Jones matrix treatment for optical Fourier processors with structured polarization.

We present a Jones matrix method useful to analyze coherent optical Fourier processors employing structured polarization. The proposed method is a generalization of the standard classical optical Fourier transform processor, but considering vectorial spatial functions with two complex components corresponding to two orthogonal linear polarizations. As a result we derive a Jones matrix that describes the polarization output in terms of two vectorial functions defining respectively the structured polarization input and the generalized polarization impulse response. We apply the method to show and analyze an experiment in which a regular scalar diffraction grating is converted into equivalent polarization diffraction gratings by means of an appropriate polarization filtering. The technique is further demonstrated to generate arbitrary structured polarizations. Excellent experimental results are presented.

[1]  M Stalder,et al.  Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters. , 1996, Optics letters.

[2]  Z. Bomzon,et al.  Formation of radially and azimuthally polarized light using space-variant subwavelength metal stripe gratings , 2001 .

[3]  Jianping Ding,et al.  Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement. , 2007, Optics letters.

[4]  J. Davis,et al.  Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator. , 2000, Applied optics.

[5]  Kimani C Toussaint,et al.  Generation of optical vector beams with a diffractive optical element interferometer. , 2005, Optics letters.

[6]  Bahram Javidi,et al.  Polarization encoding for optical security systems , 2000 .

[7]  Bahram Javidi,et al.  Optical encryption using a joint transform correlator architecture , 2000 .

[8]  F. Gori,et al.  Use of the van Cittert-Zernike theorem for partially polarized sources. , 2000, Optics letters.

[9]  Hiding binary optical data with orthogonal circular polarizations , 2008 .

[10]  Tony Wilson,et al.  Method for the generation of arbitrary complex vector wave fronts. , 2002, Optics letters.

[11]  F. Gori.  Matrix treatment for partially polarized, partially coherent beams. , 1998, Optics letters.

[12]  Juan Campos,et al.  Effects of Amplitude and Phase Mismatching Errors in the Generation of a Kinoform for Pattern Recognition , 1995 .

[13]  G Leuchs,et al.  Sharper focus for a radially polarized light beam. , 2003, Physical review letters.

[14]  Gabriella Cincotti,et al.  Polarization gratings: design and applications , 2003 .

[15]  C. Fernández-Pousa,et al.  Polarization beam splitters using polarization diffraction gratings. , 2001, Optics letters.

[16]  Ignacio Moreno,et al.  Operational modes of a ferroelectric LCoS modulator for displaying binary polarization, amplitude, and phase diffraction gratings. , 2009, Applied optics.

[17]  Chulwoo Oh,et al.  Achromatic diffraction from polarization gratings with high efficiency. , 2008, Optics letters.

[18]  Binary polarization pupil filter: Theoretical analysis and experimental realization with a liquid crystal display , 2006 .

[19]  Q. Zhan.  Cylindrical vector beams: from mathematical concepts to applications , 2009 .

[20]  Alexander Jesacher,et al.  Tailoring of arbitrary optical vector beams , 2007 .

[21]  Polarization vortices generation by diffraction from a four quadrant polarization mask , 2007 .

[22]  Digital polarization holograms with defined magnitude and orientation of each pixel's birefringence. , 2009, Optics letters.

[23]  M. Yzuel,et al.  Jones matrix treatment for polarization fourier optics , 2004 .

[24]  Chau-Jern Cheng,et al.  Optical image encryption based on polarization encoding by liquid crystal spatial light modulators , 2004 .

[25]  F. Gori.  Measuring Stokes parameters by means of a polarization grating. , 1999, Optics letters.

[26]  Jeffrey A. Davis,et al.  Polarization-multiplexed diffractive optical elements with liquid-crystal displays. , 2005, Applied optics.