Abstract

Evolution of lasers in Kerr nonlinear materials is inextricably linked with unstable behavior. Current research has investigated the growth of optical Kerr instability out of noise, which results in phenomena such as conical emission and filamentation in bulk materials, and modulation instability in optical fibers. Here, we suggest that seeding Kerr instability in dielectrics can be used for wideband optical amplification ranging from the second harmonic of the pump laser to the mid-infrared. Our theoretical feasibility analysis focuses on the infrared. We find that one- to two-cycle pulse amplification by 3–4 orders of magnitude in the wavelength range of 1–14 μm is feasible with currently available laser sources. Final output energies in the range of a few tens of μJ are achievable corresponding to about 0.25% of the pump energy. Such intense ultrashort mid-infrared radiation sources will substantially impact research in nonlinear spectroscopy, strong-field physics, attosecond science, and ultrafast laser electron accelerators.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

G. Vampa, T. J. Hammond, M. Nesrallah, A. Yu Naumov, P. B. Corkum, and T. Brabec, “Light amplification by seeded Kerr instability,” Science 359, 673–675 (2018).

2017 (1)

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
[Crossref]

2016 (3)

C. Manzoni and G. Cerullo, “Design criteria for ultrafast optical parametric amplifiers,” J. Opt. 18, 103501 (2016).
[Crossref]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352, 795–797 (2016).
[Crossref]

M. I. M. Abdul Khudus, F. De Lucia, C. Corbari, T. Lee, P. Horak, P. Sazio, and G. Brambilla, “Phase matched parametric amplification via four-wave mixing in optical microfibers,” Opt. Lett. 41, 761–764 (2016).
[Crossref]

2014 (2)

L. Gallais and M. Commandré, “Laser-induced damage thresholds of bulk and coating optical materials at 1030  nm, 500  fs,” Appl. Opt. 53, A186–A196 (2014).
[Crossref]

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

2013 (2)

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

P. Malevich, G. Andriukaitis, T. Flöry, A. J. Verhoef, A. Fernández, S. Ališauskas, A. Pugžlys, A. Baltuška, L. H. Tan, C. F. Chua, and P. B. Phua, “High energy and average power femtosecond laser for driving mid-infrared optical parametric amplifiers,” Opt. Lett. 38, 2746–2749 (2013).
[Crossref]

2011 (3)

E. Rubino, J. Darginavičius, D. Faccio, P. Di Trapani, A. Piskarskas, and A. Dubietis, “Generation of broadly tunable sub-30-fs infrared pulses by four-wave optical parametric amplification,” Opt. Lett. 36, 382–384 (2011).
[Crossref]

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

P. Béjot, B. Kibler, E. Hertz, B. Lavorel, and O. Faucher, “General approach to spatiotemporal modulational instability processes,” Phys. Rev. A 83, 013830 (2011).
[Crossref]

2010 (1)

2008 (1)

R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[Crossref]

2007 (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[Crossref]

2004 (2)

F. Min, X. Yun, W. Quing, and S. Jie-Long, “Modulation instability of non-paraxial beams for self-focusing Kerr media,” J. Shanghai Univ. 8, 159–163 (2004).
[Crossref]

X. Gu, S. Akturk, and R. Trebino, “Spatial chirp in ultrafast optics,” Opt. Commun. 242, 599–604 (2004).
[Crossref]

2002 (1)

1996 (1)

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

1992 (1)

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, “Spatiotemporal instabilities in dispersive nonlinear media,” Phys. Rev. A 46, 4202–4208 (1992).
[Crossref]

1991 (1)

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[Crossref]

1977 (1)

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[Crossref]

1976 (1)

H. H. Li, “Refractive index of alkali halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 5, 329–528 (1976).
[Crossref]

1968 (1)

J. P. Hurrell, S. P. S. Porto, T. C. Damen, and S. Mascarenhas, “Raman scattering from mixed KBr, KCl crystals,” Phys. Lett. A 26, 194–195 (1968).
[Crossref]

1967 (1)

L. A. Ostrovskii, “Propagation of wavepackets and space-time self-focusing in a nonlinear medium,” Sov. Phys. J. Exp. Theor. Phys. 24, 797–800 (1967).

1966 (2)

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exp. Theor. Phys. Lett. 3, 307–309 (1966).

