Abstract

We introduce a class of partially coherent beams with spatially varying correlation properties. It is shown that mathematically simple modifications in the coherence function of conventional Gaussian Schell-model beams lead to partially coherent fields with extraordinary free-space propagation characteristics, such as locally sharpened and laterally shifted intensity maxima. We study the properties of such fields based on an elementary-mode interpretation and by numerical simulations. The results demonstrate the potential of coherence modulation for beam shaping applications.

© 2011 Optical Society of America

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References

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1991

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1979

1967

A. C. Schell, IEEE Trans. Antennas Propag. AP-15, 187 (1967).
[CrossRef]

Arrizón, V.

Betancur, R.

Castanñeda, R.

Collett, E.

De Santis, P.

Foreman, M. R.

Friberg, A. T.

García-Guerrero, E. E.

Gbur, G.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Gori, F.

Gu, Z.-H.

Guattari, G.

Leskova, T. A.

Lim, R.

Lohmann, A. W.

Macías-Romero, C.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Maradudin, A. A.

Martínez-Herrero, R.

Martínez-Niconoff, G.

Martínez-Vara, P.

Mejías, P. M.

Méndez, E. R.

Mendlovic, D.

Olvera-Santamaría, M. A.

Ostrovsky, A. S.

Palma, C.

Rickenstorff-Parrao, C.

Santarsiero, M.

Schell, A. C.

A. C. Schell, IEEE Trans. Antennas Propag. AP-15, 187 (1967).
[CrossRef]

Shabtay, G.

Shirai, T.

Török, P.

Turunen, J.

Vahimaa, P.

Vasara, A.

Visser, T. D.

Wolf, E.

E. Collett and E. Wolf, J. Opt. Soc. Am. 69, 942 (1979).
[CrossRef]

T. Shirai and E. Wolf, J. Opt. Soc. Am. A 21, 1907.
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

IEEE Trans. Antennas Propag.

A. C. Schell, IEEE Trans. Antennas Propag. AP-15, 187 (1967).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

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Figures (2)

Fig. 1
Fig. 1

(a) Absolute value of the cross-spectral density and (b) the degree of coherence of a modified GSM beam. The corresponding functions of a GSM beam are shown in the respective insets. The width of the beams is w 0 = 0.5 mm , the coherence parameters w c = w gsm = 0.5 w 0 , and x 0 = 0.7 w 0 for the modified beam. The axes correspond to x 1 and x 2 in millimeters and their scale in the insets is the same as in the larger figures. The color scale bar is the same for all the figures.

Fig. 2
Fig. 2

Propagation of a modified GSM beam with w 0 = 0.5 mm , w c = 0.5 w 0 , and x 0 = 0 (upper row) or x 0 = 0.7 w 0 (lower row). Figures on the left-hand side show the evolution of the intensity on the x z plane. On the right-hand side, the lateral intensity distribution is shown at selected propagation distances.

Equations (9)

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W 0 ( x 1 , x 2 ) = p ( v ) H 0 * ( x 1 , v ) H 0 ( x 2 , v ) d v ,
p ( v ) = ( π a 2 ) 1 / 2 exp ( v 2 / a 2 ) ,
H 0 ( x , v ) = exp ( x 2 2 w 0 2 ) exp [ i k ( x x 0 ) 2 v ] ,
W 0 ( x 1 , x 2 ) = exp ( x 1 2 + x 2 2 2 w 0 2 ) μ ( x 1 , x 2 ) ,
μ ( x 1 , x 2 ) = exp { [ ( x 2 x 0 ) 2 ( x 1 x 0 ) 2 ] 2 w c 4 } ,
H ( x , v ; z ) = k 2 π z H ( x , v ; 0 ) exp [ i k ( x x ) 2 2 z ] d x ,
| H ( x , v ; z ) | 2 = w 0 w ( z , v ) exp [ ( x 2 v z x 0 ) 2 w 2 ( z , v ) ] ,
w 2 ( z , v ) = w 0 2 ( 1 2 v z ) 2 + ( z / k w 0 ) 2 .
S ( x , z ) = p ( v ) | H ( x , v ; z ) | 2 d v .

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