Abstract

An analysis is made of the photometrically determined ratio of the reflectances for the components, polarized parallel and perpendicular to the plane of incidence. Given the experimentally determined minimum ratio R/R. value and the angle of incidence, φB, at that minimum for a specular surface, an analytic determination of the real and imaginary parts of the dielectric constant can be made. Curves are given showing the limits for which certain successive simplifying approximations can be made that are consistent with experimental accuracy. Data for a GaSb sample at λ = 5800 Å are given with the computed values of 1, 2, and n and k.

© 1964 Optical Society of America

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References

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  1. T. S. Moss, Optical Properties of Semiconductors (Butter-worths Scientific Publications Ltd., London, 1959). Also, see standard texts which treat the Fresnel reflectance and transmittance.
  2. D. G. Avery, Proc. Phys. Soc. (London) B65, 425 (1952).
  3. R. E. Lindquist and A. W. Ewald, J. Opt. Soc. Am. 53, 247 (1963).
    [CrossRef]
  4. Subsequent to the presentation of Ref. 5 it was learned that H. B. Holl had carried out detailed calculations of the reflectances and characteristic angles (of which ϕB is one) for values of 0.1≤n≤4.0 and 0.1≤k≤6.0 in intervals of 0.1. Tabulated results appear in U. S. Army Missile Command Report No. RF-TR-63-4. I am grateful to Holl for supplying me with a copy.
  5. R. F. Potter, J. Opt. Soc. Am. 53, 1344 (1963).
    [CrossRef]

1963 (2)

1952 (1)

D. G. Avery, Proc. Phys. Soc. (London) B65, 425 (1952).

Avery, D. G.

D. G. Avery, Proc. Phys. Soc. (London) B65, 425 (1952).

Ewald, A. W.

Lindquist, R. E.

Moss, T. S.

T. S. Moss, Optical Properties of Semiconductors (Butter-worths Scientific Publications Ltd., London, 1959). Also, see standard texts which treat the Fresnel reflectance and transmittance.

Potter, R. F.

R. F. Potter, J. Opt. Soc. Am. 53, 1344 (1963).
[CrossRef]

J. Opt. Soc. Am. (2)

Proc. Phys. Soc. (London) (1)

D. G. Avery, Proc. Phys. Soc. (London) B65, 425 (1952).

Other (2)

Subsequent to the presentation of Ref. 5 it was learned that H. B. Holl had carried out detailed calculations of the reflectances and characteristic angles (of which ϕB is one) for values of 0.1≤n≤4.0 and 0.1≤k≤6.0 in intervals of 0.1. Tabulated results appear in U. S. Army Missile Command Report No. RF-TR-63-4. I am grateful to Holl for supplying me with a copy.

T. S. Moss, Optical Properties of Semiconductors (Butter-worths Scientific Publications Ltd., London, 1959). Also, see standard texts which treat the Fresnel reflectance and transmittance.

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Figures (1)

F. 1
F. 1

Curves for which certain approximation limits are valid. (21) can be used throughout the space of RB, φB in connection with Eqs. (15) and (16). Approximations are valid in regions to the right of labeled curves. IIa and IIb give limits for η2≤0.03 and 0.01, respectively. IIIa and IIIb give limits on η3 of 0.01 and 0.001, respectively, while IVa and IVb show the same limits for η4. IIc gives an upper limit for |4S0| <0.05 while IId gives an upper limit for |4S0| <0.01.

Tables (1)

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Table I Determination of optical constants of GaSb at λ = 5800 Å.

Equations (34)

