Abstract

We have developed a new ring-down technique that does not require a shutter to turn a probe laser on and off. With a rapid cavity scan we can measure a simple exponential cavity decay from which a cavity finesse can be found. When the cavity is scanned slowly, the cavity decay exhibits an amplitude modulation, and an analytic expression is derived for this modulation. With this new technique we measured the ultraslow relative velocity of the mirrors (of the order of micrometers per second) as well as the linewidth (~100 kHz) of the probe laser.

© 1995 Optical Society of America

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References

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  1. K. An, J. J. Child, R. R. Dasari, M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
    [CrossRef] [PubMed]
  2. R. J. Thompson, G. Rempe, H. J. Kimble, Phys. Rev. Lett. 66, 1132 (1992).
    [CrossRef]
  3. G. Rempe, R. J. Thompson, H. J. Kimble, Opt. Lett. 17, 363 (1992).
    [CrossRef] [PubMed]
  4. B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vol. 2, p. 1545.
  5. W. H. Parkinson, F. S. Tomkins, J. Opt. Soc. Am. 68, 535 (1978).
    [CrossRef]

1994 (1)

K. An, J. J. Child, R. R. Dasari, M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

1992 (2)

R. J. Thompson, G. Rempe, H. J. Kimble, Phys. Rev. Lett. 66, 1132 (1992).
[CrossRef]

G. Rempe, R. J. Thompson, H. J. Kimble, Opt. Lett. 17, 363 (1992).
[CrossRef] [PubMed]

1978 (1)

An, K.

K. An, J. J. Child, R. R. Dasari, M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

Child, J. J.

K. An, J. J. Child, R. R. Dasari, M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

Dasari, R. R.

K. An, J. J. Child, R. R. Dasari, M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

Feld, M. S.

K. An, J. J. Child, R. R. Dasari, M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

Kimble, H. J.

R. J. Thompson, G. Rempe, H. J. Kimble, Phys. Rev. Lett. 66, 1132 (1992).
[CrossRef]

G. Rempe, R. J. Thompson, H. J. Kimble, Opt. Lett. 17, 363 (1992).
[CrossRef] [PubMed]

Parkinson, W. H.

Rempe, G.

R. J. Thompson, G. Rempe, H. J. Kimble, Phys. Rev. Lett. 66, 1132 (1992).
[CrossRef]

G. Rempe, R. J. Thompson, H. J. Kimble, Opt. Lett. 17, 363 (1992).
[CrossRef] [PubMed]

Shore, B. W.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vol. 2, p. 1545.

Thompson, R. J.

G. Rempe, R. J. Thompson, H. J. Kimble, Opt. Lett. 17, 363 (1992).
[CrossRef] [PubMed]

R. J. Thompson, G. Rempe, H. J. Kimble, Phys. Rev. Lett. 66, 1132 (1992).
[CrossRef]

Tomkins, F. S.

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Phys. Rev. Lett. (2)

K. An, J. J. Child, R. R. Dasari, M. S. Feld, Phys. Rev. Lett. 73, 3375 (1994).
[CrossRef] [PubMed]

R. J. Thompson, G. Rempe, H. J. Kimble, Phys. Rev. Lett. 66, 1132 (1992).
[CrossRef]

Other (1)

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vol. 2, p. 1545.

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Figures (2)

Fig. 1
Fig. 1

Typical cavity decay curve obtained with the ring-down technique. The solid curve is an exponential fit to the data.

Fig. 2
Fig. 2

Cavity decay curve with a slow scan speed exhibiting an amplitude modulation. The period T12, defined in relation (12), is 0.38 μs, resulting in a mirror velocity of 6.4 μm/s.

Equations (14)

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T M [ ( 2 L 0 c ) ( λ v ) ] 1 / 2 .
L ( τ ) = L 0 + v τ .
E in ( τ ) = n = 0 t r 2 n E 0 exp { i k [ z + 2 m = 1 n L ( τ m ) ] - i ω τ } ,
m = 1 n L ( τ m ) = m = 1 n ( L 0 + v τ m ) = m = 1 n [ L 0 + v τ - v ( 2 m - 1 ) L 0 v / c ] = n [ ( 1 - n v c ) L 0 + v τ ] .
E in ( τ ) = E 0 exp [ i ( k z - ω τ ) ] × n = 0 r 2 n exp { i 2 n k [ ( 1 - n v c ) L 0 + v τ ] } .
k L 0 = N π ,             N an integer .
2 n k [ ( 1 - n v c ) L 0 + v τ ] = 2 n k [ ( 1 - n v c ) L 0 + v 2 L 0 c l ] = 2 n N π + k v ( 2 L 0 c ) n ( 2 l - n ) .
I in ( τ ) | n = 0 r 2 n exp [ i k v ( 2 L 0 c ) n ( 2 l - n ) ] | 2 .
I in ( τ ) r 4 l | n = 0 exp [ i k v ( 2 L 0 c ) n ( 2 l - n ) ] | 2 R 2 l = exp ( ln R 2 l ) = exp { 2 l ln [ 1 - ( 1 - R ) ] } exp [ - 2 ( 1 - R ) l ] = exp [ - 2 ( 1 - R ) c τ / 2 L ] = exp ( - τ / T cav ) ,
I in ( τ ) | n = 0 r 2 n exp { i k v ( 2 L 0 c ) [ l 2 - ( n - l ) 2 ] } | 2 = | n = - l r 2 ( n + l ) exp { i k v ( 2 L 0 c ) [ l 2 - n 2 ] } | 2 = | r 2 l exp [ i k v ( 2 L 0 c ) l 2 ] | 2 × | n = - 1 r 2 n exp [ - i k v ( 2 L 0 c ) n 2 ] | 2 = R 2 l | n = - 1 r 2 n exp [ - i k v ( 2 L 0 c ) n 2 ] | 2 = R 2 l | n = - 1 l r - 2 n exp [ - i k v ( 2 L 0 c ) n 2 ] + n = 0 r 2 n exp [ - i k v ( 2 L 0 c ) n 2 ] | 2 ,
k v ( 2 L 0 c ) l m 2 2 π m ,
τ m = 2 L 0 c l m [ m ( 2 L 0 c ) ( λ v ) ] 1 / 2 .
T 12 τ 2 - τ 1 ( 2 - 1 ) [ ( 2 L 0 c ) ( λ v ) ] 1 / 2 .
{ ϕ ( τ ) ϕ ( τ ) } ens = 2 Γ L δ ( τ - τ ) ,

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