Abstract

A variant of Rayleigh–Schrödinger peturbation theory is applied to the computation of the additional power losses and phase shifts caused by perturbations of optical resonators. Numerical results are given for tilted infinite-strip plane resonators. For a large range of Fresnel numbers and sufficiently small angles of tilt, there is good agreement between these and previous results. The major advantages of this technique are its applicability for both high Fresnel numbers and higher-order modes with only a minimal use of computer time.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453 (1969); T. Li, “Diffraction loss and selection of modes in maser resonators with circular mirrors,” Bell Syst. Tech. J. 44, 917–932 (1965); G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508, (1961); M. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550 (1966).
    [CrossRef] [PubMed]
  2. A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. Inst. Elect. Electron. Eng. 51, 80 (1963); W. H. Wells, “Modes of a tilted mirror optical resonator for the infrared,” IEEE J. Quantum Electron. QE-2, 94–102 (1966); R. L. Sanderson, W. Streifer, “Laser resonators with tilted reflectors,” Appl. Opt. 8, 131 (1969).
    [CrossRef] [PubMed]
  3. S. R. Barone, “Perturbed open resonators,” Appl. Opt. 10, 935 (1971).
    [CrossRef] [PubMed]
  4. E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 17.
  5. J. P. Gordon, H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 44, 2873–2887, (1965).
  6. L. A. Vainshtein, “Open resonators for lasers,” Sov. Phys. JETP 17, 709–719 (1963) [J. Exp. Theor. Phys. (USSR) 44, 1050–1067 (1963)].
  7. S. R. Barone, “Resonances of the Fabry–Perot laser,” J. Appl. Phys. 34, 831–843 (1963).
    [CrossRef]
  8. J. L. Remo, “Dependence of power loss on mirror tilt,” in preparation (1978).

1971 (1)

1969 (1)

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453 (1969); T. Li, “Diffraction loss and selection of modes in maser resonators with circular mirrors,” Bell Syst. Tech. J. 44, 917–932 (1965); G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508, (1961); M. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

1965 (1)

J. P. Gordon, H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 44, 2873–2887, (1965).

1963 (3)

L. A. Vainshtein, “Open resonators for lasers,” Sov. Phys. JETP 17, 709–719 (1963) [J. Exp. Theor. Phys. (USSR) 44, 1050–1067 (1963)].

S. R. Barone, “Resonances of the Fabry–Perot laser,” J. Appl. Phys. 34, 831–843 (1963).
[CrossRef]

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. Inst. Elect. Electron. Eng. 51, 80 (1963); W. H. Wells, “Modes of a tilted mirror optical resonator for the infrared,” IEEE J. Quantum Electron. QE-2, 94–102 (1966); R. L. Sanderson, W. Streifer, “Laser resonators with tilted reflectors,” Appl. Opt. 8, 131 (1969).
[CrossRef] [PubMed]

Barone, S. R.

S. R. Barone, “Perturbed open resonators,” Appl. Opt. 10, 935 (1971).
[CrossRef] [PubMed]

S. R. Barone, “Resonances of the Fabry–Perot laser,” J. Appl. Phys. 34, 831–843 (1963).
[CrossRef]

Fox, A. G.

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453 (1969); T. Li, “Diffraction loss and selection of modes in maser resonators with circular mirrors,” Bell Syst. Tech. J. 44, 917–932 (1965); G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508, (1961); M. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. Inst. Elect. Electron. Eng. 51, 80 (1963); W. H. Wells, “Modes of a tilted mirror optical resonator for the infrared,” IEEE J. Quantum Electron. QE-2, 94–102 (1966); R. L. Sanderson, W. Streifer, “Laser resonators with tilted reflectors,” Appl. Opt. 8, 131 (1969).
[CrossRef] [PubMed]

Gordon, J. P.

J. P. Gordon, H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 44, 2873–2887, (1965).

Kogelnik, H.

J. P. Gordon, H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 44, 2873–2887, (1965).

Li, T.

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453 (1969); T. Li, “Diffraction loss and selection of modes in maser resonators with circular mirrors,” Bell Syst. Tech. J. 44, 917–932 (1965); G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508, (1961); M. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. Inst. Elect. Electron. Eng. 51, 80 (1963); W. H. Wells, “Modes of a tilted mirror optical resonator for the infrared,” IEEE J. Quantum Electron. QE-2, 94–102 (1966); R. L. Sanderson, W. Streifer, “Laser resonators with tilted reflectors,” Appl. Opt. 8, 131 (1969).
[CrossRef] [PubMed]

Merzbacher, E.

