Abstract

A simplified method for measuring the effective photon lifetime in an optical resonator was developed. The technique requires the passage of a modulated cw laser beam through the resonator and the measurement of the resultant shift in the phase of the transmitted intensity. The method not only permits a quick and precise measurement of the mirror reflectances, but also permits these measurements to be in situ. Such an on-the-spot evaluation capability should be extremely useful in applications ranging from the investigation of new laser systems to the development of improved optical coatings. The method is also sensitive to the effects of absorption, scattering, and transmission from elements in the cavity. Cavity losses <100 ppm were detected.

© 1980 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Sanders, Appl. Opt. 16, 191 (1977).
    [CrossRef]
  2. J. Kemp, J. Opt. Soc. Am. 59, 950 (1969).
  3. W. J. Tango, R. N. Zare, J. Chem. Phys. 53, 3094 (1970).
    [CrossRef]
  4. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 325.
  5. C. R. Wylie, Advances in Engineering Mathematics (McGraw-Hill, New York, 1960), p. 697.
  6. E. P. Vance, Modern Algebra and Trigonometry (Addison-Wesley, Reading, Mass., 1962), p. 287.

1977 (1)

V. Sanders, Appl. Opt. 16, 191 (1977).
[CrossRef]

1970 (1)

W. J. Tango, R. N. Zare, J. Chem. Phys. 53, 3094 (1970).
[CrossRef]

1969 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 325.

Kemp, J.

Sanders, V.

V. Sanders, Appl. Opt. 16, 191 (1977).
[CrossRef]

Tango, W. J.

W. J. Tango, R. N. Zare, J. Chem. Phys. 53, 3094 (1970).
[CrossRef]

Vance, E. P.

E. P. Vance, Modern Algebra and Trigonometry (Addison-Wesley, Reading, Mass., 1962), p. 287.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 325.

Wylie, C. R.

C. R. Wylie, Advances in Engineering Mathematics (McGraw-Hill, New York, 1960), p. 697.

Zare, R. N.

W. J. Tango, R. N. Zare, J. Chem. Phys. 53, 3094 (1970).
[CrossRef]

Appl. Opt. (1)

V. Sanders, Appl. Opt. 16, 191 (1977).
[CrossRef]

J. Chem. Phys. (1)

W. J. Tango, R. N. Zare, J. Chem. Phys. 53, 3094 (1970).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1970), p. 325.

C. R. Wylie, Advances in Engineering Mathematics (McGraw-Hill, New York, 1960), p. 697.

E. P. Vance, Modern Algebra and Trigonometry (Addison-Wesley, Reading, Mass., 1962), p. 287.

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

Photon-lifetime measurement method.

Fig. 2
Fig. 2

Tanα vs intracavity distance.

Fig. 3
Fig. 3

Three-mirror configuration for measurement of photon lifetime.

Tables (1)

Tables Icon

Table I Results of Tests on Several Mirrors of Differing Characteristics

Equations (16)

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

tan ( α ) = 4 π f τ .
π = n τ = ( 2 n L ) / c .
R = exp ( - τ τ ) = exp ( - 1 n ) ,
R = R 1 R 2 1.
d I d t + I τ = k 1 cos ( 4 π n f t ) + k 2 ,
R = n / ( n + 1 ) .
A B = sin ( α ) cos ( α ) = tan ( α ) .
R = R 1 R 3 2 R 2
I in ( t ) = I 0 sin ( 4 π f t + ϕ 0 ) ,
I out ( t ) = T I 0 k = 1 R k sin [ 4 π f ( t - k τ ) + ϕ 0 ] ,
k = 0 R k sin [ ( k + 1 ) θ ] = sin ( θ ) 1 - 2 R cos ( θ ) + R 2 ,
k = 0 R k cos [ ( k + 1 ) θ ] = cos ( θ ) - R 1 - 2 R cos ( θ ) + R 2 ,
I out = T I 0 sin ( ω t ) - R sin ( ω t + ω τ ) 1 - 2 R cos ( ω τ ) + R 2 ,
S = a sin ( ω t + α ) + b sin ( ω t + β ) = r sin ( ω t + ϕ ) ,
I out = T I 0 sin ( ω t + ϕ ) [ 1 - 2 R cos ( ω τ ) + R 2 ] 1 / 2 ,
tan ( ϕ ) = - R sin ( ω τ ) 1 - R cos ( ω τ ) - ω τ R 1 - R - n ω τ .

Metrics