accumulated dispersion The compressor used on the photogun laser is shown in Fig Compared to the stretcher, the lens is absent The magnitude of the negative chirp is now controlled by the distance from the horizontal roof to the grating The horizontal roof, here folds the compressor geometry and eliminates a second grating As in the stretcher of Fig 5, the compressor’s vertical roof mirror double passes the beam and removes the spatial chirp Because a compressor has no curved optics, it introduces no geometric or chromatic aberrations The dispersion of a real compressor is very precisely described by the Treacy formula or its equivalent given by Eq 10 Grating Vert roof mirror in/out Hor roof mirror Fig Folded grating compressor The distance from the horizontal roof mirror to the grating determines the magnitude of the negative chirp GDD (ω ) = − L1 λ [sin (φ) + sin (ψ)]2 πc2 cos2 (φ) (10) The actual stretcher design for Velociraptor photogun laser is shown in Fig The all-reflective Offner design (Cheriaux et al., 1996) uses a convex and a concave mirror to form an imaging telescope with magnification of -1 and relay planes at the radius of curvature (ROC) center of the concave mirror The grating is placed inside the ROC to impart a positive chirp A vertical roof mirror folds the stretcher geometry and eliminates the second grating The Offner stretcher is compact and has low chromatic and geometric aberrations Consequently, its dispersion profile is nearly aberration free, meaning the GDD and higher order dispersion terms are closely predicted by Eq vertical roof Grating retro-reflector in/out convex mirror concave mirror Fig Raytraced design of the Offner stretcher for the photogun laser on Velociraptor 3.2 Fiber oscillator and amplifiers Essential to building a compact, highly stable laser system is a fiber front-end Fibers lasers are highly portable, reliable, relatively insensitive to external perturbations, provide long term hands free operation, and have been scaled to average powers above kW in a diffraction limited beam (Jeong et al., 2004) When the required pulse energy is above a mJ, a fiber oscillator and amplifiers can serve as a front end in a multi-amplifier-stage system We employ 10 58 Laser Pulses Coherence and Ultrashort Pulse Laser Emission a 10 mW Yb:doped mode-locked oscillator which, when compressed, produces 250 pJ, sub 100 fs, near transform limited pulses at 40.8 MHz repetition rate with a full bandwidth from 1035 nm to 1085 nm The oscillator, based on a design developed at Cornell (Ilday et al., 2003), fits on a rack mounted, 12”x12” breadboard (see Fig 8) On T-REX and Velociraptor, a single fiber oscillator seeds both, the photogun laser and the interaction laser systems An experimental oscillator spectrum showing the bandpass for the photogun and the interaction lasers is shown in Fig Two different chains of fiber Yb:doped fiber amplifiers tuned for peak gain at 1053 nm for PDL and 1064 nm for ILS, boost the seed pulse to ≈100 μJ/pulse The seed is chirped to a few nanosecond duration prior to amplification Each fiber amplifier stage provides 20 dB of gain The repetition rate is gradually stepped down to 10 kHz with acousto-optic modulators (AOM), inserted in between fiber amplifiers The AOMs also remove out of band amplified spontaneous emission (ASE), preserving pulse fidelity The total energy from the fiber amplifier is limited by the total stored energy and by the accumulated nonlinear phase (Eq 4) Several initial amplifier stages consist of telecom-type, 6.6 μm core polarization maintaining (PM) fibers The output from this core sized fiber is limited to ≈1μJ Next, a series of large mode field diameter, 29 μm core photonic band-gap (PBG) fibers accommodate pulse energies up to 100 μJ We are currently developing even larger core (80 μm) PBG fiber rod based amplifiers to attain over mJ per pulse at the output A major challenge with PBG and other large core fibers is careful control of the refractive index uniformity to prevent generation of higher order spatial modes, which degrade beam quality Gain fiber Pump diodes Compressor Fig The ultrashort Yb+ doped fiber oscillator fits on a 12”x12” breadboard When recompressed, the anomalous dispersion oscillator generates 100 fs pulses Amplification The action of the amplifier is