First- and second-order polarization mode dispersion generated by a two-stage emulator

A two-stage polarization mode dispersion (PMD) emulator design consisting of two variable delay lines separated by a rotatable half-wave linear retarder is analyzed and shown to generate an adjustable amount of first- and second-order PMD without any higher orders. This two-stage PMD emulator configuration provides a simple easy-to-breadboard solution for second-order PMD emulators. When compared with PMD emulators based on birefringent crystals, this two-stage emulator is simpler to calibrate.     

Free-space optical shuffle implementations by use of birefringence-customized modular optics

A stacked integration technique based on polarization optics is studied for implementing shuffle-based interconnection networks with three-dimensional solid-state modules. A basic building block of the proposed scheme consists of a hole-patterned half-wave retarder for birefringence customizations and a calcite slab for subsequent beam deflections. On the basis of a cascade of such building blocks the submodules of various shuffle-family permutations can be implemented. To minimize channel cross talk, we incorporated a collimating-relaying imaging system. To help design birefringence customization, we developed algebraic formulations of folded shuffle operations using separable shuffles. Proof-of-concept experimental results, as well as system design, fabrication, and integration issues, are discussed.     

Achromatic half-wave plate for submillimeter instruments in cosmic microwave background astronomy: experimental characterization

An achromatic half-wave plate (HWP) to be used in millimeter cosmic microwave background (CMB) polarization experiments has been designed, manufactured, and tested. The design is based on the 5-plates Pancharatnam recipe and it works in the frequency range 85-185 GHz. A model has been used to predict the transmission, reflection, absorption, and phase shift as a function of frequency. The HWP has been tested by using coherent radiation from a back-wave oscillator to investigate its modulation efficiency and with incoherent radiation from a polarizing Fourier transform spectrometer (FTS) to explore its frequency behavior. The FTS measurements have been fitted with an optical performance model which is in excellent agreement with the data. A detailed analysis of the data also allows a precise determination of the HWP fast and slow axes in the frequency band of operation. A list of the HWP performance characteristics is reported including estimates of its cross polarization.     

Orthogonal linear polarization tunable-beat ring laser with a superluminescent diode

An orthogonal linear polarization operated ring laser with a superluminescent diode has been demonstrated to generate a tunable optical beat signal. The ring cavity contains a superluminescent diode as the optical gain medium, Faraday rotators, and a variable phase retarder (Babinet-Soleil compensator). By controlling the retarder, we changed the beat frequency in the range from a few tens of megahertz to 100 MHz.     

Square-wave retarder for polarization computer-generated holography

An etched calcite square-wave retarder is designed, fabricated, and demonstrated as an illuminator for an interlaced polarization computer-generated hologram (PCGH). The calcite square-wave retarder enables alternating columns of orthogonal linear polarizations to illuminate the interlaced PCGH. Together, these components produce a speckled, tangentially polarized PCGH diffraction pattern with a measured ratio of polarization of 84% and a degree of linear polarization of 0.81. An experimental alignment tolerance analysis is also reported.     

Theory of oblique-incidence phase retarders

Phenomenological and mathematical analyses of oblique incidence in total-internal-reflection phase retarders and the procedure for constructing extremely achromatic quarter-wave retarders are presented. It is shown that the retardance can assume the same value twice at two definite spectral lines. As an example, a quarter-wave phase retarder is described that introduces a retardance of exactly 90 degrees at two He-Ne laser lines of 632.8 and 1150 nm with a maximum deviation of 0.007 degrees for other wavelengths between these two lines. This application is advantageous in conjunction with two-line and multiline lasers where the radiation is usually pumped in a state of circular polarization.     

Achromatic half-wave plate for submillimeter instruments in cosmic microwave background astronomy: modeling and simulation

We adopted an existing formalism and modified it to simulate, with high precision, the transmission, reflection, and absorption of multiple-plate birefringent devices as a function of frequency. To validate the model, we use it to compare the measured properties of an achromatic five-plate device with a broadband antireflection coating to expectations derived from the material optical constants and its geometric configuration. The half-wave plate presented here is observed to perform well with a phase shift variation of < 2 degrees from the ideal 180 degrees over a bandwidth of Deltav/v approximately 1 at millimeter wavelengths. This formalism represents a powerful design tool for birefringent polarization modulators and enables its optical properties to be specified with high accuracy.     

