Abstract

A dynamical theory for inelastic Bragg scattering of electromagnetic waves from coupled systems of acoustic lattice waves and free-carrier density waves in opaque semiconducting crystals is formulated. On basis of a quasistatic two-wave interference approximation it is predicted that sound-induced anomalous transmission of light below the plasma edge can be obtained if the radiation is incident at the Bragg angle appropriate for dynamical diffraction. This anomalous transmission is to some extent analogous to the Borrmann effect for x rays in perfect crystals.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Solid State Commun. 10, 1145 (1972).
    [CrossRef]
  2. V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Sov. Phys. Semicond. 6, 1646 (1973).
  3. G. N. Shkerdin and Yu. V. Gulyaev, Sov. Phys. Solid State 16, 2136 (1975).
  4. O. Keller, in Proceedings of the 3rd International Conference on Light Scattering in Solids, edited by M. Balkanski, R. C. C. Leite, and S. P. S. Porto (Flammarion, Paris, 1975), p. 447.
  5. O. Keller, Phys. Rev. B 13, 4612 (1976).
    [CrossRef]
  6. H. N. Spector, Solid State Phys. 19, 291 (1966).
    [CrossRef]
  7. H. Kuzmany, Phys. Stat. Sol. A 25, 9 (1974).
    [CrossRef]
  8. A. S. Pine, in Light Scattering in Solids, edited by M. Cardona (Springer-Verlag, Berlin, 1975), p. 253.
    [CrossRef]
  9. P. K. Tien, Phys. Rev. 171, 970 (1968).
    [CrossRef]
  10. G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
    [CrossRef]
  11. L. L. Hope, Phys. Rev. 166, 883 (1968).
    [CrossRef]
  12. C. Hamaguchi, J. Phys. Soc. Japan 35, 832 (1973).
    [CrossRef]
  13. O. Keller, Phys. Rev. B 11, 5059 (1975).
    [CrossRef]
  14. D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
    [CrossRef]
  15. O. Keller, Solid State Commun. 18, 1227 (1976).
    [CrossRef]
  16. O. Keller and C. Søndergaard, Japan J. Appl. Phys. 13, 1765 (1974).
    [CrossRef]
  17. The real and imaginary parts of the optical wave vector need not be collinear. In a forthcoming paper we shall study the modifications introduced by boundary effects in the theory. Thus, in a semi-infinite crystal filling half-space, the planes of constant absorption are, independent of the direction of phase propagation, parallel to the boundary.
  18. G. Borrmann, Z. Phys. 127, 297 (1950).
    [CrossRef]
  19. B. W. Battermann and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
    [CrossRef]
  20. C. Herring, Bell Sys. Tech. J. 34, 237 (1955).
    [CrossRef]
  21. A. K. Agarwal, Phys. Stat. Sol. A 25, 667 (1974).
    [CrossRef]

1976 (2)

O. Keller, Phys. Rev. B 13, 4612 (1976).
[CrossRef]

O. Keller, Solid State Commun. 18, 1227 (1976).
[CrossRef]

1975 (2)

O. Keller, Phys. Rev. B 11, 5059 (1975).
[CrossRef]

G. N. Shkerdin and Yu. V. Gulyaev, Sov. Phys. Solid State 16, 2136 (1975).

1974 (3)

H. Kuzmany, Phys. Stat. Sol. A 25, 9 (1974).
[CrossRef]

O. Keller and C. Søndergaard, Japan J. Appl. Phys. 13, 1765 (1974).
[CrossRef]

A. K. Agarwal, Phys. Stat. Sol. A 25, 667 (1974).
[CrossRef]

1973 (2)

C. Hamaguchi, J. Phys. Soc. Japan 35, 832 (1973).
[CrossRef]

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Sov. Phys. Semicond. 6, 1646 (1973).

1972 (2)

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Solid State Commun. 10, 1145 (1972).
[CrossRef]

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[CrossRef]

1968 (2)

P. K. Tien, Phys. Rev. 171, 970 (1968).
[CrossRef]

L. L. Hope, Phys. Rev. 166, 883 (1968).
[CrossRef]

1966 (2)

G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
[CrossRef]

H. N. Spector, Solid State Phys. 19, 291 (1966).
[CrossRef]

1964 (1)

B. W. Battermann and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

1955 (1)

C. Herring, Bell Sys. Tech. J. 34, 237 (1955).
[CrossRef]

1950 (1)

G. Borrmann, Z. Phys. 127, 297 (1950).
[CrossRef]

Agarwal, A. K.

A. K. Agarwal, Phys. Stat. Sol. A 25, 667 (1974).
[CrossRef]

Battermann, B. W.