illustrated in Fig 10 An input pulse with intensity Iin is amplified to output intensity Iout An amplifier can be chacterized by its small signal (undepleted) gain, G0 , saturation fluence, Jsat , and its frequency dependent lineshape function, g(ν) In general, we need to solve the laser rate equations to determine the output pulse shape, spectral distribution, and energy For a homogeneous gain medium, when (1) the temporal pulse variation and the population inversion is sufficiently small (compared to T2 coherence time) to justify rate equation analysis, and (2) transient effects relating to spontaneous emission and pumping occur on a time scale much longer than the pulse 11 59 Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources PDL ILS Power (arb u.) 0.8 0.6 0.4 0.2 1030 1040 1050 1060 (nm) 1070 1080 1090 Fig Experimental pulse spectrum of the Velociraptor oscillator of Fig The same oscillator seeds both the interaction and the photogun lasers duration, an analytical solution can be obtained using a Frantz-Nodvik approach (Frantz & Nodvik, 1963) Eq (11) is derived for a monochromatic input pulse (Planchon et al., 2005) − Iout (t) = Iin (t) × − − G0 e− Jin (t)/Jsat (t) −1 (11) t Here, Jin (t) ≡ Iin (t )dt is the instantaneous fluence Eq (11) can be modified to describe amplification of a chirped pulse This involves determining the frequency dependence of the small gain, G0 (ν) and the saturation fluence, Jsat (ν), both of which depend on the emission cross-section σe (ν) For a four-level system, Jsat (ν) = hν/σe (ν), and G0 = exp [ Nσe (ν)], where dφ(t) ¯ N is the population inversion If the instantaneous pulse frequency, ν = 2π dt is a monotonic function of t, we can define time as a function of frequency, t(ν) In this instantaneous frequency approach, we can rewrite Eq (11) as a function of ν Various aspects of chirped pulse amplification, such as total output energy, gain narrowing, square pulse distortion, and spectral sculpting can be analytically calculated using the modified form of Eq (11) Iin Iout Amplifier with gain G0 Fig 10 Basic scheme for pulse amplification A gain medium with stored energy coherently amplifies the input pulse 4.1 Chirped pulse amplification with narrowband pulses In CPA, the gain bandwidth of the amplifying medium is typically broad enough to minimize gain narrowing of the seed pulse On the photogun laser, Yb doped glass has a wide bandwidth spanning from 1000 nm to 1150 nm, and is well suited for amplifying 100 fs pulses On the interaction laser, however, bulk amplification is in Nd:YAG, which has a narrow bandwidth of 120 GHz The seed pulses gain narrow to sub nanometer bandwidths after amplification Traditional two-grating stretchers and compressors cannot provide adequate dispersion in a table-top footprint In this section, we will describe novel hyper-dispersion technology that we developed for CPA with sub-nanometer bandwidth pulses (Shverdin, Albert, Anderson, Betts, Gibson, Messerly, Hartemann, Siders & Barty, 2010) The meter-scale stretcher and compressor pair achieve 10x greater dispersion compared to standard two-grating designs Previously, D Fittinghoff, et al suggested hyper-dispersion 12 60 Laser Pulses Coherence and Ultrashort Pulse Laser Emission compressor arrangements (Fittinghoff et al., 2004) F J Duarte described a conceptually similar hyper-dispersion arrangements for a prism-based compressor (Duarte, 1987) We utilize commercial Nd:YAG amplifiers for two reasons: (1) Nd:YAG technology is extremely mature, relatively inexpensive, and provides high signal gain; (2) nominally 10 ps transform limited laser pulses are well-suited for narrowband γ-ray generation Employing a hyper-dispersion stretcher and compressor pair, we generated 750 mJ pulses at 1064 nm with 0.2 nm bandwidth, compressed to near transform limited duration of ps The nearly unfolded version of the hyper-dispersion compressor is shown in Fig 11, with a retro-mirror replacing gratings 5-8 Compared to standard Treacy design, this compressor contains two additional gratings (G2 and G3) The orientation of G2 is anti-parallel to G1: the rays dispersed at G1, are further dispersed at G2 This anti-parallel arrangement dθ enables angular dispersion, dλ , which is greater than possible with a single grating The orientation of G3 and G4 is