Embedded centrosymmetric multilayer stacks as complete-transmission quarter-wave and half-wave retarders under conditions of frustrated total internal reflection

A centrosymmetric multilayer stack of two transparent materials, which is embedded in a high-index prism, can function as a complete-transmission quarter-wave or half-wave retarder (QWR or HWR) under conditions of frustrated total internal reflection. The multilayer consists of a high-index center layer sandwiched between two identical low-index films with high-index-low-index bilayers repeated on both sides of the central trilayer, maintaining the symmetry of the entire stack and constituting a QWR (Delta(t)=90 degrees or 270 degrees ) or HWR (Delta(t)=180 degrees ) in transmission. A QWR design at wavelength lambda=1.55 microm is presented that employs an 11-layer stack of Si and SiO(2) thin films, which is embedded in a GaP cube prism. The intensity transmittances for the p and s polarizations remain >99% and Delta(t) deviates from 90 degrees by <+/-3 degrees over a 100 nm spectral bandwidth (1.5< or =lambda< or =1.6 microm), and by < or =+/-7 degrees over an internal field view of +/-1 degrees (incidence angle 44 degrees < or = phi(0)< or =46 degrees inside the prism). An HWR design at lambda=1.55 microm employs seven layers of Si and SiO(2) thin films embedded in a Si cube, has an average transmittance >93%, and Delta(t) that differs from 180 degrees by <+/-0.3 degrees over a 100 nm bandwidth (1.5< or =lambda< or =1.6 microm) and by <+/-17 degrees over an internal field view of +/-1 degree . The sensitivity of these devices to film-thickness errors is also considered.     

Simple and accurate wavemeter implemented with a polarization interferometer

A simple and accurate wavemeter for measuring the wavelength of monochromatic light is described. The device uses the wavelength-dependent phase lag between principal polarization states of a length of birefringent material (retarder) as the basis for the measurement of the optical wavelength. The retarder is sandwiched between a polarizer and a polarizing beam splitter and is oriented such that its principal axes are 45 deg to the axis of the polarizer and the principal axes of the beam splitter. As a result of the disparity in propagation velocities between the principal polarization states of the retarder, the ratio of the optical power exiting the two ports of the polarizing beam splitter is wavelength dependent. If the input wavelength is known to be within a specified range, the measurement of the power ratio uniquely determines the input wavelength. The device offers the advantage of trading wavelength coverage for increased resolution simply through the choice of the retarder length. Implementations of the device employing both bulk-optic components and fiber-optic components are described, and the results of a laboratory test of a fiber-optic prototype are presented. The prototype had a wavelength accuracy of +/-0.03 nm.     

Identification of Odd-Radius Halo Arcs and of 44 degrees /46 degrees Parhelia by Their Inner-Edge Polarization

Birefringence of ice causes the inner edges of refraction halos to be polarized. The direction of this polarization relates directly to the projection of the crystal main axis onto the sky. This implies that the inner-edge polarization can serve as an observational diagnostic for determining the actual nature of a halo arc if two competing explanations exist. The direction and the visibility of the inner-edge polarization of arcs and circular halos arising from usual ice crystals and from ice crystals with pyramidal ends are calculated. It is found that the observation of inner-edge polarization can be decisive for the identification of a spot that might be either a 44 degrees parhelion or a 46 degrees parhelion, of an arc that might be either a 22 degrees sunvex Parry arc or a 20 degrees Parroid arc arising from plate-oriented pyramidal crystals, and of an arc that might be either a 22 degrees suncave Parry arc or a 23 degrees Parroid arc from plate-oriented pyramidal crystals. (With a Parroid arc, a halo is that which arises from an ice wedge made up of two faces of a crystal that rotates about a vertically oriented spin axis, and the edge of the wedge is perpendicular to this spin axis.) Polarization properties of other rare arcs are discussed. Practical hints are given for observing visually the inner-edge polarization of halos.     

Full-field optical coherence tomography using nematic liquid-crystal phase shifter

We present a polarization Linnik interference microscope with a nematic liquid-crystal (NLC) phase shifter for full-field optical coherence tomography of high-quality images. The rotating half-wave plate in conventional achromatic phase shifters was replaced by three liquid-crystal (LC) half-wave plates for implementing three-step phase-shifting interferometry. Thus, the NLC device generates phase shifts quickly and has no vibrations. In addition, the phase shift can be set to an arbitrary value between 0 and 2π by altering the azimuth angles of the LC cells. A tomographic image is retrieved from three sequential phase-shifted interferograms by using a three-step algorithm. The experimental results confirm the feasibility of the proposed technology.     

