Dispersion of bound electron nonlinear refraction in solids

A two-hand model is used to calculate the scaling and spectrum of the nondegenerate nonlinear absorption. From this, the bound electronic nonlinear refractive index n/sub 2/ is obtained using a Kramers-Kronig transformation. The authors include the effects of two-photon and Raman transitions and the AC Stark shift (virtual band blocking). The theoretical calculation for n/sub 2/ shows excellent agreement with measured values for a five-order-of-magnitude variation in the modulus of n/sub 2/ in semiconductors and wide-gap optical solids. Beam distortion methods were used to measure n/sub 2/ in semiconductors. The observations result in a comprehensive theory that allows a prediction of n/sub 2/ at wavelengths beneath the band edge, given only the bandgap energy and the linear index of refraction. Some consequences for all-optical switching are discussed, and a wavelength criterion for the observation of switching is derived. >

[1]  Changhai Wang,et al.  Optically bistable interference filters: self-consistent modeling of nonlinear optical characteristics and optimization , 1991 .

[2]  R. C. Weast.  CRC Handbook of Chemistry and Physics , 1973 .

[3]  Brian S. Wherrett,et al.  Scaling rules for multiphoton interband absorption in semiconductors , 1984 .

[4]  J. Callaway.  Quantum theory of the solid state , 1974 .

[5]  David C. Hutchings,et al.  Optically bistable interference filters: optimization considerations , 1986 .

[6]  M. Sheik-Bahae,et al.  Semiconductor Nonlinearities For Optical Limiting , 1990, Digest on Nonlinear Optics: Materials, Phenomena and Devices.

[7]  David J. Hagan,et al.  Degenerate four-wave mixing measurements of high order nonlinearities in semiconductors , 1991 .

[8]  Howard R. Reiss,et al.  Intense-field effects in solids , 1977 .

[9]  Brian S. Wherrett,et al.  Bistable Semiconductor Elements for Optical Data Processing and Photonic Logic , 1986 .

[10]  E. Kane,et al.  Band structure of indium antimonide , 1957 .

[11]  E. W. Stryland,et al.  Sensitive Measurement of Optical Nonlinearities Using a Single Beam Special 30th Anniversary Feature , 1990 .

[12]  Kamjou Mansour,et al.  Optical limiting with semiconductors , 1988 .

[13]  Chris J. Hooker,et al.  Nonlinear properties of silica and air for picosecond ultraviolet pulses , 1990 .

[14]  C. C. Lee,et al.  Two-photon absorption with exciton effect for degenerate valence bands , 1974 .

[15]  C. Flytzanis.  Third-order optical susceptibilities in IV-IV and III–V semiconductors , 1970 .

[16]  Alan Miller,et al.  Non-linear optical effects in InSb with a c.w. CO laser , 1978 .

[17]  E. W. Stryland,et al.  Picosecond degenerate four-wave mixing studies in ZnSe , 1988 .

[18]  H S Brandi,et al.  Multiphonon absorption coefficients in solids: a universal curve , 1983 .

[19]  Payne,et al.  Nonlinear refractive index of optical crystals. , 1989, Physical review. B, Condensed matter.

[20]  Nastaran Mansour,et al.  Laser-Induced Damage And The Role Of Self-Focusing , 1989 .

[21]  T. Moss.  Theory of Intensity Dependence of Refractive Index , 1980 .

[22]  David E. Aspnes,et al.  Franz-Keldysh contributions to third-order optical susceptibilities , 1969 .

[23]  Ta-you Wu,et al.  Quantum Theory of Scattering , 1962 .

[24]  B. S. Wherrett,et al.  A comparison of theories of resonant nonlinear refraction in semiconductors , 1983, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[25]  G I Stegeman,et al.  Two-photon absorption as a limitation to all-optical switching. , 1989, Optics letters.

[26]  Haim Lotem,et al.  Absolute two-photon absorption coefficients at 355 and 266 nm , 1978 .

[27]  A. Smirl,et al.  Laser induced damage, nonlinear absorption, and doubling efficiency of LiO3 , 1984, IEEE Journal of Quantum Electronics.

[28]  E. O. Schulz-Dubois,et al.  Laser Handbook , 1972 .

[29]  G. Stegeman,et al.  Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors , 1990 .

[30]  B. S. Wherrett,et al.  The demonstration of restoring digital optical logic , 1987, Nature.

[31]  George I. Stegeman,et al.  Effect of two‐photon absorption on all‐optical guided‐wave devices , 1989 .

[32]  J. E. Sitch,et al.  All optical multiple-quantum-well waveguide switch , 1985 .

[33]  Charles C. Wang.  Empirical Relation between the Linear and the Third-Order Nonlinear Optical Susceptibilities , 1970 .

[34]  C. T. Seaton,et al.  Band-Gap—Resonant Nonlinear Refraction in III-V Semiconductors , 1981 .

[35]  A. Owyoung,et al.  Empirical relationships for predicting nonlinear refractive index changes in optical solids , 1978 .

[36]  N. Bloembergen,et al.  Nonlinear Optical Susceptibilities in Group-IV and III-V Semiconductors , 1968 .

[37]  L. Keldysh,et al.  IONIZATION IN THE FIELD OF A STRONG ELECTROMAGNETIC WAVE , 1964 .

[38]  Y. Silberberg,et al.  Femotosecond switching in a dual-core-fiber nonlinear coupler. , 1988, Optics letters.

[39]  E. W. Stryland,et al.  High-sensitivity, single-beam n(2) measurements. , 1989, Optics letters.

[40]  D. Moss,et al.  Band-structure calculation of dispersion and anisotropy in χ↔(3) for third-harmonic generation in Si, Ge, and GaAs , 1990 .

[41]  R R Neurgaonkar,et al.  Research on nonlinear optical materials: an assessment. , 1987, Applied optics.

[42]  B. Wherrett,et al.  Theory of nonlinear refraction near the band edge of a semiconductor , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[43]  Y. Yacoby.  High-Frequency Franz-Keldysh Effect , 1968 .

[44]  C. Pidgeon,et al.  Frequency dependence of two-photon absorption in InSb and Hg 1-x Cd x Te , 1980 .

[45]  T. Gold.  Two-photon spectroscopy , 1969 .

[46]  Hagan,et al.  Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption. , 1990, Physical review letters.

[47]  James G. Fujimoto,et al.  Femtosecond measurements of the nonresonant nonlinear index in AlGaAs , 1990 .

[48]  P. J. Price.  Theory of Quadratic Response Functions , 1963 .

[49]  M. J. Soileau,et al.  Two-Photon Absorption, Nonlinear Refraction and Optical Limiting in Semiconductors , 1985 .

[50]  M. Weiler,et al.  Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors , 1981 .

[51]  S. Koch,et al.  Theory of the Optical Stark Effect in Semiconductors under Ultrashort‐Pulse Excitation , 1988 .