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Showing papers on "Birefringence published in 2001"


Journal ArticleDOI
TL;DR: In this paper, it was shown that at low pump intensities, the fluorescence spectrum of the dye is modified, showing suppression of emission in the reflection band, and enhanced emission near the band edge.
Abstract: Cholesteric liquid crystals are chiral nematics, where the handedness of the constituent molecules causes the orientation of the local nematic director to vary in space. In the helical cholesteric structure, the director is perpendicular to the helix axis, and its orientation varies linearly with position along the helix axis. The spatial period of the structure is the pitch, which is determined by the concentration and the helical twisting power of the chiral constituents. As a consequence of the periodicity of the helical cholesteric structure and the birefringence of the liquid crystal, for a range of wavelengths, light propagation along the helix axis is forbidden for one of the normal modes. Since propagation is forbidden, incident light with a wavelength in this band and with the same helicity as the cholesteric is strongly reflected. The edges of this reflection band are at wavelengths that are equal to the refractive indices times the pitch. [1] Because of the existence of the selective reflection band, cholesteric liquid crystals are 1D photonic bandgap materials. The bandgap structure of cholesteric liquid crystals allows for the possibility of lasing without external mirrors that usually form a laser cavity. When a fluorescent dye is dissolved in the cholesteric host so that the peak of the fluorescent emission of the dye is in the selective reflection band of the cholesteric, propagation of one normal mode of the emitted light is forbidden. As a consequence, at low pump intensities, the fluorescence spectrum of the dye is modified, [2] showing suppression of emission in the reflection band, and enhanced emission near the band edge. As the pump intensity is increased, the linewidth of the enhanced fluorescence at the band edge narrows, and, above a pump threshold, lasing occurs. [2] Thin samples, typically 15‐30 lm in thickness, of low molecular weight cholesteric liquid crystals incorporating a variety of dyes [3] have been shown to lase. The primary role of the cholesteric liquid crystal in these systems is to act as a distributed cavity. Lasing occurs at the band edges, [2‐4] as pre

612 citations


Journal Article
TL;DR: In this article, a polarization-sensitive optical coherence-domain reflectometer capable of characterizing the phase retardation between orthogonal linear polarization modes at each reflection point in a birefringent sample is presented.
Abstract: We present a polarization-sensitive optical coherence-domain reflectometer capable of characterizing the phase retardation between orthogonal linear polarization modes at each reflection point in a birefringent sample. The device is insensitive to the rotation of the sample in the plane perpendicular to ranging. Phase measurement accuracy is ±0.86°, but the reflectometer can distinguish local variations in birefringence as small as 0.05° with a distance resolution of 10.8 μm and a dynamic range of 90 dB. Birefringence-sensitive ranging in a wave plate, an electro-optic modulator, and a calf coronary artery is demonstrated.

601 citations


Journal ArticleDOI
TL;DR: In this paper, the cutoff properties of birefringent photonic crystal fibers with respect to multimode behavior were analyzed theoretically and experimental results were presented in agreement with theoretical predictions.
Abstract: Photonic crystal fibers (PCFs) offer new possibilities of realizing highly birefringent fibers due to a higher intrinsic index contrast compared to conventional fibers. In this letter, we analyze theoretically the levels of birefringence that can be expected using relatively simple PCF designs. While extremely high degrees of birefringence may be obtained for the fibers, we demonstrate that careful design with respect to multimode behavior must be performed. We further discuss the cutoff properties of birefringent PCFs and present experimental results in agreement with theoretical predictions on both single- and multimode behavior and on levels of birefringence.

507 citations


Journal ArticleDOI
TL;DR: An improved method of polarization sensitive optical coherence tomography is presented that enables measurement and imaging of backscattered intensity, birefringence, and fast optic axis orientation simultaneously with only one single A-scan per transverse measurement location.
Abstract: We present an improved method of polarization sensitive optical coherence tomography that enables measurement and imaging of backscattered intensity, birefringence, and fast optic axis orientation simultaneously with only one single A-scan per transverse measurement location. While intensity and birefringence data are obtained in a conventional way, the optic axis orientation is determined from the phase difference recorded in two orthogonal polarization channels. We report on accuracy and precision of the method by measuring birefringence and optic axis orientation of well defined polarization states in a technical object and present maps of birefringence and, what we believe for the first time, of optic axis orientation in biological tissue.

