Abstract

Numerical solutions to the nonlinear coupled-wave equations of a counterpropagating quasi-phase-matched device are analyzed by numerical methods for both second-harmonic generation and cascaded processes. Normalized derivations for second-harmonic generation efficiency are also presented. The nonlinear phase shifts acquired in this device by cascaded second-order processes are promising in all-optical-switching applications. Specifically, a π/2 phase shift is shown to be achievable with 42 times less input intensity than the standard Type I configuration and 100% throughput. The effects of metallic mirrors are also presented. Careful use of the phase mismatch is shown to compensate for nonideal mirrors. Finally, conservation of power in this configuration is briefly investigated.

© 1998 Optical Society of America

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    [CrossRef]
  2. G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).
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    [CrossRef]
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  6. N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. 66, 806–808 (1989).
  7. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  21. M. A. Krumbugel, J. N. Sweetser, D. N. Fittinghoff, K. W. DeLong, R. Trebino, “Ultrafast optical switching by use of fully phase-matched cascaded second-order nonlinearities in a polarization-gate geometry,” Opt. Lett. 22, 245–247 (1997).
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  23. L. Torner, C. R. Menyuk, G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615–1617 (1994).
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  24. W. E. Torruellas, W. Zuo, L. Torner, G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949–1951 (1995).
    [CrossRef] [PubMed]
  25. W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
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    [CrossRef] [PubMed]
  27. V. Couderc, O. Guy, E. Roisse, A. Barthelemy, “Modelocking of CW Nd:YAG laser using nonlinear polarisation evolution in type II frequency doubling crystal,” Electron. Lett. 34, 672–673 (1998).
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  28. M. Zgonik, P. Gunter, “Cascading nonlinearities in optical four-wave mixing,” J. Opt. Soc. Am. B 13, 570–576 (1996).
    [CrossRef]
  29. M. Houe, P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
    [CrossRef]
  30. J. Pierce, D. Lowenthal, “Periodically poled materials & devices,” Lasers Optron. 16, 25–27 (1997).
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  32. M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
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  33. G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834–1836 (1997).
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    [CrossRef]
  45. K. Mizuuchi, K. Yamamoto, “Generation of 340-nm light by frequency doubling of a laser diode in bulk periodically poled LiTaO3,” Opt. Lett. 21, 107–109 (1996).
    [CrossRef] [PubMed]
  46. K. Mizuuchi, K. Yamamoto, M. Kato, “Generation of ultraviolet light by frequency doubling of a red laser diode in a first-order periodically poled bulk LiTaO3,” Appl. Phys. Lett. 70, 1201–1203 (1997).
    [CrossRef]
  47. Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
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  48. N. Hashizume, T. Tsuruzono, T. Kondo, R. Ito, “Fabrication of periodic waveguides using organic crystals and fluorinated polyimides for quasi-phase-matched second-harmonic generation,” Opt. Rev. 4, 316–320 (1997).
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1998 (2)

V. Couderc, O. Guy, E. Roisse, A. Barthelemy, “Modelocking of CW Nd:YAG laser using nonlinear polarisation evolution in type II frequency doubling crystal,” Electron. Lett. 34, 672–673 (1998).
[CrossRef]

X. Gu, R. Y. Korotkov, Y. J. Ding, J. U. Kang, J. B. Khurgin, “Backward second-harmonic generation in periodically-poled lithium niobate,” J. Opt. Soc. Am. B 15, 1561–1566 (1998).
[CrossRef]

1997 (12)

M. A. Krumbugel, J. N. Sweetser, D. N. Fittinghoff, K. W. DeLong, R. Trebino, “Ultrafast optical switching by use of fully phase-matched cascaded second-order nonlinearities in a polarization-gate geometry,” Opt. Lett. 22, 245–247 (1997).
[CrossRef] [PubMed]

M. Asobe, I. Yokohama, H. Itoh, T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes in periodically poled LiNbO3,” Opt. Lett. 22, 274–276 (1997).
[CrossRef] [PubMed]

P. Vidakovic, D. J. Lovering, J. A. Levenson, J. Webjorn, P. St. J. Russell, “Large nonlinear phase shift owing to cascaded χ(2) in quasi-phase-matched bulk LiNbO3,” Opt. Lett. 22, 277–279 (1997).
[CrossRef]

J. U. Kang, Y. J. Ding, W. K. Burns, J. S. Melinger, “Backward second-harmonic generation in periodically poled bulk LiNbO3,” Opt. Lett. 22, 862–864 (1997).
[CrossRef] [PubMed]

G. D. Landry, T. A. Maldonado, “Efficient nonlinear phase shifts due to cascaded second-order processes in a counterpropagating quasi-phase-matched configuration,” Opt. Lett. 22, 1400–1402 (1997).
[CrossRef]

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834–1836 (1997).
[CrossRef]

G. D’Alessandro, P. S. J. Russell, A. A. Wheeler, “Nonlinear dynamics of a backward quasi-phase-matched second-harmonic generator,” Phys. Rev. A 55, 3211–3218 (1997).
[CrossRef]

G. Blau, H. Hubner, B. Schnabel, “Second-harmonic generation using subwavelength gratings in planar waveguides,” Pure Appl. Opt. 6, L23–L28 (1997).
[CrossRef]

K. Mizuuchi, K. Yamamoto, M. Kato, “Generation of ultraviolet light by frequency doubling of a red laser diode in a first-order periodically poled bulk LiTaO3,” Appl. Phys. Lett. 70, 1201–1203 (1997).
[CrossRef]

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

N. Hashizume, T. Tsuruzono, T. Kondo, R. Ito, “Fabrication of periodic waveguides using organic crystals and fluorinated polyimides for quasi-phase-matched second-harmonic generation,” Opt. Rev. 4, 316–320 (1997).
[CrossRef]

J. Pierce, D. Lowenthal, “Periodically poled materials & devices,” Lasers Optron. 16, 25–27 (1997).

1996 (10)

A. Laureti-Palma, S. Trillo, G. Assanto, A. D. Capobianco, C. De Angelis, “All-optical switching via quadratic nonlinearities in a Mach–Zehnder device with soliton-like pulses,” Nonlinear Opt. Principles Mater. Phenomena Devices 16, 303–320 (1996).

