Distorted wave front produced by a high-resolution projection optical system having rotationally symmetric birefringence

The influence of birefringence caused by rotationally symmetric stress distribution in a high-resolution projection optical system is investigated. The general form of the pupil function is derived based on the Jones matrix calculation, expressing the wave front as a combination of the two orthogonal polarization components. Assuming a linearly polarized incident beam, it is found that the main polarization portion of the wave front exiting the projection lens has astigmatic aberration in the Seidel region and shows phase singularity at four pupil points at which the amplitude transmittance becomes zero.     

Measurement of birefringence for optical recording of disk substrates

We experimentally investigate the birefringence of bare and coated substrates for magneto-optical recording, using ellipsometry at wavelengths of 632.8 and 780 nm. The polarization rotation and ellipticity of reflected or transmitted light are measured for different incident angles and for different orientations of the incident linear polarization. The measured data are then fitted by the MULTILAYER computer program, which solves the Maxwell equations for a plane wave propagating in a multilayer structure. This approach makes it possible to determine, with high accuracy, the orientations of the principal axes of the substrate and the corresponding refractive indices. The results show that one of the principal axes is always along the substrate's normal direction, but the orientations of the in-plane principal axes can be much different from the radial and track directions. A special feature of the ellipsometers that were used is that a glass hemisphere is placed in contact with the substrate to eliminate refraction of the incident beam. This enables a maximum propagation angle of 70° (with respect to the normal) in the substrate and hence increases the measurement sensitivity. Certain anomalies have been observed, which we believe are associated with the variation of birefringence properties along the thickness direction.     

Dielectric tensor measurement from a single Mueller matrix image

A technique for measuring dielectric tensors in anisotropic layered structures, such as thin films of biaxial materials, is demonstrated. The ellipsometric data are collected in a quasi-monochromatic Mueller matrix image acquired over a large range of incident and azimuthal angles by illuminating a very small area on the sample with a focused beam from a modulating polarization state generator. After the beam interacts with the sample, the reflected and/or transmitted light is collected using an imaging polarization state analyzer. An image of the exit pupil of a collection objective lens is formed across a CCD such that each pixel collects light from a different angle incident on the sample, thus acquiring ellipsometric data at numerous incident angles simultaneously. The large range of angles and orientations is necessary to accurately determine dielectric tensors. The small but significant polarization aberrations of the low-polarization objective lenses used to create and collect the focused beams provide a significant challenge to accurate measurement. Measurements are presented of a thin-film E-type polarizer and a stretched plastic biaxial film.     

Axial birefringence in high-numerical-aperture optical systems and the light distribution close to focus.

The effects of birefringence on the light distribution in the focal region of a high-NA optical system are investigated with use of the Debye approach to vector diffraction theory. The attention is limited to uniaxially birefringent media with symmetry axis along the optical axis of the imaging system. The radially (p) and tangentially (s) polarized fields in the exit pupil produce spots in the focal region that are defocused with respect to each other. For small birefringence values the relative defocus causes a distortion and broadening of the spot; for larger values the two spots separate completely. As a corollary to the theory it is shown that there is a tangential tornadolike flow of energy in the focal region when the polarization in the entrance pupil is elliptical.     

Induced and form birefringence in high-frequency polarization gratings

High-frequency phase polarization gratings are fabricated holographically in dichromated gelatin dyed with malachite green. It is observed that the intensity of the -1 diffracted beam is a sinusoidal function of the incident polarization angle. In addition, we analyze the dependence of the diffracted order polarization on grating frequency. It is evident from our results that form birefringence becomes significant when the grating period is smaller than the illumination wavelength, thus modifying the optically induced birefringence. Then, in polarization hologram reconstruction, it is not possible to obtain the polarization distribution at the recording step for high-frequency objects.     

