Abstract

Chirped quasi-phase-matching (QPM) gratings offer efficient, ultra-broadband optical parametric chirped pulse amplification (OPCPA) in the mid-infrared as well as other spectral regions. Only recently, however, has this potential begun to be realized [1]. In this paper, we study the design of chirped QPM-based OPCPA in detail, revealing several important constraints which must be accounted for in order to obtain broad-band, high-quality amplification. We determine these constraints in terms of the underlying saturated nonlinear processes, and explain how they were met when designing our mid-IR OPCPA system. The issues considered include gain and saturation based on the basic three-wave mixing equations; suppression of unwanted non-collinear gain-guided modes; minimizing and characterizing nonlinear losses associated with random duty cycle errors in the QPM grating; avoiding coincidentally-phase-matched nonlinear processes; and controlling the temporal/spectral characteristics of the saturated nonlinear interaction in order to maintain the chirped-pulse structure required for OPCPA. The issues considered place constraints both on the QPM devices as well as the OPCPA system. The resulting experimental guidelines are detailed. Our results represent the first comprehensive discussion of chirped QPM devices operated in strongly nonlinear regimes, and provide a roadmap for advancing and experimentally implementing OPCPA systems based on these devices.

© 2014 Optical Society of America

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2013 (9)

B. W. Mayer, C. R. Phillips, L. Gallmann, M. M. Fejer, U. Keller, “Sub-four-cycle laser pulses directly from a high-repetition-rate optical parametric chirped-pulse amplifier at 3.4 μm,” Opt. Lett. 38, 4265–4268 (2013).
[CrossRef] [PubMed]

C. R. Phillips, C. Langrock, D. Chang, Y. W. Lin, L. Gallmann, M. M. Fejer, “Apodization of chirped quasi-phasematching devices,” J. Opt. Soc. Am. B 30, 1551–1568 (2013).
[CrossRef]

G. Porat, A. Arie, “Efficient, broadband, and robust frequency conversion by fully nonlinear adiabatic three-wave mixing,” J. Opt. Soc. Am. B 30, 1342–1351 (2013).
[CrossRef]

O. Yaakobi, M. Clerici, L. Caspani, F. Vidal, R. Morandotti, “Complete pump depletion by autoresonant second harmonic generation in a nonuniform medium,” J. Opt. Soc. Am. B 30, 1637–1642 (2013).
[CrossRef]

H. Suchowski, P. R. Krogen, S.-W. Huang, F. X. Kärtner, J. Moses, “Octave-spanning coherent mid-IR generation via adiabatic difference frequency conversion,” Opt. Express 21, 28892–28901 (2013).
[CrossRef]

C. R. Phillips, L. Gallmann, M. M. Fejer, “Design of quasi-phasematching gratings via convex optimization,” Opt. Express 21, 10139–10159 (2013).
[CrossRef] [PubMed]

V. J. Hernandez, C. V. Bennett, B. D. Moran, A. D. Drobshoff, D. Chang, C. Langrock, M. M. Fejer, M. Ibsen, “104 MHz rate single-shot recording with subpicosecond resolution using temporal imaging,” Opt. Express 21, 196–203 (2013).
[CrossRef] [PubMed]

C. R. Phillips, J. S. Pelc, M. M. Fejer, “Parametric processes in quasi-phasematching gratings with random duty cycle errors,” J. Opt. Soc. Am. B 30, 982–993 (2013).
[CrossRef]

H. Jang, G. Strömqvist, V. Pasiskevicius, C. Canalias, “Control of forward stimulated polariton scattering in periodically-poled KTP crystals,” Opt. Express 21, 27277–27283 (2013).
[CrossRef] [PubMed]

2012 (12)

C. R. Phillips, M. M. Fejer, “Adiabatic optical parametric oscillators: steady-state and dynamical behavior,” Opt. Express 20, 2466–2482 (2012).
[CrossRef] [PubMed]

H. Ishizuki, T. Taira, “Half-joule output optical-parametric oscillation by using 10-mm-thick periodically poled mg-doped congruent linbo3,” Opt. Express 20, 20002–20010 (2012).
[CrossRef] [PubMed]

C. R. Phillips, J. Jiang, C. Mohr, A. C. Lin, C. Langrock, M. Snure, D. Bliss, M. Zhu, I. Hartl, J. S. Harris, M. E. Fermann, M. M. Fejer, “Widely tunable midinfrared difference frequency generation in orientation-patterned gaas pumped with a femtosecond tm-fiber system,” Opt. Lett. 37, 2928–2930 (2012).
[CrossRef] [PubMed]

C. Heese, C. R. Phillips, L. Gallmann, M. M. Fejer, U. Keller, “Role of apodization in optical parametric amplifiers based on aperiodic quasi-phasematching gratings,” Opt. Express 20, 18066–18071 (2012).
[CrossRef] [PubMed]

