Abstract

Supercontinuum generation from nanojoule femtosecond lasers is well known in photonic-crystal fibers, channel waveguides, and micro-resonators, in which strong confinement shapes their dispersion and provides sufficient intensity for self-phase modulation, four-wave mixing, and Raman scattering to cause substantial spectral broadening. Until now, supercontinuum generation in bulk media has not been observed at equivalent energies, but here we introduce a new mechanism combining second- and third-order nonlinearities to produce broadband visible light in orientation-patterned gallium phosphide. A supercontinuum from the blue/green to the red is produced from 32 nJ 1040 nm femtosecond pulses, and a nonlinear-envelope-equation model including ${\chi ^{(2)}}$ and $ {\chi ^{(3)}} $ nonlinearities implies that high-order parametric gain pumped by the second-harmonic light of the laser and seeded by self-phase-modulated sidebands is responsible.

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References

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2018 (2)

J. Wei, J. M. Murray, J. O. Barnes, D. M. Krein, P. G. Schunemann, and S. Guha, Opt. Mater. Express 8, 485 (2018).
[Crossref]

L. Maidment, O. Kara, P. G. Schunemann, J. Piper, K. McEwan, and D. T. Reid, Appl. Phys. B 124, 143 (2018).
[Crossref]

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Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

2016 (1)

2015 (1)

L. A. Pomeranz, P. G. Schunemann, D. J. Magarrell, J. C. McCarthy, K. T. Zawilski, and D. E. Zelmon, Proc. SPIE 9347, 93470K (2015).
[Crossref]

2012 (1)

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

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[Crossref]

S. Wabnitz and V. V. Kozlov, J. Opt. Soc. Am. B 27, 1707 (2010).
[Crossref]

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[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, IEEE Photon. J. 2, 600 (2010).
[Crossref]

2007 (2)

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[Crossref]

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[Crossref]

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L. A. Ostrovskii, JETP Lett. 5, 272 (1967).

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P. J. Dean and D. G. Thomas, Phys. Rev. 150, 690 (1966).
[Crossref]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. A 127, 1918 (1962).
[Crossref]

Andreana, M.

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. A 127, 1918 (1962).
[Crossref]

Barnes, J. O.

Baronio, F.

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

M. Conforti, F. Baronio, C. De Angelis, M. Marangoni, and G. Cerullo, J. Opt. Soc. Am. B 28, 892 (2011).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, Phys. Rev. A 81, 053841 (2010).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, IEEE Photon. J. 2, 600 (2010).
[Crossref]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. A 127, 1918 (1962).
[Crossref]

Cerullo, G.

Chai, L.

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

Chihara, M.

Coleman, P. D.

Conforti, M.

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

M. Conforti, F. Baronio, C. De Angelis, M. Marangoni, and G. Cerullo, J. Opt. Soc. Am. B 28, 892 (2011).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, Phys. Rev. A 81, 053841 (2010).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, IEEE Photon. J. 2, 600 (2010).
[Crossref]

Couderc, V.

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

De Angelis, C.

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

M. Conforti, F. Baronio, C. De Angelis, M. Marangoni, and G. Cerullo, J. Opt. Soc. Am. B 28, 892 (2011).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, Phys. Rev. A 81, 053841 (2010).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, IEEE Photon. J. 2, 600 (2010).
[Crossref]

Dean, P. J.

P. J. Dean and D. G. Thomas, Phys. Rev. 150, 690 (1966).
[Crossref]

Deng, Y.

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

DeSalvo, R.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. A 127, 1918 (1962).
[Crossref]

Ebert, C. B.

C. B. Ebert, L. A. Eyres, M. M. Fejer, and J. S. Harris, J. Cryst. Growth 201–202, 187 (1999).
[Crossref]

Eyres, L. A.

C. B. Ebert, L. A. Eyres, M. M. Fejer, and J. S. Harris, J. Cryst. Growth 201–202, 187 (1999).
[Crossref]

Feinberg, J.

