Abstract

Chirped quasi-phasematching (QPM) optical devices offer the potential for ultrawide bandwidths, high conversion efficiencies, and high amplification factors across the transparency range of QPM media. In order to properly take advantage of these devices, apodization schemes are required. We study apodization in detail for many regimes of interest, including low-gain difference frequency generation (DFG), high-gain optical parametric amplification (OPA), and high-efficiency adiabatic frequency conversion (AFC). Our analysis is also applicable to second-harmonic generation, sum frequency generation, and optical rectification. In each case, a systematic and optimized approach to grating construction is provided, and different apodization techniques are compared where appropriate. We find that nonlinear chirp apodization, where the poling period is varied smoothly, monotonically, and rapidly at the edges of the device, offers the best performance. We consider the full spatial structure of the QPM gratings in our simulations, but utilize the first order QPM approximation to obtain analytical and semi-analytical results. One application of our results is optical parametric chirped pulse amplification; we show that special care must be taken in this case to obtain high gain factors while maintaining a flat gain spectrum.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  43. J. S. Pelc, C. R. Phillips, D. Chang, C. Langrock, and M. M. Fejer, “Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors,” Opt. Lett. 36, 864–866 (2011).
    [CrossRef]
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2013 (3)

2012 (6)

2011 (5)

2010 (4)

2009 (2)

H. Steigerwald, F. Luedtke, and K. Buse, “Ultraviolet light assisted periodic poling of near-stoichiometric, magnesium-doped lithium niobate crystals,” Appl. Phys. Lett. 94, 032906 (2009).
[CrossRef]

H. Suchowski, V. Prabhudesai, D. Oron, A. Arie, and Y. Silberberg, “Robust adiabatic sum frequency conversion,” Opt. Express 17, 12731–12740 (2009).
[CrossRef]

2008 (3)

2007 (3)

2006 (1)

2005 (2)

2003 (1)

2002 (3)

2001 (2)

2000 (2)

1996 (2)

M. Taya, M. C. Bashaw, and M. M. Fejer, “Photorefractive effects in periodically poled ferroelectrics,” Opt. Lett. 21, 857–859 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

1973 (1)

M. D. Crisp, “Adiabatic-Following approximation,” Phys. Rev. A 8, 2128–2135 (1973).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Adler, F.

Afeyan, B.

Alber, M. S.

Arbore, M. A.

Arie, A.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Artigas, D.

Ashihara, S.

Asobe, M.

Baronio, F.

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

Bashaw, M. C.

Bender, C. M.

C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Vol. 1 (Springer, 1999).

Bennett, C. V.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Bostani, A.

Boyd, R. W.

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

Bramati, A.

Buryak, A. V.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Buse, K.

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

H. Steigerwald, F. Luedtke, and K. Buse, “Ultraviolet light assisted periodic poling of near-stoichiometric, magnesium-doped lithium niobate crystals,” Appl. Phys. Lett. 94, 032906 (2009).
[CrossRef]

Chang, D.

Charbonneau-Lefort, M.

Chinaglia, W.

Conforti, M.

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

Conti, C.

Crisp, M. D.

M. D. Crisp, “Adiabatic-Following approximation,” Phys. Rev. A 8, 2128–2135 (1973).
[CrossRef]

De Angelis, C.

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

Deng, Y.

Di Trapani, P.

Diddams, S. A.

Drobshoff, A. D.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Falk, M.

Fattahi, H.

Fejer, M. M.

