## Effects of finite apertures on transverse eigenmodes of optical resonators

JOSA A, Vol. 16, Issue 11, pp. 2669-2674 (1999)

http://dx.doi.org/10.1364/JOSAA.16.002669

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### Abstract

We examine the properties of the transverse eigenmodes of optical resonators containing a hard aperture. We show that for orthogonal optics and arbitrary aperture shape, the trace of the ray matrix and the scaled aperture size determine the major properties of interest: loss, frequency, and distortion that is due to diffraction. We discuss three different methods of reducing the Huygen–Fresnel integral equation to a matrix equation whose eigenvalues and eigenvectors can be easily found. The dependence of loss, frequency, distortion, and required matrix order on cavity parameters is presented for cylindrically symmetrical resonators. We show that undiffracted modes inadequately approximate the actual modes in nearly unstable cavities.

© 1999 Optical Society of America

**OCIS Codes**

(050.1220) Diffraction and gratings : Apertures

(050.1940) Diffraction and gratings : Diffraction

(140.3410) Lasers and laser optics : Laser resonators

(140.4780) Lasers and laser optics : Optical resonators

(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

(230.5750) Optical devices : Resonators

**Citation**

Richard Rolleigh, Maria E. Bell, Michael Rolleigh, and D. K. Bandy, "Effects of finite apertures on transverse eigenmodes of optical resonators," J. Opt. Soc. Am. A **16**, 2669-2674 (1999)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-11-2669

