Spreading properties of beams radiated by partially coherent Schell-model sources

We derive a general law for the M2 factor of any beam generated by a partially coherent Schell-model source. The fourth power of M differs from its minimum value, attained in the coherent limit, by a term proportional to the second derivative of the modulus of the spectral degree of coherence evaluated for zero argument. Examples are given for cases of practical interest.

[1]  A. Friberg,et al.  Spatially partially coherent Fabry–Perot modes , 1994 .

[2]  A. Friberg,et al.  Interpretation and experimental demonstration of twisted Gaussian Schell-model beams , 1994 .

[3]  Dario Ambrosini,et al.  Twisted Gaussian Schell-model Beams: A Superposition Model , 1994 .

[4]  Ronald J. Sudol,et al.  Propagation parameters of gaussian Schell-model beams , 1982 .

[5]  F. Gori,et al.  Collett-Wolf sources and multimode lasers , 1980 .

[6]  Yu. A. Brychkov,et al.  Integrals and series , 1992 .

[7]  Anthony E. Siegman,et al.  Defining the effective radius of curvature for a nonideal optical beam , 1991 .

[8]  E Collett,et al.  Is complete spatial coherence necessary for the generation of highly directional light beams? , 1978, Optics letters.

[9]  Rolf Gase,et al.  The Multimode Laser Radiation as a Gaussian Schell Model Beam , 1991 .

[10]  Jari Turunen,et al.  Propagation invariance and self-imaging in variable-coherence optics , 1991 .

[11]  M. Santarsiero,et al.  Modal decomposition of partially coherent flat-topped beams produced by multimode lasers. , 1998, Optics letters.

[12]  Mj Martin Bastiaans.  Application of the Wigner distribution function to partially coherent light , 1986 .

[13]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[14]  E. Wolf,et al.  Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields , 1982 .

[15]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[16]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[17]  F. Gori,et al.  Mode propagation of the field generated by Collett-Wolf Schell-model sources , 1983 .

[18]  R. Martínez-Herrero,et al.  Relation among planar sources that generate the same radiant intensity at the output of a general optical system , 1982 .

[19]  E. Sudarshan,et al.  Partially coherent beams and a generalized ABCD-law , 1988 .

[20]  Franco Gori,et al.  Modal expansion for J0-correlated Schell-model sources , 1987 .

[21]  E. Wolf.  New theory of partial coherence in the space–frequency domain. Part I: spectra and cross spectra of steady-state sources , 1982 .

[22]  Anthony E. Siegman,et al.  New developments in laser resonators , 1990, Photonics West - Lasers and Applications in Science and Engineering.

[23]  L. Mandel,et al.  Optical Coherence and Quantum Optics , 1995 .

[24]  E. Wolf.  Coherence and radiometry , 1978 .

[25]  G. Cincotti,et al.  Beams originated by J0-correlated Schell-model planar sources , 1996 .

[26]  K. W. Cattermole.  The Fourier Transform and its Applications , 1965 .

[27]  M. Santarsiero,et al.  M(2) factor of Bessel Gauss beams. , 1997, Optics letters.

[28]  F. Gori,et al.  Bessel-Gauss beams , 1987 .

[29]  F. Gori,et al.  Partially coherent sources with helicoidal modes , 1998 .

[30]  Rosario Martínez-Herrero,et al.  Parametric characterization of general partially coherent beams propagating through ABCD optical systems , 1991 .

[31]  R. Simon,et al.  Twisted Gaussian Schell-model beams , 1993 .