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, 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]

Z. Wang, D. J. Hagan, E. W. Van Stryland, G. Assanto, “Phase-insensitive, single wavelength, all-optical transistor based on second order nonlinearities,” Electron. Lett. 32, 1135–1136 (1996).
[CrossRef]

M. Zgonik, P. Gunter, “Cascading nonlinearities in optical four-wave mixing,” J. Opt. Soc. Am. B 13, 570–576 (1996).
[CrossRef]

M. Picciau, G. Leo, G. Assanto, “Versatile bistable gate based on quadratic cascading in a Bragg periodic structure,” J. Opt. Soc. Am. B 13, 661–670 (1996).
[CrossRef]

K. Mizuuchi, K. Yamamoto, “Generation of 340-nm light by frequency doubling of a laser diode in bulk periodically poled LiTaO3,” Opt. Lett. 21, 107–109 (1996).
[CrossRef] [PubMed]

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
[CrossRef] [PubMed]

W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, R. L. Byer, “93% pump depletion, 3.5-W continuous-wave, singly resonant optical parametric oscillator,” Opt. Lett. 21, 1336–1338 (1996).
[CrossRef] [PubMed]

Y. J. Ding, J. B. Khurgin, “Second-harmonic generation based on quasi-phase matching: a novel configuration,” Opt. Lett. 21, 1445–1447 (1996).
[CrossRef] [PubMed]

1995 (7)

G. Cerullo, S. De Silvestri, A. Monguzzi, D. Segala, V. Magni, “Self-starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities,” Opt. Lett. 20, 746–748 (1995).
[CrossRef] [PubMed]

G. Assanto, “Transistor action through nonlinear cascading in Type II interactions,” Opt. Lett. 20, 1595–1597 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, W. Zuo, L. Torner, G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949–1951 (1995).
[CrossRef] [PubMed]

G. Assanto, Z. Wang, D. J. Hagan, E. W. Van Stryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[CrossRef]

L. Lefort, A. Barthelemy, “All-optical transistor action by polarisation rotation during type-II phase-matched second harmonic generation,” Electron. Lett. 31, 910–911 (1995).
[CrossRef]

W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

M. Houe, P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

1994 (5)

R. Schiek, “All-optical switching in the directional coupler caused by nonlinear refraction due to cascaded second-order nonlinearity,” Opt. Quantum Electron. 26, 415–431 (1994).
[CrossRef]

C. R. Menyuk, R. Schiek, L. Torner, “Solitary waves due to χ(2):χ(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1994).
[CrossRef]

W. P. Risk, S. D. Lau, M. A. McCord, “Third-order guided-wave distributed Bragg reflectors fabricated by ion-exchange in KTiOPO4,” IEEE Photon. Technol. Lett. 6, 406–408 (1994).
[CrossRef]

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, “Phase-controlled transistor action by cascading of second-order nonlinearities in KTP,” Opt. Lett. 19, 1305–1307 (1994).
[CrossRef] [PubMed]

L. Torner, C. R. Menyuk, G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615–1617 (1994).
[CrossRef] [PubMed]

1993 (2)

M. L. Sundheimer, C. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, “Large nonlinear phase modulation in quasi-phase-matched KTP waveguides as a result of cascaded second-order processes,” Opt. Lett. 18, 1397–1399 (1993).
[CrossRef] [PubMed]

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1326 (1993).
[CrossRef]

1992 (2)

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

1989 (1)

N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. 66, 806–808 (1989).

1983 (1)

C. Liao, P. Bundman, G. I. Stegeman, “Second harmonic generation with surface guided waves in signal processing geometries,” J. Appl. Phys. 54, 6213–6217 (1983).
[CrossRef]

1982 (1)

G. R. Meredith, “Second-order cascading in third-order nonlinear optical processes,” J. Chem. Phys. 77, 5863–5871 (1982).
[CrossRef]

1979 (1)

1972 (1)

J. M. R. Thomas, J. P. E. Taran, “Pulse distortions in mismatched second harmonic generation,” Opt. Commun. 4, 329–334 (1972).
[CrossRef]

1967 (1)

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

1962 (1)

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

1959 (1)

J. M. Manley, H. E. Rowe, “General energy in nonlinear reactances,” Proc. IRE 47, 2115–2116 (1959).

Alexander, J. I.

Amano, M.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Armstrong, J. A.

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

Asobe, M.

Assanto, G.

Z. Wang, D. J. Hagan, E. W. Van Stryland, G. Assanto, “Phase-insensitive, single wavelength, all-optical transistor based on second order nonlinearities,” Electron. Lett. 32, 1135–1136 (1996).
[CrossRef]

A. Laureti-Palma, S. Trillo, G. Assanto, A. D. Capobianco, C. De Angelis, “All-optical switching via quadratic nonlinearities in a Mach–Zehnder device with soliton-like pulses,” Nonlinear Opt. Principles Mater. Phenomena Devices 16, 303–320 (1996).

M. Picciau, G. Leo, G. Assanto, “Versatile bistable gate based on quadratic cascading in a Bragg periodic structure,” J. Opt. Soc. Am. B 13, 661–670 (1996).
[CrossRef]

G. Assanto, Z. Wang, D. J. Hagan, E. W. Van Stryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[CrossRef]

G. Assanto, “Transistor action through nonlinear cascading in Type II interactions,” Opt. Lett. 20, 1595–1597 (1995).
[CrossRef] [PubMed]

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, “Phase-controlled transistor action by cascading of second-order nonlinearities in KTP,” Opt. Lett. 19, 1305–1307 (1994).
[CrossRef] [PubMed]

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1326 (1993).
[CrossRef]

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Baboiu, D.