parallel to, respectively, G2 and G1 G3 undoes the angular dispersion of G2 and G4 undoes the angular dispersion of G1 producing a collimated, spatially chirped beam at the retro-mirror After retro-reflection, the spatial chirp is removed after four more grating reflections The number of grating reflections (8), is twice that in a Treacy compressor High diffraction efficiency gratings are essential for high throughput efficiency We utilize multi-layer-dielectric (MLD) gratings developed at LLNL with achievable diffraction efficiency >99% (Perry et al., 1995) The magnitude of the negative chirp is controlled by varying L1 , the optical path length of the central ray between G1 and G2 and L2 , the optical path length between G2 and G3 We derive an analytical formula (Eq 12) for group delay dispersion (GDD) as a function of wavelength for the compressor using Kostenbauder formalism (Kostenbauder, 1990; Lin et al., 1993) GDD = − λ [sin (φ) + sin (ψ)]2 × 2L1 cos2 (φ) + L2 [cos (φ) + cos (ψ)]2 πc2 cos4 (φ) (12) Here ψ is the angle of incidence and φ is the angle of diffraction of the central ray of wavelength λ at the first grating measured with respect to grating normal We assume that the groove density of gratings and is the same Note that the expression for GDD reduces to that of the standard two-grating compressor when L2 =0 Higher order dispersion terms can be derived by noting that φ is a function of wavelength G4 retro mirror G2 in/out G1 G3 Fig 11 Unfolded version of the hyper-dispersion compressor with anti-parallel gratings Compressor design can be folded to reduce the total number of gratings and simplify compressor alignment The compressor shown in Fig 12 has been designed for Velociraptor and is similar to the experimental design on T-REX The compressor consists of two 40x20 cm multi-layer dielectric (MLD) gratings arranged anti-parallel to each other, a vertical roof mirror (RM), and a series of two periscopes and a horizontal roof mirror These six mirrors set the height and the position of the reflected beam on the gratings and inverts the beam in the plane of diffraction The beam is incident at Littrow-3 degrees (64.8o ) on the 1740 grooves/mm 13 61 Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources gratings The vertical roof mirror here, is equivalent to the retro-mirror in Fig 11 The beam undergoes a total of grating reflections and 16 mirror reflections in the compressor The total beam path of the central ray is 22 m On T-REX, the MLD gratings had a diffraction efficiency above 97%, enabling an overall compressor throughput efficiency of 60% Here, the magnitude of the chirp is tuned by translating the horizontal roof mirror The compressor, with its relatively compact footprint of 3x0.7 m provides GDD=-4300 ps2 /rad, or a pulse dispersion of 7000 ps/nm This chirps the incident 0.2 nm bandwidth pulse to ns The two grating separation in a standard Treacy compressor with the same dispersion would be 32 m horizontal periscope horizontal roof grating vertical periscope in/out grating vertical roof mirror Fig 12 The compact hyper-dispersion compressor consisting of two 1740 grooves/mm gratings has a footprint of x 0.7 m and group delay dispersion of -4300 ps2 /rad The hyper-dispersion stretcher design is conceptually similar The unfolded version is shown in Fig 13 Compared to the standard Martinez stretcher, the hyper-dispersion design contain two extra mirrors G1 and G4, arranged anti-parallel to G2 and G3 We define L f as the path length from G2 to the first lens Then the total ray path length from G1 to the first lens (L1 + L f ) must be smaller than the lens focal length, f to produce a positive chirp The magnitude of the chirp is controlled by varying the value of L1 + L f − f We modify Eq 12 to derive the GDD formula for the aberration free hyper-dispersion stretcher shown in Fig 13: GDD = − λ [sin (φ) + sin (ψ)]2 × L1 cos2 (φ) + ( L f − f ) [cos (φ) + cos (ψ)]2 πc2 cos4 (φ) in/out G2 Lens, f G1 G4 2f (13) retro mirror Lens, f G3 Fig 13 Unfolded hyper-dispersion stretcher utilizes four gratings, as opposed to two gratings in the standard Martinez design The folded CAD version of the stretcher built for T-REX is shown in Fig 14 For high fidelity pulse recompression, the stretcher is designed with a nearly equal and opposite chirp compared