Linear Polarization Modes Research Articles

Nonlinear polarization evolution: a numerical study of the coupling between main linear normal modes

A numerical modelling of nonlinear changes of polarization by Kerr effect is presented for an optical field propagating along a birefringent silica optical fiber. The kernel of this model comes from expressing the coupled field as a sum of two linear polarization modes in the direction of the fiber principal axes. The developed model is suitable for the design of optoelectronic devices and permits easily taking into account chromatic dispersion, gain or loss, etc.

The Design of a Variable Elliptically Polarized Undulator for the Coherent THz Light Source

A coherent THz light source was built in Shanghai Institute of Nuclear Research (SINR), Chinese Academy of Science. A variable elliptically polarized undulator with Apple-II structure was designed to produce the linear polarized as well as various elliptical polarized THz radiations. The structure of the undulator corresponds to four standard Halbach-type magnet rows which consist of two pairs of planar permanent magnet rows above and below the electron orbit plane. The two rows at one diagonal can move along the longitudinal direction to provide the various polarization modes. The period and the gap are 100mm and 36 mm respectively and the number of period is five. This paper describes the magnet design, the force calculation and the stress analysis of the undulator. The magnetic fields are optimized for the horizontal linear polarization mode and the circular polarization mode.

Entanglement and squeezing in a two-mode system: theory and experiment

We report on the generation of non separable beams produced via the interaction of a linearly polarized beam with a cloud of cold cesium atoms placed in an optical cavity. We convert the squeezing of the two linear polarization modes into quadrature entanglement and show how to find out the best entanglement generated in a two-mode system using the inseparability criterion for continuous variable [Duan et al., Phys. Rev. Lett. 84, 2722 (2000)]. We verify this method experimentally with a direct measurement of the inseparability using two homodyne detections. We then map this entanglement into a polarization basis and achieve polarization entanglement.

SU5: a calibrated variable-polarization synchrotron radiation beam line in the vacuum-ultraviolet range.

SU5 is a high-resolution variable-polarization synchrotron radiation (SR) beam line with which linear and circular dichroism experiments are performed in the vacuum ultraviolet (VUV) range (5-40eV), based on an electromagnetic crossed undulator called the Onduleur Plan/Helicoidal du Lure à Induction Electromagnétique (OPHELIE). To get precise knowledge of the polarization state of the emitted SR and to take into account the polarization transformations induced by reflection on the various optics, we set up an in situ VUV polarimeter to provide a precise and complete polarization analysis of the SR atthe sample location. The overall measured polarization performances were highly satisfactory, with measured linear polarization rates of more than 98% (83%) in the vertical (horizontal) linear polarization mode and an average 92.1% (95.2%) circular polarization rate for the right- (left)-handed circular polarization mode, which, to our knowledge, are the highest reported values in the VUV range. Despite some uneven photon energy efficiency, the OPHELIE crossed undulator behaves as expected in terms of polarization, permitting full control of the emitted polarization by manipulation of the vertical-to-horizontal magnetic field ratio (rho(und)) and the relative longitudinal phase (phi(und)).

Wavelength and temperature performance of polarization-transforming fiber.

We have theoretically and experimentally investigated an optical fiber with circular polarization modes on one end and linear polarization modes on the other end. We call this fiber a polarization-transforming fiber because the local modes, or polarization states they represent, are converted from linear to circular, and visa versa, in the fiber. We have developed and implemented a postdraw process for making polarization-transforming fiber samples 30 mm long with losses less than 1 dB and a polarization-mode conversion from circular to linear greater than 20 dB. Also, we have modeled and measured the dependence on wavelength and temperature of polarization-transforming fiber samples. The measured normalized wavelength dependence of a sample fiber 30 mm long was approximately 1.4 x 10(-4) nm(-1), and the measured normalized temperature dependence was approximately 6 x 10(-4) degrees C(-1). These values are better in some cases than values for conventional high-birefringent fiber quarter-wave plates.

Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers.

A current-modulated vertical-cavity surface-emitting laser is shown to exhibit interesting nonlinear dynamics in its two orthogonal linearly polarized (LP), fundamental transverse modes. The intensities of the two LP modes may exhibit in-phase time-periodic dynamics or chaotic regimes with combination of in-phase and antiphase dynamics at two different time scales. Chaotic dynamics are found in a large range of laser and modulation parameters.

Generation and physical properties of a new form of unpolarized light

We start from our recent analysis of unpolarized light [J. Lehner et al., Phys. Rev. A 53 (1996) 2727] in which we distinguished two forms of unpolarized light, dependent on whether the field is invariant with respect to phase retardation (type I) or not (type II). First we show that optical mixing leaves the type unchanged. Our main objective is to devise a feasible experimental scheme for the generation of a new form of unpolarized light. Specifically, we point out that amplitude-stabilized unpolarized light is readily obtained with the help of two independently operated lasers. However, this light is of type II only, and we show that after passing a phase retarder it is no longer unpolarized, according to our general criteria. Experimentally, this becomes obvious from the fact that intensity fluctuations in a linear-polarization mode vary with the polarization direction.