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Baek, Y.

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
[CrossRef] [PubMed]

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).
[CrossRef]

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Barthelemy, A.

V. Couderc, O. Guy, E. Roisse, A. Barthelemy, “Modelocking of CW Nd:YAG laser using nonlinear polarisation evolution in type II frequency doubling crystal,” Electron. Lett. 34, 672–673 (1998).
[CrossRef]

L. Lefort, A. Barthelemy, “All-optical transistor action by polarisation rotation during type-II phase-matched second harmonic generation,” Electron. Lett. 31, 910–911 (1995).
[CrossRef]

Batchko, R. G.

Baumann, I.

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).
[CrossRef]

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
[CrossRef] [PubMed]

Belashenkov, N. R.

N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. 66, 806–808 (1989).

Bierlein, J. D.

Blau, G.

G. Blau, H. Hubner, B. Schnabel, “Second-harmonic generation using subwavelength gratings in planar waveguides,” Pure Appl. Opt. 6, L23–L28 (1997).
[CrossRef]

Bloembergen, N.

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

Bosenberg, W. R.

Bosshard, C.

Boyd, R. W.

See, for example, R. W. Boyd, Nonlinear Optics (Academic, San Diego, 1992).

Bundman, P.

C. Liao, P. Bundman, G. I. Stegeman, “Second harmonic generation with surface guided waves in signal processing geometries,” J. Appl. Phys. 54, 6213–6217 (1983).
[CrossRef]

Burns, W. K.

Byer, R. L.

Capobianco, A. D.

A. Laureti-Palma, S. Trillo, G. Assanto, A. D. Capobianco, C. De Angelis, “All-optical switching via quadratic nonlinearities in a Mach–Zehnder device with soliton-like pulses,” Nonlinear Opt. Principles Mater. Phenomena Devices 16, 303–320 (1996).

Cerullo, G.

Couderc, V.

V. Couderc, O. Guy, E. Roisse, A. Barthelemy, “Modelocking of CW Nd:YAG laser using nonlinear polarisation evolution in type II frequency doubling crystal,” Electron. Lett. 34, 672–673 (1998).
[CrossRef]

D’Alessandro, G.

G. D’Alessandro, P. S. J. Russell, A. A. Wheeler, “Nonlinear dynamics of a backward quasi-phase-matched second-harmonic generator,” Phys. Rev. A 55, 3211–3218 (1997).
[CrossRef]

De Angelis, C.

A. Laureti-Palma, S. Trillo, G. Assanto, A. D. Capobianco, C. De Angelis, “All-optical switching via quadratic nonlinearities in a Mach–Zehnder device with soliton-like pulses,” Nonlinear Opt. Principles Mater. Phenomena Devices 16, 303–320 (1996).

De Silvestri, S.

DeLong, K. W.

DeSalvo, R.

Ding, Y. J.

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed. (Springer, Berlin, 1997).
[CrossRef]

Drobshoff, A.

Ducuino, J.

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

Fejer, M. M.

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834–1836 (1997).
[CrossRef]

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Fittinghoff, D. N.

Gagarskii, S. V.

N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. 66, 806–808 (1989).

Gase, T.

T. Gase, W. Karthe, “Cascading the second-order susceptibility in poled polymers by quasi-phase matching,” in Quantum Electronics and Laser Science Conference, Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 78.

Gu, X.

Gunter, P.

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed. (Springer, Berlin, 1997).
[CrossRef]

Guy, O.

V. Couderc, O. Guy, E. Roisse, A. Barthelemy, “Modelocking of CW Nd:YAG laser using nonlinear polarisation evolution in type II frequency doubling crystal,” Electron. Lett. 34, 672–673 (1998).
[CrossRef]

Hagan, D.

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Hagan, D. J.

Z. Wang, D. J. Hagan, E. W. Van Stryland, G. Assanto, “Phase-insensitive, single wavelength, all-optical transistor based on second order nonlinearities,” Electron. Lett. 32, 1135–1136 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, 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]

G. Assanto, Z. Wang, D. J. Hagan, E. W. Van Stryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[CrossRef]

W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, “Phase-controlled transistor action by cascading of second-order nonlinearities in KTP,” Opt. Lett. 19, 1305–1307 (1994).
[CrossRef] [PubMed]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

Hashizume, N.

N. Hashizume, T. Tsuruzono, T. Kondo, R. Ito, “Fabrication of periodic waveguides using organic crystals and fluorinated polyimides for quasi-phase-matched second-harmonic generation,” Opt. Rev. 4, 316–320 (1997).
[CrossRef]

Hikita, M.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Houe, M.

M. Houe, P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

Hubner, H.

G. Blau, H. Hubner, B. Schnabel, “Second-harmonic generation using subwavelength gratings in planar waveguides,” Pure Appl. Opt. 6, L23–L28 (1997).
[CrossRef]

Inochkin, M. V.

N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, “Nonlinear refraction of light on second-harmonic generation,” Opt. Spectrosc. 66, 806–808 (1989).

Ito, R.

N. Hashizume, T. Tsuruzono, T. Kondo, R. Ito, “Fabrication of periodic waveguides using organic crystals and fluorinated polyimides for quasi-phase-matched second-harmonic generation,” Opt. Rev. 4, 316–320 (1997).
[CrossRef]

Itoh, H.

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Kaino, T.

Kang, J. U.

Karthe, W.

T. Gase, W. Karthe, “Cascading the second-order susceptibility in poled polymers by quasi-phase matching,” in Quantum Electronics and Laser Science Conference, Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 78.

Kato, M.

K. Mizuuchi, K. Yamamoto, M. Kato, “Generation of ultraviolet light by frequency doubling of a red laser diode in a first-order periodically poled bulk LiTaO3,” Appl. Phys. Lett. 70, 1201–1203 (1997).
[CrossRef]

Khurgin, J. B.

Kondo, T.