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### References

- N. B. Abraham and W. J. Firth, “Overview of transverse effects in nonlinear-optical systems,” J. Opt. Soc. Am. B 7, 951–961 (1990) and references therein.
- A. W. Yu, G. P. Agrawal, and R. Roy, “Power spectra and spatial pattern dynamics of a ring laser,” J. Stat. Phys. 54, 1223–1241 (1989).
- N. N. Rasonov and V. E. Semenov, “The kinetics of the hysteresis change of the beam profile in nonlinear interferometers,” Opt. Commun. 38, 435–438 (1981).
- F. Hollinger, C. Jung, and H. Weber, “Simple mathematical model describing multi-transversal solid-state lasers,” J. Opt. Soc. Am. B 7, 1013–1018 (1990).
- L. A. Lugiato, F. Pratt, L. M. Narducci, P. Ru, J. R. Tredicce, and D. K. Bandy, “Role of transverse effects in laser instabilities,” Phys. Rev. A 37, 3847–3866 (1988).
- L. A. Lugiato, G. L. Oppo, J. R. Tredicce, L. M. Narducci, and M. A. Pernigo, “Instabilities and spatial complexity in a laser,” J. Opt. Soc. Am. B 7, 1019–1033 (1990).
- L. A. Lugiato, “Spatio-temporal structures. Part I,” Phys. Rep. 219, 293–310 (1992).
- H. Adachihara, O. Hess, E. Abraham, P. Ru, and J. V. Moloney, “Spatiotemporal chaos in broad-area semiconductor lasers,” J. Opt. Soc. Am. B 10, 658–665 (1993).
- W. Kaige, N. B. Abraham, and L. A. Lugiato, “Leading role of optical phase instabilities in the formation of certain laser transverse patterns,” Phys. Rev. A 47, 1263–1273 (1993).
- A. M. Dunlop, W. J. Firth, and E. M. Wright, “Master equation for spatio-temporal beam propagation and Kerr lens mode-locking,” Opt. Commun. 138, 211–226 (1997).
- J. Martin-Regalado, S. Balle, and M. San Miguel, “Polarization and transverse mode dynamics of gain-guided vertical-cavity surface emitting lasers,” Opt. Lett. 22, 460–462 (1997).
- D. J. Jones and D. K. Bandy, “Hysteresis effects attributed to free-space diffraction in a passive optical system,” Opt. Commun. 92, 376–384 (1992).
- M. Brambilla, F. Battipede, L. A. Lugiato, V. Penns, F. Prati, C. Tamm, and C. O. Weiss, “Transverse laser patterns. II. Phase singularity crystals,” Phys. Rev. A 43, 5090–5113 (1991).
- T. N. Danilova, A. P. Danilova, O. G. Ershov, A. N. Imenkov, V. V. Sherstnev, and Yu. P. Yakovlev, “Spatial distribution of the radiation in the far zone of InAsSb/InAsAbP mesastrip lasers as a function of current,” Semiconductors 32, 339–342 (1998).
- T. Burkhard, M. O. Ziegler, I. Fischer, and W. Elsaber, “Spatio-temporal dynamics of broad area semiconductor lasers and its characterization,” Chaos, Solitons and Fractals 10, 845–850 (1999).
- M. A. Rippin and G. H. C. New, “Excess noise factors in circular unstable resonators,” J. Mod. Opt. 43, 993–1008 (1996).
- A. E. Siegman, “Excess spontaneous emission in non-Hermitian optical systems. I. Laser amplifiers,” Phys. Rev. A 39, 1253–1263 (1989).
- A. E. Siegman, “Excess spontaneous emission in non-Hermitian optical systems. II. Laser oscillators,” Phys. Rev. A 39, 1264–1268 (1989).
- M. Brunel, G. Ropars, A. L. Floch, and F. Bretenaker, “Transverse excess noise factor in geometrically stable resonators,” Phys. Rev. A 55, 4563–4567 (1997).
- K. Joosten and G. Nienhuis, “Combined longitudinal and transverse noise enhancement in lasers,” Phys. Rev. A 58, 4937–4945 (1998).
- Yuh-Jen Cheng, C. G. Fanning, and A. E. Siegman, “Experimental observation of a large excess quantum noise factor in the linewidth of a laser oscillator having nonorthogonal modes,” Phys. Rev. Lett. 77, 627–630 (1996).
- M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, “Resonance of quantum noise in an unstable cavity laser,” Phys. Rev. Lett. 77, 4314–4317 (1996).
- M. A. van Eijkelenborg, M. P. van Exter, and J. P. Woerdman, “Threshold characteristics and intensity fluctuations of lasers with excess quantum noise,” Phys. Rev. A 57, 571–579 (1998).
- Å. M. Lindberg, M. A. van Eijkelenborg, K. Joosten, G. Nienhuis, and J. P. Woerdman, “Observation of excess quantum noise in a geometrically stable laser,” Phys. Rev. A 57, 3036–3039 (1998).
- O. Emile, M. Brunel, F. Bretenaker, and A. Le Floch, “Direct measurement of the transverse excess noise factor in a geometrically stable resonator,” Phys. Rev. A 57, 4889–4893 (1998).
- A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 626–652.
- O. Haderka, “Properties of the transverse eigenmode set in optical resonators with apertures,” J. Opt. Soc. Am. A 12, 340–345 (1995).
- S. Ruschin, T. Hurvits, and M. Keselbrener, “Properties of the transverse eigenmode set in optical resonators with apertures: comment,” J. Opt. Soc. Am. A 13, 1287–1288 (1996).
- O. Haderka, “Properties of the transverse eigenmode set in optical resonators with apertures: reply to comment,” J. Opt. Soc. Am. A 13, 1289–1290 (1996).
- P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), pp. 904–913.
- A. E. Siegman, “Orthogonality properties of optical resonator eigenmodes,” Opt. Commun. 31, 369–373 (1979).
- A. G. Fox and T. Li, “Resonant modes in a maser interferometer,” Bell Syst. Tech. J. 40, 453–488 (1961).
- A. E. Siegmann and H. Y. Miller, “Unstable optical resonator loss calculations using the Prony method,” Appl. Opt. 9, 2729–2735 (1970); see also pages 570–577 of Ref. 12.
- M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1965), pp. 887–890.
- G. D’Alessandro and G. L. Oppo, “Gauss–Laguerre modes: a ‘sensible’ basis for laser dynamics,” Opt. Commun. 88, 130–136 (1992).

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