to that of the compressor The small difference accounts for other dispersive elements in the system We again use two large 1740 grooves/mm MLD gratings, with footprints of 20x10 cm and 35x15 cm The beam is incident at the same Littrow-3o angle as in the compressor A large, 175 mm diameter, f = 3099 mm lens accommodates the large footprint of the spatially chirped beam A folding retro-mirror is placed f away from the lens, forming a 2- f telescope seen in the unfolded version of Fig 13 The beam height changes through off-center incidence on the lens After grating reflections, the beam is incident on the vertical roof mirror, which is equivalent to the retro-mirror in Fig 13 The two 450 14 62 Laser Pulses Coherence and Ultrashort Pulse Laser Emission mirrors fold the beam path, rendering a more compact footprint After grating reflections, the compressed pulse arrives and 2nd pass retro mirror The beam is then retro-reflected through the stretcher, undergoing a total of 16 grating reflections We double pass through the stretcher to double the total pulse chirp Beam clipping on the lens prevents reducing the lens to G2 distance to match compressor dispersion in a single pass Chromatic and geometric lens aberrations modify higher order dispersion terms in the stretcher, requiring raytracing for more accurate computation We use a commercial ray-tracing software (FRED by Photon Engineering, LLC) to compute ray paths in the stretcher and in the compressor From raytrace analysis, the GDD for the stretcher is 4300 ps2 /rad, and the TOD/GDD ratio is -115 fs, at the 1064 nm central wavelength; for the compressor, the TOD/GDD ratio is -84 fs The TOD mismatch would result in a 3% reduction in the temporal Strehl ratio of the compressed pulse We can match the GDD and the TOD of the stretcher/compressor pair by a 1o increase of the angle of incidence on gratings and in the stretcher folding retro mirror folding mirror vertical roof lens G2 2nd pass retro G1 beam sizing fiber input/output Fig 14 The compact hyper-dispersion stretcher matches the GDD of the compressor We employed the hyper-dispersion stretcher-compressor pair in our interaction laser Commercial Q-switched bulk Nd:YAG laser heads amplified stretched pulses from the fiber chain to 1.3 J, with 800 mJ remaining after pulse recompression We characterize the compressed pulse temporal profile using multi-shot second harmonic generation (SHG) frequency resolved optical gating (FROG) (Kane & Trebino, 1993; Kane et al., 1994) technique FROG is a commonly used method for measurement of ultrashort pulses Compared to autocorrelation which cannot measure the actual pulse intensity, FROG measures both the intensity and the phase of the recompressed pulse In its multi-shot, SHG implementation, a FROG measurement consists of measuring the frequency spectrum of the auto-correlation signal at each relative delay between the two pulse replicas Mathematically, ∞ SHG we determine IFROG (ω, τ ) = | −∞ E(t) E(t − τ ) exp(−iωt)dt|2 , which is a 2D spectrogram plotting delay, τ vs frequency (Trebino, 2000) Several inversion algorithms exist to process the FROG data and extract pulse intensity and phase In the measurement, we use a 0.01 nm resolution m spectrometer (McPherson Model 2061) to resolve the narrow bandwidth pulse spectrum at the output of a background free SHG auto-correlator The measured field of the FROG spectrogram, I (ω, τ ) is shown in Fig 15(a) Numerical processing then symmetrizes the trace and removes spurious background and noise The FROG algorithm converges to the spectrogram shown in Fig 15(b) The FROG algorithm discretizes the measurement into a 512x512 array The FROG error between the measured and the converged calculated profile, defined as EFROG ≡ N2 N meas calculated ∑i,j=1 IFROG (ωi , τj ) − IFROG (ωi , τj ) , where N=512 is the array dimension, is 5.3x10−3 The intensity profile corresponding to FROG spectrum of Fig 15(b) is shown in Fig 16(a) The 15 63 Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources (a) (b) Fig 15 Experimental measurement of the 800 mJ pulse duation (a) Field of the experimentally measured FROG spectrogram (b) Lowest error field obtained by a FROG algorithm using a 512×512 discretization grid pulse is slightly asymmetric and contains a small pre-pulse, caused by a small