A. Bostani, A. Tehranchi, R. Kashyap, “Engineering of effective second-order nonlinearity in uniform and chirped gratings,” J. Opt. Soc. Am. B 29, 2929–2934 (2012).
[CrossRef]

T. W. Neely, L. Nugent-Glandorf, F. Adler, S. A. Diddams, “Broadband mid-infrared frequency upconversion and spectroscopy with an aperiodically poled LiNbO3 waveguide,” Opt. Lett. 37, 4332–4334 (2012).
[CrossRef] [PubMed]

J. Rothhardt, S. Demmler, S. Hädrich, J. Limpert, A. Tünnermann, “Octave-spanning OPCPA system delivering CEP-stable few-cycle pulses and 22 W of average power at 1 MHz repetition rate,” Opt. Express 20, 10870–10878 (2012).
[CrossRef] [PubMed]

S. Witte, K. Eikema, “Ultrafast optical parametric chirped-pulse amplification,” Selected Topics in IEEE J. Quant. Electron. 18, 296–307 (2012).
[CrossRef]

C. T. Middleton, P. Marek, P. Cao, C.-c. Chiu, S. Singh, A. M. Woys, J. J. de Pablo, D. P. Raleigh, M. T. Zanni, “Two-dimensional infrared spectroscopy reveals the complex behaviour of an amyloid fibril inhibitor,” Nature chemistry 4, 355–360 (2012).
[CrossRef] [PubMed]

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mcke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernndez-Garca, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef] [PubMed]

C. Heese, C. R. Phillips, B. W. Mayer, L. Gallmann, M. M. Fejer, U. Keller, “75 MW few-cycle mid-infrared pulses from a collinear apodized APPLN-based OPCPA,” Opt. Express 20, 26888–26894 (2012).
[CrossRef] [PubMed]

Y. Deng, A. Schwarz, H. Fattahi, M. Ueffing, X. Gu, M. Ossiander, T. Metzger, V. Pervak, H. Ishizuki, T. Taira, T. Kobayashi, G. Marcus, F. Krausz, R. Kienberger, N. Karpowicz, “Carrier-envelope-phase-stable, 1.2 mJ, 1.5 cycle laser pulses at 2.1 μm,” Opt. Lett. 37, 4973–4975 (2012).
[CrossRef] [PubMed]

2011 (11)

B. E. Schmidt, A. D. Shiner, P. Lassonde, J.-C. Kieffer, P. B. Corkum, D. M. Villeneuve, F. Légaré, “CEP stable 1.6 cycle laser pulses at 1.8 μm,” Opt. Express 19, 6858–6864 (2011).
[CrossRef] [PubMed]

G. Andriukaitis, T. Balciunas, S. Aliauskas, A. Puglys, A. Baltuka, T. Popmintchev, M. Chen, M. M. Murnane, H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36, 2755–2757 (2011).
[CrossRef] [PubMed]

C. Li, D. Wang, L. Song, J. Liu, P. Liu, C. Xu, Y. Leng, R. Li, Z. Xu, “Generation of carrier-envelope phase stabilized intense 1.5 cycle pulses at 1.75 μm,” Opt. Express 19, 6783–6789 (2011).
[CrossRef] [PubMed]

C. Heese, A. E. Oehler, L. Gallmann, U. Keller, “High-energy picosecond Nd:YVO4 slab amplifier for OPCPA pumping,” Applied Physics B 103, 5–8 (2011).
[CrossRef]

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-Samha, L. B. Madsen, U. Keller, “Atto-clock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Physics 8, 76–80 (2011).
[CrossRef]

T. Rohwer, S. Hellmann, M. Wiesenmayer, C. Sohrt, A. Stange, B. Slomski, A. Carr, Y. Liu, L. M. Avila, M. Kalläne et al., “Collapse of long-range charge order tracked by time-resolved photoemission at high momenta,” Nature 471, 490–493 (2011).
[CrossRef] [PubMed]

C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, I. Hartl, M. E. Fermann, “Supercontinuum generation in quasi-phasematched waveguides,” Opt. Express 19, 18754–18773 (2011).
[CrossRef] [PubMed]

D. T. Reid, “Ultra-broadband pulse evolution in optical parametric oscillators,” Opt. Express 19, 17979–17984 (2011).
[CrossRef] [PubMed]

C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, J. Jiang, M. E. Fermann, I. Hartl, “Supercontinuum generation in quasi-phase-matched LiNbO3 waveguide pumped by a Tm-doped fiber laser system,” Opt. Lett. 36, 3912–3914 (2011).
[CrossRef] [PubMed]

J. R. Schwesyg, M. Falk, C. R. Phillips, D. H. Jundt, K. Buse, M. M. Fejer, “Pyroelectrically induced photorefractive damage in magnesium-doped lithium niobate crystals,” J. Opt. Soc. Am. B 28, 1973–1987 (2011).
[CrossRef]

