## Analysis of eigenfields in the axicon-based Bessel–Gauss resonator by the transfer-matrix method

JOSA A, Vol. 23, Issue 4, pp. 912-918 (2006)

http://dx.doi.org/10.1364/JOSAA.23.000912

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### Abstract

The axicon-based-Bessel–Gauss resonator (ABGR) has been proposed for the production of Bessel–Gauss beams. To analyze eigenfields of the ABGR with a plane or spherical output coupler, we present and demonstrate the transfer-matrix method. Since the method is slow to converge to eigenmodes of the ABGR by use of the Fox and Li iterative algorithm, in this paper the Huygens–Fresnel diffraction integral equations associated with ray matrices are converted into finite-sum matrix equations, and mode-fields and corresponding losses are described as eigenvectors and eigenvalues of a transfer matrix according to the self-reproducing principle of the laser field. By solving the transfer matrix for eigenvectors and eigenvalues, we obtain field distributions and losses of the dominant eigenmodes. Moreover, eigenfields across arbitrary interfaces between the axicon and the output coupler, and the propagation of output beams, are simulated by using the fast-Fourier transform (FFT). The calculation results reveal that because of the ABGR’s poor transverse mode discrimination the ABGR should be improved to produce good-quality Bessel–Gauss beams.

© 2006 Optical Society of America

**OCIS Codes**

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(140.3300) Lasers and laser optics : Laser beam shaping

(140.3410) Lasers and laser optics : Laser resonators

(140.4130) Lasers and laser optics : Molecular gas lasers

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: September 9, 2005

Manuscript Accepted: September 30, 2005

**Citation**

Dongxiong Ling, Junchang Li, and Junruo Chen, "Analysis of eigenfields in the axicon-based Bessel-Gauss resonator by the transfer-matrix method," J. Opt. Soc. Am. A **23**, 912-918 (2006)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-4-912

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### References

- J. Durnin, J. J. Micely, Jr., and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987). [CrossRef] [PubMed]
- J. Durnin, "Exact solutions for nondiffracting beams. I. The scalar theory," J. Opt. Soc. Am. A 4, 651-654 (1987). [CrossRef]
- F. Gori, G. Guattari, and C. Padovani, "Bessel-Gauss beams," Opt. Commun. 64, 491-495 (1987). [CrossRef]
- J. K. Jabczynski, "A 'diffraction-free' resonator," Opt. Commun. 77, 292-294 (1990). [CrossRef]
- J. Rogel-Salazar, G. H. C. New, and S. Chávez-Cerda, "Bessel-Gauss beam optical resonator," Opt. Commun. 190, 117-122 (2001). [CrossRef]
- J. Rogel-Salazar, G. H. C. New, P. Muys, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, "Bessel-Gauss resonators," in Laser Resonators IV, A.V.Kudryashov and A.H.Paxton, eds., Proc. SPIE 4270, 52-63 (2001).
- A. N. Khilo, E. G. Katranji, and A. A. Ryzhevich, "Axicon-based Bessel resonator: analytical description and experiment," J. Opt. Soc. Am. A 18, 1986-1992 (2001). [CrossRef]
- J. C. Gutiérrez-Vega, R. Rodríguez-Masegosa, and S. Chávez-Cerda, "Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis," J. Opt. Soc. Am. A 20, 2113-2122 (2003). [CrossRef]
- P. Baues, "The connection of geometric optics with the propagation of Gaussian beams and the theory of optical resonators," Opto-electronics (London) 1, 103-118 (1969). [CrossRef]
- P. Baues, "Huygens's principle in inhomogeneous isotropic media and a general integral equation applicable to optical resonators," Opto-electronics (London) 1, 37-44 (1969). [CrossRef]
- S. A. Collins, Jr., "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Am. 60, 1168-1177 (1970). [CrossRef]
- B. Lü, Propagation and Control of High-power Lasers (National Defense Industry Press, Beijing, 1999), p. 23.
- L. Dongxiong, L. Junchang, and L. Xingyi, "Numerical simulation of laser field across the diffraction-limited optics system," Laser Technol. 26, 284-286 (2002).
- A. G. Fox and T. Li, "Resonant modes in a maser interferometer," Bell Syst. Tech. J. 40, 453-458 (1961).
- A. G. Fox and T. Li, "Resonant modes in an optical maser," Proc. IRE 48, 1904-1905 (1960).
- W. Zaifu, W. Runwen, and W. Zhijiang, "Numerical analysis of mode-fields of unstable ring resonators 90° beam rotation," Acta Opt. Sin. 15, 696-702 (1995).
- D. Ling, Y. Fu, D. Xu, and Y. Guan, "Finite-sum matrix analysis of eigen-mode fields of the Gaussian-reflectivity plano-concave resonator," in High-Power Lasers and Applications II, DianyuanFan, KeithA.Truesdell, and KojiYasui, eds., Proc. SPIE 4914, 371-381 (2002).

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