Abstract

Analysis of an optical ring resonator consisting of a prism and two mirrors demonstrates that such a resonator can have adjustable dispersion of either sign. The dispersion is proportional to the second derivative of the optical path length in the resonator with respect to wavelength. Adjustable dispersion may have important application to the production of ultrashort laser pulses.

© 1984 Optical Society of America

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References

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  1. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [CrossRef]
  2. A. Hagegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  3. W. Dietel, J. J. Fontaine, J. C. Diels, Opt. Lett. 8, 4 (1983).
    [CrossRef] [PubMed]
  4. S. DeSilvestri, P. LaPorta, O. Svelto, Centro di Elettronica Quantistica e Strumentazione Elettronica del CNR, Istituto di Fisica del Politechnico, Milano, Italy (personal communication).
  5. D. Marcuse, Appl. Opt. 19, 1653 (1980).
    [CrossRef] [PubMed]

1983 (1)

1980 (2)

D. Marcuse, Appl. Opt. 19, 1653 (1980).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1973 (1)

A. Hagegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

DeSilvestri, S.

S. DeSilvestri, P. LaPorta, O. Svelto, Centro di Elettronica Quantistica e Strumentazione Elettronica del CNR, Istituto di Fisica del Politechnico, Milano, Italy (personal communication).

Diels, J. C.

Dietel, W.

Fontaine, J. J.

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Hagegawa, A.

A. Hagegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

LaPorta, P.

S. DeSilvestri, P. LaPorta, O. Svelto, Centro di Elettronica Quantistica e Strumentazione Elettronica del CNR, Istituto di Fisica del Politechnico, Milano, Italy (personal communication).

Marcuse, D.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Svelto, O.

S. DeSilvestri, P. LaPorta, O. Svelto, Centro di Elettronica Quantistica e Strumentazione Elettronica del CNR, Istituto di Fisica del Politechnico, Milano, Italy (personal communication).

Tappert, F.

A. Hagegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Hagegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Other (1)

S. DeSilvestri, P. LaPorta, O. Svelto, Centro di Elettronica Quantistica e Strumentazione Elettronica del CNR, Istituto di Fisica del Politechnico, Milano, Italy (personal communication).

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Figures (3)

Fig. 1
Fig. 1

Ring resonator incorporating a prism. The optical path for a ray having a deviation angle θ is shown by the solid line. The optical path for a ray having a smaller deviation angle is shown by the dashed line.

Fig. 2
Fig. 2

Construction for the optical path length through the prism. In (a), AB and ED are possible wave fronts. Hence paths AE and BCD have equal optical lengths. Length BD of (b) is equal to AE of (a) by construction. Points A and D are common to both diagrams.

Fig. 3
Fig. 3

Right half of the resonator of Fig. 1. Point A is the apex of the prism. By the construction of Fig. 2, length BDE is half of the optical length of the resonator.

Equations (12)

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T = d ( 2 π P / λ ) d ω = c 1 ( P λ d P / d λ ) ,
D = l 1 d T / d λ = ( λ / c l ) d 2 P / d λ 2 ,
B D = A E sin θ + E D cos θ ,
P = 2 [ A E sin θ + E D ( 1 + cos θ ) ] .
d P / d θ = 2 [ A E cos θ E D sin θ ] = 2 A B , d 2 P / d θ 2 = R c o s ( θ / 2 ) 2 B D = 2 ( f B D ) ,
d P d λ = d n d λ d P d n , d 2 P d λ 2 = d 2 n d λ 2 d P d n + ( d n d λ ) 2 d 2 P d n 2 ,
d 2 P d λ 2 = [ d 2 n d λ 2 d θ d n + ( d n d λ ) 2 d 2 θ d n 2 ] d P d θ + ( d n d λ d θ d n ) 2 d 2 P d θ 2 .
θ = sin 1 ( n sin α ) α , d θ / d n = [ ( sin α ) 2 n 2 ] 1 / 2 , d 2 θ / d n 2 = n ( d θ / d n ) 3 .
d 2 P / d λ 2 = [ d 2 n d λ 2 + n ( d n d λ ) 2 ] 2 A B + ( d n d λ ) 2 2 ( f B D ) .
n = 1 . 457 , d n / d λ = 0 . 03059 μ m 1 , d 2 n / d λ 2 = 0 . 1267 μ m 2 ,
d 2 P / d λ 2 = 0 . 256 A B + 1 . 87 × 10 3 ( f B D ) .
d 2 P / d λ 2 = 0 . 4292 ,

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