Analysis of the receiver response for a noncoaxial lidar system with fiber-optic output

The return signal of a noncoaxial lidar system with fiber-optic output is examined. The dependence of the overlap regions and the overlap factor of the system on the fiber diameter is calculated for several inclination angles between the laser beam and the optical receiver axes. The effect of central obstruction is included and both cases of Gaussian and quasi-Gaussian laser beam profiles are treated. The irradiance spatial distribution on the focal plane of the system is calculated and experimentally determined. Finally, an alignment procedure of the lidar system is described based on the comparison between the range-corrected lidar signal and the range-corrected exponentially attenuated Rayleigh backscattered coefficient.     

Ocular aberrations with ray tracing and Shack-Hartmann wave-front sensors: does polarization play a role?

Ocular aberrations were measured in 71 eyes by using two reflectometric aberrometers, employing laser ray tracing (LRT) (60 eyes) and a Shack-Hartmann wave-front sensor (S-H) (11 eyes). In both techniques a point source is imaged on the retina (through different pupil positions in the LRT or a single position in the S-H). The aberrations are estimated by measuring the deviations of the retinal spot from the reference as the pupil is sampled (in LRT) or the deviations of a wave front as it emerges from the eye by means of a lenslet array (in the S-H). In this paper we studied the effect of different polarization configurations in the aberration measurements, including linearly polarized light and circularly polarized light in the illuminating channel and sampling light in the crossed or parallel orientations. In addition, completely depolarized light in the imaging channel was obtained from retinal lipofuscin autofluorescence. The intensity distribution of the retinal spots as a function of entry (for LRT) or exit pupil (for S-H) depends on the polarization configuration. These intensity patterns show bright corners and a dark area at the pupil center for crossed polarization, an approximately Gaussian distribution for parallel polarization and a homogeneous distribution for the autofluorescence case. However, the measured aberrations are independent of the polarization states. These results indicate that the differences in retardation across the pupil imposed by corneal birefringence do not produce significant phase delays compared with those produced by aberrations, at least within the accuracy of these techniques. In addition, differences in the recorded aerial images due to changes in polarization do not affect the aberration measurements in these reflectometric aberrometers.     

Polarization aberrations. 1. Rotationally symmetric optical systems

The polarization in isotropic radially symmetric lens and mirror systems in the paraxial approximation is examined. Polarized aberrations are variations in the phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear diattenuation, and linear retardance aberrations are derived in terms of the chief and marginal ray angles of incidence and the Taylor series expansion coefficients of the Fresnel equations for reflection and transmission at uncoated and thin-film-coated interfaces. Applications to polarization ray tracing are discussed.     

All-optical controlling of the focal intensity of a liquid crystal polymer microlens array

The current work demonstrates a liquid crystalline polymer microlens array (LCP MLA) with an all-optically tunable and multistable focal intensity through photochemical phase transition. The operational mechanism of the optical tuning is associated with the photoisomerization effect. The proposed LCP MLA device has a focusing unit based on a birefringence LCP and a tuning unit with a light responsive material to control the polarization state of the incident probe beam. The optically variable refractive indices of LCP enable a positive or negative MLA that can control the polarization of incident light to be realized.     

Measuring distribution of the ellipsoid of birefringence through the thickness of optical disk substrates

We have measured the birefringence of polycarbonate optical disk substrates, using ellipsometry. For a more comprehensive characterization, the probe beam was incident upon substrates in a wide range of polar angles and from different azimuths relative to track direction (?). Our measurements show that the ellipsoid of birefringence is tilted in the plane of radial (r) and normal (z) directions. The tilt angle varies through thickness, with a maximum value of approximately 10°. For beams passing through the substrate in the ?-z plane and at large incident angles, this tilt causes significant conversion (up to 100%) between p- and s-polarized components. Distributions of other parameters, such as the values of in-plane and vertical birefringence, are obtained simultaneously in the measurements.     

