## Paraxial propagation of a partially coherent Hermite–Gaussian beam through aligned and misaligned *ABCD* optical systems

JOSA A, Vol. 24, Issue 8, pp. 2394-2401 (2007)

http://dx.doi.org/10.1364/JOSAA.24.002394

Enhanced HTML Acrobat PDF (299 KB)

### Abstract

Paraxial propagation of a partially coherent Hermite–Gaussian beam through aligned and misaligned *ABCD* optical systems is investigated based on the generalized Collins formula for treating the propagation of a partially coherent beam through such optical systems. Analytical formulas for the cross-spectral density of a partially coherent Hermite–Gaussian beam propagating through such optical systems are derived. As an application example, we derive the propagation formulas for a partially coherent flattened Gaussian beam by expressing it as a superposition of a series of partially coherent Hermite–Gaussian beams by using polynomial expansion. The focusing properties of a partially coherent Hermite–Gaussian beam focused by a thin lens are studied as a numerical example.

© 2007 Optical Society of America

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(140.3300) Lasers and laser optics : Laser beam shaping

(350.5500) Other areas of optics : Propagation

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: February 13, 2007

Revised Manuscript: April 13, 2007

Manuscript Accepted: April 16, 2007

Published: July 11, 2007

**Citation**

Yangjian Cai and Chiyi Chen, "Paraxial propagation of a partially coherent Hermite-Gaussian beam through aligned and misaligned ABCD optical systems," J. Opt. Soc. Am. A **24**, 2394-2401 (2007)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-8-2394