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

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

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

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

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

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

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

C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, J. Jiang, M. E. Fermann, and 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]

J. S. Pelc, C. R. Phillips, D. Chang, C. Langrock, and M. M. Fejer, “Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors,” Opt. Lett. 36, 864–866 (2011).
[CrossRef]

J. R. Schwesyg, M. Falk, C. R. Phillips, D. H. Jundt, K. Buse, and 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, and M. M. Fejer, “Continuous wave monolithic quasi-phase-matched optical parametric oscillator in periodically poled lithium niobate,” Opt. Lett. 36, 2973–2975 (2011).
[CrossRef]

C. Heese, C. R. Phillips, L. Gallmann, M. M. Fejer, and U. Keller, “Ultrabroadband, highly flexible amplifier for ultrashort midinfrared laser pulses based on aperiodically poled Mg:LiNbO3,” Opt. Lett. 35, 2340–2342 (2010).
[CrossRef]

C. R. Phillips and M. M. Fejer, “Efficiency and phase of optical parametric amplification in chirped quasi-phase-matched gratings,” Opt. Lett. 35, 3093–3095 (2010).
[CrossRef]

C. R. Phillips and M. M. Fejer, “Stability of the singly resonant optical parametric oscillator,” J. Opt. Soc. Am. B 27, 2687–2699 (2010).
[CrossRef]

M. Charbonneau-Lefort, B. Afeyan, and 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]

M. Charbonneau-Lefort, B. Afeyan, and 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]

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

J. Huang, X. P. Xie, C. Langrock, R. V. Roussev, D. S. Hum, and M. M. Fejer, “Amplitude modulation and apodization of quasi-phase-matched interactions,” Opt. Lett. 31, 604–606 (2006).
[CrossRef]

M. Charbonneau-Lefort, M. M. Fejer, and 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]

G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B 18, 534–539 (2001).
[CrossRef]

L. Gallmann, G. Steinmeyer, U. Keller, G. Imeshev, M. M. Fejer, and J. Meyn, “Generation of sub-6 fs blue pulses by frequency doubling with quasi-phase-matching gratings,” Opt. Lett. 26, 614–616 (2001).
[CrossRef]

G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, “Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping,” J. Opt. Soc. Am. B 17, 304–318 (2000).
[CrossRef]

M. Taya, M. C. Bashaw, and M. M. Fejer, “Photorefractive effects in periodically poled ferroelectrics,” Opt. Lett. 21, 857–859 (1996).
[CrossRef]

Fermann, M.

Fermann, M. E.

Gallmann, L.

Galvanauskas, A.

Goldman, R.

R. Goldman, “Curvature formulas for implicit curves and surfaces,” Comput. Aided Geom. Des. 22, 632–658 (2005).
[CrossRef]

Gu, X.

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Harter, D.

Hartl, I.

Heese, C.

Hellström, J.

Hernandez, V. J.

Huang, J.

Hum, D. S.

Ibsen, M.

Imeshev, G.

Ishizuki, H.

Jiang, J.

Jundt, D. H.

Karpowicz, N.

Kashyap, R.

Keller, U.

Kienberger, R.

Kilius, J.

Kobayashi, T.

Krausz, F.

Kuroda, K.

Langrock, C.

Laurell, F.

Luedtke, F.

H. Steigerwald, F. Luedtke, and K. Buse, “Ultraviolet light assisted periodic poling of near-stoichiometric, magnesium-doped lithium niobate crystals,” Appl. Phys. Lett. 94, 032906 (2009).
[CrossRef]

Luther, G. G.

Magari, K.

Marcus, G.

Marsden, J. E.

Mayer, B. W.

Metzger, T.

Meyn, J.

Miller, G. D.

G. D. Miller, “Periodically poled lithium niobate: modeling, fabrication, and nonlinear-optical performance,” Ph.D. dissertation (Stanford University, 1998).

Minardi, S.

Moran, B. D.

Neely, T. W.

Nishida, Y.

Nishina, J.

Nugent-Glandorf, L.

Oron, D.

Orszag, S. A.

C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Vol. 1 (Springer, 1999).

Ossiander, M.

Pasiskevicius, V.

Pelc, J. S.

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918–1939 (1962).
[CrossRef]

Pervak, V.

Phillips, C. R.

