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Frontiers of Optoelectronics

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Front Optoelec    2013, Vol. 6 Issue (1) : 89-96    https://doi.org/10.1007/s12200-012-0307-5
REVIEW ARTICLE
Stress engineering and the applications of inhomogeneously polarized optical fields
Thomas G. BROWN1(), Amber M. BECKLEY2
1. The Institute of Optics, University of Rochester, Rochester, NY 14627, USA; 2. Department of Engineering Physics, école Polytechnique de Montréal, Montréal, QC H3C 3A7, Canada
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Abstract

Spatial inhomogeneities in the polarization of a light field can show fascinating effects in focusing, propagation, illumination, and imaging. This paper provides examples of these effects and describes how deterministic stress on the periphery of an optical element can be used in fundamental studies of beam propagation, as well as applications such as polarimetry.
Keywords polarization      birefringence      physical optics     
Corresponding Author(s): BROWN Thomas G.,Email:thomas.brown@rochester.edu   
Issue Date: 05 March 2013
 Cite this article:   
Thomas G. BROWN,Amber M. BECKLEY. Stress engineering and the applications of inhomogeneously polarized optical fields[J]. Front Optoelec, 2013, 6(1): 89-96.
 URL:  
https://academic.hep.com.cn/foe/EN/10.1007/s12200-012-0307-5
https://academic.hep.com.cn/foe/EN/Y2013/V6/I1/89
Fig.1  Azimuthal (left) and radial (right) polarization states are locally plane-polarized in a way that retains cylindrical symmetry about the beam axis in both polarization and phase
Fig.1  Azimuthal (left) and radial (right) polarization states are locally plane-polarized in a way that retains cylindrical symmetry about the beam axis in both polarization and phase
Fig.1  Azimuthal (left) and radial (right) polarization states are locally plane-polarized in a way that retains cylindrical symmetry about the beam axis in both polarization and phase
Fig.1  Azimuthal (left) and radial (right) polarization states are locally plane-polarized in a way that retains cylindrical symmetry about the beam axis in both polarization and phase
Fig.2  Scheme of Youngworth and Brown to form a cylindrical vector beam (radial illustrated here) based on Mach-Zehnder interferometer. The right hand side shows a photograph of the interferometer
Fig.2  Scheme of Youngworth and Brown to form a cylindrical vector beam (radial illustrated here) based on Mach-Zehnder interferometer. The right hand side shows a photograph of the interferometer
Fig.2  Scheme of Youngworth and Brown to form a cylindrical vector beam (radial illustrated here) based on Mach-Zehnder interferometer. The right hand side shows a photograph of the interferometer
Fig.2  Scheme of Youngworth and Brown to form a cylindrical vector beam (radial illustrated here) based on Mach-Zehnder interferometer. The right hand side shows a photograph of the interferometer
Fig.3  Poincaré sphere representation of two polarization states superimposed with relative amplitude and phase. The phase difference determines the longitude and the relative amplitude the latitude when pictured on a sphere
Fig.3  Poincaré sphere representation of two polarization states superimposed with relative amplitude and phase. The phase difference determines the longitude and the relative amplitude the latitude when pictured on a sphere
Fig.3  Poincaré sphere representation of two polarization states superimposed with relative amplitude and phase. The phase difference determines the longitude and the relative amplitude the latitude when pictured on a sphere
Fig.3  Poincaré sphere representation of two polarization states superimposed with relative amplitude and phase. The phase difference determines the longitude and the relative amplitude the latitude when pictured on a sphere
Fig.4  Comparison of finite element computation (a), analytic solution of Yiannopoulos [] (b), and experimental image (c), showing contours of equal half wave retardance for trigonally-stressed optical element
Fig.4  Comparison of finite element computation (a), analytic solution of Yiannopoulos [] (b), and experimental image (c), showing contours of equal half wave retardance for trigonally-stressed optical element
Fig.4  Comparison of finite element computation (a), analytic solution of Yiannopoulos [] (b), and experimental image (c), showing contours of equal half wave retardance for trigonally-stressed optical element
Fig.4  Comparison of finite element computation (a), analytic solution of Yiannopoulos [] (b), and experimental image (c), showing contours of equal half wave retardance for trigonally-stressed optical element
Fig.5  Retardance (normalized) as function of radius for = 3, 4, and 5. The insets show the contours of equal retardance based on the analytic model of Iannopolis
Fig.5  Retardance (normalized) as function of radius for = 3, 4, and 5. The insets show the contours of equal retardance based on the analytic model of Iannopolis
Fig.5  Retardance (normalized) as function of radius for = 3, 4, and 5. The insets show the contours of equal retardance based on the analytic model of Iannopolis
Fig.5  Retardance (normalized) as function of radius for = 3, 4, and 5. The insets show the contours of equal retardance based on the analytic model of Iannopolis
Fig.6  Twyman Green interferometer for characterizing phase vortex
Fig.6  Twyman Green interferometer for characterizing phase vortex
Fig.6  Twyman Green interferometer for characterizing phase vortex