Sort: Year | Journal | Reset

### References

- A. E. Siegman, Lasers (University Science Books, 1986).
- W. H. Carter, "Spot size and divergence for Hermite-Gaussian beams of any order," Appl. Opt. 19, 1027-1029 (1980). [CrossRef] [PubMed]
- S. Saghafi and C. J. R. Sheppard, "The beam propagation factor for higher-order Gaussian beams," Opt. Commun. 153, 207-210 (1998). [CrossRef]
- M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, "Astigmatic laser mode converters and transfer of orbital angular momentum," Opt. Commun. 96, 123-132 (1993). [CrossRef]
- A. N. Alekseev, K. N. Alekseev, O. S. Borodavka, A. V. Volyar, and Yu. A. Fridman, "Conversion of Hermite-Gaussian and Laguerre-Gaussian beams in an astigmatic optical system. 1. Experiment," Tech. Phys. Lett. 24, 694-696 (1998). [CrossRef]
- T. Kojima, "Diffraction of Hermite-Gaussian beams from a sinusoidal conducting grating," J. Opt. Soc. Am. A 7, 1740-1744 (1990). [CrossRef]
- O. Mata-Mendez and F. Chavez-Rivas, "New property in the diffraction of Hermite-Gaussian beams by a finite grating in the scalar diffraction regime: constant-intensity angles in the far field when the beam center is displaced through the grating," J. Opt. Soc. Am. A 15, 2698-2704 (1998). [CrossRef]
- O. Mata-Mendez and F. Chavez-Rivas, "Diffraction of Gaussian and Hermite-Gaussian beams by finite gratings," J. Opt. Soc. Am. A 18, 537-545 (2001). [CrossRef]
- O. Mata-Mendez and F. Chavez-Rivas, "Diffraction of Hermite-Gaussian beams by a slit," J. Opt. Soc. Am. A 12, 2440-2445 (1995). [CrossRef]
- M. Yokota, T. Takenaka, and O. Fukumitsu, "Scattering of a Hermite-Gaussian beam mode by parallel dielectric circular cylinders," J. Opt. Soc. Am. A 3, 580-586 (1986). [CrossRef]
- M. Yokota, S. He, and T. Takenaka, "Scattering of a Hermite-Gaussian beam field by a chiral sphere," J. Opt. Soc. Am. A 18, 1681-1689 (2001). [CrossRef]
- K. M. Luk and P. K. Yu, "Generation of Hermite-Gaussian beam modes by multipoles with complex source points," J. Opt. Soc. Am. A 2, 1818-1820 (1985). [CrossRef]
- Y. F. Chen, T. M. Huang, C. F. Kao, C. L. Wang, and S. C. Wang, "Generation of Hermite-Gaussian modes in fiber-coupled laser-diode end-pumped lasers," IEEE J. Quantum Electron. 33, 1025-1030 (1997). [CrossRef]
- H. Laabs, "Propagation of Hermite-Gaussian-beams beyond the paraxial approximation," Opt. Commun. 147, 1-4 (1998). [CrossRef]
- K. Duan, B. Wang, and B. Lu, "Propagation of Hermite-Gaussian and Laguerre-Gaussian beams beyond the paraxial approximation," J. Opt. Soc. Am. A 22, 1976-1982 (2005). [CrossRef]
- B. Lu and P. Peng, "Focal shift in Hermite-Gaussian beams based on the encircled-power criterion," Opt. Laser Technol. 35, 435-440 (2003).
- B. Lu, X. Tao, and Y. Nie, "Effect of quartic-phase aberrations on the focal switch of Hermite-Gaussian beams," Optik (Stuttgart) 116, 454-458 (2005). [CrossRef]
- T. P. Meyrath, F. Schreck, J. L. Hanssen, C. S. Chuu, and M. G. Raizen, "A high frequency optical trap for atoms using Hermite-Gaussian beams," Opt. Express 13, 2843-2851 (2005). [CrossRef]
- S. Saghafi and C. J. R. Sheppard, "Near field and far field of elegant Hermite-Gaussian and Laguerre-Gaussian modes," J. Mod. Opt. 45, 1999-2009 (1998). [CrossRef]
- S. Yu and W. Gu, "Generation of elegant Hermite-Gaussian beams using the graded-phase mirror," Opt. Laser Technol. 5, 460-463 (2003).
- C. Y. Young, Y. V. Gilchrest, and B. R. Macon, "Turbulence-induced beam spreading of higher-order mode optical waves," Opt. Eng. 41, 1097-1103 (2002). [CrossRef]
- Y. Cai and Q. Lin, "The elliptical Hermite-Gaussian beam and its propagation through paraxial systems," Opt. Commun. 207, 139-147 (2002).
- Y. Cai and Q. Lin, "Decentered elliptical Hermite-Gaussian beam," J. Opt. Soc. Am. A 20, 1111-1119 (2003). [CrossRef]
- F. Gori, "Flattened Gaussian beams," Opt. Commun. 107, 335-341 (1994). [CrossRef]
- B. Lu and H. Ma, "Beam combination of a radial laser array: Hermite-Gaussian model," Opt. Commun. 178, 395-403 (2000). [CrossRef]
- Y. Baykal, "Formulation of correlations for general-type beams in atmospheric turbulence," J. Opt. Soc. Am. A 23, 889-893 (2006). [CrossRef]
- C. Arpali, C. Yazicioglu, H. T. Eyyuboglu, S. A. Arpali, and Y. Baykal, "Simulator for general-type beam propagation in turbulent atmosphere," Opt. Express 14, 8918-8928 (2006). [CrossRef] [PubMed]
- Y. Qiu, H. Guo, and Z. Chen, "Paraxial propagation of partially coherent Hermite-Gauss beams," Opt. Commun. 245, 21-26 (2005). [CrossRef]
- S. A. Collins, "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Am. 60, 1168-1177 (1970). [CrossRef]
- Q. Lin and Y. Cai, "Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams," Opt. Lett. 27, 216-218 (2002). [CrossRef]
- A. Erdelyi, W. Magnus, and F. Oberhettinger, Tables of Integral Transforms (McGraw-Hill, 1954).
- M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U. S. Department of Commerce, 1970).
- R. Simon, N. Mukunda, and E. C. G. Sudarshan, "Partially coherent beams and a generalized ABCD-law," Opt. Commun. 65, 322-328 (1988). [CrossRef]
- S. Wang and L. Ronchi, "Principles and design of optical arrays," in Progress in Optics, Vol. XXV, E.Wolf, ed. (Elsevier Science, 1988), p. 279.
- Y. Cai and Q. Lin, "Propagation of partially coherent twisted anisotropic Gaussian Schell-model beams through misaligned optical systems," Opt. Commun. 211, 1-8 (2002). [CrossRef]
- V. Bagini, R. Borghi, F. Gori, A. M. Pacileo, and M. Santarsiero, "Propagation of axially symmetric flattened Gaussian beams," J. Opt. Soc. Am. A 13, 1385-1394 (1996). [CrossRef]
- Y. Cai and Q. Lin, "Properties of a flattened Gaussian beam in the fractional Fourier transform plane," J. Opt. A, Pure Appl. Opt. 5, 272-275 (2003). [CrossRef]
- Y. Cai and Q. Lin, "Light beams with elliptical flat-topped profiles," J. Opt. A, Pure Appl. Opt. 6, 390-395 (2004). [CrossRef]
- Y. Cai, "Propagation of various flat-topped beams in a turbulent atmosphere," J. Opt. A, Pure Appl. Opt. 8, 537-545 (2006). [CrossRef]
- X. Lu and Y. Cai, "Analytical formulas for a circular or non-circular flat-topped beam propagating through an apertured paraxial optical system," Opt. Commun. 269, 39-46 (2007). [CrossRef]
- Y. Cai and S. He, "Partially coherent flattened Gaussian beam and its paraxial propagation properties," J. Opt. Soc. Am. A 23, 2623-2628 (2006). [CrossRef]
- D. W. Coutts, "Double-pass copper vapor laser master-oscillator power-amplifier systems: generation of flat-top focused beams for fiber coupling and percussion drilling," IEEE J. Quantum Electron. 38, 1217-1224 (2002). [CrossRef]
- Y. G. Basov, "Divergence of excimer laser beams: a review," J. Commun. Technol. Electron. 46, 1-6 (2001).
- L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).

## 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.

### Figures

Fig. 1 |

« Previous Article | Next Article »

OSA is a member of CrossRef.