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

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

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

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

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

J. R. Schwesyg, M. Falk, C. R. Phillips, D. H. Jundt, K. Buse, and 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, C. Langrock, J. S. Pelc, M. M. Fejer, J. Jiang, M. E. Fermann, and 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]

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

J. S. Pelc, C. R. Phillips, D. Chang, C. Langrock, and M. M. Fejer, “Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors,” Opt. Lett. 36, 864–866 (2011).
[CrossRef]

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

C. Heese, C. R. Phillips, L. Gallmann, M. M. Fejer, and U. Keller, “Ultrabroadband, highly flexible amplifier for ultrashort midinfrared laser pulses based on aperiodically poled Mg:LiNbO3,” Opt. Lett. 35, 2340–2342 (2010).
[CrossRef]

C. R. Phillips and M. M. Fejer, “Efficiency and phase of optical parametric amplification in chirped quasi-phase-matched gratings,” Opt. Lett. 35, 3093–3095 (2010).
[CrossRef]

C. R. Phillips and M. M. Fejer, “Stability of the singly resonant optical parametric oscillator,” J. Opt. Soc. Am. B 27, 2687–2699 (2010).
[CrossRef]

Prabhudesai, V.

Reid, D. T.

Robbins, J. M.

Roussev, R. V.

Schwarz, A.

Schwesyg, J. R.

Shimura, T.

Silberberg, Y.

Skryabin, D. V.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
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Steigerwald, H.

H. Steigerwald, F. Luedtke, and K. Buse, “Ultraviolet light assisted periodic poling of near-stoichiometric, magnesium-doped lithium niobate crystals,” Appl. Phys. Lett. 94, 032906 (2009).
[CrossRef]

Steinmeyer, G.

Suchowski, H.

Suzuki, H.

Tadanaga, O.

Taira, T.

Taya, M.

Tehranchi, A.

Tillman, K. A.

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Trapani, P. D.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

Trillo, S.

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–857 (2002).
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Ueffing, M.

Umeki, T.

Valiulis, G.

White, R. B.

R. B. White, Asymptotic Analysis of Differential Equations (World Scientific, 2005).

Xie, X. P.

Yanagawa, T.

Appl. Phys. Lett. (1)

H. Steigerwald, F. Luedtke, and K. Buse, “Ultraviolet light assisted periodic poling of near-stoichiometric, magnesium-doped lithium niobate crystals,” Appl. Phys. Lett. 94, 032906 (2009).
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Comput. Aided Geom. Des. (1)

R. Goldman, “Curvature formulas for implicit curves and surfaces,” Comput. Aided Geom. Des. 22, 632–658 (2005).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (11)

M. Charbonneau-Lefort, B. Afeyan, and 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]

C. R. Phillips and M. M. Fejer, “Stability of the singly resonant optical parametric oscillator,” J. Opt. Soc. Am. B 27, 2687–2699 (2010).
[CrossRef]

J. R. Schwesyg, M. Falk, C. R. Phillips, D. H. Jundt, K. Buse, and M. M. Fejer, “Pyroelectrically induced photorefractive damage in magnesium-doped lithium niobate crystals,” J. Opt. Soc. Am. B 28, 1973–1987 (2011).
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G. Imeshev, M. A. Arbore, M. M. Fejer, A. Galvanauskas, M. Fermann, and D. Harter, “Ultrashort-pulse second-harmonic generation with longitudinally nonuniform quasi-phase-matching gratings: pulse compression and shaping,” J. Opt. Soc. Am. B 17, 304–318 (2000).
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G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, “Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media,” J. Opt. Soc. Am. B 17, 932–941 (2000).
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G. Imeshev, M. M. Fejer, A. Galvanauskas, and D. Harter, “Pulse shaping by difference-frequency mixing with quasi-phase-matching gratings,” J. Opt. Soc. Am. B 18, 534–539 (2001).
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M. Charbonneau-Lefort, B. Afeyan, and 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).
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C. Conti, S. Trillo, P. Di Trapani, J. Kilius, A. Bramati, S. Minardi, W. Chinaglia, and G. Valiulis, “Effective lensing effects in parametric frequency conversion,” J. Opt. Soc. Am. B 19, 852–857 (2002).
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S. Ashihara, J. Nishina, T. Shimura, and K. Kuroda, “Soliton compression of femtosecond pulses in quadratic media,” J. Opt. Soc. Am. B 19, 2505–2510 (2002).
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A. Bostani, A. Tehranchi, and R. Kashyap, “Engineering of effective second-order nonlinearity in uniform and chirped gratings,” J. Opt. Soc. Am. B 29, 2929–2934 (2012).
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C. R. Phillips, J. S. Pelc, and M. M. Fejer, “Parametric processes in quasi-phasematching gratings with random duty cycle errors,” J. Opt. Soc. Am. B 30, 982–993 (2013).
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Opt. Express (7)