Fig.6  Twyman Green interferometer for characterizing phase vortex
Fig.7  Left: (a) Interferogram of phase vortex; (b) irradiance of vortex. Right: Reconstructed phase of vortex obtained by Fourier analysis of interferogram
Fig.7  Left: (a) Interferogram of phase vortex; (b) irradiance of vortex. Right: Reconstructed phase of vortex obtained by Fourier analysis of interferogram
Fig.7  Left: (a) Interferogram of phase vortex; (b) irradiance of vortex. Right: Reconstructed phase of vortex obtained by Fourier analysis of interferogram
Fig.7  Left: (a) Interferogram of phase vortex; (b) irradiance of vortex. Right: Reconstructed phase of vortex obtained by Fourier analysis of interferogram
Fig.8  (a) Arrangement for examining effects of stressed window apodization in focal region of lens; (b) arrangement for studying propagation of Bessel-like beams transmitted through high-stress window
Fig.8  (a) Arrangement for examining effects of stressed window apodization in focal region of lens; (b) arrangement for studying propagation of Bessel-like beams transmitted through high-stress window
Fig.8  (a) Arrangement for examining effects of stressed window apodization in focal region of lens; (b) arrangement for studying propagation of Bessel-like beams transmitted through high-stress window
Fig.8  (a) Arrangement for examining effects of stressed window apodization in focal region of lens; (b) arrangement for studying propagation of Bessel-like beams transmitted through high-stress window
Fig.9  Focal splitting from threefold stress at low numerical aperture. (a-c) show the point spread functions at the inner focus, the paraxial focus, and the outer focus; (d) shows a comparison of the measured axial irradiance with that calculated from a numerical estimate based on the power law model
Fig.9  Focal splitting from threefold stress at low numerical aperture. (a-c) show the point spread functions at the inner focus, the paraxial focus, and the outer focus; (d) shows a comparison of the measured axial irradiance with that calculated from a numerical estimate based on the power law model
Fig.9  Focal splitting from threefold stress at low numerical aperture. (a-c) show the point spread functions at the inner focus, the paraxial focus, and the outer focus; (d) shows a comparison of the measured axial irradiance with that calculated from a numerical estimate based on the power law model
Fig.9  Focal splitting from threefold stress at low numerical aperture. (a-c) show the point spread functions at the inner focus, the paraxial focus, and the outer focus; (d) shows a comparison of the measured axial irradiance with that calculated from a numerical estimate based on the power law model
Fig.10  Axial irradiance patterns for a range of stress parameters . Because the focal splitting expands in proportional to the stress, the highest stress case has an expanded horizontal scale
Fig.10  Axial irradiance patterns for a range of stress parameters . Because the focal splitting expands in proportional to the stress, the highest stress case has an expanded horizontal scale
Fig.10  Axial irradiance patterns for a range of stress parameters . Because the focal splitting expands in proportional to the stress, the highest stress case has an expanded horizontal scale
Fig.10  Axial irradiance patterns for a range of stress parameters . Because the focal splitting expands in proportional to the stress, the highest stress case has an expanded horizontal scale
Fig.11  Photographs showing irradiance pattern of non-vortex (a) and vortex (b) Bessel-like beams. The inset shows a measurement of the central lobe under propagation compared with a Gaussian beam of equivalent size
Fig.11  Photographs showing irradiance pattern of non-vortex (a) and vortex (b) Bessel-like beams. The inset shows a measurement of the central lobe under propagation compared with a Gaussian beam of equivalent size
Fig.11  Photographs showing irradiance pattern of non-vortex (a) and vortex (b) Bessel-like beams. The inset shows a measurement of the central lobe under propagation compared with a Gaussian beam of equivalent size
Fig.11  Photographs showing irradiance pattern of non-vortex (a) and vortex (b) Bessel-like beams. The inset shows a measurement of the central lobe under propagation compared with a Gaussian beam of equivalent size
Fig.12  Polarization dependent point spread functions using stress engineered optical element. In each case, the input state of polarization is listed above the image
Fig.12  Polarization dependent point spread functions using stress engineered optical element. In each case, the input state of polarization is listed above the image
Fig.12  Polarization dependent point spread functions using stress engineered optical element. In each case, the input state of polarization is listed above the image
Fig.12  Polarization dependent point spread functions using stress engineered optical element. In each case, the input state of polarization is listed above the image
input statesBoldItalic1BoldItalic2BoldItalic3error/radDoP
horizontal0.97120.00940.02040.02320.9715
vertical-0.98810.00370.01860.01920.9883
+45 linear0.01000.9781-0.00950.01410.9782
45 linear0.0051-0.97580.00940.01090.9758
right circular0.00000.00001.000001.0000
left circular0.00000.0000-1.000001.0000
elliptical-0.40560.7529-0.50400.03190.9927
Tab.1  Representative Stokes measurements using star test polarimetry according to calibration procedure in Ref. []
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