Fejer, M. M.

Fermann, M. E.

Guha, S.

Hagan, D. J.

Harris, J. S.

C. B. Ebert, L. A. Eyres, M. M. Fejer, and J. S. Harris, J. Cryst. Growth 201–202, 187 (1999).
[Crossref]

Hartl, I.

Hu, M.

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

Itoh, M.

Jiang, J.

Kara, O.

L. Maidment, O. Kara, P. G. Schunemann, J. Piper, K. McEwan, and D. T. Reid, Appl. Phys. B 124, 143 (2018).
[Crossref]

Kondo, T.

T. Matsushita, T. Yamamoto, and T. Kondo, Jpn. J. Appl. Phys. 46, L408 (2007).
[Crossref]

Kozlov, V. V.

Krein, D. M.

Kuroda, K.

Langrock, C.

Lee, N. P.

Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

Leproux, P.

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

Li, Y.

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

Liu, F.

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

Loparo, Z. E.

Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

Magarrell, D. J.

L. A. Pomeranz, P. G. Schunemann, D. J. Magarrell, J. C. McCarthy, K. T. Zawilski, and D. E. Zelmon, Proc. SPIE 9347, 93470K (2015).
[Crossref]

Maidment, L.

L. Maidment, O. Kara, P. G. Schunemann, J. Piper, K. McEwan, and D. T. Reid, Appl. Phys. B 124, 143 (2018).
[Crossref]

L. Maidment, P. G. Schunemann, and D. T. Reid, Opt. Lett. 41, 4261 (2016).
[Crossref]

Marangoni, M.

Matsushita, T.

T. Matsushita, T. Yamamoto, and T. Kondo, Jpn. J. Appl. Phys. 46, L408 (2007).
[Crossref]

McCarthy, J. C.

L. A. Pomeranz, P. G. Schunemann, D. J. Magarrell, J. C. McCarthy, K. T. Zawilski, and D. E. Zelmon, Proc. SPIE 9347, 93470K (2015).
[Crossref]

McEwan, K.

L. Maidment, O. Kara, P. G. Schunemann, J. Piper, K. McEwan, and D. T. Reid, Appl. Phys. B 124, 143 (2018).
[Crossref]

Mirov, S. B.

Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

Modotto, D.

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

Murray, J. M.

Ogura, I.

Okamura, H.

Okazaki, Y.

Ostrovskii, L. A.

L. A. Ostrovskii, JETP Lett. 5, 272 (1967).

Parsons, D. F.

Pelc, J. S.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. A 127, 1918 (1962).
[Crossref]

Phillips, C. R.

Piper, J.

L. Maidment, O. Kara, P. G. Schunemann, J. Piper, K. McEwan, and D. T. Reid, Appl. Phys. B 124, 143 (2018).
[Crossref]

Pomeranz, L. A.

L. A. Pomeranz, P. G. Schunemann, D. J. Magarrell, J. C. McCarthy, K. T. Zawilski, and D. E. Zelmon, Proc. SPIE 9347, 93470K (2015).
[Crossref]

Reid, D. T.

L. Maidment, O. Kara, P. G. Schunemann, J. Piper, K. McEwan, and D. T. Reid, Appl. Phys. B 124, 143 (2018).
[Crossref]

L. Maidment, P. G. Schunemann, and D. T. Reid, Opt. Lett. 41, 4261 (2016).
[Crossref]

Ru, Q.

Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

Schunemann, P. G.

J. Wei, J. M. Murray, J. O. Barnes, D. M. Krein, P. G. Schunemann, and S. Guha, Opt. Mater. Express 8, 485 (2018).
[Crossref]

L. Maidment, O. Kara, P. G. Schunemann, J. Piper, K. McEwan, and D. T. Reid, Appl. Phys. B 124, 143 (2018).
[Crossref]

Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

L. Maidment, P. G. Schunemann, and D. T. Reid, Opt. Lett. 41, 4261 (2016).
[Crossref]

L. A. Pomeranz, P. G. Schunemann, D. J. Magarrell, J. C. McCarthy, K. T. Zawilski, and D. E. Zelmon, Proc. SPIE 9347, 93470K (2015).
[Crossref]

Sheik-Bahae, M.