B. W. Battermann and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Benedek, G. B.

G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
[CrossRef]

Borrmann, G.

G. Borrmann, Z. Phys. 127, 297 (1950).
[CrossRef]

Cole, H.

B. W. Battermann and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Fritsch, K.

G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
[CrossRef]

Gulyaev, Yu. V.

G. N. Shkerdin and Yu. V. Gulyaev, Sov. Phys. Solid State 16, 2136 (1975).

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Sov. Phys. Semicond. 6, 1646 (1973).

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Solid State Commun. 10, 1145 (1972).
[CrossRef]

Hamaguchi, C.

C. Hamaguchi, J. Phys. Soc. Japan 35, 832 (1973).
[CrossRef]

Herring, C.

C. Herring, Bell Sys. Tech. J. 34, 237 (1955).
[CrossRef]

Hope, L. L.

L. L. Hope, Phys. Rev. 166, 883 (1968).
[CrossRef]

Keller, O.

O. Keller, Phys. Rev. B 13, 4612 (1976).
[CrossRef]

O. Keller, Solid State Commun. 18, 1227 (1976).
[CrossRef]

O. Keller, Phys. Rev. B 11, 5059 (1975).
[CrossRef]

O. Keller and C. Søndergaard, Japan J. Appl. Phys. 13, 1765 (1974).
[CrossRef]

O. Keller, in Proceedings of the 3rd International Conference on Light Scattering in Solids, edited by M. Balkanski, R. C. C. Leite, and S. P. S. Porto (Flammarion, Paris, 1975), p. 447.

Kuzmany, H.

H. Kuzmany, Phys. Stat. Sol. A 25, 9 (1974).
[CrossRef]

Lax, M.

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[CrossRef]

Lazay, P. D.

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[CrossRef]

Nelson, D. F.

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[CrossRef]

Pine, A. S.

A. S. Pine, in Light Scattering in Solids, edited by M. Cardona (Springer-Verlag, Berlin, 1975), p. 253.
[CrossRef]

Proklov, V. V.

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Sov. Phys. Semicond. 6, 1646 (1973).

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Solid State Commun. 10, 1145 (1972).
[CrossRef]

Shkerdin, G. N.

G. N. Shkerdin and Yu. V. Gulyaev, Sov. Phys. Solid State 16, 2136 (1975).

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Sov. Phys. Semicond. 6, 1646 (1973).

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Solid State Commun. 10, 1145 (1972).
[CrossRef]

Søndergaard, C.

O. Keller and C. Søndergaard, Japan J. Appl. Phys. 13, 1765 (1974).
[CrossRef]

Spector, H. N.

H. N. Spector, Solid State Phys. 19, 291 (1966).
[CrossRef]

Tien, P. K.

P. K. Tien, Phys. Rev. 171, 970 (1968).
[CrossRef]

Bell Sys. Tech. J. (1)

C. Herring, Bell Sys. Tech. J. 34, 237 (1955).
[CrossRef]

J. Phys. Soc. Japan (1)

C. Hamaguchi, J. Phys. Soc. Japan 35, 832 (1973).
[CrossRef]

Japan J. Appl. Phys. (1)

O. Keller and C. Søndergaard, Japan J. Appl. Phys. 13, 1765 (1974).
[CrossRef]

Phys. Rev. (3)

P. K. Tien, Phys. Rev. 171, 970 (1968).
[CrossRef]

G. B. Benedek and K. Fritsch, Phys. Rev. 149, 647 (1966).
[CrossRef]

L. L. Hope, Phys. Rev. 166, 883 (1968).
[CrossRef]

Phys. Rev. B (3)

O. Keller, Phys. Rev. B 11, 5059 (1975).
[CrossRef]

D. F. Nelson, P. D. Lazay, and M. Lax, Phys. Rev. B 6, 3109 (1972).
[CrossRef]

O. Keller, Phys. Rev. B 13, 4612 (1976).
[CrossRef]

Phys. Stat. Sol. A (2)

H. Kuzmany, Phys. Stat. Sol. A 25, 9 (1974).
[CrossRef]

A. K. Agarwal, Phys. Stat. Sol. A 25, 667 (1974).
[CrossRef]

Rev. Mod. Phys. (1)

B. W. Battermann and H. Cole, Rev. Mod. Phys. 36, 681 (1964).
[CrossRef]

Solid State Commun. (2)

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Solid State Commun. 10, 1145 (1972).
[CrossRef]

O. Keller, Solid State Commun. 18, 1227 (1976).
[CrossRef]

Solid State Phys. (1)