491 citations


Journal ArticleDOI
TL;DR: PS-OCT has potential use for noninvasive assessment of burn depth because it can measure the reduction in collagen birefringence using depth resolved changes in the polarization state of light propagated in, and reflected from, the tissue.
Abstract: We report the first application of high-speed fiber-based polarization sensitive optical coherence tomography (PS-OCT) to image burned tissue in vivo. Thermal injury denatures collagen in skin and PS-OCT can measure the reduction in collagen birefringence using depth resolved changes in the polarization state of light propagated in, and reflected from, the tissue. Stokes vectors were calculated for each point in a scan and birefringence relative to incident polarization determined using four incident polarization states. Using a high-speed fiber-based PS-OCT system on rat skin burned for varying periods of time, a correlation between birefringence and actual burn depth determined by histological analysis was established. In conclusion, PS-OCT has potential use for noninvasive assessment of burn depth.

362 citations


Journal ArticleDOI
12 Apr 2001-Nature
TL;DR: The approach can be used to form a wide range of other functional polymer thin films with isotropic as well as anisotropic topologies, and films can be produced whose optical birefringence exceeds that of the bireFringence of the polymer material itself.
Abstract: Light reflection from computer monitors, car dashboards and any other optical surface can impair the legibility of displays, degrade transmission of optical components and in some cases may even pose safety hazards. Antireflective coatings are therefore widely used, but existing antireflection technologies often perform sub-optimally or are expensive to implement. Here we present an alternative approach to antireflection coatings, based on an extension of our photo-aligning and photo-patterning technology for liquid-crystal displays (LCDs) and liquid-crystal polymer films with smooth surfaces to optical polymer films with controlled surface topologies. Nano- and micro-corrugated topologies are shown to result from optically induced monomer phase-separation on the polymer surfaces. The properties of the resulting films make them suitable high-performance and low-cost antireflection coatings for optical components of virtually any size, shape and material. Moreover, the approach can be used to form a wide range of other functional polymer thin films with isotropic as well as anisotropic topologies. For example, films can be produced whose optical birefringence exceeds that of the birefringence of the polymer material itself. These new films can also be used as diffractive thin films, diffusers, and directional reflectors which preserve light polarization, or as substrates for aligning liquid crystals to produce bright, low-power-consumption LCDs with integrated optical functions and memory.

290 citations


Journal ArticleDOI
TL;DR: This work studies the dispersive properties of photonic crystal fibers with elliptical air holes with unusual guidance, which leads to novel behavior of the birefringence, group-velocity walk-off, and dispersion parameters, including the possibility of zeroWalk-off with high bireFringence in the single-mode regime.
Abstract: We study the dispersive properties of photonic crystal fibers (PCF's) with elliptical air holes. The unusual guidance of PCF leads to novel behavior of the birefringence, group-velocity walk-off, and dispersion parameters, including the possibility of zero walk-off with high birefringence in the single-mode regime. A number of these effects are closely tied to the underlying radiation states of the air-hole lattice.

258 citations


Journal ArticleDOI
TL;DR: In this article, the optical properties of a cyclic olefin copolymer, Topas™, made by Celanese AG, are presented and compared with other commonly used thermoplastics, namely, polycarbonate and polymethyl methacrylate.
Abstract: The optical properties of a cyclic olefin copolymer, Topas™, made by Celanese AG, are presented. This class of materials is attractive on account of their high use temperature, excellent optical transmission, low birefringence, and low moisture uptake. These materials are compared with other commonly used thermoplastics, namely, polycarbonate and polymethyl methacrylate. Finally, Topas™ is compared with a number of other optical polymers being studied for optical waveguiding applications. It is found that at 830 nm Topas™ has low losses (less than 0.5 dB/cm), so that it may be useful for datacom applications. At the telecommunication wavelength of 1550 nm the losses are in the range of 0.7 dB/cm.

253 citations


Journal ArticleDOI
TL;DR: In this article, the authors survey the properties of photonic crystal fibers with elliptical air holes, examining mode shapes, birefringence, group velocity walkoff and dispersion, and cutoff conditions.
Abstract: We survey the properties of photonic crystal fibers with elliptical air holes, examining mode shapes, birefringence, group velocity walkoff and dispersion, and cutoff conditions. We find new types of behavior for each quantity and demonstrate the possibility achieving large birefringence with zero walkoff in the single-mode regime. We show that the dispersive properties of the vector modes are closely tied to those of the so-called fundamental space filling modes, and that at long wavelengths, the fibers exhibit a single-polarization single-mode regime of propagation without the presence of material anisotropy.

