Abstract
A simple, two parabolic band model is shown to give the correct bandgap scaling, dispersion, and magnitude of bound electronic optical nonlinearities in semiconductors and certain large gap dielectrics. Essential to this formalism is a generalized Kramers-Kronig transformation that unifies the optical Kerr effect (n 2) with third-order absorptive nonlinearities: two-photon absorption, Raman effect, and quadratic Stark effect. Experimental results obtained with semiconductors and dielectrics have energy band-gaps ranging from 0.7 to 11eV show remarkable agreement with this simple theory. Extensions of t his model successfully predict the nondegenerate optical Kerr effect and nonlinearities in active semiconductors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Adair, L.L. Chase, and S.A. Payne, Nonlinear Refractive Index of Optical Crystals, Phys. Rev. B, 39, 3337–3350 (1989).
M.J. LaGasse, K.K. Anderson, C.A. Wang, H.A. Haus, and J.G. Fujimuto, Femtosecond Measurements of the Nonresonant Nonlinear Index in AlGaAs, Appl. Phys. Lett. 56, 417–419 (1990).
M. Sheik-Bahae, D.J. Hagan, and E.W. Van Stryland, Dispersion and Band-gap Scaling of the Electronic Kerr Effect in Solids associated with Two-Photon Absorption, Phys. Rev. Lett.
M. Sheik-Bahae, D.C. Hutchings, D.J. Hagan, and E.W. Van Stryland, Dispersion of Bound-Electronic Nonlinear Refraction in Solids, IEEE J. Quantum Electron. QE-27, 1296–1309 (1991).
G.P. Agrawal, Nonlinear Fiber Optics, Academic Press, 1989
D.E. Spence, P.N. Kean, and W. Sibbett, Opt. Lett. 19, 4 (1991).
H.M. Gibbs, Optical Bistability: Controlling Light with Light, Academic Press, 1985.
M. Sheik-Bahae, A.A. Said, T.H. Wei, D.J. Hagan, and E.W. Van Stryland, Sensitive measurements of optical nonlinearities using a single beam, IEEE J. Quantum Electron., QE-26, 760–769 (1990).
M. Sheik-Bahae, A.A. Said, and E.W. Van Stryland, High Sensitivity, Single Beam n 2 Measurements, Opt. Lett. 14, 955–957 (1989).
M. Sheik-Bahae, J. Wang, E. W. Van Stryland, IEEE J. Quantum Electron. 30, 249–255 (1994).
D.C. Hutchings, M. Sheik-Bahae, D.J. Hagan, E.W. Van Stryland, Kramers-Kronig Dispersion Relations in Nonlinear Optics, Opt. Quantum Electron., 24, 1–30 (1992).
N. Bloembergen, Nonlinear Optics, Benjamin (1971), also S.S. Jha and N. Bloembergen, Nonlinear Optical Susceptibility in Group-IV and III-V Semiconductors, Phys. Rev. 171, 891–898 (1968).
R.W. Hellwarth, Third-order optical susceptibilities of liquids and solids, in Progress in Quantum Electronics, Volume 5, Part 1, Pergamon Press 1977.
P.J. Price, Phys. Rev. 130, 1792 (1964).
D.A.B. Miller, C.T. Seaton, M.E. Prise, and S.D. Smith, Band-gap resonant nonlinear refraction in III-V semiconductors, Phys. Rev. Lett., 47, 197–200 (1981).
B.S. Wherrett, A.C. Walker, and F.A.P. Tooley, Nonlinear refraction for cw optical bistability, in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, Eds., Academic Press., 1988.
B.S. Wherrett, Scaling rules for multiphoton interband absorption in semiconductors, J. Opt. Soc. Am. B, 1, 67–72 (1984)
L.V. Keldysh, Ionization in the field of a strong electromagnetic wave, Sov. Phys. JETP, 20, 1307–1314 (1965).
H.D. Jones and H. R. Reiss, Intense-field effects in solids, Phys. Rev. B. 16, 2466–2473 (1977).
H.S. Brandi and C.B. de Araujo, Multiphoton Absorption Coefficients in Solids: a Universal Curve, J. Phys. C 16, 5929–5936 (1983).
D.M. Volkov, Concerning a class of solution of the Dirac equation, Z. Phys. 94, 250–260 (1935).
T.-Y. Wu and T Ohmura, Quantum Theory of Scattering, Englewood Cliffs, NJ, Prentice Hall (1962).
I.N. Ross, W. T. Toner, C.J. Hooker, J.R. Barr, and I. Coffey, Nonlinear properties of silica and air for picosecond ultraviolet pulses, J. Modern Opt., 37, 555–573 (1990).
G.I. Stegeman, E.M. Wright, All-optical waveguide switching, Optical and Quantum Electronics, 22, 95–122 (1990).
C.T. Haltgren, E.P. Ippen, Ultrafast refractive index dynamics in AlGaAs diode laser amplifiers, Appl. Phys. Lett. 59, 635–638 (1991). K. L. Hall, G. Lenz, E.P. Ippen, G. Raybon, Heterodyne pump-probe technique for time-domain studies of optical nonlinearities in waveguides, Opt. Lett. 17, 874-877 (1992).
C.T. Hultgren and E.P. Ippen, Femtosecond band-edge index nonlinearities in active AlGaAs waveguides, Technical Digest of IQEC-994, paper QThG3, Optical Society of America, Anaheim, CA, May 8-13, 1994.
M. Sheik-Bahae and E.W. Van Stryland, Ultrafast nonlinear refraction in semiconductor laser amplifiers, Ultrafast Phenomena VIII, J.-L. Martin, A. Migus, G.A. Mourou, A.H. Zewail, Eds. Springer Verlag, Vol. 55, 426–4299 (1993).
M. Sheik-Bahae and E.W. Van Stryland, Ultrafast nonlinearities in semiconductor laser amplifiers, Phys. Rev. B, 50, 14171–14178 (1994)
S.G. Lee, B.P. McGinnis, R. Jin, J. Yumoto, G. Khitrova, H. M. Gibbs, N. Peyghambarian, paper CTuC4, CLEO94 Technical Digest, pp. 55.
R. Binder, D. Scott, A.E. Paul, M. Lindberg, K. Henneberger, S.W. Koch, Carrier-carrier scattering and optical dephasing in highly excited semiconductors, Phys. Rev. B, 45, 1107–1115 (1992).
C. Aversa, J.E. Sipe, M. Sheik-Bahae, E.W. Van Stryland, Third-order optical susceptibilities in semiconductors: The two-band model, Phys. Rev. B 50, 18073–18082 (1994)
E.W. Van Stryland, M.A. Woodall, H. Vanherzeele, and M.J. Soileau, Energy Band-gap Dependence of Two-Photon Absorption, Opt. Lett. 10, 490–492 (1985).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Sheik-Bahae, M. (1998). Nonlinear Optics of Bound Electrons in Solids. In: Moloney, J.V. (eds) Nonlinear Optical Materials. The IMA Volumes in Mathematics and its Applications, vol 101. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1714-5_8
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1714-5_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7253-3
Online ISBN: 978-1-4612-1714-5
eBook Packages: Springer Book Archive