Optical properties of polarization-dependent geometric phase elements with partially polarized light

The behavior of geometric phase elements illuminated with partially polarized monochromatic beams is investigated both theoretically and experimentally. The element discussed in this paper is composed of wave plates withp-retardation and a space-variant orientation angle. We found that a beam emerging from such an element comprises two polarization orders; right-and left-handed circularly polarized states with conjugate geometric phase modification. This phase equals twice the orientation angle of the space-variant wave plate comprising the element. Apart from the two polarization orders, the emerging beam coherence polarization matrix includes a ‘‘vectorial interference matrix’’ which contains information concerning the correlation between the two orthogonal, circularly polarized portions of the incident beam. In this paper we measure this correlation by a simple interference experiment. In addition, we found that the equivalent mutual intensity of the emerging beam is modulated according to the geometric phase induced by the element. Other interesting phenomena concerning propagation will be discussed theoretically and demonstrated experimentally. The experiment made use of a spherical geometric phase element that was realized by use of a space-variant subwavelength grating illuminated with CO2 laser radiation of 10.6 lm wavelength. � 2006 Elsevier B.V. All rights reserved.

[1]  G. Nordin,et al.  Micropolarizer Array for Infrared Imaging Polarimetry , 1999 .

[2]  Erez Hasman,et al.  Geometrical phase image encryption obtained with space-variant subwavelength gratings. , 2005, Optics letters.

[3]  Erez Hasman,et al.  Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings. , 2002, Optics letters.

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

[5]  Y Fainman,et al.  Form-birefringent computer-generated holograms. , 1996, Optics letters.

[6]  E Hasman,et al.  Pancharatnam--Berry phase in space-variant polarization-state manipulations with subwavelength gratings. , 2001, Optics letters.

[7]  Michael Mishchenko,et al.  Fundamentals of Polarized Light , 2003 .

[8]  Jani Tervo,et al.  Design of space-variant diffractive polarization elements. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[9]  G. Biener,et al.  Chapter 4 – Space-variant polarization manipulation , 2005 .

[10]  K. Kinnstatter,et al.  Amplitude detection for the focus error in optical disks using a birefringent lens. , 1990, Applied optics.

[11]  N. Murakami,et al.  Nulling interferometry by use of geometric phase. , 2001, Optics letters.

[12]  E. Wolf.  Unified theory of coherence and polarization of random electromagnetic beams , 2003 .

[13]  Andrew G. Glen,et al.  APPL , 2001 .

[14]  Philippe Lalanne,et al.  Design and fabrication of blazed binary diffractive elements with sampling periods smaller than the structural cutoff , 1999 .

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

[16]  Erez Hasman,et al.  Rotating vectorial vortices produced by space-variant subwavelength gratings. , 2005, Optics letters.

[17]  Erez Hasman,et al.  Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics , 2003 .

[18]  Erez Hasman,et al.  Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures , 2002 .

[19]  G. Biener,et al.  Space-variant polarization manipulation for far-field polarimetry by use of subwavelength dielectric gratings. , 2005, Optics letters.

[20]  E. Wolf,et al.  Coherence and polarization of electromagnetic beams modulated by random phase screens and their changes on propagation in free space. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[21]  James R. Leger,et al.  Interferometric measurement of the geometric phase in space-variant polarization manipulations , 2002 .

[22]  Emil Wolf,et al.  Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation. , 2003, Optics letters.

[23]  A. Dubra,et al.  Conversion of bright nondiffracting beams into dark nondiffracting beams by use of the topological properties of polarized light. , 2000, Optics letters.

[24]  G. Biener,et al.  Spiral phase elements obtained by use of discrete space-variant subwavelength gratings , 2005 .

[25]  Phase modulation by polarization recording in bacteriorhodopsin: application to phase-shifting interferometry. , 2004, Optics letters.

[26]  C. Brosseau.  Fundamentals of Polarized Light: A Statistical Optics Approach , 1998 .

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

[28]  G. Biener,et al.  Space-variant polarization manipulation , 2005 .

[29]  M. Berry.  The Adiabatic Phase and Pancharatnam's Phase for Polarized Light , 1987 .

[30]  M. Berry.  Quantal phase factors accompanying adiabatic changes , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[31]  Daniel F. V. James,et al.  Change of polarization of light beams on propagation in free space , 1994 .

[32]  Rajendra Bhandari,et al.  Polarization of light and topological phases , 1997 .

[33]  Franco Gori,et al.  Beam coherence-polarization matrix , 1998 .

[34]  J Turunen,et al.  Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings. , 2000, Optics letters.

[35]  E. Wolf,et al.  Changes in the state of polarization of a random electromagnetic beam on propagation , 2005 .

[36]  Samuel,et al.  Observation of topological phase by use of a laser interferometer. , 1988, Physical review letters.

[37]  Y Fainman,et al.  Fabrication, modeling, and characterization of form-birefringent nanostructures. , 1995, Optics letters.

[38]  Erez Hasman,et al.  Near-field Fourier transform polarimetry by use of a discrete space-variant subwavelength grating. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[39]  J. Goodman.  Introduction to Fourier optics , 1969 .

[40]  G. Agarwal,et al.  Generation of complete coherence in Young's interference experiment with random mutually uncorrelated electromagnetic beams. , 2005, Optics letters.