Abstract

Using accurate band structures of InAs, InSb, and two Hg1xCdxTe alloys, we calculate the change in refractive index caused by the photoexcited electrons and holes. The effects of both free-carrier absorption (FCA) and one-photon absorption are considered. We find that the change in refractive index varies nonlinearly with the density of photoexcited carriers and that the generally neglected FCA contribution is significant in InAs, owing to its weak spin-orbit coupling.

© 2006 Optical Society of America

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  1. W. S. Pelouch and L. A. Schlie, "Ultrafast carrier dynamics and saturable absorption in HgCdTe," Appl. Phys. Lett. 68, 1389-1391 (1996).
    [CrossRef]
  2. S. Kono, P. Gu, M. Tani, and K. Sakai, "Temperature dependence of terahertz radiation from n-type InSb and n-type InAs surfaces," Appl. Phys. B 71, 901-904 (2000).
    [CrossRef]
  3. For a review, see D. M. Kovsh, S. Yong, D. J. Hagan, and E. Van Stryland, "Nonlinear optical liquid for power limiting," Proc. SPIE 3472, 163-177 (1998).
    [CrossRef]
  4. D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, "Picosecond spectroscopy of semiconductors," Solid-State Electron. 21, 147-150 (1978).
    [CrossRef]
  5. 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).
    [CrossRef]
  6. E. W. van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, "Optical limiting with semiconductors," J. Opt. Soc. Am. A 5, 1980-1989 (1988).
  7. P. P. Paskov and K. R. Koynov, "A theoretical analysis of absorption and refractive index changes in optically excited In1−xGaxSb," Semicond. Sci. Technol. 9, 1584-1590 (1994).
    [CrossRef]
  8. 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. 27, 1296-1309 (1991).
    [CrossRef]
  9. P. Paskov, "Refractive indices of InSb, InAs, GaSb, InAsSb and InGaSb: effects of free carriers, J. Appl. Phys. 81, 1890-1898 (1997).
    [CrossRef]
  10. J. I. Pankove, Optical Processes in Semiconductors (Dover, 1975), p. 90.
  11. A. B. Chen and A. Sher, Semiconductor Alloys (Plenum, 1995), Chap. 5.
  12. Z. Kucera, "Dispersion of the refractive index of Hg1−xCdxTe," Phys. Status Solidi A 100, 659-665 (1987).
    [CrossRef]
  13. S. Rolland, "Dielectric constant and refractive index of HgCdTe," in Properties of Narrow Gap Cadmium-Based Compounds, P.Capper, ed. (INSPEC, IEE, 1994), pp. 80-85.
  14. E. D. Palik and R. T. Holm, "Indium arsenide," in Handbook of Optical Constants of Solids, D.Palik, ed. (Academic, 1998), pp. 479-489.
  15. R. T. Holm, "Indium antimonide," in Handbook of Optical Constants of Solids, D.Palik, ed. (Academic, 1998), pp. 490-502.

2000

S. Kono, P. Gu, M. Tani, and K. Sakai, "Temperature dependence of terahertz radiation from n-type InSb and n-type InAs surfaces," Appl. Phys. B 71, 901-904 (2000).
[CrossRef]

1998

For a review, see D. M. Kovsh, S. Yong, D. J. Hagan, and E. Van Stryland, "Nonlinear optical liquid for power limiting," Proc. SPIE 3472, 163-177 (1998).
[CrossRef]

1997

P. Paskov, "Refractive indices of InSb, InAs, GaSb, InAsSb and InGaSb: effects of free carriers, J. Appl. Phys. 81, 1890-1898 (1997).
[CrossRef]

1996

W. S. Pelouch and L. A. Schlie, "Ultrafast carrier dynamics and saturable absorption in HgCdTe," Appl. Phys. Lett. 68, 1389-1391 (1996).
[CrossRef]

1994

P. P. Paskov and K. R. Koynov, "A theoretical analysis of absorption and refractive index changes in optically excited In1−xGaxSb," Semicond. Sci. Technol. 9, 1584-1590 (1994).
[CrossRef]

1991

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. 27, 1296-1309 (1991).
[CrossRef]

1988

E. W. van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, "Optical limiting with semiconductors," J. Opt. Soc. Am. A 5, 1980-1989 (1988).