residual TOD mismatch We calculate that the FWHM is 8.3 ps, with 84% of the pulse energy contained in the 20 ps wide bin indicated by the dashed box, and the temporal strehl ratio is 0.78 The temporal strehl is the ratio of the peak measured intensity, and the peak transform limited intensity for the measured spectral profile The temporal waveform on the logarithmic scale (Fig 16(b)) shows a post pulse at 160 ps, 100 dB lower than the main pulse This post-pulse causes the satellite wings and the fringing in the FROG measurement Frequency doubling will further improve the pulse contrast FROG also measures the pulse spectrum (Fig 17) Comparing the FROG measured spectrum with the direct IR spectral measurement performed with an f =1 m spectrometer indicates good agreement Intensity arb u Intensity arb u 1.0 0.8 0.6 0.4 0.2 0.0 40 20 Time ps (a) 20 40 0.1 0.01 0.001 10 200 100 Time ps 100 200 (b) Fig 16 Temporal pulse intensity obtained by analyzing a numerically processed FROG spectrogram on the linear scale (a) and log scale (b) FWHM of the pulse duration is 8.3 ps, and 84% of the energy is contained in the 20 ps bin (dashed box) Frequency conversion High power, high energy laser technology is well developed in the 800 nm to 1.1 μm wavelength range One can generate other wavelengths through a nonlinear conversion process Fundamentally, the response of a dielectric medium to an applied electric field can be described by an induced polarization, P = χ(1) E + χ(2) EE + , where is the free space permittivity, χ(n) is the nth order susceptibility, and E is the vector electric field Because 16 64 Laser Pulses Coherence and Ultrashort Pulse Laser Emission Fig 17 Pulse spectrum from FROG (red dots) and spectrometer (solid line) measurements χ(2) for an off-resonant medium, higher order terms become important only when χ (1) the applied electric field is sufficiently high In a χ(2) process, EE term produces excitation at twice the fundamental frequency Let E = A cos(ωt), then E2 = A (1 + cos(2ωt)) The magnitude of the nonlinear susceptibility varies with the applied frequency and depends on the electronic level structure of the material Under well-optimized conditions harmonic efficiencies can exceed 80% When selecting an appropriate nonlinear crystal, we consider various application dependent factors such as the magnitude of the nonlinear coefficient, acceptance bandwidth, absorption, thermal acceptance, thermal conductivity, walk-off angle, damage threshold, and maximum clear aperture For pulse durations in the 200 fs to 10 ps range and for the fundamental wavelength ≈1 μm, beta barium borate (BBO) is an excellent candidate for 2ω, 3ω, and 4ω generation The main draw back, is that the largest clear crystal aperture is ≈20 mm which limits its use to low pulse energies (< 10 − 100 mJ) For higher pulse energies, deuterated and non-deuterated potassium dihydrogen phosphate (DKDP and KDP), lithium triborate (LBO) and yttrium calcium oxyborate (YCOB) can be grown to much larger apertures YCOB is particularly attractive for its high average power handling, high damage threshold, and large effective nonlinearity (Liao et al., 2006) For frequency doubling, typical required laser intensities are in the 100 MW/cm2 to 10 GW/cm2 range The crystal must be cut along an appropriate plane to allow phase matching and to maximize the effective nonlinear coefficient, de f f , which is related to χ(2) and the crystal orientation The interacting waves at ω and 2ω acquire different phases, φ(ω ) = k ω z = nω ωz/c and φ(2ω ) = k2ω z = 2n2ω ωz/c as they propagate along the crystal in z direction An interaction is phase matched when k2ω = 2k ω A uniaxial crystal contains two polarization eigenvectors, one parallel to the optic axis (the axis of rotation symmetry) and one perpendicular to it An electric field inside the crystal contains a component perpendicular to the optic axis (ordinary polarization) and a component in the plane defined by the optic axis and the direction of propagation (extraordinary polarization), as illustrated in Fig (18) The refractive index of the extraordinary polarization, ne , varies with θ, the angle between the direction of propagation and the optic axis; the ordinary refractive index, no has no angular dependence In the e example shown in Fig (18), the crystal