N. Hashizume, T. Tsuruzono, T. Kondo, R. Ito, “Fabrication of periodic waveguides using organic crystals and fluorinated polyimides for quasi-phase-matched second-harmonic generation,” Opt. Rev. 4, 316–320 (1997).
[CrossRef]

Korotkov, R. Y.

Krijnen, G.

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).
[CrossRef]

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
[CrossRef] [PubMed]

Krumbugel, M. A.

Landry, G. D.

Lau, S. D.

W. P. Risk, S. D. Lau, M. A. McCord, “Third-order guided-wave distributed Bragg reflectors fabricated by ion-exchange in KTiOPO4,” IEEE Photon. Technol. Lett. 6, 406–408 (1994).
[CrossRef]

Laureti-Palma, A.

A. Laureti-Palma, S. Trillo, G. Assanto, A. D. Capobianco, C. De Angelis, “All-optical switching via quadratic nonlinearities in a Mach–Zehnder device with soliton-like pulses,” Nonlinear Opt. Principles Mater. Phenomena Devices 16, 303–320 (1996).

Lefort, L.

L. Lefort, A. Barthelemy, “All-optical transistor action by polarisation rotation during type-II phase-matched second harmonic generation,” Electron. Lett. 31, 910–911 (1995).
[CrossRef]

Leo, G.

Levenson, J. A.

Liao, C.

C. Liao, P. Bundman, G. I. Stegeman, “Second harmonic generation with surface guided waves in signal processing geometries,” J. Appl. Phys. 54, 6213–6217 (1983).
[CrossRef]

Lovering, D. J.

Lowenthal, D.

J. Pierce, D. Lowenthal, “Periodically poled materials & devices,” Lasers Optron. 16, 25–27 (1997).

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Magni, V.

Maldonado, T. A.

Manley, J. M.

J. M. Manley, H. E. Rowe, “General energy in nonlinear reactances,” Proc. IRE 47, 2115–2116 (1959).

McCord, M. A.

W. P. Risk, S. D. Lau, M. A. McCord, “Third-order guided-wave distributed Bragg reflectors fabricated by ion-exchange in KTiOPO4,” IEEE Photon. Technol. Lett. 6, 406–408 (1994).
[CrossRef]

Melinger, J. S.

Menyuk, C. R.

W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

L. Torner, C. R. Menyuk, G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615–1617 (1994).
[CrossRef] [PubMed]

C. R. Menyuk, R. Schiek, L. Torner, “Solitary waves due to χ(2):χ(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1994).
[CrossRef]

Meredith, G. R.

G. R. Meredith, “Second-order cascading in third-order nonlinear optical processes,” J. Chem. Phys. 77, 5863–5871 (1982).
[CrossRef]

Miller, G. D.

Miyata, S.

H. S. Nalwa, T. Watanabe, S. Miyata, “Organic materials for second-order nonlinear optics,” in Nonlinear Optics of Organic Molecules and Polymers, H. S. Nalwa, S. Miyata, eds. (CRC, Boca Raton, Fla., 1997), pp. 166–167.

Mizuuchi, K.

K. Mizuuchi, K. Yamamoto, M. Kato, “Generation of ultraviolet light by frequency doubling of a red laser diode in a first-order periodically poled bulk LiTaO3,” Appl. Phys. Lett. 70, 1201–1203 (1997).
[CrossRef]

K. Mizuuchi, K. Yamamoto, “Generation of 340-nm light by frequency doubling of a laser diode in bulk periodically poled LiTaO3,” Opt. Lett. 21, 107–109 (1996).
[CrossRef] [PubMed]

Monguzzi, A.

Myers, L. E.

Nalwa, H. S.

H. S. Nalwa, T. Watanabe, S. Miyata, “Organic materials for second-order nonlinear optics,” in Nonlinear Optics of Organic Molecules and Polymers, H. S. Nalwa, S. Miyata, eds. (CRC, Boca Raton, Fla., 1997), pp. 166–167.

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed. (Springer, Berlin, 1997).
[CrossRef]

Normandin, R.

Ostrovskii, L. A.

L. A. Ostrovskii, “Self-action of light in crystals,” JETP Lett. 5, 272–275 (1967).

Paquin, R. A.

R. A. Paquin, “Properties of metals,” in Handbook of Optics, Vol II: Devices, Measurements, and Properties, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), p. 35.19.

Pershan, P. S.

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

Picciau, M.

Pierce, J.

J. Pierce, D. Lowenthal, “Periodically poled materials & devices,” Lasers Optron. 16, 25–27 (1997).

Risk, W. P.

W. P. Risk, S. D. Lau, M. A. McCord, “Third-order guided-wave distributed Bragg reflectors fabricated by ion-exchange in KTiOPO4,” IEEE Photon. Technol. Lett. 6, 406–408 (1994).
[CrossRef]

Roisse, E.

V. Couderc, O. Guy, E. Roisse, A. Barthelemy, “Modelocking of CW Nd:YAG laser using nonlinear polarisation evolution in type II frequency doubling crystal,” Electron. Lett. 34, 672–673 (1998).
[CrossRef]

Rowe, H. E.

J. M. Manley, H. E. Rowe, “General energy in nonlinear reactances,” Proc. IRE 47, 2115–2116 (1959).

Russell, P. S. J.

G. D’Alessandro, P. S. J. Russell, A. A. Wheeler, “Nonlinear dynamics of a backward quasi-phase-matched second-harmonic generator,” Phys. Rev. A 55, 3211–3218 (1997).
[CrossRef]

Russell, P. St. J.

Schiek, R.

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
[CrossRef] [PubMed]

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).
[CrossRef]

R. Schiek, “All-optical switching in the directional coupler caused by nonlinear refraction due to cascaded second-order nonlinearity,” Opt. Quantum Electron. 26, 415–431 (1994).
[CrossRef]

C. R. Menyuk, R. Schiek, L. Torner, “Solitary waves due to χ(2):χ(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1994).
[CrossRef]

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Schnabel, B.