1987

Z. Kucera, "Dispersion of the refractive index of Hg1−xCdxTe," Phys. Status Solidi A 100, 659-665 (1987).
[CrossRef]

1981

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).
[CrossRef]

1978

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, "Picosecond spectroscopy of semiconductors," Solid-State Electron. 21, 147-150 (1978).
[CrossRef]

Auston, D. H.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, "Picosecond spectroscopy of semiconductors," Solid-State Electron. 21, 147-150 (1978).
[CrossRef]

Chen, A. B.

A. B. Chen and A. Sher, Semiconductor Alloys (Plenum, 1995), Chap. 5.

Gu, P.

S. Kono, P. Gu, M. Tani, and K. Sakai, "Temperature dependence of terahertz radiation from n-type InSb and n-type InAs surfaces," Appl. Phys. B 71, 901-904 (2000).
[CrossRef]

Hagan, D. J.

For a review, see D. M. Kovsh, S. Yong, D. J. Hagan, and E. Van Stryland, "Nonlinear optical liquid for power limiting," Proc. SPIE 3472, 163-177 (1998).
[CrossRef]

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. 27, 1296-1309 (1991).
[CrossRef]

E. W. van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, "Optical limiting with semiconductors," J. Opt. Soc. Am. A 5, 1980-1989 (1988).

Holm, R. T.

E. D. Palik and R. T. Holm, "Indium arsenide," in Handbook of Optical Constants of Solids, D.Palik, ed. (Academic, 1998), pp. 479-489.

R. T. Holm, "Indium antimonide," in Handbook of Optical Constants of Solids, D.Palik, ed. (Academic, 1998), pp. 490-502.

Hutchings, D. C.

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. 27, 1296-1309 (1991).
[CrossRef]

Ippen, E. P.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, "Picosecond spectroscopy of semiconductors," Solid-State Electron. 21, 147-150 (1978).
[CrossRef]

Kono, S.

S. Kono, P. Gu, M. Tani, and K. Sakai, "Temperature dependence of terahertz radiation from n-type InSb and n-type InAs surfaces," Appl. Phys. B 71, 901-904 (2000).
[CrossRef]

Kovsh, D. M.

For a review, see D. M. Kovsh, S. Yong, D. J. Hagan, and E. Van Stryland, "Nonlinear optical liquid for power limiting," Proc. SPIE 3472, 163-177 (1998).
[CrossRef]

Koynov, K. R.

P. P. Paskov and K. R. Koynov, "A theoretical analysis of absorption and refractive index changes in optically excited In1−xGaxSb," Semicond. Sci. Technol. 9, 1584-1590 (1994).
[CrossRef]

Kucera, Z.

Z. Kucera, "Dispersion of the refractive index of Hg1−xCdxTe," Phys. Status Solidi A 100, 659-665 (1987).
[CrossRef]

Mansour, K.

E. W. van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, "Optical limiting with semiconductors," J. Opt. Soc. Am. A 5, 1980-1989 (1988).

McAffee, S.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, "Picosecond spectroscopy of semiconductors," Solid-State Electron. 21, 147-150 (1978).
[CrossRef]

Miller, D. A. B.

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).
[CrossRef]

Palik, E. D.

E. D. Palik and R. T. Holm, "Indium arsenide," in Handbook of Optical Constants of Solids, D.Palik, ed. (Academic, 1998), pp. 479-489.

Pankove, J. I.

J. I. Pankove, Optical Processes in Semiconductors (Dover, 1975), p. 90.

Paskov, P.

P. Paskov, "Refractive indices of InSb, InAs, GaSb, InAsSb and InGaSb: effects of free carriers, J. Appl. Phys. 81, 1890-1898 (1997).
[CrossRef]

Paskov, P. P.

P. P. Paskov and K. R. Koynov, "A theoretical analysis of absorption and refractive index changes in optically excited In1−xGaxSb," Semicond. Sci. Technol. 9, 1584-1590 (1994).
[CrossRef]

Pelouch, W. S.

W. S. Pelouch and L. A. Schlie, "Ultrafast carrier dynamics and saturable absorption in HgCdTe," Appl. Phys. Lett. 68, 1389-1391 (1996).
[CrossRef]

Prise, M. E.

