Chirped pulse amplification OPO OVERVIEW Second harmonic, difference frequency, optical parametric oscillation :Phase matching :Phase matching with periodically poled crystals Broadband parametric amplification Chirped pulse amplification Fourier plane optical parametric amplification (FOPA)

LOSS GAIN GAIN SF DF OPG or OPO or OPA Second harmonic, difference frequency, optical parametric oscillation LOSS GAIN GAIN SF DF OPG or OPO or OPA

What is the difference between population inversion gain Second harmonic, difference frequency, optical parametric oscillation What is the difference between population inversion gain and optical parametric gain? Population inversion OPG Lasts after the pump Instantaneous Energy dissipation no dissipation in matter (relaxation mechanisms) Analogy?

Analogy: population inversion gain versus optical parametric gain TIME Ip TIME Ip G A I N TIME G A I N TIME

TYPE I Phase matching Phase matching in second harmonic generation Fundamental Phase matching Second harmonic dE2 dz = a E12 SHG E2 Different wavelengths dE1 dz = -a E2E1* ENERGY EXCHANGE ALWAYS FROM 1 TO 2 Distance z

TYPE II Phase matching Phase matching in second harmonic generation SHG dE2 dz = a EoEe Phase matching dEo dz = -a E2Ee* Eo dEe dz = -a E2Eo* Ee THE SIGN OF ENERGY EXCHANGE CAN CHANGE Distance z

Tuning the crystal length for optimum short pulse compression LONG CRYSTALS = HIGHER CONVERSION LONG CRYSTALS = NARROWER BANDWIDTH The obvious solution for short pulses: short crystals? Not always! One can use long crystals to compress pulses down to femtoseconds. THE GENERATED PULSES ARE SHORTER THAN THE FUNDAMENTAL, AND THAN THE INVERSE BANDWIDTH OF THE SECOND HARMONIC PROCESS. Where does one get the bandwidth? From the amplitude modulation of the pump, as the pump is depleted at a faster rate than the pump risetime.

Compression in SHG Motion of pulses in the frame of reference of the second harmonic Weak pulses: the second harmonic broadens as the overlap of the two fundamental pulses increases

Strong pulses Compression in SHG Motion of pulses in the frame of reference of the second harmonic Strong pulses The trick: sum frequency group velocity between that of fundamental o and fundamental e

Phase matching with periodically poled crystals Use the orientation for maximum NL coefficient. Periodically reverse the sign of the coefficient (a), when SHG E2 sin Dk z = sin (k2 - 2k1z) changes sign Distance z dE2 dz = a E12 Advantage: Large nonlinearity dE1 dz = -a E2E1* Disadvantage: Periodic structure Narrow band

(a) (b) (c)

Find the angles? SNLO CHIRP AMPLIFICATION

There are two solutions to the narrow bandwidth of Periodically Poled crystals: 1. Pole the crystal “non-periodically” “ENGINEERABLE COMPRESSION OF ULTRASHORT PULSES BY USE OF SECOND HARMONIC GENERATION IN CHIRPED-PERIOD-POLED LITHIUM NIOBATE”, Optics Letters 22, 1341 (1997) “SIMULTANEOUS FEMTOSECOOND-PULSE COMPRESSION AND SHG IN APERIODICALLY POLED KTiOPO4”, Optics Letters 24, 1071 (1999) 2. Convert the spectrum piece by piece x Periodically poled crystal of period changing with x.

Other solution: use many crystals for each wavelength range grating Laser source y grating This is part of OPCPA

CHIRPED PULSE AMPLIFICATION LASER DAMAGE CHIRPED PULSE AMPLIFICATION LINEAR DISPERSION (+) LINEAR DISPERSION (-) AMPLIFIED SHORT PULSE SHORT PULSE GAIN If the parametric gain is sufficiently broad for the short pulse, it is also sufficiently broad for the dispersed pulse. THE PARAMETRIC GAIN HAS NO ENERGY STORAGE: THE DURATION OF HAVE TO BE MATCHED PUMP SIGNAL PUMP DEPLETION: “DIP” IN PUMP. TECHNICAL CHALLENGE: PUMP 100 ps OR LESS SIGNAL STRETCHED TO > 100 ps.