A. R. Gee, D. C. O’shea, and H. Z. Cummins, “Raman scattering and fluorescence in calcium fluoride,” Solid State Commun. 4, 43–46 (1966).
[Crossref]

1963 (1)

Abdul Khudus, M. I. M.

Agostini, P.

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

Agrawal, G. P.

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, “Spatiotemporal instabilities in dispersive nonlinear media,” Phys. Rev. A 46, 4202–4208 (1992).
[Crossref]

Akturk, S.

X. Gu, S. Akturk, and R. Trebino, “Spatial chirp in ultrafast optics,” Opt. Commun. 242, 599–604 (2004).
[Crossref]

Alam, M. Z.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352, 795–797 (2016).
[Crossref]

Ališauskas, S.

Andriukaitis, G.

Apalkov, V.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Baltuška, A.

Béjot, P.

P. Béjot, B. Kibler, E. Hertz, B. Lavorel, and O. Faucher, “General approach to spatiotemporal modulational instability processes,” Phys. Rev. A 83, 013830 (2011).
[Crossref]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exp. Theor. Phys. Lett. 3, 307–309 (1966).

Boivin, M.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Bothschafter, E.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Boyd, R. W.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352, 795–797 (2016).
[Crossref]

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Brabec, T.

G. Vampa, T. J. Hammond, M. Nesrallah, A. Yu Naumov, P. B. Corkum, and T. Brabec, “Light amplification by seeded Kerr instability,” Science 359, 673–675 (2018).

Brambilla, G.

Campillo, A. J.

A. J. Campillo, “Small-scale self focusing,” in Self Focusing: Past and Present, R. W. Boyd, ed. (Springer, 2009).

Cao, X. D.

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, “Spatiotemporal instabilities in dispersive nonlinear media,” Phys. Rev. A 46, 4202–4208 (1992).
[Crossref]

Cerullo, G.

C. Manzoni and G. Cerullo, “Design criteria for ultrafast optical parametric amplifiers,” J. Opt. 18, 103501 (2016).
[Crossref]

Chua, C. F.

Climent, V.

Commandré, M.

Corbari, C.

Corkum, P. B.

G. Vampa, T. J. Hammond, M. Nesrallah, A. Yu Naumov, P. B. Corkum, and T. Brabec, “Light amplification by seeded Kerr instability,” Science 359, 673–675 (2018).

Couairon, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[Crossref]

Cummins, H. Z.

A. R. Gee, D. C. O’shea, and H. Z. Cummins, “Raman scattering and fluorescence in calcium fluoride,” Solid State Commun. 4, 43–46 (1966).
[Crossref]

Damen, T. C.

J. P. Hurrell, S. P. S. Porto, T. C. Damen, and S. Mascarenhas, “Raman scattering from mixed KBr, KCl crystals,” Phys. Lett. A 26, 194–195 (1968).
[Crossref]

Darginavicius, J.

De Leon, I.

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352, 795–797 (2016).
[Crossref]

De Lucia, F.

DeSalvo, R.

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

Di Trapani, P.

Dichiara, A. D.

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

Dimauro, L. F.

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

Dubietis, A.

Faccio, D.

Fan, D.

Faucher, O.

P. Béjot, B. Kibler, E. Hertz, B. Lavorel, and O. Faucher, “General approach to spatiotemporal modulational instability processes,” Phys. Rev. A 83, 013830 (2011).
[Crossref]

Fernández, A.

Fiess, M.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Flemens, N.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
[Crossref]

Flöry, T.

Gallais, L.

Gattass, R.

R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[Crossref]

Gee, A. R.

A. R. Gee, D. C. O’shea, and H. Z. Cummins, “Raman scattering and fluorescence in calcium fluoride,” Solid State Commun. 4, 43–46 (1966).
[Crossref]

Ghimire, S.

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

Glass, A. J.

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[Crossref]

Gu, X.

X. Gu, S. Akturk, and R. Trebino, “Spatial chirp in ultrafast optics,” Opt. Commun. 242, 599–604 (2004).
[Crossref]

Hagan, D. J.

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

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[Crossref]

Hammond, T. J.

G. Vampa, T. J. Hammond, M. Nesrallah, A. Yu Naumov, P. B. Corkum, and T. Brabec, “Light amplification by seeded Kerr instability,” Science 359, 673–675 (2018).