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 17.

Remo, J. L.

J. L. Remo, “Dependence of power loss on mirror tilt,” in preparation (1978).

Vainshtein, L. A.

L. A. Vainshtein, “Open resonators for lasers,” Sov. Phys. JETP 17, 709–719 (1963) [J. Exp. Theor. Phys. (USSR) 44, 1050–1067 (1963)].

Appl. Opt. (1)

Bell Syst. Tech. J. (2)

A. G. Fox, T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453 (1969); T. Li, “Diffraction loss and selection of modes in maser resonators with circular mirrors,” Bell Syst. Tech. J. 44, 917–932 (1965); G. D. Boyd, J. P. Gordon, “Confocal multimode resonator for millimeter through optical wavelength masers,” Bell Syst. Tech. J. 40, 489–508, (1961); M. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550 (1966).
[CrossRef] [PubMed]

J. P. Gordon, H. Kogelnik, “Equivalence relations among spherical mirror optical resonators,” Bell Syst. Tech. J. 44, 2873–2887, (1965).

J. Appl. Phys. (1)

S. R. Barone, “Resonances of the Fabry–Perot laser,” J. Appl. Phys. 34, 831–843 (1963).
[CrossRef]

Proc. Inst. Elect. Electron. Eng. (1)

A. G. Fox, T. Li, “Modes in a maser interferometer with curved and tilted mirrors,” Proc. Inst. Elect. Electron. Eng. 51, 80 (1963); W. H. Wells, “Modes of a tilted mirror optical resonator for the infrared,” IEEE J. Quantum Electron. QE-2, 94–102 (1966); R. L. Sanderson, W. Streifer, “Laser resonators with tilted reflectors,” Appl. Opt. 8, 131 (1969).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

L. A. Vainshtein, “Open resonators for lasers,” Sov. Phys. JETP 17, 709–719 (1963) [J. Exp. Theor. Phys. (USSR) 44, 1050–1067 (1963)].

Other (2)

J. L. Remo, “Dependence of power loss on mirror tilt,” in preparation (1978).

E. Merzbacher, Quantum Mechanics (Wiley, New York, 1970), Chap. 17.

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

Symmetrically perturbed Fabry–Perot resonator of length L, mirror width 2a, and tilt α.

Fig. 2
Fig. 2

Total power loss for tilted (tilt angle α = λ/144) infinite-strip plane mirrors as a function of Fresnel number N = a2/2L compared with Fox and Li.2

Fig. 3
Fig. 3

Phase shift as a function of Fresnel number; this work compared with that of Fox and Li.2

Equations (17)

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

γ m ( 0 ) Ψ m ( 0 ) = K ^ Ψ m ( 0 ) ,
γ m ( 0 ) Ψ m ( 0 ) ( X ) = - a a K ( X , X ) Ψ m ( 0 ) ( X ) d X ,
γ m Ψ m ( X ) = exp [ i 2 Φ ( X ) ] - a a K ( X , X ) Ψ m ( X ) d X ,
γ m Ψ m = exp ( i 2 Φ ) K ^ Ψ m ,
Φ α K X = α ( 2 π / λ ) X ,
exp ( i 2 Φ ) = 1 + i 2 Φ - 2 Φ 2 + ,
Ψ m = Ψ m ( 0 ) + Ψ m ( 1 ) + Ψ m ( 2 ) + ,
γ m = γ m ( 0 ) + γ m ( 1 ) + γ m ( 2 ) + ,
Ψ m ( 1 ) = m n n ; a m n Ψ n ( 0 ) ,
Ψ m ( 2 ) = l m l , b m l Ψ l ( 0 ) .
- a a Ψ m ( 0 ) ( X ) Ψ n ( 0 ) ( X ) d X = δ m , n .
γ m ( 1 ) = i 2 γ m ( 0 ) m Φ m ,
γ m ( 2 ) = γ m ( 0 ) [ - 2 m Φ 2 m + 4 m n n ( Φ m n ) 2 1 - γ m ( 0 ) / γ n ( 0 ) ] .
Δ P m = γ m ( 0 ) 2 - γ m 2 ,
δ Φ = Im ln ( γ m / γ m ( 0 ) ) .
P m sp = 1 - γ m 2 ,
P m RT = 1 - γ m γ m 2 .

Metrics