228 citations


Journal ArticleDOI
TL;DR: In this article, a new type of permanent damage obtained in bulk fused silica by focusing IR femtosecond laser pulses with microjoule energy was reported, which consists of an uniaxial birefringence zone over a lateral size of a few microns and a depth of several tens of microns.

207 citations


Journal ArticleDOI
TL;DR: In this article, a simple model for the dependence of thermal lensing and degradation in beam quality on the transverse intensity profile of the pump beam is presented, and the role of energy transfer upconversion as a mechanism for additional heat loading under non-lasing conditions is considered.
Abstract: Degradation in beam quality due to aberrated thermal lensing and depolarization loss due to stress induced birefringence in end-pumped edge-cooled solid-state lasers are investigated. A simple model for the dependence of thermal lensing and degradation in beam quality on the transverse intensity profile of the pump beam is presented. Experimental measurements of thermal lensing, degradation in beam quality and depolarization loss in a diode-bar-end-pumped Nd:YAG rod support the main predictions of the model and, in addition, show that there can be significant extra heating under non-lasing conditions compared to lasing conditions. The role of energy transfer upconversion as a mechanism for additional heat loading under non-lasing conditions is considered. Finally, various strategies for limiting the impact of thermal lensing and thermally induced birefringence on laser performance in simple end-pumped cavity configurations are reviewed.

Journal ArticleDOI
TL;DR: Coupled plasmon-waveguide resonance (CPWR) spectroscopy is shown to provide a convenient means of evaluating parameters in a single lipid bilayer, and provide a powerful tool for analyzing lipid-protein, protein- protein, and protein-ligand interactions in proteolipid films.

Journal ArticleDOI
TL;DR: A method for extracting the birefringence properties of biological samples with micrometer-scale resolution in three dimensions, using a new form of polarization-sensitive optical coherence tomography, which measures net retardance, net fast axis, and total reflectivity as a function of depth into the sample.
Abstract: We report a method for extracting the birefringence properties of biological samples with micrometer-scale resolution in three dimensions, using a new form of polarization-sensitive optical coherence tomography. The method measures net retardance, net fast axis, and total reflectivity as a function of depth into the sample. Polarization sensing is accomplished by illumination of the sample with at least three separate polarization states during consecutive acquisitions of the same pixel, A scan, or B scan. The method can be implemented by use of non-polarization-maintaining fiber and a single detector. In a calibration test of the system, net retardance was measured with an average error of 7.5° (standard deviation 2.2°) over the retardance range 0° to 180°, and a fast axis with average error of 4.8° over the range 0° to 180°.

Patent
13 Dec 2001
TL;DR: In this paper, an organic optical waveguide with a patterned, light transmissive perfluoropolymer core composition and a light reflecting cladding composition on the pattern of the core was proposed.
Abstract: The invention provides organic optical waveguide devices which employ perfluoropolymeric materials having low optical loss and low birefringence. An optical element has a substrate; a patterned, light transmissive perfluoropolymer core composition; and a light reflecting cladding composition on the pattern of the core. Writing of high-efficiency waveguide gratings is also disclosed.

Journal ArticleDOI
TL;DR: In this paper, a high-power continuous-wave polycrystalline 1% Nd:Y3Al5O12 (Nd :YAG) rod laser was demonstrated.
Abstract: A high-power continuous-wave polycrystalline 1% Nd:Y3Al5O12 (Nd:YAG) ceramic rod laser was demonstrated. With 290 W/808 nm laser diode pumping, cw laser output of 72 W was obtained at 1064 nm. The optical-to-optical conversion efficiency is 24.8%. Thermally induced birefringence properties of Nd:YAG ceramic was also investigated.

Patent
22 Aug 2001
TL;DR: In this article, an optical element and a manufacturing method therefor, an exposure apparatus, and a device manufacturing method that can reduce the effect of intrinsic birefringence under high NA conditions were presented.
Abstract: An optical element and a manufacturing method therefor, an exposure apparatus, and a device manufacturing method that can reduce the effect of intrinsic birefringence under high NA conditions. According to an optical element as one aspect of the present invention, an angle between a [0 0 1] axis of an isometric crystal and an optical axis is less than 10°, and preferably 0°.