Hertz, E.

P. Béjot, B. Kibler, E. Hertz, B. Lavorel, and O. Faucher, “General approach to spatiotemporal modulational instability processes,” Phys. Rev. A 83, 013830 (2011).
[Crossref]

Hofstetter, M.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Holzner, S.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Hong, K.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
[Crossref]

Horak, P.

Hurrell, J. P.

J. P. Hurrell, S. P. S. Porto, T. C. Damen, and S. Mascarenhas, “Raman scattering from mixed KBr, KCl crystals,” Phys. Lett. A 26, 194–195 (1968).
[Crossref]

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[Crossref]

Ibrahim, H.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Jie-Long, S.

F. Min, X. Yun, W. Quing, and S. Jie-Long, “Modulation instability of non-paraxial beams for self-focusing Kerr media,” J. Shanghai Univ. 8, 159–163 (2004).
[Crossref]

Kärtner, F. X.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
[Crossref]

Kibler, B.

P. Béjot, B. Kibler, E. Hertz, B. Lavorel, and O. Faucher, “General approach to spatiotemporal modulational instability processes,” Phys. Rev. A 83, 013830 (2011).
[Crossref]

Kienberger, R.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Krausz, F.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Krogen, P.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
[Crossref]

Lanzis, J.

Laramée, A.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Lavorel, B.

P. Béjot, B. Kibler, E. Hertz, B. Lavorel, and O. Faucher, “General approach to spatiotemporal modulational instability processes,” Phys. Rev. A 83, 013830 (2011).
[Crossref]

Lebrun, G.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Lee, T.

Légaré, F.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Li, H. H.

H. H. Li, “Refractive index of alkali halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 5, 329–528 (1976).
[Crossref]

Liang, H.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
[Crossref]

Liou, L. W.

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, “Spatiotemporal instabilities in dispersive nonlinear media,” Phys. Rev. A 46, 4202–4208 (1992).
[Crossref]

Malevich, P.

Malitson, I. H.

Manzoni, C.

C. Manzoni and G. Cerullo, “Design criteria for ultrafast optical parametric amplifiers,” J. Opt. 18, 103501 (2016).
[Crossref]

Mascarenhas, S.

J. P. Hurrell, S. P. S. Porto, T. C. Damen, and S. Mascarenhas, “Raman scattering from mixed KBr, KCl crystals,” Phys. Lett. A 26, 194–195 (1968).
[Crossref]

Mazur, E.

R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[Crossref]

McKinstrie, C. J.

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, “Spatiotemporal instabilities in dispersive nonlinear media,” Phys. Rev. A 46, 4202–4208 (1992).
[Crossref]

Mendoza-Yero, O.

Milam, D.

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[Crossref]

Min, F.

F. Min, X. Yun, W. Quing, and S. Jie-Long, “Modulation instability of non-paraxial beams for self-focusing Kerr media,” J. Shanghai Univ. 8, 159–163 (2004).
[Crossref]

Minguez-Vega, G.

Moses, J.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
[Crossref]

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[Crossref]

Nesrallah, M.

G. Vampa, T. J. Hammond, M. Nesrallah, A. Yu Naumov, P. B. Corkum, and T. Brabec, “Light amplification by seeded Kerr instability,” Science 359, 673–675 (2018).

O’shea, D. C.

A. R. Gee, D. C. O’shea, and H. Z. Cummins, “Raman scattering and fluorescence in calcium fluoride,” Solid State Commun. 4, 43–46 (1966).
[Crossref]

Ostrovskii, L. A.

L. A. Ostrovskii, “Propagation of wavepackets and space-time self-focusing in a nonlinear medium,” Sov. Phys. J. Exp. Theor. Phys. 24, 797–800 (1967).

Ozaki, T.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids II (Academic, 1991).

Phua, P. B.

Piskarskas, A.

Poitras, F.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Porto, S. P. S.

J. P. Hurrell, S. P. S. Porto, T. C. Damen, and S. Mascarenhas, “Raman scattering from mixed KBr, KCl crystals,” Phys. Lett. A 26, 194–195 (1968).
[Crossref]

Pugžlys, A.

Quing, W.

F. Min, X. Yun, W. Quing, and S. Jie-Long, “Modulation instability of non-paraxial beams for self-focusing Kerr media,” J. Shanghai Univ. 8, 159–163 (2004).
[Crossref]

Reis, D. A.