Rank Prize Funds Minisymposium on Non-classical Light for Communication

Abstract

We studied both experimentally and theoretically the transmission and polarization characteristics of a Cr⁴⁺ : YAG saturable absorber crystal as a function of the intensity and polarization state of an incident laser beam. We found that a birefringent absorption behaviour is induced and we show that the experimental results are well described by a full numerical model which includes excited-state absorption as well as a ground-state cross-absorption term. By using pump-probe measurements we show that a finite cross-saturation of the absorption is achieved along the crystal axes orthogonal to the polarization of the optical radiation. No induced refractive index birefringence is observed.     

Self-healing of tightly focused scalar and vector Bessel-Gauss beams at the focal plane

The property of self-healing at the focal plane for both scalar and vector Bessel-Gauss (BG) beams is investigated in the tight focusing condition. For the BG beam, which is partially obstructed at the pupil plane, the spatial intensity distribution at the focal plane is well recovered. Furthermore, recovery of not only intensity but also polarization distribution is observed for an obstructed vector BG beam. This self-healing effect for both the intensity and polarization components is recognized even when the half of the beam is obstructed by a semicircular obstacle. The effect of the size of the obstacle on recovery of polarization and intensity distribution is studied. The role of the beam size at the pupil plane is also discussed.     

Axial irradiance of a focused beam

The principal maximum of axial irradiance of a focused beam with a low Fresnel number does not lie at its focal point; instead it lies at a point that is closer to the focusing pupil. It has been shown by the numerical example of a weakly truncated Gaussian beam that its value increases and its location moves closer to the pupil when spherical aberration is introduced into the beam. Such an increase has been referred to as "beyond the conventional diffraction limit." Similarly, an increase in the value and a shift in the location of the principal maximum of axial irradiance of a uniform beam toward the pupil by the introduction of some spherical aberration has been characterized as an unexpected result. We explain why and how such a result comes about and that it neither invalidates any diffraction limit nor is it unexpected. We illustrate this for uniform as well as Gaussian beams of various truncation ratios. Both focused and collimated beams aberrated by spherical aberration or astigmatism are considered.     

Polarization averaged short-time Fourier transform technique for distributed fiber birefringence characterization using Brillouin gain

A polarization averaged short-time Fourier transform (PASTFT) technique is developed for distributed fiber birefringence characterization based on counterpropagating stimulated Brillouin scattering (SBS) gain signal. This technique can be used for the birefringence characterization of the general elliptical birefringent fiber. A theoretical model on polarization matching of counterpropagating SBS process is established. The performance of the short-time Fourier transform (STFT) method and the PASTFT technique is analyzed by using the simulation of the theoretical model. Simulation results show that the process of polarization average could effectively reduce the birefringence characterization error caused by the polarization dependence of the local period of SBS gain. A less than 8% normalized root mean square error is achieved for the characterization of the length of the birefringence vector on elliptical birefringent fibers. The PASTFT technique is experimentally verified by the distributed measurement of beat length and differential group delay of a standard single-mode fiber via the Brillouin optical time domain analysis system.     

Thermo-optical model of repetitively pumped solid-state lasers

A thermo-optical model describing the cavity stability and TEM00-mode volume of a repetitively pumped solid-state laser is developed and verified experimentally. The model predicts a maximum theoretical TEM00 Gaussian-mode radius in the laser rod. This maximum mode radius is caused by a bifocusing of the cavity mode and is present even in gain-polarized materials that nominally suppress the effect of birefringence on beam polarization. The mode limitation effect is not eliminated by conventional optics and is reduced only marginally by the often-described technique of placing a second identical laser head in the cavity. A maximum mode radius implies a fundamental limit on the TEM00-mode energy that can be extracted from a given laser cavity.     