is rotated along the y-axis until n2ω (θ ) = no The ω illustrated phase matching condition, where both incident photons have the same polarization is known as type I phase matching In Type II phase matching, the incident field has both an ordinary and an extraordinary polarization component Coupled Eqs (14-15), given in SI units, describe Type I, 2ω generation process relevant for 200 fs - 10 ps duration pulses Here, we make a plane wave approximation, justified when we are not focusing into the crystal, and when the crystal is sufficiently thin to ignore beam walk-off effects We also ignore pulse dispersion in the crystal, justified for our pulse bandwidth and crystal thickness We can account for two-photon absorption, which becomes Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources 17 65 important for 4ω generation in BBO, by adding β| A2ω |2 A2ω term to the left hand side of Eq (15) ∂Aω ∂Aω αω 2ω + + Aω = i d A∗ A exp(−iΔkz) ∂z v g,ω ∂t n(ω )c e f f ω 2ω (14) 2ω ∂A2ω ∂A2ω α + + 2ω A2ω = i d A2 exp(iΔkz) ∂z v g,2ω ∂t n(2ω )c e f f ω (15) Fig 18 Frequency doubling with OOE type phasematching in a uniaxial nonlinear crystal θ is the phasematching angle between the optic axis and the propagation direction We obtain an analytical solution assuming qausi-CW pulse duration, which eliminates the time dependent terms, and a low conversion efficiency, or a constant Aω The efficiency of 2ω harmonic generation, η2ω = I2ω /Iω , reduces to Eq (16): η2ω = 8π d2 f f L2 Iω sin2 (ΔkL/2) e 2 nω n2ω cλω ( ΔkL/2) (16) In our laser systems, we implement frequency conversion on both, the photogun and the interaction laser systems (Gibson et al., 2010) On T-REX, we generate the 4th harmonic of the fundamental frequency by cascading two BBO crystals The first, mm thick crystal cut for Type I phase matching, frequency doubles the incident pulse from 1053 nm to 527 nm The second 0.45 mm thick BBO crystal cut for Type I phase matching,frequency doubles 527 nm pusle to 263 nm The overall conversion efficiency from IR to UV is 10%, yielding 100 μJ at 263 nm Here, frequency conversion is primarily limited by two-photon absorption in the UV and the group velocity mismatch (GVM) between the 2ω and the 4ω pulses GVM results in temporal walk-off of the pulse envelopes and, in the frequency domain, is equivalent to the acceptance bandwidth On the interaction laser, we frequency double the high energy pulses to increase the final γ-ray energy On T-REX we use a large aperture (30x30 mm) mm thick DKDP crystal to frequency double 800 mJ pulse from 1064 nm to 532 nm with up to 40% conversion efficiency Here, the pulse bandwidth is relatively narrow (≈0.2 nm) and group velocity walk-off is insignificant The conversion efficiency is primarily limited by beam quality and temporal pulse shape Generated 532 nm pulse energy is plotted vs the compressed input pulse energy in Fig 19 18 66 Laser Pulses Coherence and Ultrashort Pulse Laser Emission At maximum IR energy, the conversion efficiency unexpectedly decreases This may indicate onset of crystal damage, degradation in pulse quality, or an increase in phase mismatch Energy at 532 nm (mJ) 300 250 200 150 100 50 0 200 400 600 800 Energy at 1064 nm (mJ) 1000 Fig 19 Frequency doubling of the 10 ps T-REX ILS laser with a peak efficiency of 40% Pulse shaping A uniform elliptical laser shape in space and time minimizes the contribution of space-charge force on the electron beam emittance (Kapchinskij & Vladimirskij, 1959; Li & Lewellen, 2008) Due to technical difficulties of generating this shape, simulations suggest that a uniform cylindrical pulse in space and time is an alternative (Cornacchia & et al., 1998) We generate the cylindrical shape by time-stacking the UV laser pulse in a Hyper-Michelson interferometer (Siders et al., 1998) and clipping the UV beam with a hard edge aperture It is also possible to mode-convert the UV beam from a Gaussian to a flat-top with a commercial refractive beam shaper based on aspheric lenses The pulse shaper is a Michelson-based ultrafast multiplexing device having nearly 100% throughput and designed for high energy shaped pulse generation The pulse train generates a train of replicas of the input pulse delayed with respect to each other with femtosecond precision The pulse stacker used in T-REX (Gibson