Losses of bound and unbound custom resonator modes

doi:10.1364/OE.15.013463

Optics Express

Editor: C. Martijn de Sterke
Vol. 15, Iss. 21 — Oct. 17, 2007
pp: 13463–13475

Losses of bound and unbound custom resonator modes

Brad Tiffany and James Leger »View Author Affiliations

Optics Express, Vol. 15, Issue 21, pp. 13463-13475 (2007)
http://dx.doi.org/10.1364/OE.15.013463

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Abstract
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References (12)
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Abstract

We analyze a class of custom-mode laser cavities with aspheric mirrors that become either asymptotically flat or hemispheric away from the optical axis. Previous work classifies the modes of such cavities as either bound or unbound. We develop an analytic approximation for the losses and frequencies of such modes. The bound modes have losses that diminish exponentially as the size of the cavity mirror increases and have frequencies that become independent of the mirror size. On the other hand, unbound modes have losses that diminish asymptotically as the inverse third power of the mirror width and frequencies that converge toward those of the unperturbed (flat or hemispheric) cavity with increasing mirror width. Finally, we show good agreement between our model and numeric cavity eigenvalue calculations.

OCIS Codes
(140.3300) Lasers and laser optics : Laser beam shaping
(140.3410) Lasers and laser optics : Laser resonators
(140.4780) Lasers and laser optics : Optical resonators

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 5, 2007
Revised Manuscript: September 5, 2007
Manuscript Accepted: September 23, 2007
Published: October 1, 2007

Citation
Brad Tiffany and James Leger, "Losses of bound and unbound custom resonator modes," Opt. Express 15, 13463-13475 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-13463

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References

P. A. Bélanger and C. Paré, "Optical resonators using graded-phase mirrors," Opt. Lett. 16(14), 1057-1059 (1991). [CrossRef] [PubMed]
J. R. Leger, D. Chen, and G. Mowry, "Design and performance of diffractive optics for custom laser resonators," Appl. Opt. 34, 2498-2509 (1995). [CrossRef] [PubMed]
C. Paré, L. Gagnon, and P. A. Bélanger, "Aspherical laser resonators: An analogy with quantum mechanics," Phys. Rev. A 46, 4150-4160 (1992). [CrossRef] [PubMed]
M. Kuznetsov, M. Stern, and J. Coppeta, "Single transverse mode optical resonators," Opt. Express 13, 171-181 (2005). [CrossRef] [PubMed]
L. A. Weinstein, Open Resonators and Open Waveguides (Golem, Boulder, 1969).
L. A. Weinstein, The Theory of Diffraction and the Factorization Method (Golem, Boulder, 1969).
V. V. Lyubimov and I. B. Orlova, "Approximate Calculation of Oscillations in Resonators with Concave Mirrors," Opt. Spectrosc. 29, 310-313 (1970).
L.-W. Chen and L. B. Felsen, "Coupled-Mode Theory of Unstable Resonators," IEEE J. Quantum Electron. 9, 1102-1113 (1973). [CrossRef]
G. N. Vinokurov, V. V. Lyubimov, and I. B. Orlova, "Investigation of the selective properties of open unstable cavities," Opt. Spectrosc. 34, 427-432 (1973).
J. Goodman, Fourier Optics, 2nd ed. (McGraw Hill, 1995).
V. V. Lyubimov and I. B. Orlova, "Oscillations in a Tilted-Mirror Resonator," Opt. Spectrosc. 30, 409-411 (1971).
C. E. Santana and L. B. Felsen, "Ray-Optical Calculation of Edge Diffraction in Unstable Resonators," IEEE Trans. Microwave Theory Tech. MTT-26, 101-108 (1978). [CrossRef]

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[1] P. A. Bélanger and C. Paré, "Optical resonators using graded-phase mirrors," Opt. Lett. 16(14), 1057-1059 (1991). [CrossRef] [PubMed]

[2] J. R. Leger, D. Chen, and G. Mowry, "Design and performance of diffractive optics for custom laser resonators," Appl. Opt. 34, 2498-2509 (1995). [CrossRef] [PubMed]

[3] C. Paré, L. Gagnon, and P. A. Bélanger, "Aspherical laser resonators: An analogy with quantum mechanics," Phys. Rev. A 46, 4150-4160 (1992). [CrossRef] [PubMed]

[4] M. Kuznetsov, M. Stern, and J. Coppeta, "Single transverse mode optical resonators," Opt. Express 13, 171-181 (2005). [CrossRef] [PubMed]

[5] L. A. Weinstein, Open Resonators and Open Waveguides (Golem, Boulder, 1969).

[6] L. A. Weinstein, The Theory of Diffraction and the Factorization Method (Golem, Boulder, 1969).

[7] V. V. Lyubimov and I. B. Orlova, "Approximate Calculation of Oscillations in Resonators with Concave Mirrors," Opt. Spectrosc. 29, 310-313 (1970).

[8] L.-W. Chen and L. B. Felsen, "Coupled-Mode Theory of Unstable Resonators," IEEE J. Quantum Electron. 9, 1102-1113 (1973). [CrossRef]

[9] G. N. Vinokurov, V. V. Lyubimov, and I. B. Orlova, "Investigation of the selective properties of open unstable cavities," Opt. Spectrosc. 34, 427-432 (1973).

[10] J. Goodman, Fourier Optics, 2nd ed. (McGraw Hill, 1995).

[11] V. V. Lyubimov and I. B. Orlova, "Oscillations in a Tilted-Mirror Resonator," Opt. Spectrosc. 30, 409-411 (1971).

[12] C. E. Santana and L. B. Felsen, "Ray-Optical Calculation of Edge Diffraction in Unstable Resonators," IEEE Trans. Microwave Theory Tech. MTT-26, 101-108 (1978). [CrossRef]

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Losses of bound and unbound custom resonator modes