Generation of high quality Airy beams with blazed micro-optical cubic phase plates

We design and fabricate a hybrid refractive-diffractive cubic phase plate (CPP) with a combined conventional blazed grating for generating high quality Airy beams. The grating enables elimination of direct incident illumination in the reconstructed beam. The CPP is fabricated in a negative photoresist on a substrate by laser direct writing lithography with precise exposure control of gray scales. Experimentally measured intensity distribution of the Airy beam is found in good agreement with the theoretical predictions. Furthermore, self-healing and nondiffraction properties of the Airy beam are verified experimentally. The proposed method gives rise to a simple, reliable, and low-cost micro-optical element solution for the generation of high quality Airy beams.     

Enhancement of Two-Wave Coupling in a Ce:KNSBN Crystal with Optimum Polarization of the Writing Beams

We have improved the two-wave coupling amplification and the signal-to-noise ratio of an amplified signal with photorefractive cerium-doped potassium sodium strontium barium niobate (Ce:KNSBN) by employing optimum polarization orientation of the pump beam while the signal beam retains extraordinary polarization. The optimum polarization angle of the pump beam was found experimentally to be 30 degrees with respect to the extraordinary polarization direction in a symmetrically incident system. Nearly 1.9-times enhancement of the gain and nearly 3-times enhancement of the signal-to-noise ratio were achieved at a signal-to-pump beam intensity ratio of 1:40. At a beam intensity ratio of 1:2000, a two-wave coupling gain of nearly 500 was obtained, which is much higher than the gain previously reported. Modified coupled-wave equations that involve beam fanning with certain assumptions concerning the fanning parameters were used. The numerical solution is in good agreement with the experimental data. The results are compared with those obtained with a 45 degrees -cut BaTiO(3) crystal.     

Polarization properties of fiber lasers with twist-induced circular birefringence

We have experimentally observed and theoretically analyzed the polarization properties of fiber lasers with twist-induced birefringence. Twisting a fiber induces the circular birefringence of a fiber laser cavity, and this birefringence reduces the effects of intrinsic linear birefringence on the polarization properties of fiber lasers. The frequencies of their polarization eigenmodes coincide with each other gradually as the twist rate increases, and the directions of polarization eigenmodes deviate from the birefringence axis at a much larger twist rate than the magnitude of intrinsic linear birefringence. We describe the successful experimental results for Nd and Er fiber lasers.     

Contrast mechanisms in polarization-sensitive Mueller-matrix optical coherence tomography and application in burn imaging

We investigate the various contrast mechanisms provided by polarization-sensitive (PS) Mueller-matrix optical coherence tomography (OCT). Our PS multichannel Mueller-matrix OCT is the first, to our knowledge, to offer simultaneously comprehensive polarization-contrast mechanisms, including the amplitude of birefringence, the orientation of birefringence, and the diattenuation in addition to the polarization-independent intensity contrast, all of which can be extracted from the measured Jones or the equivalent Mueller matrix. Theoretical analysis shows that when diattenuation is negligible, the round-trip Jones matrix represents a linear retarder, which is the foundation of conventional PS-OCT, and can be calculated with a single incident polarization state, although the one-way Jones matrix generally represents an elliptical retarder; otherwise, two incident polarization states are needed. The experimental results obtained from rat skin samples, which conform well with the histology, show that Mueller OCT provides complementary structural and functional information on biological samples and reveal that polarization contrast is more sensitive to thermal degeneration of biological tissue than amplitude-based contrast. Thus, Mueller OCT has significant potential for application in the noninvasive assessment of burn depth.     

Serial bideposition of anisotropic thin films with enhanced linear birefringence

We describe a serial bideposition technique in which a tilted substrate is rotated stepwise by half a turn about a normal axis during the evaporation of a metal oxide from a single electron-beam source. Coatings formed by the new method develop a columnar nanostructure that is perpendicular to the substrate and has greatest width or bunching perpendicular to the common deposition plane. With appropriate choice of deposition parameters, the method produces biaxial films with large birefringence, principal axes aligned parallel and perpendicular to the substrate, and improved uniformity. Measured phase retardances for light incident normally on the films are double the corresponding values for tilted-columnar films.