Shimura, T.

Stegeman, G.

Sun, Q.

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

Thomas, D. G.

P. J. Dean and D. G. Thomas, Phys. Rev. 150, 690 (1966).
[Crossref]

Tonello, A.

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

Van Stryland, E. W.

Vanherzeele, H.

Vasilyev, S.

Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

Vodopyanov, K. L.

Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

Wabnitz, S.

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

S. Wabnitz and V. V. Kozlov, J. Opt. Soc. Am. B 27, 1707 (2010).
[Crossref]

Wang, C.

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

Wei, J.

Xing, Q.

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

Yamamoto, T.

T. Matsushita, T. Yamamoto, and T. Kondo, Jpn. J. Appl. Phys. 46, L408 (2007).
[Crossref]

Zawilski, K. T.

L. A. Pomeranz, P. G. Schunemann, D. J. Magarrell, J. C. McCarthy, K. T. Zawilski, and D. E. Zelmon, Proc. SPIE 9347, 93470K (2015).
[Crossref]

Zelmon, D. E.

L. A. Pomeranz, P. G. Schunemann, D. J. Magarrell, J. C. McCarthy, K. T. Zawilski, and D. E. Zelmon, Proc. SPIE 9347, 93470K (2015).
[Crossref]

Zhong, K.

Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

Appl. Opt. (1)

Appl. Phys. B (1)

L. Maidment, O. Kara, P. G. Schunemann, J. Piper, K. McEwan, and D. T. Reid, Appl. Phys. B 124, 143 (2018).
[Crossref]

IEEE Photon. J. (1)

M. Conforti, F. Baronio, and C. De Angelis, IEEE Photon. J. 2, 600 (2010).
[Crossref]

J. Cryst. Growth (1)

C. B. Ebert, L. A. Eyres, M. M. Fejer, and J. S. Harris, J. Cryst. Growth 201–202, 187 (1999).
[Crossref]

J. Opt. (1)

F. Liu, Y. Li, Q. Xing, L. Chai, M. Hu, C. Wang, Y. Deng, Q. Sun, and C. Wang, J. Opt. 12, 95201 (2010).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

L. A. Ostrovskii, JETP Lett. 5, 272 (1967).

Jpn. J. Appl. Phys. (1)

T. Matsushita, T. Yamamoto, and T. Kondo, Jpn. J. Appl. Phys. 46, L408 (2007).
[Crossref]

Opt. Express (1)

Opt. Fiber Technol. (1)

F. Baronio, M. Conforti, C. De Angelis, D. Modotto, S. Wabnitz, M. Andreana, A. Tonello, P. Leproux, and V. Couderc, Opt. Fiber Technol. 18, 283 (2012).
[Crossref]

Opt. Lett. (5)

Opt. Mater. Express (1)

Phys. Rev. (1)

P. J. Dean and D. G. Thomas, Phys. Rev. 150, 690 (1966).
[Crossref]

Phys. Rev. A (2)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. A 127, 1918 (1962).
[Crossref]

M. Conforti, F. Baronio, and C. De Angelis, Phys. Rev. A 81, 053841 (2010).
[Crossref]

Proc. SPIE (2)

Q. Ru, K. Zhong, N. P. Lee, Z. E. Loparo, P. G. Schunemann, S. Vasilyev, S. B. Mirov, and K. L. Vodopyanov, Proc. SPIE 10088, 1008809 (2017).
[Crossref]

L. A. Pomeranz, P. G. Schunemann, D. J. Magarrell, J. C. McCarthy, K. T. Zawilski, and D. E. Zelmon, Proc. SPIE 9347, 93470K (2015).
[Crossref]