G. Blau, H. Hubner, B. Schnabel, “Second-harmonic generation using subwavelength gratings in planar waveguides,” Pure Appl. Opt. 6, L23–L28 (1997).
[CrossRef]

Segala, D.

Sheik-Bahae, M.

Shuto, Y.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Sohler, W.

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).
[CrossRef]

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
[CrossRef] [PubMed]

Stegeman, G.

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, “Phase-controlled transistor action by cascading of second-order nonlinearities in KTP,” Opt. Lett. 19, 1305–1307 (1994).
[CrossRef] [PubMed]

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1326 (1993).
[CrossRef]

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Stegeman, G. I.

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
[CrossRef] [PubMed]

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, 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]

W. E. Torruellas, W. Zuo, L. Torner, G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949–1951 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

L. Torner, C. R. Menyuk, G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615–1617 (1994).
[CrossRef] [PubMed]

M. L. Sundheimer, C. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, “Large nonlinear phase modulation in quasi-phase-matched KTP waveguides as a result of cascaded second-order processes,” Opt. Lett. 18, 1397–1399 (1993).
[CrossRef] [PubMed]

C. Liao, P. Bundman, G. I. Stegeman, “Second harmonic generation with surface guided waves in signal processing geometries,” J. Appl. Phys. 54, 6213–6217 (1983).
[CrossRef]

R. Normandin, G. I. Stegeman, “Nondegenerate four-wave mixing in integrated optics,” Opt. Lett. 4, 58–59 (1979).
[CrossRef] [PubMed]

Sundheimer, M. L.

Sweetser, J. N.

Taran, J. P. E.

J. M. R. Thomas, J. P. E. Taran, “Pulse distortions in mismatched second harmonic generation,” Opt. Commun. 4, 329–334 (1972).
[CrossRef]

Thomas, J. M. R.

J. M. R. Thomas, J. P. E. Taran, “Pulse distortions in mismatched second harmonic generation,” Opt. Commun. 4, 329–334 (1972).
[CrossRef]

Tomaru, S.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Torner, L.

G. I. Stegeman, D. J. Hagan, 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]

W. E. Torruellas, W. Zuo, L. Torner, G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949–1951 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

L. Torner, C. R. Menyuk, G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615–1617 (1994).
[CrossRef] [PubMed]

C. R. Menyuk, R. Schiek, L. Torner, “Solitary waves due to χ(2):χ(2) cascading,” J. Opt. Soc. Am. B 11, 2434–2443 (1994).
[CrossRef]

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Torruellas, W.

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Torruellas, W. E.

W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, W. Zuo, L. Torner, G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949–1951 (1995).
[CrossRef] [PubMed]

Townsend, P. D.

M. Houe, P. D. Townsend, “An introduction to methods of periodic poling for second-harmonic generation,” J. Phys. D 28, 1747–1763 (1995).
[CrossRef]

Trebino, R.

Trillo, S.

A. Laureti-Palma, S. Trillo, G. Assanto, A. D. Capobianco, C. De Angelis, “All-optical switching via quadratic nonlinearities in a Mach–Zehnder device with soliton-like pulses,” Nonlinear Opt. Principles Mater. Phenomena Devices 16, 303–320 (1996).

Tsuruzono, T.

N. Hashizume, T. Tsuruzono, T. Kondo, R. Ito, “Fabrication of periodic waveguides using organic crystals and fluorinated polyimides for quasi-phase-matched second-harmonic generation,” Opt. Rev. 4, 316–320 (1997).
[CrossRef]

Tulloch, W. M.

van Stryland, E.

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1326 (1993).
[CrossRef]

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Van Stryland, E. W.

Vanherzeele, H.

VanStryland, E. W.

W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Vidakovic, P.

Wang, Z.

Z. Wang, D. J. Hagan, E. W. Van Stryland, G. Assanto, “Phase-insensitive, single wavelength, all-optical transistor based on second order nonlinearities,” Electron. Lett. 32, 1135–1136 (1996).
[CrossRef]

G. Assanto, Z. Wang, D. J. Hagan, E. W. Van Stryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[CrossRef]

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, “Phase-controlled transistor action by cascading of second-order nonlinearities in KTP,” Opt. Lett. 19, 1305–1307 (1994).
[CrossRef] [PubMed]

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

Watanabe, T.

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

H. S. Nalwa, T. Watanabe, S. Miyata, “Organic materials for second-order nonlinear optics,” in Nonlinear Optics of Organic Molecules and Polymers, H. S. Nalwa, S. Miyata, eds. (CRC, Boca Raton, Fla., 1997), pp. 166–167.

Webjorn, J.

Weise, D. R.

Wheeler, A. A.

G. D’Alessandro, P. S. J. Russell, A. A. Wheeler, “Nonlinear dynamics of a backward quasi-phase-matched second-harmonic generator,” Phys. Rev. A 55, 3211–3218 (1997).
[CrossRef]

Yamamoto, K.

K. Mizuuchi, K. Yamamoto, M. Kato, “Generation of ultraviolet light by frequency doubling of a red laser diode in a first-order periodically poled bulk LiTaO3,” Appl. Phys. Lett. 70, 1201–1203 (1997).
[CrossRef]

K. Mizuuchi, K. Yamamoto, “Generation of 340-nm light by frequency doubling of a laser diode in bulk periodically poled LiTaO3,” Opt. Lett. 21, 107–109 (1996).
[CrossRef] [PubMed]

Yokohama, I.

M. Asobe, I. Yokohama, H. Itoh, T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes in periodically poled LiNbO3,” Opt. Lett. 22, 274–276 (1997).
[CrossRef] [PubMed]

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[CrossRef]

Zgonik, M.

Zuo, W.

W. E. Torruellas, W. Zuo, L. Torner, G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949–1951 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

Zwillinger, D.