H. N. Spector, Solid State Phys. 19, 291 (1966).
[CrossRef]

Sov. Phys. Semicond. (1)

V. V. Proklov, G. N. Shkerdin, and Yu. V. Gulyaev, Sov. Phys. Semicond. 6, 1646 (1973).

Sov. Phys. Solid State (1)

G. N. Shkerdin and Yu. V. Gulyaev, Sov. Phys. Solid State 16, 2136 (1975).

Z. Phys. (1)

G. Borrmann, Z. Phys. 127, 297 (1950).
[CrossRef]

Other (3)

O. Keller, in Proceedings of the 3rd International Conference on Light Scattering in Solids, edited by M. Balkanski, R. C. C. Leite, and S. P. S. Porto (Flammarion, Paris, 1975), p. 447.

A. S. Pine, in Light Scattering in Solids, edited by M. Cardona (Springer-Verlag, Berlin, 1975), p. 253.
[CrossRef]

The real and imaginary parts of the optical wave vector need not be collinear. In a forthcoming paper we shall study the modifications introduced by boundary effects in the theory. Thus, in a semi-infinite crystal filling half-space, the planes of constant absorption are, independent of the direction of phase propagation, parallel to the boundary.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

FIG. 1
FIG. 1

Schematic representation of the mutual phase shifts of the quasistanding electric field-intensity wave patterns for the anomalously transmitted fundamental Fourier mode (dashed line), the corresponding mode suffering enhanced absorption (full line), and a Gaussian free-carrier density modulation (shaded area).

FIG. 2
FIG. 2

Normalized optical wave vectors, k N ±, (dashed lines) and amplitude attenuation coefficients, γ N ±, (full lines) for the Bragg configurations of enhanced (−) and reduced (+) absorption as a function of the normalized optical frequency, ψ ˜, for a collisionless plasma. The shaded area shows the region ( ψ ˜ B , n + 1) of anomalous transmission. The normalized dispersion relation, k O N + ( ω ), for the forward diffracted beam is given by the dotted line. The coefficients k N 0 and γ N 0 refer to unperturbed optical wave propagation.

FIG. 3
FIG. 3

Normalized amplitude attenuation coefficients, γ 0 N +, for the anomalously transmitted mode as a function of the reduced frequency, ψ ˜, with the degree of free-carrier density modulation, | Δ ˜ K , n u|, as a parameter. The scattering takes place from a T2-phonon excited plasma wave in the basal plane of CdS.

FIG. 4
FIG. 4

Normalized wave vectors, k 0 N 0 +, (dashed lines) and amplitude attenuation coefficients, γ 0 N 0 +, (full lines) as a function of the reduced frequency, ψ ˜, for the limiting cases of free-carrier density modulation Δ ˜ K , n u = 0 , 1. Scattering from a T2-phonon excited plasma in the basal phane of CdS. The insert shows the Bragg angle θ B , n + for anomalous transmission as a function of ψ ˜.

Equations (41)

Equations on this page are rendered with MathJax. Learn more.