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Figures (6)

Fig. 1.
Fig. 1. Supercontinuum generation experiment. Stretched pulses from an Yb:fiber laser were de-chirped in a grating compressor before being focused into an OPGaP crystal (X). The resulting supercontinuum was measured using a visible spectrometer and optical spectrum analyzer (OSA), and also with a beam profiling camera. Intense pump light was rejected using two attenuators (A), and beam profiling employed different color filters (C) to isolate: (a) pump light at 1040 nm; (b) all visible outputs; (c) wavelengths $ \lt {500}\;{\rm nm}$; (d) wavelengths at ${520}\;{\rm nm}{\rm \pm }{10}\;{\rm nm}$; and (e) wavelengths $ \gt {600}\;{\rm nm}$. Profiles were measured at different observation planes, so their relative sizes are not comparable.
Fig. 2.
Fig. 2. (a) Upper panels: output spectra at maximum pump power, recorded using a visible spectrometer and an optical spectrum analyzer. Lower panels: evolution of the supercontinuum for average pump powers from zero to 3.2 W. (b) Photograph of the visible output corresponding to approximately 450–600 nm. A weak violet color is visible at the short-wavelength edge of the image.
Fig. 3.
Fig. 3. Fundamental and high-order ($m={3 - 17}$) phase-matching loci for difference-frequency mixing in a 27 µm period OPGaP crystal of length 1 mm. Interaction efficiency, proportional to ${{\rm sinc}^2}( {\Delta kL/2} )/{m^2}$, is represented by the color map. Strong second-harmonic light centered at 520 nm (dashed line) acts as a pump to amplify neighboring longer wavelengths that satisfy a high-order phase-matching condition. The bandwidth of the 520 nm pump pulses is transferred into these signal pulses, which have sufficient spectral width to form a supercontinuum. This process is illustrated by considering how a narrow 520 nm pump spectrum (right axis) is mapped into multiple signal pulses (top axis, green). For comparison, the top axis shows in red the experimentally measured spectrum, whose maxima agree well with those predicted for $m = 5$, 7, and 9. At higher values of $m$, the experimental and calculated behaviors are more sensitive to uncertainties in the OPGaP fabrication and in the Sellmeier equations, leading to differences in the positions of the conversion maxima.
Fig. 4.
Fig. 4. Simulated evolution of the visible and near-infrared spectra after propagation through a 1 mm long OPGaP crystal fabricated with a grating period of 27 µm. The upper panels show the spectra obtained at maximum pump power (3.2 W) and the effect on these of switching off either the ${\chi ^{( 2 )}}$ or ${\chi ^{( 3 )}}$ nonlinearity.
Fig. 5.
Fig. 5. Profiles of the fundamental beam after the OPGaP crystal, showing a power-dependent self-defocusing effect, which we attribute to cascaded second-order effects. Panels (a) and (b) show, respectively, the $x$ and $y$ beam profiles at minimum (blue) and maximum (red) powers. The corresponding color maps show the beam intensity on a linear scale, indicating a divergence that approximately doubles as the power is increased from 60 mW to 3.38 W.
Fig. 6.
Fig. 6. Full-spectrum NEE simulation, showing long-wave infrared generation above 7 µm, corresponding to idler radiation from difference-frequency mixing between 520 nm and wavelengths shorter than 562 nm.

Equations (2)

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A z + i D A = i ω o 2 n o c ε o ( 1 i ω o τ ) × ( ε o χ ( 2 ) 2 [ A 2 e i ω o τ + i ω o β 1 z i β o z + 2 | A | 2 e i ω o τ i ω o β 1 z + i β o z ] + ε o χ ( 3 ) 4 [ 3 | A | 2 A + A 3 e 2 i ω o τ + i 2 ω o β 1 z 2 i β o z ] ) ,
D = n = 2 n = i n + 1 n ! β n n t n .

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