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).
[CrossRef]

Rolland, S.

S. Rolland, "Dielectric constant and refractive index of HgCdTe," in Properties of Narrow Gap Cadmium-Based Compounds, P.Capper, ed. (INSPEC, IEE, 1994), pp. 80-85.

Sakai, K.

S. Kono, P. Gu, M. Tani, and K. Sakai, "Temperature dependence of terahertz radiation from n-type InSb and n-type InAs surfaces," Appl. Phys. B 71, 901-904 (2000).
[CrossRef]

Schlie, L. A.

W. S. Pelouch and L. A. Schlie, "Ultrafast carrier dynamics and saturable absorption in HgCdTe," Appl. Phys. Lett. 68, 1389-1391 (1996).
[CrossRef]

Seaton, C. T.

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).
[CrossRef]

Shank, C. V.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, "Picosecond spectroscopy of semiconductors," Solid-State Electron. 21, 147-150 (1978).
[CrossRef]

Sheik-Bahae, M.

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. 27, 1296-1309 (1991).
[CrossRef]

Sher, A.

A. B. Chen and A. Sher, Semiconductor Alloys (Plenum, 1995), Chap. 5.

Smith, S. D.

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).
[CrossRef]

Soileau, M. J.

E. W. van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, "Optical limiting with semiconductors," J. Opt. Soc. Am. A 5, 1980-1989 (1988).

Tani, M.

S. Kono, P. Gu, M. Tani, and K. Sakai, "Temperature dependence of terahertz radiation from n-type InSb and n-type InAs surfaces," Appl. Phys. B 71, 901-904 (2000).
[CrossRef]

Teschke, O.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, "Picosecond spectroscopy of semiconductors," Solid-State Electron. 21, 147-150 (1978).
[CrossRef]

Van Stryland, E.

For a review, see D. M. Kovsh, S. Yong, D. J. Hagan, and E. Van Stryland, "Nonlinear optical liquid for power limiting," Proc. SPIE 3472, 163-177 (1998).
[CrossRef]

van Stryland, E. W.

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. 27, 1296-1309 (1991).
[CrossRef]

E. W. van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, "Optical limiting with semiconductors," J. Opt. Soc. Am. A 5, 1980-1989 (1988).

Wu, Y. Y.

E. W. van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, "Optical limiting with semiconductors," J. Opt. Soc. Am. A 5, 1980-1989 (1988).

Yong, S.

For a review, see D. M. Kovsh, S. Yong, D. J. Hagan, and E. Van Stryland, "Nonlinear optical liquid for power limiting," Proc. SPIE 3472, 163-177 (1998).
[CrossRef]

Appl. Phys. B

S. Kono, P. Gu, M. Tani, and K. Sakai, "Temperature dependence of terahertz radiation from n-type InSb and n-type InAs surfaces," Appl. Phys. B 71, 901-904 (2000).
[CrossRef]

Appl. Phys. Lett.

W. S. Pelouch and L. A. Schlie, "Ultrafast carrier dynamics and saturable absorption in HgCdTe," Appl. Phys. Lett. 68, 1389-1391 (1996).
[CrossRef]

IEEE J. Quantum Electron.

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. 27, 1296-1309 (1991).
[CrossRef]

J. Appl. Phys.

P. Paskov, "Refractive indices of InSb, InAs, GaSb, InAsSb and InGaSb: effects of free carriers, J. Appl. Phys. 81, 1890-1898 (1997).
[CrossRef]

J. Opt. Soc. Am. A

E. W. van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, "Optical limiting with semiconductors," J. Opt. Soc. Am. A 5, 1980-1989 (1988).

Phys. Rev. Lett.

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).
[CrossRef]

Phys. Status Solidi A

Z. Kucera, "Dispersion of the refractive index of Hg1−xCdxTe," Phys. Status Solidi A 100, 659-665 (1987).
[CrossRef]

Proc. SPIE

For a review, see D. M. Kovsh, S. Yong, D. J. Hagan, and E. Van Stryland, "Nonlinear optical liquid for power limiting," Proc. SPIE 3472, 163-177 (1998).
[CrossRef]

Semicond. Sci. Technol.