Patent
06 Feb 2001
TL;DR: In this paper, a polarized sample beam of broadband radiation is focused onto the surface of a sample and the radiation modified by the sample is collected by means of a mirror system in different planes of incidence.
Abstract: A polarized sample beam of broadband radiation is focused onto the surface of a sample and the radiation modified by the sample is collected by means of a mirror system in different planes of incidence. The sample beam focused to the sample has a multitude of polarization states. The modified radiation is analyzed with respect to a polarization plane to provide a polarimetric spectrum. Thickness and refractive information may then be derived from the spectrum. Preferably the polarization of the sample beam is altered only by the focusing and the sample, and the analyzing is done with respect to a fixed polarization plane. In the preferred embodiment, the focusing of the sample beam and the collection of the modified radiation are repeated employing two different apertures to detect the presence or absence of a birefringence axis in the sample. In another preferred embodiment, the above-described technique may be combined with ellipsometry for determining the thicknesses and refractive indices of thin films.

Journal ArticleDOI
TL;DR: In this paper, the double-start-screw nanostructure was used to construct multilayered fabrication of birefringent thin-film materials for the circular Bragg resonance at visible and near infrared wavelengths.
Abstract: Recent advances in birefringent thin-film technology have led to vacuum-deposited inorganic chiral materials of significance for optics. The new materials have a double-start-screw nanostructure and exhibit large optical activity. At the circular Bragg resonance, which can be engineered for visible or near infrared wavelengths, the materials tend to transmit circularly polarized light of one handedness and reflect the other. A large range of standard thin-film materials can be used, but best results are achieved with evaporants that yield large form birefringence, such as tantalum oxide, titanium oxide, and zirconium oxide for visible wavelengths and silicon for the near infrared. Multilayered fabrication has been demonstrated, and potential applications include solid-state sources, reflectors, filters, and detectors for circularly polarized light.

Journal ArticleDOI
TL;DR: A Monte Carlo model was used to analyze the propagation of polarized light in linearly birefringent turbid media, such as fibrous tissues, and videos of spatially distributed polarization states of light backscattered from or propagating in bireFringent media are presented.
Abstract: A Monte Carlo model was used to analyze the propagation of polarized light in linearly birefringent turbid media, such as fibrous tissues. Linearly and circularly polarized light sources were used to demonstrate the change of polarizations in turbid media with different birefringent parameters. Videos of spatially distributed polarization states of light backscattered from or propagating in birefringent media are presented.

Journal ArticleDOI
TL;DR: In this paper, the effects of 1-d photonic band-gap materials on the fluorescence spectrum of dyes dissolved in cholesteric liquid crystal, as well as on the fluorescent spectrum of the liquid crystal itself were studied.
Abstract: Cholesteric liquid crystals, due to their periodic structure and large birefringence, are 1-d photonic band-gap materials. Circularly polarized light of the same handedness as the cholesteric structure cannot propagate in the reflection band. We have studied the effects of this band-gap structure on the fluorescence spectrum of dyes dissolved in the cholesteric liquid crystal, as well as on the fluorescence spectrum of the liquid crystal itself. We have found that emission is enhanced at the band edges, and, above a certain pump threshold, lasing occurs both in dye-doped and in pure liquid crystals. Extremely low lasing thresholds and high efficiencies were observed in dye-doped systems. The results suggest an active energy transfer mechanism between the LC host and the fluorescent dye molecules.

Journal ArticleDOI
TL;DR: In this article, the authors used the diameter reduced type of polarization maintaining fibers to generate a 340-fs soliton pulse at a wavelength of around 2 /spl mu/m using a frequency-resolved optical gating method.
Abstract: Characteristics of widely wavelength tunable ultrashort pulse generation using several types of polarization maintaining fibers have been experimentally analyzed. Using the diameter reduced type of polarization maintaining fibers, the wavelength tunable soliton pulse is generated from 1.56 to 2.03 /spl mu/m. It is confirmed that the almost transform-limited 340-fs soliton pulse is generated at a wavelength of around 2 /spl mu/m using a frequency-resolved optical gating method. When low-birefringence fibers are used, it is observed that the orthogonally polarized small pulse spectrum is trapped by the soliton pulse and is also shifted toward the longer wavelength side in the process of soliton self-frequency shift. The wavelength of the orthogonally polarized pulse spectrum is 40-50 nm longer than that of the soliton pulse, and the birefringence of the fiber is compensated by the chromatic dispersion. Finally, a polarization maintaining highly nonlinear dispersion-shifted fiber is used as the sample fiber. When the fiber input power is low, the wavelength-tunable soliton and anti-Stokes pulses are generated. As the fiber input power is increased, the pulse spectra are gradually overlapped and the 1.1-2.1 /spl mu/m widely broadened supercontinuum spectra are generated by only 520 pJ pulse energy.

