### Abstract

Many laser interaction models assume that incident focused laser fields are Gaussian and use either the approximate TEM_{00} series model or the exact integral Gaussian angular-spectrum solution. Many practical laser systems, however, produce flat-top transverse intensity profiles, and indeed, such profiles are often desired. Here, an exact, integral solution is derived for all of the vector components having a general flattened Gaussian profile using the angular-spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The resulting integrals are solved for tight focusing conditions exactly by making use of a Fourier-Gegenbauer expansion. This technique follows closely that of Sepke and Umstadter [Opt. Lett. 31, 1447 (2006)] but, by redefining the expansion coefficients, the simplicity of the model is greatly enhanced and the computation time reduced by roughly a factor of 2 beyond the 2 orders of magnitude improvement obtained previously. This series solution is stable at all points and converges after S ∼ 20w_{0} terms, where w_{0} is the 1/e waist normalized to the laser wavelength.

Original language | English (US) |
---|---|

Pages (from-to) | 2157-2165 |

Number of pages | 9 |

Journal | Journal of the Optical Society of America B: Optical Physics |

Volume | 23 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2006 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Atomic and Molecular Physics, and Optics

### Cite this

**Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes. I. Small F-number laser focusing.** / Sepke, Scott M.; Umstadter, Donald P.

Research output: Contribution to journal › Article

*Journal of the Optical Society of America B: Optical Physics*, vol. 23, no. 10, pp. 2157-2165. https://doi.org/10.1364/JOSAB.23.002157

}

TY - JOUR

T1 - Analytical solutions for the electromagnetic fields of flattened and annular Gaussian laser modes. I. Small F-number laser focusing

AU - Sepke, Scott M.

AU - Umstadter, Donald P.

PY - 2006/10

Y1 - 2006/10

N2 - Many laser interaction models assume that incident focused laser fields are Gaussian and use either the approximate TEM00 series model or the exact integral Gaussian angular-spectrum solution. Many practical laser systems, however, produce flat-top transverse intensity profiles, and indeed, such profiles are often desired. Here, an exact, integral solution is derived for all of the vector components having a general flattened Gaussian profile using the angular-spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The resulting integrals are solved for tight focusing conditions exactly by making use of a Fourier-Gegenbauer expansion. This technique follows closely that of Sepke and Umstadter [Opt. Lett. 31, 1447 (2006)] but, by redefining the expansion coefficients, the simplicity of the model is greatly enhanced and the computation time reduced by roughly a factor of 2 beyond the 2 orders of magnitude improvement obtained previously. This series solution is stable at all points and converges after S ∼ 20w0 terms, where w0 is the 1/e waist normalized to the laser wavelength.

AB - Many laser interaction models assume that incident focused laser fields are Gaussian and use either the approximate TEM00 series model or the exact integral Gaussian angular-spectrum solution. Many practical laser systems, however, produce flat-top transverse intensity profiles, and indeed, such profiles are often desired. Here, an exact, integral solution is derived for all of the vector components having a general flattened Gaussian profile using the angular-spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The resulting integrals are solved for tight focusing conditions exactly by making use of a Fourier-Gegenbauer expansion. This technique follows closely that of Sepke and Umstadter [Opt. Lett. 31, 1447 (2006)] but, by redefining the expansion coefficients, the simplicity of the model is greatly enhanced and the computation time reduced by roughly a factor of 2 beyond the 2 orders of magnitude improvement obtained previously. This series solution is stable at all points and converges after S ∼ 20w0 terms, where w0 is the 1/e waist normalized to the laser wavelength.

UR - http://www.scopus.com/inward/record.url?scp=33751243309&partnerID=8YFLogxK

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U2 - 10.1364/JOSAB.23.002157

DO - 10.1364/JOSAB.23.002157

M3 - Article

AN - SCOPUS:33751243309

VL - 23

SP - 2157

EP - 2165

JO - Journal of the Optical Society of America B: Optical Physics

JF - Journal of the Optical Society of America B: Optical Physics

SN - 0740-3224

IS - 10

ER -