C. R. Phillips, J. S. Pelc, M. M. Fejer, “Continuous wave monolithic quasi-phase-matched optical parametric oscillator in periodically poled lithium niobate,” Opt. Lett. 36, 2973–2975 (2011).
[CrossRef] [PubMed]

2010 (6)

2009 (5)

2008 (9)

F. Druon, M. Hanna, G. Lucas-Leclin, Y. Zaouter, D. Papadopoulos, P. Georges, “Simple and general method to calculate the dispersion properties of complex and aberrated stretchers-compressors,” J. Opt. Soc. Am. B 25, 754–762 (2008).
[CrossRef]

M. Charbonneau-Lefort, B. Afeyan, M. M. Fejer, “Optical parametric amplifiers using nonuniform quasi-phase-matched gratings. II. space-time evolution of light pulses,” J. Opt. Soc. Am. B 25, 683–700 (2008).
[CrossRef]

C. Lynch, D. Bliss, T. Zens, A. Lin, J. Harris, P. Kuo, M. Fejer, “Growth of mm-thick orientation-patterned GaAs for IR and THz generation,” Journal of Crystal Growth 310, 5241–5247 (2008).
[CrossRef]

K. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser & Photonics Reviews 2, 11–25 (2008).
[CrossRef]

O. Gayer, Z. Sacks, E. Galun, A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B: Lasers Opt. 91, 343–348 (2008).
[CrossRef]

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nature Physics 4, 386–389 (2008).
[CrossRef]

M. Charbonneau-Lefort, B. Afeyan, M. M. Fejer, “Optical parametric amplifiers using chirped quasi-phase-matching gratings I: practical design formulas,” J. Opt. Soc. Am. B 25, 463–480 (2008).
[CrossRef]

M. Charbonneau-Lefort, B. Afeyan, M. M. Fejer, “Competing collinear and noncollinear interactions in chirped quasi-phase-matched optical parametric amplifiers,” J. Opt. Soc. Am. B 25, 1402–1413 (2008).
[CrossRef]

Ł. Kornaszewski, M. Kohler, U. K. Sapaev, D. T. Reid, “Designer femtosecond pulse shaping using grating-engineered quasi-phase-matching in lithium niobate,” Opt. Lett. 33, 378–380 (2008).
[CrossRef] [PubMed]

2007 (7)

C. Langrock, M. M. Fejer, I. Hartl, M. E. Fermann, “Generation of octave-spanning spectra inside reverse-proton-exchanged periodically poled lithium niobate waveguides,” Opt. Lett. 32, 2478–2480 (2007).
[CrossRef] [PubMed]

M. Conforti, F. Baronio, C. D. Angelis, “From femtosecond infrared to picosecond visible pulses: temporal shaping with high-efficiency conversion,” Opt. Lett. 32, 1779–1781 (2007).
[CrossRef] [PubMed]

K. A. Tillman, D. T. Reid, “Monolithic optical parametric oscillator using chirped quasi-phase matching,” Opt. Lett. 32, 1548–1550 (2007).
[CrossRef] [PubMed]

A. Cavalieri, N. Müller, T. Uphues, V. Yakovlev, A. Baltuška, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[CrossRef] [PubMed]

T. Umeki, M. Asobe, Y. Nishida, O. Tadanaga, K. Magari, T. Yanagawa, H. Suzuki, “Widely tunable 3.4 μm band difference frequency generation using apodized χ(2) grating,” Opt. Lett. 32, 1129–1131 (2007).
[CrossRef] [PubMed]

P. Reckenthaeler, D. Maxein, T. Woike, K. Buse, B. Sturman, “Separation of optical Kerr and free-carrier nonlinear responses with femtosecond light pulses in LiNbO3 crystals,” Physical Review B 76, 195117 (2007).
[CrossRef]

D. S. Hum, R. K. Route, M. M. Fejer, “Quasi-phase-matched second-harmonic generation of 532 nm radiation in 25°-rotated, x-cut, near-stoichiometric, lithium tantalate fabricated by vapor transport equilibration,” Opt. Lett. 32, 961–963 (2007).
[CrossRef] [PubMed]

2005 (2)

M. Charbonneau-Lefort, M. M. Fejer, B. Afeyan, “Tandem chirped quasi-phase-matching grating optical parametric amplifier design for simultaneous group delay and gain control,” Opt. Lett. 30, 634–636 (2005).
[CrossRef] [PubMed]

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

2004 (1)

M. Kolesik, J. V. Moloney, “Nonlinear optical pulse propagation simulation: from maxwell’s to unidirectional equations,” Physical Review. E 70, 036604 (2004).
[CrossRef]

2003 (2)

2002 (1)

2001 (2)

1999 (1)