D. Zwillinger, Handbook of Differential Equations, 2nd ed. (Academic, San Diego, 1992).

Appl. Phys. Lett. (4)

G. Assanto, Z. Wang, D. J. Hagan, E. W. Van Stryland, “All-optical modulation via nonlinear cascading in type II second-harmonic generation,” Appl. Phys. Lett. 67, 2120–2122 (1995).
[CrossRef]

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. van Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett. 62, 1323–1326 (1993).
[CrossRef]

Y. Baek, R. Schiek, G. I. Stegeman, G. Krijnen, I. Baumann, W. Sohler, “All-optical integrated Mach–Zehnder switching due to cascaded nonlinearities,” Appl. Phys. Lett. 68, 2055–2057 (1996).
[CrossRef]

K. Mizuuchi, K. Yamamoto, M. Kato, “Generation of ultraviolet light by frequency doubling of a red laser diode in a first-order periodically poled bulk LiTaO3,” Appl. Phys. Lett. 70, 1201–1203 (1997).
[CrossRef]

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[CrossRef]

Z. Wang, D. J. Hagan, E. W. Van Stryland, G. Assanto, “Phase-insensitive, single wavelength, all-optical transistor based on second order nonlinearities,” Electron. Lett. 32, 1135–1136 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. Shuto, T. Watanabe, S. Tomaru, I. Yokohama, M. Hikita, M. Amano, “Quasi-phase-matched second-harmonic generation in diazo-dye-substituted polymer channel waveguides,” IEEE J. Quantum Electron. 33, 349–357 (1997).
[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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Nonlinear Opt. Principles Mater. Phenomena Devices (1)

A. Laureti-Palma, S. Trillo, G. Assanto, A. D. Capobianco, C. De Angelis, “All-optical switching via quadratic nonlinearities in a Mach–Zehnder device with soliton-like pulses,” Nonlinear Opt. Principles Mater. Phenomena Devices 16, 303–320 (1996).

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[CrossRef]

Opt. Lett. (18)

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, “Self-focusing and self-defocusing by cascaded second-order effects in KTP,” Opt. Lett. 17, 28–30 (1992).
[CrossRef] [PubMed]

M. L. Sundheimer, C. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, “Large nonlinear phase modulation in quasi-phase-matched KTP waveguides as a result of cascaded second-order processes,” Opt. Lett. 18, 1397–1399 (1993).
[CrossRef] [PubMed]

D. J. Hagan, Z. Wang, G. Stegeman, E. W. Van Stryland, M. Sheik-Bahae, G. Assanto, “Phase-controlled transistor action by cascading of second-order nonlinearities in KTP,” Opt. Lett. 19, 1305–1307 (1994).
[CrossRef] [PubMed]

L. Torner, C. R. Menyuk, G. I. Stegeman, “Excitation of solitons with cascaded χ(2) nonlinearities,” Opt. Lett. 19, 1615–1617 (1994).
[CrossRef] [PubMed]

G. Cerullo, S. De Silvestri, A. Monguzzi, D. Segala, V. Magni, “Self-starting mode locking of a cw Nd:YAG laser using cascaded second-order nonlinearities,” Opt. Lett. 20, 746–748 (1995).
[CrossRef] [PubMed]

G. Assanto, “Transistor action through nonlinear cascading in Type II interactions,” Opt. Lett. 20, 1595–1597 (1995).
[CrossRef] [PubMed]

W. E. Torruellas, W. Zuo, L. Torner, G. I. Stegeman, “Observation of mutual trapping and dragging of two-dimensional spatial solitary waves in a quadratic medium,” Opt. Lett. 20, 1949–1951 (1995).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

M. A. Krumbugel, J. N. Sweetser, D. N. Fittinghoff, K. W. DeLong, R. Trebino, “Ultrafast optical switching by use of fully phase-matched cascaded second-order nonlinearities in a polarization-gate geometry,” Opt. Lett. 22, 245–247 (1997).
[CrossRef] [PubMed]

M. Asobe, I. Yokohama, H. Itoh, T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency-generation and difference-frequency-generation processes in periodically poled LiNbO3,” Opt. Lett. 22, 274–276 (1997).
[CrossRef] [PubMed]

P. Vidakovic, D. J. Lovering, J. A. Levenson, J. Webjorn, P. St. J. Russell, “Large nonlinear phase shift owing to cascaded χ(2) in quasi-phase-matched bulk LiNbO3,” Opt. Lett. 22, 277–279 (1997).
[CrossRef]

J. U. Kang, Y. J. Ding, W. K. Burns, J. S. Melinger, “Backward second-harmonic generation in periodically poled bulk LiNbO3,” Opt. Lett. 22, 862–864 (1997).
[CrossRef] [PubMed]

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[CrossRef]

G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. 22, 1834–1836 (1997).
[CrossRef]

K. Mizuuchi, K. Yamamoto, “Generation of 340-nm light by frequency doubling of a laser diode in bulk periodically poled LiTaO3,” Opt. Lett. 21, 107–109 (1996).
[CrossRef] [PubMed]

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, W. Sohler, “All-optical switching in lithium niobate directional couplers with cascaded nonlinearity,” Opt. Lett. 21, 940–942 (1996).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Opt. Quantum Electron. (2)

G. I. Stegeman, D. J. Hagan, 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]

R. Schiek, “All-optical switching in the directional coupler caused by nonlinear refraction due to cascaded second-order nonlinearity,” Opt. Quantum Electron. 26, 415–431 (1994).
[CrossRef]

Opt. Rev. (1)

N. Hashizume, T. Tsuruzono, T. Kondo, R. Ito, “Fabrication of periodic waveguides using organic crystals and fluorinated polyimides for quasi-phase-matched second-harmonic generation,” Opt. Rev. 4, 316–320 (1997).
[CrossRef]

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[CrossRef]

Phys. Rev. A (1)

G. D’Alessandro, P. S. J. Russell, A. A. Wheeler, “Nonlinear dynamics of a backward quasi-phase-matched second-harmonic generator,” Phys. Rev. A 55, 3211–3218 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

W. E. Torruellas, W. Zuo, D. J. Hagan, E. W. VanStryland, G. I. Stegeman, L. Torner, C. R. Menyuk, “Observation of two-dimensional spatial solitary waves in a quadratic medium,” Phys. Rev. Lett. 74, 5036–5039 (1995).
[CrossRef] [PubMed]

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[CrossRef]

Other (7)

V. G. Dmitriev, G. G. Gurzadyan, D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed. (Springer, Berlin, 1997).
[CrossRef]

See, for example, R. W. Boyd, Nonlinear Optics (Academic, San Diego, 1992).