et al., 2010) consists of stages, stacking 16 pulses The laser pulse passes through a series of beam splitters, each time being recombined following an adjustable delay path The built pulse stacker is shown in Fig 20 At the output of the pulse stacker, two orthogonally polarized pulse trains are recombined and interleaved in time at a polarizing beamsplitter The individual pulses must be sufficiently delayed to avoid high frequency intensity modulation that results from interferences of same-polarized pulses An example of a stacked flat-top pulse from the pulse stacker is shown in Fig 21 The figure shows a cross-correlation of the stacked UV pulse obtained on T-REX The 15 ps stacked UV (4ω) pulse is cross-correlated with the ≈0.75 ps IR (1ω) pulse (blue line) The predicted cross-correlation on the basis of the pulse energies of each of the 16 stacked pulses is shown by the dashed line Cross-correlations between the IR and the 16 individual UV pulses are shown below the main pulse High energy laser pulse recirculation In this section we describe a novel technique for recirculating high power, high energy, picosecond laser pulses, akin to the interaction laser pulses on T-REX The motivation for laser recirculation for compton-scattering sources is two-fold First, a major fundamental limitation of these sources is the extremely small Thomson scattering cross-section, σT = 8π −25 cm2 , where r classical electron radius, which leads to low conversion e re = 6.65 × 10 Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources Laser Technology for Compact, Narrow-bandwidth Gamma-ray Sources 19 67 input HW output BS BC BS BS BS Intensity (a u.) Fig 20 Photograph of the pulse stacker on T-REX photogun laser Time (ps) Fig 21 Cross-correlation measurement of the temporally shaped UV pulse from T-REX photogun laser indicates a 15 ps FWHM pulse duration efficiency from laser photons to γ rays Only in 1010 of laser photons is doppler upshifted to γ-ray energy The overall efciency of the compton-scattering source could be increased by reusing the laser photons after each interaction with the electron bunch Second, the joule-class, short pulse lasers operate at a few Hz to 100 Hz type of repetition rates Linacs can operate at kHz and higher repetition rates Increasing the repetition rate of the interaction laser would increase the average brightness of the γ-ray source The pulse recirculation scheme that we have developed is general and could be applied to various other phenomena that involve high intensity lasers interacting with an optically thin medium such as cavity ring down spectroscopy, high-harmonic generation in short gas jets, or laser based plasma diagnostics The pulse recirculation scheme is based on injection and trapping a single laser pulse inside a passive optical cavity A thin nonlinear crystal acts as an optical switch, trapping the frequency converted light This technique, termed recirculation injection by nonlinear gating (RING) is compatible with joule class, 100s of Watts of average power, picosecond laser pulses In the simplest implementation of this technique, the incident laser pulse at the fundamental frequency enters the resonator and is efficiently frequency doubled The resonator mirrors are dichroic, coated to transmit the 1ω light and reflect at 2ω (see Fig 22) The upconverted 2ω pulse becomes trapped inside the cavity After many roundtrips, the laser pulse decays primarily due to Fresnel losses at the crystal faces and cavity mirrors The crystal thickness is optimized for high conversion efficiency Current pulse recirculation schemes are based on either resonant cavity coupling (Gohle et al., 2005; Jones et al., 2005) or active (electro-optic or acousto-optic) pulse switching (Yu & Stuart, 20 68 Laser Pulses Coherence and Ultrashort Pulse Laser Emission M NL crystal M M Fig 22 Conceptual design of the RING picosecond pulse recirculation cavity 1997; Mohamed et al., 2002) into and out of the resonator Active pulse switching schemes are suitable for low intensity, nanosecond duration pulses (Meng et al., 2007) Resonant cavity coupling requires interferometric cavity alignment and MHz and higher repetition rates To date, researchers have attained up to 100x enhancement for W average power, ≈50 fs duration incident pulses with per pulse energy