Motivation for 5-fs (2-cycle) lasers Relativistic HHG 5 fs cos Generation of single attosecond light and electron pulses in gas and plasma medium 20 fs 5 fs cos 5 fs sin Gas harmonics l3 regime A. Baltuska et al., IEEE J. of Sel. Top. in Quantum Electronics 9, 972 (2003) G. D. Tsakiris et al., New J. Phys. 8, 19 (2006) A. Baltuska et al., IEEE J. of Sel. Top. in Quantum Electronics 9, 972 (2003) N. M.Naumova et al., Phys. Plas. 12, 056707 (2005) G. D. Tsakiris et al., New J. Phys. 8, 19 (2006) A. Baltuska et al., IEEE J. of Sel. Top. in Quantum Electronics 9, 972 (2003)

Optical parametric chirped pulse amplification (OPCPA) Pump Signal Idler BBO Advantages Broad gain bandwidth, supporting few-cycle pulses Good contrast achievable ... * D. Herrmann et al. Opt. Lett., 34, 2459 (2009) F. Tavella et al. Opt. Lett. 32, 2227 (2007) S. Witte et al. Opt. Express 14, 8168 (2006) S. Adachi et al. Opt. Express 16, 14341 (2008)

Synthesizer principles Parallel synthesis Pro: Shorter „beam path“ Simple narrow bandwidth mirrors Contra: Interferometric stability needed Very sensitive  high rep.rate Broad bandwidth mirrors after beam combination Similar principle: frequency domain OPA l Il Serial synthesis Pro: No special requirements on stability Insensitive Contra: Longer „beam path“ Broad bandwidth mirrors S.-W. Huang et al. Nat. Photon 5, 475 (2011) C. Manzoni et al. Opt. Lett. 37, 1880 (2012) B. E. Schmidt et al. Nat. Commun. 5, 3643 (2014) D. Herrmann et al., Opt. Exp. 18, p. 18752 (2010) A. Harth et al. Opt. Express 20, 3076 (2012) 19

Multi-10-TW sub-5-fs Optical Parametric Synthesizer − Relativistic intensity sub-5-femtosecond laser pulses and their applications Laszlo Veisz1, Daniel Rivas1, Gilad Marcus1, Xun Gu1, Daniel Cardenas1, Jiancai Xu1, Julia Mikhailova1, Alexander Buck1,2, Tibor Wittmann1, Christopher M. S. Sears1, Daniel Herrmann3, Olga Razskazovskaya2, Vladimir Pervak2, Ferenc Krausz1,2 1 Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany 2 Ludwig-Maximilians-Universität München, Am Coulombwall 1, 85748 Garching, Germany 3 Lehrstuhl für BioMolekulare Optik, Department für Physik, Ludwig-Maximilians-Universität,Oettingenstrasse 67, 80538 München, Germany 20

Fourier plane optical parametric amplification (FOPA) Faux pas L grating Laser source y grating This is part of OPCPA PUMP

A collimated Gaussian beam of 2 mm diameter FWHM, 800 nm, is incident on a pair of gratings of 1700 grooves/mm, at an angle of incidence of 30 degrees (see Fig. ). The spacing between the gratings is L = 10 cm. After the gratings, the diffracted beam is incident on 4 independent modulators, each of height Δy = 2 mm. Assuming a Gaussian pulse of g = 40 fs duration, calculate the duration and chirp of the pulse entering each 2 mm section (you are sampling a fraction of the spectrum of the pulse diffracted by the gratings). You can make abstraction of the spatial problem for this question. Two approaches possible: (a) see which wavelength correspond to each section boundaries. That defines the spectrum. The inverse of the spectrum gives the pulse duration (b) Calculate the second order dispersion of the pair of gratings. That give the pulse broadening and chirp introduced by the pair of gratings.

(b) Calculate the second order dispersion of the pair of gratings (b) Calculate the second order dispersion of the pair of gratings. That give the pulse broadening and chirp introduced by the pair of gratings.

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the pulse broadening and chirp introduced by the pair of gratings. (b) Calculate the second order dispersion of the pair of gratings. That give the pulse broadening and chirp introduced by the pair of gratings. If m is the order of diffraction, the angle of incidence and the diffraction angle are related through the grating equation

(a) see which wavelength correspond to each section boundaries. That defines the spectrum. The inverse of the spectrum gives the pulse duration