A note on the general solution of the paraxial wave equation: A Lie algebra view

Journal of Optics A: Pure and Applied Optics

Volumn 10, Issue 5, 2008, Pages

  Torre, A ^a  

^a ENEA   (Italy)

Author keywords

Gaussian optical beams; Paraxial wave equation; Su(1, 1) Lie algebra

Indexed keywords

ALGEBRA; NUMERICAL METHODS; PROBLEM SOLVING;

CARTESIAN COORDINATES; GAUSSIAN OPTICAL BEAMS; PARAXIAL WAVE EQUATION;

WAVE EQUATIONS;

EID: 44449112351     PISSN: 14644258     EISSN: 17413567     Source Type: Journal    
DOI: 10.1088/1464-4258/10/5/055006     Document Type: Article

References (17)

1. Bandres M A and Gutiérrez-Vega J C 2007 Cartesian beams Opt. Lett. 32 3459-61
2. Bandres M A and Gutiérrez-Vega J C 2008 Circular beams Opt. Lett. 33 177-9
3. 2U = 0 J. Math. Phys. 15 1728-37
4. Kotlyar V V, Skidanov R V, Khonina S N and Soifer V A 2007 Hypergeometric modes Opt. Lett. 32 742-4
5. Karimi E, Zito G, Piccirillo B, Marrucci L and Santamato E 2007 Hypergeometric-Gaussian modes Opt. Lett. 32 3053-5
6. Pratesi R and Ronchi L 1977 Generalized Gaussian beams in free space J. Opt. Soc. Am. 67 1274-6
7. Gutiérrez-Vega J C 2007 Fractionalization of optical beams: I. Planar analysis Opt. Lett. 32 1521-3
8. Vilenkin N Y 1968 Special Functions and the Theory of Group Representations (Providence, RI: AMS Transl.)
9. Erdélyi A, Magnus W, Oberhettinger F and Tricomi F G 1953 Higher Transcendental Functions vol I and II (New York: McGraw-Hill)
10. Buccholz H 1969 The Confluent Hypergeometric Function (Berlin: Springer)
11. Cherry T M 1949 Expansions in terms of parabolic cylinder functions Proc. Edinburgh Math. Soc. 8 50-65
12. Srivastava H M, Vu K T and Yakubovich S B 2000 The Cherry transform and its relationship with a singular Sturm-Liouville problem Q. J. Math. Oxford 51 371-83
13. Torre A 2003 Linear and radial transforms of fractional order J. Comput. Appl. Math. 153 477-86
14. Magnus W 1941 Zur theorie des zylindrisch-parabolischen Spiegels Z. Phys. Berlin 11 343-56
15. Ban M 1993 Decomposition formulas for su(1,1) and su(2) Lie algebras and their applications to quantum optics J. Opt. Soc. Am. B 10 1347-59
16. Enderlein J and Pampaloni F 2004 Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes J. Opt. Soc. Am. 21 1553-8
17. 2U = 0 J. Math. Phys. 16 499-511