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

Rubino, E.

Said, A. A.

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

Sazio, P.

Schmidt, B. E.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Schultze, M.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Schweinberger, W.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Sheik Bahae, M.

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

Sheik-Bahae, M.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[Crossref]

Sistrunk, E.

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

Sommer, A.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Stockman, M. I.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Suchowski, H.

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
[Crossref]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exp. Theor. Phys. Lett. 3, 307–309 (1966).

Tan, L. H.

Thiré, N.

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Trebino, R.

X. Gu, S. Akturk, and R. Trebino, “Spatial chirp in ultrafast optics,” Opt. Commun. 242, 599–604 (2004).
[Crossref]

Vampa, G.

G. Vampa, T. J. Hammond, M. Nesrallah, A. Yu Naumov, P. B. Corkum, and T. Brabec, “Light amplification by seeded Kerr instability,” Science 359, 673–675 (2018).

Van Stryland, A. W.

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

Van Stryland, E. W.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[Crossref]

Verhoef, A. J.

Weber, M. J.

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[Crossref]

Wen, S.

Yakovlev, V. S.

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Yu Naumov, A.

G. Vampa, T. J. Hammond, M. Nesrallah, A. Yu Naumov, P. B. Corkum, and T. Brabec, “Light amplification by seeded Kerr instability,” Science 359, 673–675 (2018).

Yun, X.

F. Min, X. Yun, W. Quing, and S. Jie-Long, “Modulation instability of non-paraxial beams for self-focusing Kerr media,” J. Shanghai Univ. 8, 159–163 (2004).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. Milam, M. J. Weber, and A. J. Glass, “Nonlinear refractive index of fluoride crystals,” Appl. Phys. Lett. 31, 822–825 (1977).
[Crossref]

IEEE J. Quantum Electron. (2)

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

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[Crossref]

J. Exp. Theor. Phys. Lett. (1)

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” J. Exp. Theor. Phys. Lett. 3, 307–309 (1966).

J. Opt. (1)

C. Manzoni and G. Cerullo, “Design criteria for ultrafast optical parametric amplifiers,” J. Opt. 18, 103501 (2016).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. Ref. Data (1)

H. H. Li, “Refractive index of alkali halides and its wavelength and temperature derivatives,” J. Phys. Chem. Ref. Data 5, 329–528 (1976).
[Crossref]

J. Shanghai Univ. (1)

F. Min, X. Yun, W. Quing, and S. Jie-Long, “Modulation instability of non-paraxial beams for self-focusing Kerr media,” J. Shanghai Univ. 8, 159–163 (2004).
[Crossref]

Nat. Commun. (1)

B. E. Schmidt, N. Thiré, M. Boivin, A. Laramée, F. Poitras, G. Lebrun, T. Ozaki, H. Ibrahim, and F. Légaré, “Frequency domain optical parametric amplification,” Nat. Commun. 5, 3643 (2014).
[Crossref]

Nat. Photonics (2)

R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[Crossref]

P. Krogen, H. Suchowski, H. Liang, N. Flemens, K. Hong, F. X. Kärtner, and J. Moses, “Generation and multi-octave shaping of mid-infrared intense single-cycle pulses,” Nat. Photonics 11, 222–226 (2017).
[Crossref]

Nat. Phys. (1)

S. Ghimire, A. D. Dichiara, E. Sistrunk, P. Agostini, L. F. Dimauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7, 138–141 (2011).
[Crossref]

Nature (1)

M. Schultze, E. Bothschafter, A. Sommer, S. Holzner, W. Schweinberger, M. Fiess, M. Hofstetter, R. Kienberger, V. Apalkov, V. S. Yakovlev, M. I. Stockman, and F. Krausz, “Controlling dielectrics with the electric field of light,” Nature 493, 75–78 (2013).
[Crossref]

Opt. Commun. (1)

X. Gu, S. Akturk, and R. Trebino, “Spatial chirp in ultrafast optics,” Opt. Commun. 242, 599–604 (2004).
[Crossref]

Opt. Lett. (4)

Phys. Lett. A (1)

J. P. Hurrell, S. P. S. Porto, T. C. Damen, and S. Mascarenhas, “Raman scattering from mixed KBr, KCl crystals,” Phys. Lett. A 26, 194–195 (1968).
[Crossref]