A. Shirakawa, I. Sakane, M. Takasaka, T. Kobayashi, “Sub-5-fs visible pulse generation by pulse-front-matched noncollinear optical parametric amplification,” Appl. Phys. Lett. 74, 2268–2270 (1999).
[CrossRef]

1997 (1)

1996 (1)

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quant. Electron. 32, 1324–1333 (1996).
[CrossRef]

1993 (1)

1979 (1)

R. A. Baumgartner, R. Byer, “Optical parametric amplification,” Quantum Electronics, IEEE Journal of 15, 432–444 (1979).
[CrossRef]

Abu-Samha, M.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-Samha, L. B. Madsen, U. Keller, “Atto-clock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Physics 8, 76–80 (2011).
[CrossRef]

Adler, F.

Afeyan, B.

Agostini, P.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nature Physics 4, 386–389 (2008).
[CrossRef]

Aliauskas, S.

Alisauskas, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mcke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernndez-Garca, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef] [PubMed]

Andersen, T. V.

Andriukaitis, G.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mcke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernndez-Garca, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef] [PubMed]

G. Andriukaitis, T. Balciunas, S. Aliauskas, A. Puglys, A. Baltuka, T. Popmintchev, M. Chen, M. M. Murnane, H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36, 2755–2757 (2011).
[CrossRef] [PubMed]

Angelis, C. D.

Arie, A.

Arpin, P.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mcke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernndez-Garca, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef] [PubMed]

Artigas, D.

Asobe, M.

Avila, L. M.

T. Rohwer, S. Hellmann, M. Wiesenmayer, C. Sohrt, A. Stange, B. Slomski, A. Carr, Y. Liu, L. M. Avila, M. Kalläne et al., “Collapse of long-range charge order tracked by time-resolved photoemission at high momenta,” Nature 471, 490–493 (2011).
[CrossRef] [PubMed]

Balciunas, T.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mcke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernndez-Garca, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef] [PubMed]

G. Andriukaitis, T. Balciunas, S. Aliauskas, A. Puglys, A. Baltuka, T. Popmintchev, M. Chen, M. M. Murnane, H. C. Kapteyn, “90 GW peak power few-cycle mid-infrared pulses from an optical parametric amplifier,” Opt. Lett. 36, 2755–2757 (2011).
[CrossRef] [PubMed]

Baltuka, A.

Baltuska, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mcke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernndez-Garca, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef] [PubMed]

Baltuška, A.

A. Cavalieri, N. Müller, T. Uphues, V. Yakovlev, A. Baltuška, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[CrossRef] [PubMed]

Baronio, F.

M. Conforti, F. Baronio, C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Physical Review A 81, 053841 (2010).
[CrossRef]

M. Conforti, F. Baronio, C. D. Angelis, “From femtosecond infrared to picosecond visible pulses: temporal shaping with high-efficiency conversion,” Opt. Lett. 32, 1779–1781 (2007).
[CrossRef] [PubMed]

Baumgartner, R. A.

R. A. Baumgartner, R. Byer, “Optical parametric amplification,” Quantum Electronics, IEEE Journal of 15, 432–444 (1979).
[CrossRef]

Becker, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mcke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernndez-Garca, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef] [PubMed]

Bennett, C. V.

Beyer, O.

O. Beyer, D. Maxein, K. Buse, B. Sturman, H. T. Hsieh, D. Psaltis, “Investigation of nonlinear absorption processes with femtosecond light pulses in lithium niobate crystals,” Phys. Rev. E 71, 056603 (2005).
[CrossRef]

Blaga, C. I.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nature Physics 4, 386–389 (2008).
[CrossRef]

Bliss, D.

Blümel, L.

A. Cavalieri, N. Müller, T. Uphues, V. Yakovlev, A. Baltuška, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[CrossRef] [PubMed]

Bostani, A.

Breunig, I.

Brown, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mcke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernndez-Garca, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef] [PubMed]

Buse, K.

Byer, R.

R. A. Baumgartner, R. Byer, “Optical parametric amplification,” Quantum Electronics, IEEE Journal of 15, 432–444 (1979).
[CrossRef]

Camara Mayorga, I.

Canalias, C.

Cao, P.

C. T. Middleton, P. Marek, P. Cao, C.-c. Chiu, S. Singh, A. M. Woys, J. J. de Pablo, D. P. Raleigh, M. T. Zanni, “Two-dimensional infrared spectroscopy reveals the complex behaviour of an amyloid fibril inhibitor,” Nature chemistry 4, 355–360 (2012).
[CrossRef] [PubMed]

Carr, A.

T. Rohwer, S. Hellmann, M. Wiesenmayer, C. Sohrt, A. Stange, B. Slomski, A. Carr, Y. Liu, L. M. Avila, M. Kalläne et al., “Collapse of long-range charge order tracked by time-resolved photoemission at high momenta,” Nature 471, 490–493 (2011).
[CrossRef] [PubMed]

Caspani, L.