Patent
21 Sep 2001
TL;DR: In this article, the effect of the index profile around a waveguide can be used to change the polarization dependence or birefringence of the resonators, which allows one to control the polarization in the waveguide.
Abstract: Methods of tuning, switching or modulating, or, in general, changing the resonance of waveguide micro-resonators. Changes in the resonance can be brought about, permanently or temporarily, by changing the size of the micro-resonator with precision, by changing the local physical structure of the device or by changing the effective and group indices of refraction of the mode in the micro-resonator. Further changing the asymmetry of the index profile around a waveguide can alter the birefringence of the waveguide and allows one to control the polarization in the waveguide. This change in index profile may be used to change the polarization dependence or birefringence of the resonators.

Journal ArticleDOI
TL;DR: The results of modeling show that the temperature and pressure sensitivity of elliptical-core fiber are associated primarily with variations in stress induced by these parameters.
Abstract: Modal birefringence and its sensitivity to temperature and hydrostatic pressure were measured versus wavelength in three elliptical-core fibers and one fiber with stress-induced birefringence. We carried out the measurements in the spectral range from 633 to 843 nm by using interferometric methods. In fibers with elliptical cores all the measured parameters showed high chromatic dependence, whereas in fibers with stress-induced birefringence this dependence was weak. We modeled the dispersion characteristics of two elliptical-core fibers by using the modified perturbation approach first proposed by Kumar. The modification consists of introducing into the expression for the normalized propagation constants an additional perturbation term that contains information about stress-induced birefringence. The results of modeling show that the temperature and pressure sensitivity of elliptical-core fiber are associated primarily with variations in stress induced by these parameters. The agreement between measured and calculated values of sensitivity in the worst case was equal to 20% for modal birefringence and temperature sensitivity and 50% for pressure sensitivity. Lower agreement between measured and calculated values of pressure sensitivity is most probably associated with uncertainties in the material constants used in modeling.

Journal ArticleDOI
TL;DR: Polarization selection in small-area vertical-cavity surface-emitting lasers is studied experimentally in dependence of injection current and substrate temperature in the vicinity of the minimum threshold condition as mentioned in this paper.
Abstract: Polarization selection in small-area vertical-cavity surface-emitting lasers is studied experimentally in dependence of injection current and substrate temperature in the vicinity of the minimum threshold condition. Polarization switching from the low to the high frequency fundamental spatial mode is demonstrated. The effective birefringence displays a minimum in the transition region. The observation of dynamical transition states hints to the relevance of nonlinear effects. A comparison to the predictions of the San Miguel–Feng–Moloney model based on phase-amplitude coupling is given.

Journal ArticleDOI
TL;DR: In this article, the birefringence of two-dimensional photonic crystals in the spectral region below the first photonic band gap was measured using transmission spectroscopy.
Abstract: We report an experimental and theoretical study of the birefringence of two-dimensional photonic crystals in the spectral region below the first photonic band gap. Transmission spectroscopy is used to measure the birefringence of a sample composed of a triangular lattice of air cylinders in silicon, with a cylinder radius of $0.644 \ensuremath{\mu}\mathrm{m}$ and a lattice pitch of $1.5 \ensuremath{\mu}\mathrm{m}.$ The measured birefringence (defined as the difference in the effective refractive indices of the electric fields polarized parallel and perpendicular to the cylinder axis) reaches a maximum value of 0.366 near the first photonic band edge at a wavelength of $6.52 \ensuremath{\mu}\mathrm{m}.$ The results show excellent agreement with theory and demonstrate the potential use of two-dimensional photonic crystals for highly birefringent optically integrated devices.

Patent
04 Sep 2001
TL;DR: In this paper, the frequency periodicity measurements are derived from differential delays induced by in-process glass elements between beam components in a polarization interferometer unit and from progressive wavelength scanning across a wavelength band of interest.
Abstract: Optical components, particularly microoptic glass components used in synthesizing birefringence in filter systems based on polarization interferometer techniques, are fabricated using systems and methods which provide accurate frequency periodicity measurements. These measurements are derived from differential delays induced by in-process glass elements between beam components in a polarization interferometer unit and from progressive wavelength scanning across a wavelength band of interest. The consequent sinusoidal output variation has peak to peak spacings which are measured to provide frequency periodicity values from which precise length corrections for the optical elements can be calculated.

