Abstract

Frustrated total internal reflection calculations show that after a certain thickness of the second medium the wavepacket transit time does not depend on thickness.

© 1989 Optical Society of America

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References

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  1. A. K. Ghatak, M. R. Shenoy, I. C. Goyal, K. Thyagarajan, “Beam Propagation Under Frustrated Total Reflection,” Opt. Commun. 56, 313 (1986).
    [Crossref]
  2. J. J. Cowan, B. Anicin, “Longitudinal and Transverse Displacements of a Bounded Microwave Beam at Total Internal Reflection,” J. Opt. Soc. Am. 67, 1307–1314 (1977).
    [Crossref]
  3. L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960).

1986 (1)

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, K. Thyagarajan, “Beam Propagation Under Frustrated Total Reflection,” Opt. Commun. 56, 313 (1986).
[Crossref]

1977 (1)

Anicin, B.

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960).

Cowan, J. J.

Ghatak, A. K.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, K. Thyagarajan, “Beam Propagation Under Frustrated Total Reflection,” Opt. Commun. 56, 313 (1986).
[Crossref]

Goyal, I. C.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, K. Thyagarajan, “Beam Propagation Under Frustrated Total Reflection,” Opt. Commun. 56, 313 (1986).
[Crossref]

Shenoy, M. R.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, K. Thyagarajan, “Beam Propagation Under Frustrated Total Reflection,” Opt. Commun. 56, 313 (1986).
[Crossref]

Thyagarajan, K.

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, K. Thyagarajan, “Beam Propagation Under Frustrated Total Reflection,” Opt. Commun. 56, 313 (1986).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

A. K. Ghatak, M. R. Shenoy, I. C. Goyal, K. Thyagarajan, “Beam Propagation Under Frustrated Total Reflection,” Opt. Commun. 56, 313 (1986).
[Crossref]

Other (1)

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960).

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Figures (2)

Fig. 1
Fig. 1

FTIR ray picture and refractive index distribution.

Fig. 2
Fig. 2

Normalized time delay τ/τmax as a function of thickness d of the second medium. The parameters are described in the text. τmax is found to have a value of 3.879 fs.

Equations (15)

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E y = A exp [ i ( k 1 x x + k 1 z z ω t ) ] + B exp [ i ( k 1 x x k 1 z z ω t ) ] , z < 0 , = C exp [ i ( k 1 x x ω t ) ] exp ( K z ) + D exp [ i ( k 1 x x ω t ) ] exp ( K z ) , 0 < z < d , = F exp [ i ( k 1 x x + k 1 z z ω t ) ] + G exp [ i ( k 1 x x k 1 z z ω t ) ] , z > d ,
k 1 x = k 1 sin θ i ; k 1 z = k 1 cos θ i ; K = k 1 x 2 k 2 2 k 1 = ω c n 1 ; k 2 = ω c n 2 ,
ψ i ( x , z , t ) = 1 2 π + d ω + + d k x A ( k x , ω ) × exp i [ k x x + k 1 z z ω t + θ ( k x , ω ) ] ,
ψ t ( x , z , t ) = 1 2 π + d ω + d k x A ( k x , ω ) t ( k x , ω ) × exp { i [ k x x + k 1 z ( z d ) ω t + θ + ϕ ] } ,
t ( k x , ω ) = 2 k 1 z K cosech ( d K ) [ ( k 1 z 2 K 2 ) ] 2 + 4 k 1 z 2 K 2 coth 2 ( K d ) 1 / 2 ,
ϕ ( k x , ω ) = π 2 tan 1 [ 2 k 1 z K coth ( K d ) ( k 1 z 2 K 2 ) ] .
ψ i ( x , z , t ) = χ i exp [ i ( k x 0 x ω 0 t + θ ( k x 0 , ω 0 ) ) ] ,
χ i = 1 2 π + d ω + d k x A ( k x , ω ) × exp [ i ( k x k x 0 ) ( x + k 1 z k x | k x 0 z + θ k x | k x 0 ) ] × exp [ i ( ω ω 0 ) ( t k 1 z ω | ω 0 z θ ω | ω 0 ) ]
x + k 1 z k x | k x 0 z + θ k x | k x 0 = 0 ,
t k 1 z ω | ω 0 z θ ω | ω 0 = 0 .
x + k 1 z k x | k x 0 ( z d ) + θ k x | k x 0 + ϕ k x | k x 0 = 0 ,
t k 1 z ω | ω 0 ( z d ) θ ω | ω 0 ϕ ω | ω 0 = 0 .
τ = ϕ ω | ω 0 = 2 ( k 1 z 2 K 2 ) 2 + 4 k 1 z 2 K 2 coth 2 ( K d ) × [ ( k 1 z 2 + K 2 ) ] coth ( K d ) k 1 z K ( k 1 υ 1 K 2 + k 2 υ 2 k 1 z 2 ) d υ 2 k 1 z k 2 cos ech 2 ( K d ) ( k 1 z 2 K 2 ) ,
τ max = 2 ( k 1 z 2 + K 2 ) [ 1 k 1 z K ( k 1 ν 1 K 2 + k 2 ν 2 k 1 z 2 ) ] ,
n 1 = 1 . 442 , ν 1 = c n 1 ( 1 λ 0 n 1 d n 1 d λ 0 ) 1 = 2 . 06 × 10 8 m / s , n 2 = 1 . 0 , ν 2 = c .

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