Catoire, F.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nature Physics 4, 386–389 (2008).
[CrossRef]

Cavalieri, A.

A. Cavalieri, N. Müller, T. Uphues, V. Yakovlev, A. Baltuška, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[CrossRef] [PubMed]

Cerullo, G.

G. Cerullo, S. De Silvestri, “Ultrafast optical parametric amplifiers,” Review of Scientific Instruments 74, 1–18 (2003).
[CrossRef]

Chang, D.

Charbonneau-Lefort, M.

Chen, M.

Chen, M.-C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mcke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernndez-Garca, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef] [PubMed]

Chirla, R.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nature Physics 4, 386–389 (2008).
[CrossRef]

Chiu, C.-c.

C. T. Middleton, P. Marek, P. Cao, C.-c. Chiu, S. Singh, A. M. Woys, J. J. de Pablo, D. P. Raleigh, M. T. Zanni, “Two-dimensional infrared spectroscopy reveals the complex behaviour of an amyloid fibril inhibitor,” Nature chemistry 4, 355–360 (2012).
[CrossRef] [PubMed]

Cirelli, C.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-Samha, L. B. Madsen, U. Keller, “Atto-clock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Physics 8, 76–80 (2011).
[CrossRef]

Clerici, M.

Colosimo, P.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nature Physics 4, 386–389 (2008).
[CrossRef]

Conforti, M.

M. Conforti, F. Baronio, C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Physical Review A 81, 053841 (2010).
[CrossRef]

M. Conforti, F. Baronio, C. D. Angelis, “From femtosecond infrared to picosecond visible pulses: temporal shaping with high-efficiency conversion,” Opt. Lett. 32, 1779–1781 (2007).
[CrossRef] [PubMed]

Corkum, P. B.

De Angelis, C.

M. Conforti, F. Baronio, C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Physical Review A 81, 053841 (2010).
[CrossRef]

de Pablo, J. J.

C. T. Middleton, P. Marek, P. Cao, C.-c. Chiu, S. Singh, A. M. Woys, J. J. de Pablo, D. P. Raleigh, M. T. Zanni, “Two-dimensional infrared spectroscopy reveals the complex behaviour of an amyloid fibril inhibitor,” Nature chemistry 4, 355–360 (2012).
[CrossRef] [PubMed]

De Silvestri, S.

G. Cerullo, S. De Silvestri, “Ultrafast optical parametric amplifiers,” Review of Scientific Instruments 74, 1–18 (2003).
[CrossRef]

Demmler, S.

Deng, Y.

DeSalvo, R.

R. DeSalvo, A. Said, D. Hagan, E. Van Stryland, M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quant. Electron. 32, 1324–1333 (1996).
[CrossRef]

Diddams, S. A.

Dierolf, V.

DiMauro, L. F.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nature Physics 4, 386–389 (2008).
[CrossRef]

Dimitrovski, D.

A. N. Pfeiffer, C. Cirelli, M. Smolarski, D. Dimitrovski, M. Abu-Samha, L. B. Madsen, U. Keller, “Atto-clock reveals natural coordinates of the laser-induced tunnelling current flow in atoms,” Nature Physics 8, 76–80 (2011).
[CrossRef]

Doumy, G.

P. Colosimo, G. Doumy, C. I. Blaga, J. Wheeler, C. Hauri, F. Catoire, J. Tate, R. Chirla, A. M. March, G. G. Paulus, H. G. Muller, P. Agostini, L. F. DiMauro, “Scaling strong-field interactions towards the classical limit,” Nature Physics 4, 386–389 (2008).
[CrossRef]

Drescher, M.

A. Cavalieri, N. Müller, T. Uphues, V. Yakovlev, A. Baltuška, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[CrossRef] [PubMed]

Drobshoff, A. D.

Druon, F.

Echenique, P. M.

A. Cavalieri, N. Müller, T. Uphues, V. Yakovlev, A. Baltuška, B. Horvath, B. Schmidt, L. Blümel, R. Holzwarth, S. Hendel, M. Drescher, U. Kleineberg, P. M. Echenique, R. Kienberger, F. Krausz, U. Heinzmann, “Attosecond spectroscopy in condensed matter,” Nature 449, 1029–1032 (2007).
[CrossRef] [PubMed]

Eidam, T.

Eikema, K.

S. Witte, K. Eikema, “Ultrafast optical parametric chirped-pulse amplification,” Selected Topics in IEEE J. Quant. Electron. 18, 296–307 (2012).
[CrossRef]

Falk, M.

Fattahi, H.

Fejer, M.