D. Zwillinger, Handbook of Differential Equations, 2nd ed. (Academic, San Diego, 1992).

H. S. Nalwa, T. Watanabe, S. Miyata, “Organic materials for second-order nonlinear optics,” in Nonlinear Optics of Organic Molecules and Polymers, H. S. Nalwa, S. Miyata, eds. (CRC, Boca Raton, Fla., 1997), pp. 166–167.

R. A. Paquin, “Properties of metals,” in Handbook of Optics, Vol II: Devices, Measurements, and Properties, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), p. 35.19.

T. Gase, W. Karthe, “Cascading the second-order susceptibility in poled polymers by quasi-phase matching,” in Quantum Electronics and Laser Science Conference, Vol. 10 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 78.

G. Stegeman, R. Schiek, L. Torner, W. Torruellas, Y. Baek, D. Baboiu, Z. Wang, E. Van Stryland, D. Hagan, G. Assanto, “Cascading: a promising approach to nonlinear optical phenomena,” in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, C. Umeton, eds. (Wiley, New York, 1997).

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Figures (12)

Fig. 1
Fig. 1

Wave-vector matching diagrams for (a) FQPM, (b) BQPM, (c) CQPM. There are two simultaneously phase-matchable processes for cases (a) and (b), whereas there are six for case (c). The FF and SH wave vectors are represented by thin black and thin gray arrows, respectively. The grating wave vector K = 2π/Λ is represented by a thick black arrow. A dashed arrow represents the conjugate of the fundamental wave.

Fig. 2
Fig. 2

Schematic of the CQPM device under study. The input–output interface is located at z = 0. A highly reflective mirror is located at z = L. The domain inversion period is Λ.

Fig. 3
Fig. 3

SHG conversion efficiency ηSHG as a function of the normalized input intensity Γ2 I 0 for the (a) CQPM device with mirror reflectivities r ω = r = 1 (solid curve), (b) CQPM device with mirror reflectivities r ω = r = 0.8 (dashed curve), (c) FQPM (dotted curve).

Fig. 4
Fig. 4

Normalized field profiles inside the device for Δκ = 0 and (a) Γ2 I 0 = 0.2, (b) Γ2 I 0 = (π/4)2, (c) Γ2 I 0 = 3, (d) Γ2 I 0 = 5. The field magnitudes are |A(ρ)| (solid black curve), |B(ρ)| (dashed black curve), |C(ρ)| (solid gray curve), and |D(ρ)| (dashed gray curve). The reflectivities are taken to be r ω = r = 0.9. Note that the output SH field is maximum for the input intensity of (b).

Fig. 5
Fig. 5

Total intensity in the +ρ direction (black curve) and -ρ direction (gray curve) for (a) Γ2 I 0 = 0.2 and (b) Γ2 I 0 = 3. The reflectivities are taken to be r ω = r = 0.9. The offset is equal to the leakage at the mirror I leak.

Fig. 6
Fig. 6

Fundamental nonlinear phase shift (in units of π) as a function of normalized input intensity Γ2 I 0 and phase mismatch Δκ (in units of π) for the CQPM device under study with r ω = r = 1. The dashed line represents the NLPS solutions found by a different numerical method (i.e., the relaxation method).

Fig. 7
Fig. 7

Fundamental throughput as a function of normalized input intensity Γ2 I 0 and phase mismatch Δκ (in units of π) for the CQPM device under study with r ω = r = 1. The viewpoint in this figure is different from that of Fig. 6 to improve legibility. The dashed line represents the throughput solutions found by a different numerical method (i.e., the relaxation method).

Fig. 8
Fig. 8

Normalized input intensity (solid curve) necessary to generate a ±π/2 phase shift and the associated fundamental throughput (dashed curve) for a FQPM configuration.

Fig. 9
Fig. 9

Normalized field profiles inside the device for Δκ = π and (a) Γ2 I 0 = 0.2, (b) Γ2 I 0 = (π/4)2, (c) Γ2 I 0 = 3, (d) Γ2 I 0 = 5. The field magnitudes are |A(ρ)| (solid black curve), |B(ρ)| (dashed black curve), |C(ρ)| (solid gray curve), and |D(ρ)| (dashed gray curve). The reflectivities are taken to be r ω = r = 0.9.

Fig. 10
Fig. 10

SHG efficiency as a function of the mirror FF phase ϕFF and SH phase ϕSH (in degrees). The magnitude of the reflectivities are set to unity, |r ω| = |r | = 1. Also, Γ2 I 0 = (π/4)2 and Δκ = 0.

Fig. 11
Fig. 11

SHG efficiency as a function of the mirror FF phase ϕFF and SH phase ϕSH (in degrees). The magnitude of the reflectivities are set to unity, |r ω| = |r | = 1. Also, Γ2 I 0 = (π/4)2 and Δκ = π.

Fig. 12
Fig. 12

SHG efficiency as a function of Δκ (in units of π) for silver mirrors on KTP with a 1.064-μm FF: r ω = 0.98 exp(j151°) and r = 0.97 exp(j119°).

