## Electromagnetic coherence theory of laser resonator modes

JOSA A, Vol. 22, Issue 1, pp. 103-108 (2005)

http://dx.doi.org/10.1364/JOSAA.22.000103

Acrobat PDF (155 KB)

### Abstract

A theory of open laser resonators is formulated within the framework of the electromagnetic coherence theory. It is shown that if only one Fox-Li mode contributes to the field at a given frequency, then the field at that frequency is necessarily completely coherent in view of the space-frequency counterpart of the recently introduced degree of coherence of electromagnetic fields [Opt. Express 11, 1137 (2003)]. It is also shown that the relation between the number of Fox-Li modes and the new degree of coherence is analogous to the relation established in the scalar theory of laser resonator modes. Difficulties that arise with the formerly introduced visibility-based definition of the electromagnetic degree of coherence are briefly discussed.

© 2005 Optical Society of America

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(140.4780) Lasers and laser optics : Optical resonators

(260.2110) Physical optics : Electromagnetic optics

(260.5430) Physical optics : Polarization

**Citation**

Toni Saastamoinen, Jari Turunen, Jani Tervo, Tero Setälä, and Ari T. Friberg, "Electromagnetic coherence theory of laser resonator modes," J. Opt. Soc. Am. A **22**, 103-108 (2005)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-1-103

Sort: Year | Journal | Reset

### References

- M. Born and E. Wolf, Principles of Optics , 7th (expanded) ed. (Cambridge U. Press, Cambridge, UK, 1999), historical introduction.
- E. Wolf and G. S. Agarwal, "Coherence theory of laser resonator modes," J. Opt. Soc. Am. A 1, 541-546 (1984).
- D. Pohl, "Operation of a ruby laser in the purely transverse electric mode TE01," Appl. Phys. Lett. 20, 266-267 (1972).
- R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
- A. V. Nesterov, V. G. Niziev, and V. P. Yakunin, "Generation of high-power radially polarized beam," J. Phys. D Appl. Phys. 32, 2871-2875 (1999).
- A. V. Nesterov and V. G. Niziev, "Laser beams with axially symmetric polarization," J. Phys. D Appl. Phys. 33, 1817-1822 (2000).
- I. Moshe, S. Jackel, and A. Meir, "Production of radially or azimuthally polarized beams in solid-state lasers and the elimination of thermally induced birefringence effects," Opt. Lett. 28, 807-809 (2003).
- J. R. Leger, D. Chen, and G. Mowry, "Design and performance of diffractive optics for custom laser resonators," Appl. Opt. 34, 2498-2509 (1995).
- J. Tervo and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," Opt. Lett. 25, 785-786 (2000).
- J. Tervo, V. Kettunen, M. Honkanen, and J. Turunen, "Design of space-variant diffractive polarization elements," J. Opt. Soc. Am. A 20, 282-289 (2003).
- F. Zernike, "The concept of degree of coherence and its application to optical problems," Physica 5, 785-795 (1938).
- J. Tervo, T. Setälä, and A. T. Friberg, "Degree of coherence for electromagnetic fields," Opt. Express 11, 1137-1143 (2003); www.opticsexpress.org.
- T. Setälä, J. Tervo, and A. T. Friberg, "Complete electromagnetic coherence in the space-frequency domain," Opt. Lett. 29, 328-330 (2004).
- T. Setälä, J. Tervo, and A. T. Friberg, "Theorems on complete electromagnetic coherence in the space-time domain," Opt. Commun. 238 , 229-236 (2004).
- R. J. Glauber, "The quantum theory of optical coherence," Phys. Rev. 130, 2529-2539 (1963).
- J. Tervo, T. Setälä, and A. T. Friberg, "Theory of partially coherent electromagnetic fields in the space-frequency domain," J. Opt. Soc. Am. A 21, 2205-2215 (2004).
- P. Roman and E. Wolf, "Correlation theory of stationary electromagnetic fields. Part I - the basic field equations," Nuovo Cimento 17, 462-476 (1960).
- P. Roman and E. Wolf, "Correlation theory of stationary electromagnetic fields. Part II - conservation laws," Nuovo Cimento 17, 477-490 (1960).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
- E. Wolf, "New theory of partial coherence in the space-frequency domain. Part I: spectra and cross-spectra of steady-state sources," J. Opt. Soc. Am. 72, 343-351 (1982).
- F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, "Coherent-mode decomposition of partially polarized, partially coherent sources," J. Opt. Soc. Am. A 20, 78-84 (2003).
- H. Kogelnik and T. Li, "Laser beams and resonators," Appl. Opt. 5, 1550-1567 (1966).
- A. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).
- A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-488 (1961).
- P. M. Morse and H. Feshbach, Methods of Mathematical Physics (McGraw-Hill, New York, 1953).
- F. Smithies, Integral Equations (Cambridge U. Press, Cambridge, UK, 1970).
- The exact conditions for the existence and validity of the biothogonal expansion in Eq. (22 ) do not appear to be known. However, it is readily shown that if the Fox-Li modes are complete in the sense that the field Fj+1 (rho, omega) on the left-hand side of Eq. (15 ) is expressible as their linear combination, then the resonator kernel admits the biorthogonal series representation as given in Eq. (22 ). A similar assumption (though stated slightly differently) was also invoked in Footnote 15 of Ref. 2 .
- The steps are essentially identical to those made in Ref. 2 but with the scalar functions replaced by appropriate vector- or tensor-valued functions. The vectorial formulation is given in detail in Ref. 29 .
- J. Tervo, T. Saastamoinen, J. Turunen, T. Setälä, and A. T. Friberg, "Degree of coherence and electromagnetic resonators," in Photon Management, F. Wyrowski, ed., Proc. SPIE 5456, 28-35 (2004).
- The same result holds also within the scalar theory, although it is not explicitly mentioned in Refs. 2 and 19.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.