C. Lynch, D. Bliss, T. Zens, A. Lin, J. Harris, P. Kuo, M. Fejer, “Growth of mm-thick orientation-patterned GaAs for IR and THz generation,” Journal of Crystal Growth 310, 5241–5247 (2008).
[CrossRef]

Fejer, M. M.

C. R. Phillips, J. S. Pelc, M. M. Fejer, “Parametric processes in quasi-phasematching gratings with random duty cycle errors,” J. Opt. Soc. Am. B 30, 982–993 (2013).
[CrossRef]

V. J. Hernandez, C. V. Bennett, B. D. Moran, A. D. Drobshoff, D. Chang, C. Langrock, M. M. Fejer, M. Ibsen, “104 MHz rate single-shot recording with subpicosecond resolution using temporal imaging,” Opt. Express 21, 196–203 (2013).
[CrossRef] [PubMed]

C. R. Phillips, C. Langrock, D. Chang, Y. W. Lin, L. Gallmann, M. M. Fejer, “Apodization of chirped quasi-phasematching devices,” J. Opt. Soc. Am. B 30, 1551–1568 (2013).
[CrossRef]

C. R. Phillips, L. Gallmann, M. M. Fejer, “Design of quasi-phasematching gratings via convex optimization,” Opt. Express 21, 10139–10159 (2013).
[CrossRef] [PubMed]

B. W. Mayer, C. R. Phillips, L. Gallmann, M. M. Fejer, U. Keller, “Sub-four-cycle laser pulses directly from a high-repetition-rate optical parametric chirped-pulse amplifier at 3.4 μm,” Opt. Lett. 38, 4265–4268 (2013).
[CrossRef] [PubMed]

C. Heese, C. R. Phillips, B. W. Mayer, L. Gallmann, M. M. Fejer, U. Keller, “75 MW few-cycle mid-infrared pulses from a collinear apodized APPLN-based OPCPA,” Opt. Express 20, 26888–26894 (2012).
[CrossRef] [PubMed]

C. Heese, C. R. Phillips, L. Gallmann, M. M. Fejer, U. Keller, “Role of apodization in optical parametric amplifiers based on aperiodic quasi-phasematching gratings,” Opt. Express 20, 18066–18071 (2012).
[CrossRef] [PubMed]

C. R. Phillips, J. Jiang, C. Mohr, A. C. Lin, C. Langrock, M. Snure, D. Bliss, M. Zhu, I. Hartl, J. S. Harris, M. E. Fermann, M. M. Fejer, “Widely tunable midinfrared difference frequency generation in orientation-patterned gaas pumped with a femtosecond tm-fiber system,” Opt. Lett. 37, 2928–2930 (2012).
[CrossRef] [PubMed]

C. R. Phillips, M. M. Fejer, “Adiabatic optical parametric oscillators: steady-state and dynamical behavior,” Opt. Express 20, 2466–2482 (2012).
[CrossRef] [PubMed]

C. R. Phillips, J. S. Pelc, M. M. Fejer, “Continuous wave monolithic quasi-phase-matched optical parametric oscillator in periodically poled lithium niobate,” Opt. Lett. 36, 2973–2975 (2011).
[CrossRef] [PubMed]

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Nature (2)

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Supplementary Material (2)

» Media 1: AVI (2748 KB)     
» Media 2: AVI (2870 KB)     

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Figures (7)

Fig. 1
Fig. 1

Schematic overview of the mid-infrared OPCPA setup. DM: dichroic mirrors. DM1: reflective 1064 nm / transmissive 1560 nm & 3400 nm, DM2: reflective 1560 nm / transmissive 3400 nm. The OPA2 and OPA3 amplification stages are seeded by the 1560-nm signal output beams from OPA1 and OPA2, respectively; the 3400-nm idler output beams from OPA1 and OPA2 are discarded. For OPA3, the signal output is discarded, and the idler output is compressed in a bulk sapphire rod.

Fig. 2
Fig. 2

(a) Example evolution of the three waves in a cw OPA interaction. For small ρ, the amplification corresponds closely to Eqs. (9) and (10). For larger ρ, the interaction approaches the adiabatic frequency conversion case [8, 9], and for ρ ≫ 1 (corresponding to DFG or SFG rather than OPA), correspond to the case considered in [7]. The predicted conversion efficiency increases with both ΛR,p and ρ, as can be seen from (b). The turning points ztp,j appearing in Eq. (10) are the two points where the normalized position coordinate (zzpm)/(2γp) = ±1: the ρ = 10−8 curve in the figure clearly shows that the exponential gain takes place between these two points. Note also that zpm is frequency dependent due to the dispersion of the material, so different wavelengths are amplified around different longitudinal positions. (b) Simulated pump depletion ηp = |Ap(L)/Ap(0)|2 as a function of ΛR,p (which determines the small-signal OPA gain) and ρ (which denotes the ratio of input signal and pump photon fluxes, and hence how much gain is required in order to saturate the pump). Contours are labelled with values of ηp. The grating length is chosen such that L ≫ 2Ldeph in each case [Ldeph defined in Eq. (14)], and hence has L negligible impact on the pump depletion .