Equations (41)

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E ω + z = α z exp - jk ω z , E ω - z = β z exp + jk ω z , E 2 ω + z = γ z exp - jk 2 ω z , E 2 ω - z = ζ z exp + jk 2 ω z ,
d z = d 0 m = - 2 | m | π exp jmKz d 0 2 π exp jKz + exp - jKz ,
P ω + z = 2 0 d z β * z γ z exp - jk ω z - jk 2 ω z + ζ z exp - jk ω z + jk 2 ω z , P ω - z = 2 0 d z α * z γ z exp + jk ω z - jk 2 ω z + ζ z exp + jk ω z + jk 2 ω z , P 2 ω z = 2 0 d z α z β z exp - jk ω z + jk ω z = 2 0 d z α z β z ,
P ω + z = 4 π   0 d 0 β * z γ z exp + jKz - jk 2 ω z + ζ z exp - jKz + jk 2 ω z × exp - jk ω z , P + - z = 4 π   0 d 0 α * z γ z exp + jKz - jk 2 ω z + ζ z exp - jKz + jk 2 ω z × exp + jk ω z , P 2 ω + z = 4 π   0 d 0 α z β z exp - jKz , P 2 ω - z = 4 π   0 d 0 α z β z exp + jKz .
d 2 d z 2   E ω + z = - ω 2 μ 0 0 n ω 2 E ω + z + P ω + z , d 2 d z 2   E ω - z = - ω 2 μ 0 0 n ω 2 E ω - z + P ω - z , d 2 d z 2   E 2 ω + z = - 2 ω 2 μ 0 0 n 2 ω 2 E 2 ω + z + P 2 ω + z , d 2 d z 2   E 2 ω - z = - 2 ω 2 μ 0 0 n 2 ω 2 E 2 ω - z + P 2 ω - z ,
d α z d z = - j   ω 2 / π d 0 cn ω   β * z γ z exp - j Δ kz + ζ z exp + j Δ kz , d β z d z = + j   ω 2 / π d 0 cn ω   α * z γ z exp - j Δ kz + ζ z exp + j Δ kz , d γ z d z = - j   2 ω 2 / π d 0 cn 2 ω   α z β z exp + j Δ kz , d ζ z d z = + j   2 ω 2 / π d 0 cn 2 ω   α z β z exp - j Δ kz ,
Δ k = k 2 ω - K .
n 2 ω / 2 Z 0 1 / 2   exp ± j Δ kL ρ ,
A ρ = α ρ L n ω 2 Z 0 1 / 2 , B ρ = β ρ L n ω 2 Z 0 1 / 2 , C ρ = γ ρ L exp - j Δ kL ρ n 2 ω 2 Z 0 1 / 2 , D ρ = ζ ρ L exp j Δ kL ρ n 2 ω 2 Z 0 1 / 2 .
d A ρ d ρ = - j Γ B * z C ρ + D ρ ,
d B ρ d ρ = + j Γ A * z C ρ + D ρ ,
d C ρ d ρ = - j 2 Γ A ρ B ρ - j Δ κ C ρ ,
d D ρ d ρ = + j 2 Γ A ρ B ρ + j Δ κ D ρ ,
Γ = ω 2 / π d 0 L cn ω 2 Z 0 n 2 ω 1 / 2 , Δ κ = k 2 ω - K L = Δ kL .
A 0 = I 0 ,
C 0 = 0 ,
B 1 = r ω A 1 ,
D 1 = r 2 ω C 1 ,
C ρ + D ρ = Ω ,
D 0 = Ω - C 0 = Ω ,
C 1 = Ω 1 + r 2 ω .
d A ρ d ρ = - j Γ Ω B * z , d B ρ d ρ = + j Γ Ω A * z .
A ρ = a 0   cos b 0 ρ + c 0 , B ρ = a 1   sin b 0 ρ + c 0 ,
a 1 = j   Ω | Ω |   a 0 * ,
b 0 = Γ | Ω | .
c 0 = arctan r ω - Γ | Ω | ,
C ρ = - Ω a 0 2 2 | Ω | 2 cos 2 b o ρ + 2 c 0 - cos 2 c 0 .
D ρ = Ω 1 + a 0 2 2 | Ω | 2 cos 2 b 0 ρ + 2 c 0 - cos 2 c 0 .
| Ω | 2 = a 0 2 1 + r 2 ω 2 cos 2 c 0 - cos 2   arctan r ω .
a 0 2 = I 0 / cos 2 c 0 .
| Ω | 2 = I 0 1 + r 2 ω 2 cos 2 c 0 - cos 2   arctan r ω cos 2 c 0 = I 0 1 + r 2 ω 2 1 - tan 2 c 0 - cos 2   arctan r ω cos 2 c 0 .
η SHG = | D 0 | 2 | A 0 | 2 = | Ω | 2 I 0
η SHG = 1 + r 2 ω 2 1 - tan 2 arctan r ω - Γ 2 I 0 η SHG 1 / 2 - cos 2   arctan r ω cos 2 arctan r ω - Γ 2 I 0 η SHG 1 / 2 .
η std = tanh 2 Γ 2 I 0 1 / 2 .
η SHG = 1 - tan 2 π 4 - Γ 2 I 0 η SHG 1 / 2 .
I leak = | A 1 | 2 1 - r ω 2 + | C 1 | 2 1 - r 2 ω 2 .
| A ρ | 2 - | B ρ | 2 + | C ρ | 2 - | D ρ | 2 = I leak .
d | A ρ | 2 d ρ + d | B ρ | 2 d ρ = d A ρ d ρ   A * ρ + d A * ρ d ρ   A ρ + d B ρ d ρ   B * ρ + d B * ρ d ρ   B ρ = 0 .
| A ρ | 2 + | B ρ | 2 = I FF .
d | A ρ | 2 d ρ + d | C ρ | 2 d ρ = d | B ρ | 2 d ρ + d | D ρ | 2 d ρ .
- d | A ρ | 2 d ρ = d | B ρ | 2 d ρ = 1 2 d | C ρ | 2 d ρ - 1 2 d | D ρ | 2 d ρ .

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