Journal ArticleDOI
TL;DR: In this article, the intrinsic optical anisotropy of Si induced by its dielectric patterning was investigated and an in-plane birefringence for nanostructured (110) Si surfaces was found to be 104 times stronger than that observed in bulk silicon crystals.
Abstract: We report on a strong intrinsic optical anisotropy of Si induced by its dielectric patterning. As a result, an in-plane birefringence for nanostructured (110) Si surfaces is found to be 104 times stronger than that observed in bulk silicon crystals. We found the value of birefringence to be strongly dependent on the dielectric surrounding of the silicon nanoparticles assembling these layers. Beyond numerous potential implications for realization of optical devices and sensors, this gives a favorable route for studying the physics of condensation phenomena in a mesoscopic geometrical scale.

Patent
29 Mar 2001
TL;DR: In this paper, a variable reflectance mirror employing a super-twisted nematic (STN) liquid crystal cell to control reflectivity is presented, where a polymer alignment layer is formed over the electrodes so as to orient the STN liquid crystal material to possess a twist angle between 180° and approximately 270°.
Abstract: A variable reflectance mirror employing a super-twisted nematic (STN) liquid crystal cell to control reflectivity. The STN liquid crystal cell includes a layer of STN liquid crystal material formed between a pair of transparent electrodes, where a polymer alignment layer is formed over the electrodes so as to orient the STN liquid crystal material to possess a twist angle between approximately 180° and approximately 270°. A pair of crossed polarizers are respectively positioned on the outer surfaces of the front and rear plates. A layer of reflective material is further formed adjacent to the outer surface of the polarizer adjacent to the rear plate. The transparent electrodes are connected to a voltage source to apply an electrical bias across the STN liquid crystal layer, where the transmitivity of the STN liquid crystal layer to light can be varied by varying the electrical bias applied across the transparent electrodes to vary the birefringence of the STN liquid crystal layer. The degree of reflection provided by the variable reflectance mirror is adjusted by adjusting the electrical bias applied across the STN liquid crystal layer. A stacked IC control circuit is provided for controlling the electrical bias applied across the STN liquid crystal layer.

Journal ArticleDOI
TL;DR: In this article, the potential of all commercially available optical crystals is evaluated on the basis of the specific requirements in the high-power femtosecond regime, and a comparative experimental study of a number of materials (birefringent and quasi-phase-matched) employed in a seeded optical parametric amplifier pumped near 800-nm is presented, where the generated idler is tunable between 3 and 4µm.
Abstract: We review methods for frequency conversion of amplified femtosecond laser pulses from the near- to the mid-infrared. The potential of all commercially available optical crystals is evaluated on the basis of the specific requirements in the high-power femtosecond regime. A comparative experimental study of a number of materials (birefringent and quasi-phase-matched) employed in a seeded optical parametric amplifier pumped near 800 nm is presented, where the generated idler is tunable between 3 and 4 µm. Internal conversion efficiencies as high as 40% and pulse energies as high as 20 µJ are achieved in this spectral range. Wavelength tunability up to 12 µm with energies exceeding 1 µJ is demonstrated by pumping optical parametric amplifiers and generators near 1.25 and 2 µm, as well as by difference frequency generation with a quantum efficiency of 40-80%. In all cases the generated mid-infrared pulses are almost bandwidth limited with a duration of 100-200 fs.

Journal ArticleDOI
TL;DR: In this paper, a nonlinear, birefringent optical fiber with twist was analyzed and the authors derived a simplified set of equations to describe the nonlinear evolution of the phase.
Abstract: We analyze propagation in a nonlinear, birefringent optical fiber with twist. The results show that the polarization evolution is periodic, and they are applied to the analysis of a Sagnac interferometer. The period is calculated by using perturbation theory, and we find a condition for it to be independent of the initial polarization state. We derive a simplified set of equations to describe the nonlinear evolution of the phase. We give a useful way to visualize the behavior of the nonlinear optical loop mirror (as a function of birefringence, twist, length, and input polarization) in terms of the Poincare sphere.