Fig. 3
Fig. 3

(a) Simulated normalized gain rate Γ/γp0 of non-collinear gain guided modes, for different normalized angles and values of ΛR,p. The Λ R , p 1 = 0 case corresponds to an unchirped grating. This figure is adapted from Fig. 2 of [3] and Fig. 12 of [52], with minor modifications to notation. (b) Geometric mean angle θis versus idler wavelength, for two particular grating k-vectors (chosen to satisfy collinear phase-matching for 3 or 4 μm). The maximum angle occurs at degeneracy.

Fig. 4
Fig. 4

(a) Schematic of a QPM grating with random duty cycle (RDC) errors. Horizontal dashed lines indicate the ideal, equally-spaced domain boundary positions. Elements of the domain boundary vectors z (with RDC errors) and z0 (ideal) are indicated. (b) Fourier spectra |(k)|2 with parameters σz = 0.5 μm and a 10-mm crystal, and approximately a 30 μm average period. For the averaged case (black curve), averaging is performed over 250 gratings. The vertical dashed lines show the spatial frequencies corresponding to phase-matching for some additional processes (signal-pump SFG; idler-pump SFG; and pump SHG). (c) The same curves as (b), but shown on a linear scale in the vicinity of first-order QPM. This plot reveals the influence of RDC errors on the nominal ’tuning curve’ of the device.

Fig. 5
Fig. 5

Coincidentally phase-matched processes, assuming a pump wavelength of 1.064 μm, as a function of the long-wave idler wavelength. The legend indicates the type of interaction (SHG, OPA, or SFG) and the frequencies involved. The desired OPA interaction is ωp = ωi + ωs; the corresponding curve is indicated. For each process, we consider phase-matching for the nearest-odd-order of QPM (except for pump SHG process, for which we show 4th- and 5th-order QPM).

Fig. 6
Fig. 6

Numerical example including several carrier waves. The pump and seeded idler wavelengths are 1.064-μm and 3.8-μm, respectively. The legend shows the frequency of each wave included in the model. The sign of the chirp rate (sgn(Δk′)) is (a) positive (showing significant coupling to unwanted field envelopes and hence distortion of the desired OPA process), and (b) negative (showing negligible distortions). The parameters are given in the text

Fig. 7
Fig. 7

Illustration of group velocity walk-off effects in saturated-pump OPCPA. (a) Negative signal GDD ( Media 1), (b) Positive signal GDD ( Media 2). The figures and movies show the evolution of cross- frequency resolved optical gating (FROG) spectrograms (dB scale; 400 fs gate pulse) of the unseeded wave (in this case, the long-wavelength idler) as it propagates through the QPM grating. The pump pulse is 12 ps long and the 1.55-μm signal input is stretched from 30 fs to 6 ps with pure second-order phase. The z-dependence of Kg is shown in the inset. The first ∼10 mm of the grating is a highly phase mismatched region, added to illustrate the relevant dynamics: this region allows the secondary pulse to propagate away from the main pulse, making it easier to distinguish; in a practical device, this region would not be included. The current position in the grating is marked for each frame.

Tables (4)

Tables Icon

Table 1 Summary of basic quantities defined in the paper

Tables Icon

Table 2 Summary of basic chirped QPM OPCPA related quantities

Tables Icon

Table 3 Summary of definitions used primarily in sections 4, 5, and 6.

Tables Icon

Table 4 Summary of definitions used primarily in section 7.

Equations (38)