P. P. Paskov and K. R. Koynov, "A theoretical analysis of absorption and refractive index changes in optically excited In1−xGaxSb," Semicond. Sci. Technol. 9, 1584-1590 (1994).
[CrossRef]

Solid-State Electron.

D. H. Auston, S. McAffee, C. V. Shank, E. P. Ippen, and O. Teschke, "Picosecond spectroscopy of semiconductors," Solid-State Electron. 21, 147-150 (1978).
[CrossRef]

Other

J. I. Pankove, Optical Processes in Semiconductors (Dover, 1975), p. 90.

A. B. Chen and A. Sher, Semiconductor Alloys (Plenum, 1995), Chap. 5.

S. Rolland, "Dielectric constant and refractive index of HgCdTe," in Properties of Narrow Gap Cadmium-Based Compounds, P.Capper, ed. (INSPEC, IEE, 1994), pp. 80-85.

E. D. Palik and R. T. Holm, "Indium arsenide," in Handbook of Optical Constants of Solids, D.Palik, ed. (Academic, 1998), pp. 479-489.

R. T. Holm, "Indium antimonide," in Handbook of Optical Constants of Solids, D.Palik, ed. (Academic, 1998), pp. 490-502.

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Figures (6)

Fig. 1
Fig. 1

Refractive index change due to the FCA and OPA as a function of the photon wavelength in InSb with Δ N = 10 16 and 10 17 cm 3 at room temperature.

Fig. 2
Fig. 2

Refractive index change at λ = 9.5 μ m due to the FCA and OPA as a function of Δ N in InSb and Hg 0.762 Cd 0.238 Te (HCT) at room temperature.

Fig. 3
Fig. 3

Refractive index change at λ = 4.8 μ m due to the FCA and OPA as a function of Δ N in InAs and Hg 0.656 Cd 0.344 Te (HCT) at room temperature.

Fig. 4
Fig. 4

Cross section of the FCA σ as a function of the photon wavelength in InAs and Hg 0.656 Cd 0.344 Te (HCT) at room temperature.

Fig. 5
Fig. 5

Energy difference between the heavy-hole and light-hole valence bands as a function of wave vector for InAs and Hg 0.656 Cd 0.344 Te (HCT) at room temperature.

Fig. 6
Fig. 6

Total change in the refractive index Δ n 1 at λ = 4.8 μ m for InSb and Hg 0.762 Cd 0.238 Te (HCT-238) and at λ = 9.5 μ m for InAs and Hg 0.656 Cd 0.344 Te (HCT-344) as a function of Δ N at room temperature.

Tables (1)

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Table 1 Fit Parameters to Obtain the Calculated Change in Refractive Index at 300 K

Equations (9)

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n 1 ( ω ) 1 = c π P 0 α ( ω ) d ω ω 2 ω 2 ,
Δ n 1 ( ω ) = c π P 0 α ( ω , Δ N ) α ( ω , 0 ) ω 2 ω 2 d ω ,
α ( ω , Δ N ) α 0 ( ω ) = ω n 1 0 ( ω ) c [ ϵ 2 ( ω , Δ N ) ϵ 2 ( ω , 0 ) ] ,
ϵ 2 ( ω , Δ N ) = 4 π 2 e 2 3 m 0 2 ω 2 n m k p n m ( k ) 2 f ( E m k ) [ 1 f ( E n k ) ] δ ( E n k E m k ω ) ,
f ( E m k ) = [ 1 + e β ( E m k μ h ) ] 1 ,
f ( E n k ) = [ 1 + e β ( E n k μ e ) ] 1 ,
ϵ 2 ( ω , Δ N ) = 8 π 3 e 4 ω LO ω 3 m 0 2 V ( 1 κ 1 κ 0 ) n k f ( E n k ) R n k ,
R n k = n q ± ( N LO + 1 2 1 2 ) n k ± q e i q r q n k ( n k j e j p n k n k + q j e j p n k + q ) ,
ϵ 2 ( ω , Δ N ) = 4 π 2 e 2 3 m 0 2 ω 2 m m k p m m ( k ) 2 f ( E m k ) [ 1 f ( E m k ) ] δ ( E m k E m k ω ) ,

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