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R = R R = | [ cos φ r cos φ i sin φ r sin φ i cos φ r cos φ i + sin φ r sin φ i ] | 2 ,
sin φ i = ( N / N 0 ) sin φ , ( Snell’s law ) ,
N N 0 cos φ r = N ( 1 sin 2 φ r ) 1 2 N 0 = N N 0 [ 1 ( N 0 N ) 2 sin 2 φ i ] 1 2 = α + i β ,
α 2 β 2 = [ ( n 2 k 2 ) / N 0 2 ] sin 2 φ i , α 2 β 2 = ( n 2 k 2 ) / N 0 4 .
R = | [ ( N / N 0 ) cos φ r cos φ i sin 2 φ i ( N / N 0 ) cos φ r cos φ i + sin 2 φ i ] | 2 , = | [ α + i β sin φ i tan φ i α + i β + sin φ i tan φ i ] | 2 .
R = [ ( α X ) 2 + β 2 ] / [ ( α + X ) 2 + β 2 ] .
( α d α / d φ ) ( β d β / d φ ) = sin φ cos φ ,
β d α + α d β = 0 ,
( α 2 + β 2 ) ( 1 / α ) ( d α / d φ ) = sin φ cos φ ,
( 1 / X ) ( d X / d φ ) = ( 2 + tan 2 φ ) / tan φ .
( α 2 X 2 ) X d α d φ ( α 2 X 2 ) α d X d φ β 2 ( X d α d φ + α d X d φ ) + 2 α β X d β d φ = 0 .
α 0 2 + β 0 2 = X 0 2 at φ B ,
( X 0 2 4 β 0 2 X B 2 ) 1 α d α d φ | B = ( X 0 2 X B 2 ) ( 1 X B d X d φ ) | B ,
X 0 2 X B 2 = 4 β 0 2 ( d α / α 0 ) ( X / d X ) | B 1 ( d α / α 0 ) ( X / d X ) | B = 4 β 0 2 γ B ,
X 0 2 = X B 2 [ 1 ( 4 β 0 2 γ B / X B 2 ) ] , γ B = ( d α / α 0 ) ( X / d X ) | B 1 ( d α / α 0 ) ( X / d X ) | B .
α 0 2 / X B 2 = p 2 , β 0 2 / X B 2 = q 2
X 0 2 = X B 2 ( 1 4 q 2 γ B ) ,
R B = α 0 2 + β 0 2 2 β 0 X B + X B 2 α 0 2 + β 0 2 + 2 α 0 X B + X B 2 = X 0 2 2 α 0 X B + X B 2 X 0 2 + 2 α 0 X B + X B 2
R B = X B 2 ( 1 2 q 2 γ B ) α 0 X B X B 2 ( 1 2 q 2 γ B ) + α 0 X B = X B ( 1 2 q 2 γ B ) α 0 X B ( 1 2 q 2 γ B ) + α 0 .
α 0 2 / X B 2 = p 2 = ( 1 2 q 2 γ B ) 2 [ ( 1 R B ) / ( 1 + R B ) ] 2 = ( 1 2 q 2 γ B ) 2 c 2
β 0 2 / X B 2 = ( X 0 2 / X B 2 ) p 2 = q 2 = 1 4 q 2 γ B ( 1 2 q 2 γ B ) 2 c 2
β 0 2 / X B 2 = q 2 = d 2 ( 1 4 q 2 γ B ) 4 γ B 2 q 4 c 2 c 2 = [ ( 1 R B ) / ( 1 + R B ) ] 2 ; d 2 = 4 R B / ( 1 + R B ) 2 ; c 2 + d 2 = 1 .
γ B = K / ( 1 K ) ,
K = d α α 0 X d X | B = sin 2 φ B ( 2 + tan 2 φ B ) X 0 2 = 1 ( 2 + tan 2 φ B ) tan 2 φ B ( 1 4 q 2 γ B ) = 1 ( 1 4 q 2 γ B ) f .
γ B = 1 / [ 1 + ( 1 4 q 2 γ B ) f ] ,
q 2 γ B = q 2 / [ 1 + ( 1 4 q 2 γ B ) f ] .
q 2 = S ( 1 + f ) + 4 f S 2 ,
q 2 = d 2 ( 1 4 S ) 4 S 2 c 2 .
4 S 2 ( 1 + S 0 ) ( 1 + 4 S 0 ) S + S 0 = 0 .
S = [ 1 / 8 ( 1 + S 0 ) ] [ 1 + 4 S 0 ( 1 8 S 0 ) 1 2 ]
S 0 = d 2 / ( 1 + f ) ; for small values of S 0 q 2 d 2 ; γ B 1 / ( 1 + f ) .
S = S 0 { 1 + 4 S 0 2 [ ( 1 + 5 S 0 ) / ( 1 + S 0 ) ] } = S 0 ( 1 + η 2 ) η 2 4 S 0 2 ( 1 + 4 S 0 ) ; S 0 1 8 .
q 2 = d 2 ( 1 4 S 0 ) ( 1 η 3 ) ; η 3 ( 4 c 2 d 2 ) / [ ( 1 + f ) 2 ( 1 4 S 0 ) ] ,
p 2 = c 2 ( 1 2 S 0 ) 2 ( 1 + η 4 ) ; η 4 16 S 0 3 ( 1 + 2 S 0 ) .