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A ˜ j ( ω ω j ) z + L ^ j ( ω ) A ˜ j ( ω ω j ) = i ω 2 u ( ω ) k e ( ω ) c 2 ε 0 [ P N L , j ] ( ω ω j ) .
L ^ j ( ω ) = i 2 ( k e ( ω ) k o ( ω ) 2 2 x 2 + 1 k e ( ω ) 2 y 2 ) + i [ k e ( ω ) k e ( ω j ) ω ω j v ref ] .
E ˜ ( ω ) u ( ω ) = 1 2 j A ˜ j ( ω ω j ) e i k e ( ω j ) z ,
P N L , j ( t ) ε 0 = d 33 2 k , l m d m ¯ [ ( X j , k l e + i ( Δ k j , k l z m ϕ G ( z ) ) ) A k ( t ) A l ( t ) + ( 2 X k , j l e i ( Δ k j , k l z m ϕ G ( z ) ) ) A k ( t ) A l ( t ) * ] ,
X j , k l = { 0 , ω j ω k + ω l 1 , ω j = ω k + ω l .
Δ k j , k l = k e ( ω j ) k e ( ω k ) k e ( ω l ) .
d ( z ) d 33 = sgn [ cos ( ϕ G ( z ) ) cos ( π D ( z ) ) ] d 0 ¯ ( z ) + m = m 0 d m ¯ ( z ) exp ( i m ϕ G ( z ) )
d A i , s d z = i ω i , s ( d 33 d 1 ¯ ) n i , s c A p A s , i * exp [ i 0 z Δ β ( z ) d z ]
d A p d z = i ω p ( d 33 d 1 ¯ ) n p c A i A s exp [ + i 0 z Δ β ( z ) d z ] ,
G s = exp ( 2 π γ p 2 | Δ k | )
G s ( Ω ) exp [ 2 z t p , 1 ( Ω ) z t p , 2 ( Ω ) γ p ( Ω ) 2 ( Δ k 0 ( Ω ) K g ( z ) 2 ) 2 d z ] ,
γ p ( Ω ) 2 = ( ω i Ω ) ( ω s + Ω ) ( d 1 ¯ d 33 ) 2 n e ( ω i Ω ) n e ( ω s + Ω ) c 2 2 n e ( ω p ) ε 0 c I p ( τ s ( ω s + Ω ) ) ,
Δ k 0 ( Ω ) = k e ( ω p ) k e ( ω s + Ω ) k e ( ω i Ω ) ,
Δ k 0 ( Ω ) K g ( z p m ( Ω ) ) = 0 .
L deph = 2 γ p | Δ k | .
Δ k OPA | Δ k | L 4 γ p 0 Δ k B W 4 γ p 0 .
Λ R , p γ p 0 2 | Δ k | = 4 ω i ω s ω p ( d 1 ¯ d 33 ) 2 π ε 0 c 4 n i n s ξ p P p k | Δ k | L .
Δ k = k p k s k i K g
k j z ^ k e 1 1 2 [ ( k j x ^ k o ) 2 + ( k j y ^ k e ) 2 ] .
Δ k z ^ Δ β + j = i , s [ k e ( ω j ) 2 k o ( ω j ) 2 k x 2 + 1 2 k e ( ω j ) k y 2 ]
θ i s = ± | k | k e ( ω i ) k e ( ω s ) ,
Δ k z ^ Δ β + k e ( ω p ) 2 θ i s 2 .
θ i s γ p w p 1 π Λ R , p .
θ i s , max ( Ω ) Re 2 ( K g , max Δ k 0 ( Ω ) ) k p ,
P p k > π 3 ε 0 n i n s n p c 3 4 ω i ω s d 33 2 d 1 2 ( Λ R , p θ i s , max ) 2 ,
P p k > ( 0.56 MW ) × Λ R , p 2 .
| g ˜ z ( k ) | 2 = e k 2 σ z 2 | g ˜ z 0 ( k ) | 2 + N ( π k L ) 2 ( 1 e k 2 σ z 2 ) ,
U S H U p 1 3 ( 1 e Δ k SHG 2 σ z 2 Δ k SHG 2 σ z 2 ) ( π σ z l D ) 2 ( n i n s n S H n p ω p 2 ω i ω s d SHG 2 d OPA 2 ) ( γ p 2 L l D ) .
U TPA U p 24 35 ( U S H U p ) 2 ( β TPA I p , p k L )
Δ k s i ( DFG ) = k e ( ω s ) k e ( ω s ω i ) k e ( ω i ) ,
τ u w , eff ( z ) = τ u w ( 0 , Ω p m ( z ) ) + v u w ( Ω p m ( z ) ) 1 z ,
v u w , eff ( z ) 1 = d τ u w , eff d z = 1 v u w ( Ω p m ( z ) ) + ( d τ s w ( 0 , Ω ) d Ω | Ω = Ω p m β u w , G V D ( Ω p m ( z ) ) z ) d Ω p m d z .
d Ω p m d z = d K g d z d Δ k 0 d Ω | Ω = Ω p m 1 = Δ k ( z ) δ ν u w , s w ( Ω p m ) 1
v amp ( z ) 1 = d d z ( τ s w ( z , Ω p m ( z ) ) ) = 1 v s w ( Ω p m ( z ) ) ( τ s w Ω | Ω = Ω p m ( z ) + β s w , GVD ( Ω p m ( z ) ) z ) Δ k ( z ) δ ν u w , s w ( Ω p m ( z ) ) .
( v u w , eff ( z ) 1 v amp ( z ) 1 ) ( v amp ( z ) 1 v p 1 ) < 0 .
β s w , GDD Δ k > ( v u w 1 v s w 1 ) ( v s w 1 v p 1 ) .
τ p ( Δ k OPA γ p 0 2 c + 4 γ p 0 c ) δ n g Λ R , p ,
χ T ( 3 ) ( Ω ) = 16 d T 2 3 n T c Ω α T + i ( n T + n g ) ( Ω Ω p m ) .

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