Opt. Lett. (15)

C. Heese, C. R. Phillips, L. Gallmann, M. M. Fejer, and U. Keller, “Ultrabroadband, highly flexible amplifier for ultrashort midinfrared laser pulses based on aperiodically poled Mg:LiNbO3,” Opt. Lett. 35, 2340–2342 (2010).
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C. R. Phillips and M. M. Fejer, “Efficiency and phase of optical parametric amplification in chirped quasi-phase-matched gratings,” Opt. Lett. 35, 3093–3095 (2010).
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C. R. Phillips, J. S. Pelc, and M. M. Fejer, “Continuous wave monolithic quasi-phase-matched optical parametric oscillator in periodically poled lithium niobate,” Opt. Lett. 36, 2973–2975 (2011).
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J. S. Pelc, C. R. Phillips, D. Chang, C. Langrock, and M. M. Fejer, “Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors,” Opt. Lett. 36, 864–866 (2011).
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L. Gallmann, G. Steinmeyer, U. Keller, G. Imeshev, M. M. Fejer, and J. Meyn, “Generation of sub-6 fs blue pulses by frequency doubling with quasi-phase-matching gratings,” Opt. Lett. 26, 614–616 (2001).
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M. Taya, M. C. Bashaw, and M. M. Fejer, “Photorefractive effects in periodically poled ferroelectrics,” Opt. Lett. 21, 857–859 (1996).
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K. A. Tillman, D. T. Reid, D. Artigas, J. Hellström, V. Pasiskevicius, and F. Laurell, “Low-threshold femtosecond optical parametric oscillator based on chirped-pulse frequency conversion,” Opt. Lett. 28, 543–545 (2003).
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M. Charbonneau-Lefort, M. M. Fejer, and 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).
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J. Huang, X. P. Xie, C. Langrock, R. V. Roussev, D. S. Hum, and M. M. Fejer, “Amplitude modulation and apodization of quasi-phase-matched interactions,” Opt. Lett. 31, 604–606 (2006).
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T. Umeki, M. Asobe, Y. Nishida, O. Tadanaga, K. Magari, T. Yanagawa, and H. Suzuki, “Widely tunable 3.4 μm band difference frequency generation using apodized χ(2) grating,” Opt. Lett. 32, 1129–1131 (2007).
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K. A. Tillman and D. T. Reid, “Monolithic optical parametric oscillator using chirped quasi-phase matching,” Opt. Lett. 32, 1548–1550 (2007).
[CrossRef]

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

C. R. Phillips, C. Langrock, J. S. Pelc, M. M. Fejer, J. Jiang, M. E. Fermann, and 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]

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, and N. Karpowicz, “Carrier-envelope-phase-stable, 1.2 mJ, 1.5 cycle laserpulses at 2.1 μm,” Opt. Lett. 37, 4973–4975 (2012).
[CrossRef]

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

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, “χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons,” Opt. Quantum Electron. 28, 1691–1740 (1996).
[CrossRef]

Phys. Rep. (1)

A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[CrossRef]

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M. Conforti, F. Baronio, and C. De Angelis, “Nonlinear envelope equation for broadband optical pulses in quadratic media,” Phys. Rev. A 81, 053841 (2010).
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R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

G. D. Miller, “Periodically poled lithium niobate: modeling, fabrication, and nonlinear-optical performance,” Ph.D. dissertation (Stanford University, 1998).

C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Vol. 1 (Springer, 1999).

R. B. White, Asymptotic Analysis of Differential Equations (World Scientific, 2005).

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