Electrostatic deposition of graphene

Loose graphene sheets, one to a few atomic layers thick, are often observed on freshly cleaved HOPG surfaces. A straightforward technique using electrostatic attraction is demonstrated to transfer these graphene sheets to a selected substrate. Sheets from one to 22?layers thick have been transferred by this method. One sheet after initial deposition is measured by atomic force microscopy to be only an atomic layer thick (～0.35?nm). A few weeks later, this height is seen to increase to ～0.8?nm. Raman spectroscopy of a single layer sheet shows the emergence of an intense D band which dramatically decreases as the number of layers in the sheet increase. The intense D band in monolayer graphene is attributed to the graphene conforming to the roughness of the substrate. The disruption of the C-C bonds within the single graphene layer could also contribute to this intense D band as evidenced by the emergence of a new band at 1620?cm(-1).     

Difference Frequency Generation of 5-18 mum in a AgGaSe(2) Crystal

Mid-infrared radiation in the 5-18-mum range has been obtained by difference frequency generation in a AgGaSe(2) crystal by pumping with the output of a type I LiNbO(3) optical parametric oscillator (OPO). Here we suggest the use of a LiTaO(3) retarder to achieve an orthogonal state of polarization between OPO outputs that are necessary for efficient pumping of a AgGaSe(2) crystal. Several tens of kilowatts of peak power near 8 mum and continuously tunable operation in the above range have been obtained.     

Fiber-optic polarization and phase modulator utilizing transparent piezofilm with indium tin oxide electrodes

A highly efficient optical polarization and phase modulator formed by the placement of a thin transparent piezofilm with indium tin oxide electrodes directly in the path of the output from an optical fiber is presented. Various configurations that differ in the clamping conditions, utilization of epoxy, and optical arrangement are presented. For a film thickness of 63.9 μm, a linear phase-shifting coefficient of 0.131 rad/voltage peak (Vp) at 2 kHz and of 0.508 rad/Vp at 7.4 kHz is demonstrated. An intrinsic birefringence of 0.0328 between the directions along the stretch and its perpendicular in the plane of the film has been measured. The polarization modulation coefficient was determined to be 0.323 rad/Vp at 8.423 kHz, corresponding to a half-wave voltage of 8.353 Vp. Applications of the device involving concurrent spatiotemporal polarization and phase modulation are indicated.     

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.     

Accurate interferometric retardance measurements

A two-polarization Michelson interferometer with a low-retardance beam splitter and digital signal processing is used to measure the retardance of optical devices. Error analysis of the improved optical system and data processing shows that the measurement has an uncertainty of 0.039 degrees for measurements of nominally 90 degrees retarders. Retardance variations arising from coherent reflections in the retarder used for intercomparison add an uncertainty of from 0.005 degrees to 0.03 degrees , increasing the combined measurement uncertainty to as much as 0.049 degrees .     

Rotating-polarizer polarimeter for accurate retardance measurement

We demonstrate an automated polarimeter based on a rotating polarizer for the measurement of linear retardance independent of laser power and detector gain. The retardance is found when a curve is fitted to a unique normalization of the intensity response of the polarimeter over a range of input polarizer orientations. The performance of this polarimeter is optimal for measurements of quarter-wave retardance and minimal for half-wave retardance. Uncertainties are demonstrated by measurements on six stable double Fresnel rhombs of nominal quarter-wave retardance, yielding expanded uncertainties between 0.031 degrees and 0.067 degrees . The accuracy has also been verified by blind comparisons with interferometric and modified null retardance measurement techniques.     

The design,preparation and optical measurement of thin film polarizers

The general approach to the design of thin film polarizers is outlined by reference to the principle of equivalent layers, and an analytical expression is derived for the number of quarter-wave layers required in a mirror structure to provide a specified polarization transmittance ratio $\text{(ifP =}\text{T}{}_{\mathrm{?}}\text{T}{}_{\mathrm{\perp }}\text{)}$. It is shown that the high polarization ratio and the small sensitivity of this parameter to the angle of incidence are conflicting specifications which require a compromise solution in practice. Also, to achieve simple and precise monitoring of the optical properties of the layers during deposition, double half-wave filter systems are shown to be preferable to multilayer quarter-wave mirrors as polarizers.The results of measurements on double half-wave polarizers for use with large aperture Pockel's cell shutters and Faraday isolators in high power neodymium glass lasers are presented with particular reference to transmittance, polarization ratio, superficial unifromity and laser damage threshold.