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[Crossref]

Phys. Rev. A (2)

L. W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, “Spatiotemporal instabilities in dispersive nonlinear media,” Phys. Rev. A 46, 4202–4208 (1992).
[Crossref]

P. Béjot, B. Kibler, E. Hertz, B. Lavorel, and O. Faucher, “General approach to spatiotemporal modulational instability processes,” Phys. Rev. A 83, 013830 (2011).
[Crossref]

Science (2)

G. Vampa, T. J. Hammond, M. Nesrallah, A. Yu Naumov, P. B. Corkum, and T. Brabec, “Light amplification by seeded Kerr instability,” Science 359, 673–675 (2018).

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352, 795–797 (2016).
[Crossref]

Solid State Commun. (1)

A. R. Gee, D. C. O’shea, and H. Z. Cummins, “Raman scattering and fluorescence in calcium fluoride,” Solid State Commun. 4, 43–46 (1966).
[Crossref]

Sov. Phys. J. Exp. Theor. Phys. (1)

L. A. Ostrovskii, “Propagation of wavepackets and space-time self-focusing in a nonlinear medium,” Sov. Phys. J. Exp. Theor. Phys. 24, 797–800 (1967).

Other (5)

G. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

A. J. Campillo, “Small-scale self focusing,” in Self Focusing: Past and Present, R. W. Boyd, ed. (Springer, 2009).

E. D. Palik, Handbook of Optical Constants of Solids II (Academic, 1991).

https://doi.org/10.6084/m9.figshare.5878747 .

Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. Schematic of KIA. Left: parametric four-wave mixing of type 2ωp(ωp±Ωs)=ωpΩs, where ωp is the pump frequency and ωp<Ωs<ωp is the seed frequency. Right: there exist transverse wavevectors for which unstable behavior occurs. Gain is maximum for the transverse wavevector k¯(Ωs). The instability evolves as ϵx(Ωs)=exp(i(ωp+Ωs)tiK(Ωs)x) and ϵx*(Ωs)=exp(i(ωpΩs)t+iK(Ωs)x). Here, K(Ωs)=(k¯(Ωs),0,Kz(Ωs)). In contrast to conventional four wave mixing, phase matching of the instability is automatically fulfilled as the wavevector of the instability K(Ωs) fulfills the relation K(Ωs)=2Kp+K(Ωs). For a more detailed discussion, see Eq. (12) and below.
Fig. 2.
Fig. 2. Plane wave amplification in a CaF2 crystal with Kerr coefficient n2=2×1016  cm2/W and pump peak intensity Ip=50  TW/cm2. (a) Kerr instability gain g versus ωs/ωp (seed over pump frequency) and k/kp (transverse over pump wavevector). Pump wavelength λp=0.85  μm. The white line indicates k¯ at which maximum gain g¯=g(k¯) [Eq. (9)] occurs. (b) g¯ versus seed frequency νs (bottom) and seed wavelength λs (top). The red dotted line represents absorption. [(b), (c)] λp=0.85 and 2.1 μm correspond to the blue full and green dashed curves, respectively. (c) Angle of inclination θs between pump and seed beam [Eq. (13)] at which maximum amplification takes place versus νs and λs.
Fig. 3.
Fig. 3. Plane wave amplification in a KBr crystal. Panels (a)–(c) correspond to those in Fig. 2. Here we have a nonlinear refractive index of n2=6×1016  cm2/W and a pump peak intensity of Ip=8  TW/cm2. In panel (a), the pump wavelength is λp=2.1  μm. All other parameters and definitions in panels (a)–(c) are the same as those in the caption of Fig. 2.
Fig. 4.
Fig. 4. KIA of a single-cycle pulse τ(0)=Ts=2π/ωs in CaF2. Here n2=2×1016  cm2/W, pump peak intensity Ip=50  TW/cm2, pump wavelength λp=0.85  μm, and amplifier length l=8/g¯. Pump beam radius and duration are denoted with, respectively, wp and τp [see text above Eq. (20)]. Initial seed beam radii, wx(0)=wy(0), are determined from Eq. (20). (a) Seed pulse energy increase, Ws(l)/Ws(0), from Eq. (19) versus ωs/ωp (seed over pump frequency). The black dashed line corresponds to the cw limit exp(g¯l)=exp(8)3000. (b) Amplified seed pulse duration τ(l)/Ts (blue, full); transform-limited amplified seed pulse duration τg(l)/Ts [defined above Eq. (19)] (green, dashed); and group velocity walk-off between pump and seed, |Δβ1|l/Ts, versus ωs/ωp (red, dotted). (c) Amplified seed beam radii wx(l)/λs (blue, full) and wy(l)/λs (green, dashed) versus ωs/ωp. Initial beam radius is not plotted as wy(l)wx(0)=wy(0). Shift of seed beam center, |ξcr|, is defined below Eq. (18) (red dotted). (d) Minimum required pump energy Wp (blue, full) [see text above Eq. (20)] and corresponding seed energy Ws(l) (green, dashed) versus ωs/ωp. (e) Dispersive length ld/l (blue, full) and nonlinear length ln/l (green, dashed) versus ωs/ωp. (f) Damage threshold intensity Ith versus ωs/ωp. The dashed lines indicate Ip=Ith.
Fig. 5.
Fig. 5. KIA of a single-cycle pulse τ(0)=Ts in KBr. Here n2=6×1016  cm2/W, pump peak intensity is Ip=8  TW/cm2, and pump wavelength is λp=2.1  μm. Panels (a)–(f) correspond to those in Fig. 4 (see the caption of Fig. 4 for a complete description).
Fig. 6.
Fig. 6. [(a), (c)] Spatio-spectral and [(b), (d)] spatiotemporal intensity profiles of seed pulses amplified in CaF2 for ωs/ωp=0.2 and 0.4, respectively. The parameters are the same as in Fig. 4. Peaks are normalized to unity. Time is shown with reference to time t0 of the pulse peak and is normalized to the optical cycle Ts. The white lines indicate the transverse pulse maximum.