_ ( ω , r , t ) = μ K [ _ K L , μ + i ( σ _ K μ / 0 ω ) ] e i ( K · r - Ω K μ t ) ,
σ _ K μ = m σ _ K , m μ e i m ( K · r - Ω K μ t ) ,
_ K L , μ = _ K D , μ + m _ K , m S I , μ e i m ( K · r - Ω K μ t ) .
ω d = ω i + m Ω K μ ,
L c / n m Ω K μ ,
· E ( r , ω ) - 2 E ( r , ω ) = ( ω / c ) 2 _ ( r , ω ) · E ( r , ω ) ,
E ( r , ω ) = n E n ( ω , k n ) e ( i k n - γ n ) · r ,
k n = k 0 + n K ,
[ ( k n + i γ n ) · ( k n + i γ n ) 1 _ - ( k n + i γ n ) ( k n + i γ n ) ] · E n - ( ω / c ) 2 m _ K , n - m μ · E m = 0 ,             n = 0 , ± 1 , ± 2 ,
_ K , n μ = _ K , n D , μ p = 0 , ± 1 δ n , p + _ K , n S I , μ + i ( σ _ K , n μ / 0 ω ) .
I ( Q n ) I ( 0 ) = i = 1 3 sin 2 ( Q i L i / 2 ) ( Q i L i / 2 ) 2 .
{ ( c / ω ) 2 [ ( k 0 + i γ 0 ) · ( k 0 + i γ 0 ) 1 _ - ( k 0 + i γ 0 ) ( k 0 + i γ 0 ) ] - _ 0 } · E 0 = ( _ K , n μ ) * · E n ,
{ ( c / ω ) 2 [ ( k n + i γ n ) · ( k n + i γ n ) 1 _ - ( k n + i γ n ) ( k n + i γ n ) ] - _ 0 } · E n = _ K , n μ · E 0 ,
det { ( c / ω ) 2 ( k 0 + i γ 0 ) 2 - ˜ 0 - ( ˜ K , n μ ) * - ˜ K , n μ ( c / ω ) 2 ( k n + i γ n ) 2 - ˜ 0 } = 0 ,
k n ± = ( ω / c ) { 1 2 [ ( ˜ 0 2 + ˜ K , n μ 2 ± 2 Re [ ˜ 0 ] ˜ K , n μ ) 1 / 2 + Re [ ˜ 0 ] ± ˜ K , n μ ] } 1 / 2 ,
γ n ± = ( ω / c ) { 1 2 [ ( ˜ 0 2 + ˜ K , n μ 2 ± 2 Re [ ˜ 0 ] ˜ K , n μ ) 1 / 2 - Re [ ˜ 0 ] ˜ K , n μ ] } 1 / 2 ,
E ˜ n ± E ˜ 0 ± = ± e + i φ n ,             tan φ n = Im [ ˜ K , n μ ] Re [ ˜ K , n μ ] ,
E ˜ ± ( r , ω ) = 2 E ˜ 0 ± e i ( k 0 n ± ŝ · r + φ n / 2 ) e - γ 0 n ± ŝ · r × { cos [ ( 1 + i γ n + k n + )             n K 2 · r + φ n 2 ] - i sin [ ( 1 + i γ n - k n - )             n K 2 · r + φ n 2 ] } .
k 0 n ± ( ω ) = k n ± ( ω ) cos θ B , n ± ( ω ) ,
γ 0 n ± ( ω ) = γ n ± ( ω ) cos θ B , n ± ( ω ) ,
sin θ B , n ± = n K / 2 k n ± .
k n ± γ n ± = k 0 γ 0 = 1 2 ( ω / c ) 2 Im [ ˜ 0 ] ,
k 0 n ± γ 0 n ± = k 0 γ 0 cos 2 θ B , n ± ,
0 < Im [ ˜ 0 ] Re [ ˜ 0 ] ± ˜ K , n μ 1.
˜ 0 = ˜ 0 L ( 1 + 1 v 2 v 2 Ã ψ ˜ i - Ã ψ ˜ 1 + ( Ã ψ ˜ ) 2 ) ,
˜ K , n μ = ˜ 0 L v 2 v 2 Ã ψ ˜ i - Ã ψ ˜ 1 + ( Ã ψ ˜ ) 2 Δ ˜ K , n μ ,
˜ 0 ˜ 0 L [ 1 - ( ω ˜ p / ω ) 2 ] ,
˜ K , n μ - ˜ 0 L ( ω ˜ p / ω ) 2 Δ ˜ K , n μ ,
γ n ± 0 ,
k n ± ( ˜ 0 L ) 1 / 2 ( ω / c ) [ 1 - ( ω ˜ p / ω ) 2 ( 1 Δ ˜ K , n μ ) ] 1 / 2 ,
γ n ± ( ˜ 0 L ) 1 / 2 ( ω / c ) [ ( ω ˜ p / ω ) 2 ( 1 Δ ˜ K , n μ ) - 1 ] 1 / 2 ,
k n ± 0 ,
ω ˜ B , n + = ( ω ˜ p 2 ( 1 - Δ ˜ K , n μ ) + n 2 c 2 4 ˜ 0 L ( V p , K μ ) 2 Ω 2 ) 1 / 2 ω ω ˜ p ,
ω ˜ p ω ( ω p 2 ( 1 + Δ ˜ K , n μ ) + n 2 c 2 4 ˜ 0 L ( V p , K μ ) 2 Ω 2 ) 1 / 2 = ω ˜ B ˜ , n ,
k 0 N ± = [ ψ ˜ 2 - 1 ± Δ ˜ K , n μ - ( k N min ) 2 ] 1 / 2 ,             Ã ψ ˜ 1
γ 0 N ± = [ 1 Δ ˜ K , n μ - ψ ˜ 2 - ( k N min ) 2 ] 1 / 2 ,             Ã ψ ˜ 1
k N min = n c 2 ( ˜ 0 L ) 1 / 2 V p , K μ Ω ω ˜ p ,
ω ˜ p τ ˜ p .
Ω τ ˜ p .
( γ n + ) 2 + ( γ n - ) 2 = 2 ( γ 0 ) 2 ,
( k n + ) 2 + ( k n - ) 2 = 2 ( k 0 ) 2 .