Abstract

The well-known problem of penetration through an internally reflecting barrier is treated as it relates to the extraction of a laser beam from an internally reflecting cavity. A quantity d logT/d logn which relates the fractional change of transmittance to the fractional change of refractive index is defined and is shown to be large for large barrier spacing. It is suggested that this strong dependence of transmittance on the value of n may be used in studying and controlling laser beams.

© 1963 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. H. Maiman, Nature 187, 493 (1960).
    [Crossref]
  2. Advertised commercially by Trion Corporation.
  3. E. R. Peck, J. Opt. Soc. Am. 52, 253 (1962).
    [Crossref]
  4. P. Rabinowitz, J. Opt. Soc. Am. 52, 452 (1962).
    [Crossref]
  5. G. Gould, S. F. Jacobs, P. Rabinowitz, and T. Shultz, J. Opt. Soc. Am. 51, 1467 (1961).
  6. L. Berstein, W. Kahn, and C. Shulman, Proc. IRE 50, 1833 (1962).

1962 (3)

1961 (1)

G. Gould, S. F. Jacobs, P. Rabinowitz, and T. Shultz, J. Opt. Soc. Am. 51, 1467 (1961).

1960 (1)

T. H. Maiman, Nature 187, 493 (1960).
[Crossref]

Berstein, L.

L. Berstein, W. Kahn, and C. Shulman, Proc. IRE 50, 1833 (1962).

Gould, G.

G. Gould, S. F. Jacobs, P. Rabinowitz, and T. Shultz, J. Opt. Soc. Am. 51, 1467 (1961).

Jacobs, S. F.

G. Gould, S. F. Jacobs, P. Rabinowitz, and T. Shultz, J. Opt. Soc. Am. 51, 1467 (1961).

Kahn, W.

L. Berstein, W. Kahn, and C. Shulman, Proc. IRE 50, 1833 (1962).

Maiman, T. H.

T. H. Maiman, Nature 187, 493 (1960).
[Crossref]

Peck, E. R.

Rabinowitz, P.

P. Rabinowitz, J. Opt. Soc. Am. 52, 452 (1962).
[Crossref]

G. Gould, S. F. Jacobs, P. Rabinowitz, and T. Shultz, J. Opt. Soc. Am. 51, 1467 (1961).

Shulman, C.

L. Berstein, W. Kahn, and C. Shulman, Proc. IRE 50, 1833 (1962).

Shultz, T.

G. Gould, S. F. Jacobs, P. Rabinowitz, and T. Shultz, J. Opt. Soc. Am. 51, 1467 (1961).

J. Opt. Soc. Am. (3)

E. R. Peck, J. Opt. Soc. Am. 52, 253 (1962).
[Crossref]

P. Rabinowitz, J. Opt. Soc. Am. 52, 452 (1962).
[Crossref]

G. Gould, S. F. Jacobs, P. Rabinowitz, and T. Shultz, J. Opt. Soc. Am. 51, 1467 (1961).

Nature (1)

T. H. Maiman, Nature 187, 493 (1960).
[Crossref]

Proc. IRE (1)

L. Berstein, W. Kahn, and C. Shulman, Proc. IRE 50, 1833 (1962).

Other (1)

Advertised commercially by Trion Corporation.

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 (3)

Fig. 1
Fig. 1

Diagram of the internally reflecting laser cavity shown with a beam extractor. Roof prisms are indicated.

Fig. 2
Fig. 2

Ray paths at the boundary face A, B.

Fig. 3
Fig. 3

Ray path configuration used for analyzing the effect of the barrier. Media I and III are the same.

Tables (1)

Tables Icon

Table I Values of the modulation sensitivity d logT/d logn for various spacings (n = 1.4264 calcium fluoride, λ = 1.4733, θ = 45°).

Equations (17)

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

E 1 = 1 z e i l y ( A e i m x + B e i m x ) , E 2 = 1 z e i l y ( C e k x + D e k x ) , E 3 = 1 z e i l y ( F e i m x + G e i m x ) .
H 1 = 1 z e i l y ( A e i m x + B e i m x ) , H 2 = 1 z e i l y ( C e k x + D e k x ) , H 3 = 1 z e i l y ( F e i m x + G e i m x ) .
l = ( 2 π n / λ ) sin θ , m = ( 2 π n / λ ) cos θ ,
( A B ) M 1 = ( C D ) M 2 M 1 = { e i m δ e i m δ e i m δ e i m δ } M 2 = { e k δ ( i k / m ) e k δ e k δ ( i k / m ) e k δ } ( C D ) M 3 = ( F G ) M 4 M 3 = { e k δ ( i k / m ) e k δ e k δ ( i k / m ) e k δ } M 4 = { e i m δ e i m δ e i m δ e i m δ } ,
( A B ) M 1 = ( C D ) M 5 M 5 = { e k δ ( k n 2 / i m ) e k δ e k δ ( k n 2 / i m ) e k δ } ( C D ) M 6 = ( F G ) M 4 M 6 = { e k δ ( k n 2 / i m ) e k δ e k δ ( k n 2 / i m ) e k δ } .
F A = 4 e i 2 m δ / [ 4 cos h 2 k δ + 2 i ( k m m k ) sin h 2 k δ ] ;
F A = 4 e i 2 m δ / [ 4 cos h 2 k δ + 2 i ( n 2 k m m n 2 k ) sin h 2 k δ ] .
T = | F A | 2 = 16 / { 16 + [ 16 + 4 ( k m m k ) 2 ] sin h 2 2 k δ } ,
T = | F A | 2 = 16 / { 16 + [ 16 + 4 ( n 2 k m m n 2 k ) 2 ] sin h 2 2 k δ } .
T 16 k 2 m 2 e 4 k δ / ( k 2 + m 2 ) 2 ,
T 16 n 4 k 2 m 2 e 4 k δ / ( n 4 k 2 + m 2 ) 2 .
T = 16 n 2 cos 2 θ ( n 2 sin 2 θ 1 ) ( n 2 1 ) 2 exp [ 4 π λ ( n 2 sin 2 θ 1 ) 1 2 Δ ] ,
T = 16 n 2 cos 2 θ ( n 2 sin 2 θ 1 ) [ sin 2 θ ( n 4 1 ) ( n 2 1 ) ] 2 exp [ 4 π λ ( n 2 sin 2 θ 1 ) 1 2 Δ ] .
d log T d log n = ( 4 π Δ / λ ) n 2 sin 2 θ ( n 2 sin 2 θ 1 ) 1 2 + 2 ( 1 + n 2 cos 2 θ ) ( n 2 1 ) ( n 2 sin 2 θ 1 ) ;
d log T d log n = ( 4 π Δ / λ ) n 2 sin 2 θ ( n 2 sin 2 θ 1 ) 1 2 + 2 2 n 2 sin 2 θ 1 n 2 sin 2 θ 1 4 n 2 ( 2 n 2 sin 2 θ 1 ) ( n 2 1 ) [ ( n 2 + 1 ) sin 2 θ 1 ] .
d log T d log n = 4 π 2 Δ n 2 λ ( n 2 2 ) 1 2 + 4 ( n 2 1 ) ( n 2 2 ) ;
d log T d log n = 4 2 π Δ n 2 λ ( n 2 2 ) 1 2 + 4 ( n 4 + 2 n 2 + 1 ) ( n 2 1 ) ( n 2 2 ) .