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

(z2+2t2c2n2)ϵx=Ep2t2c2χ(3)P(ϵx),
[(zikp)2+kv2k2]v˜x=kn2v˜x()*,
[(z+ikp)2+kv()2k2]v˜x()*=kn()2v˜x.
Dg(Ω)=c1(ηg(Ω)ωp+ηu(Ω)Ω),
Du(Ω)=c1((ηp+ηg(Ω))Ω+ηu(Ω)ωp).
[(Kv2Du2σ2)+(Du2kp2)(σ21)+k2]24kp2(Kv+Duσ)2kn2kn()2=0
4(Kv+σDu)2(kp2(σDu)2)4(Kv+σDu)×σDu(κ2k2)(κ2k2)2+(knkn())2=0.
Ku(k,Ω)=σDu[112κ2k2kp2(σDu)2],
Kg(k,Ω)=12kp(κ2k2)2δ4kp2(σDu)2.
k¯(Ω)={κforκ200forκ2<0
g¯(Ω)={kpδ4(κ2k¯2)2kp2(σDu)2elsewhere0for  κ2<0,κ4>δ4.
δ2(Ω)=knkn()kpkp2(σDu)2.
v˜x(z=0)=(2π)3/2Esδ(kxk¯s)δ(ky)δ(ΩΩs)
ϵx(x,t)=Esexp(12g¯(Ωs)liKsx+iωst).
θs=θ(Ωs)=arctan(k¯s/Kzs).
v˜x(0)=23/2Esf(Ω)ΔxΔyΔωexp((kxk¯sΔx)2(kyΔy)2),
gg¯g2(kxk¯)2,g2=2kpk¯2[δ2(kp2(σDu)2)]1.
v˜x(k,l,Ω)=v˜x(0)exp(iσDul+12g¯l)exp(i2αlky2)×exp(l2(g2+iα)(kxk¯)2iαlk¯(kxk¯)),
v˜x(x,y,l,Ω)=Esτwxwy2qxqyf(Ω)exp((γ2iϰ)l+ik¯sx)×exp((xxc)2qxy2qy)
|v˜x(x,y,l,Ω)|2=(Esτwxwy)22|qxqy||f(Ω)|2exp(Γl)×exp(2(xξcr)2wx2(l)2y2wy2(l)).
Ws(l)Ws(0)=wxRe[qx(Ωs)]ττg(l)exp(Γsl+(Γsl)22τg2(l)),
lsf2nnnp=wp=r(wx(l)+0.5|ξcr|)

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