Measuring a two-mode optical fiber using modulation of the spectrum of a low-coherence source at its output

It is demonstrated experimentally at the output of an optical fiber excited by a low-coherence source that the mutual interference of two linearly polarized (LP) modes can be resolved in the spectral domain when the optical path difference between both LP modes exceeds the source coherence length. The spectral interference between two LP modes, which shows up as a periodic modulation of the source spectrum, serves as an illustration of the feasibility of a novel measuring technique utilizing a high-resolution spectrometer in the evaluation of the group delay time difference between both LP modes. Moreover, it is shown that the spectral analysis performed across the output modal pattern of the two-mode optical fiber leads to spectral modulations in which the effects of both polarization properties and overlaps of modes are inscribed.

Far zone spectral shifts in light propagation from the exit face of a few-mode fibre waveguide guiding the frequency-dependent linearly polarized modes

Far zone spectral shifts, including free space propagation of light from a planar secondary, partially coherent source represented by the exit face of a few-mode fibre waveguide, are investigated in the paraxial regime by using frequency-dependent linearly polarized (LP) modes guided by the fibre waveguide. The origin of the far zone blue or red spectral shift of individual frequency-dependent LP modes, as well as of their superposition at the particular observation point, is clarified. In particular, the dependence of the wavelength shifts of spectra on the position of the observation point in the far zone plane and the primary source linewidth is studied for the two-mode, weakly guiding, step-index fibre waveguide.

Experimental demonstration of the spectral interference between two linearly polarized modes at the output of a fibre waveguide excited by a low-coherence source

The mutual interference of two linearly polarized (LP) modes in the frequency domain has been demonstrated experimentally at the output of a fibre waveguide excited by a low-coherence source when the optical path difference between both LP modes exceeds the coherence length of the source. The spectral interference between two LP modes, which shows up a periodic modulation of the source spectrum, serves as an illustration of the experimental verification of conclusions we have made in previous theoretical works. Consequently, the feasibility of a novel experimental method utilizing a high-resolution spectrometer in the evaluation of the group-delay time difference between both LP modes has been confirmed.

Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence

Polarization mode dispersion and the polarization decorrelation and diffusion lengths are calculated in fibers with randomly varying birefringence. Two different physical models in which the birefringence orientation varies arbitrarily are studied and are shown to yield nearly identical results. These models are appropriate for communication fibers. We show that both the length scales for polarization mode dispersion and polarization decorrelation measured with respect to the local axes of birefringence are equal to the fiber autocorrelation length. We also show that the coupled nonlinear Schrodinger equation which describes wave evolution over long length along a communication fiber can be reduced to the Manakov equation. The appropriate averaging length for the linear polarization mode dispersion is just the fiber autocorrelation length but the appropriate averaging length for the nonlinear terms is the diffusion length in the azimuthal direction along the Poincare sphere which can be different, The implications for the nonlinear evolution are discussed.

Holographically written reflective polarization filter in single-mode optical fibers

A new type of internally written grating filter is proposed and demonstrated in single-mode optical fibers. A photoinduced rocking birefringence is created by polarization interference between two counterpropagating and orthogonal linear-polarization modes at 514.5 nm. This birefringent grating has the correct submicrometer pitch for efficient phase-matched reflection of a linearly polarized mode into the orthogonally polarized counterpropagating mode. The phenomenon represents a new form of holography in which the image (the orthogonal counterpropagating mode) is reconstructed by scattering off a hologram consisting of a periodic birefringence.

Polarization-sensitive low-coherence reflectometer for birefringence characterization and ranging

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.

Polarization diversity detection performance of 2.5-Gb/s CPFSK regenerators intended for field use

2.5-Gb/s continuous-phase frequency-shift keying (CPFSK) regenerators are studied in laboratory and field experiments. A polarization diversity receiver is constructed with newly designed automatic gain and automatic frequency controllers. It achieves a sensitivity fluctuation of about 0.5 dB against all input signal polarization states. The automatic gain control is used in the intermediate-frequency circuits of the receiver and stably operates over 15 dB of input signal power variation. The automatic frequency control (AFC) is sufficiently stable to withstand a 30-kHz input signal polarization variation between two orthogonal linear polarization modes. AFC stability is maintained even if the environmental temperature of the laser diode modules fluctuates from 15 to 35 C. The polarization fluctuation in both cases results in only 0.1-dB degradation in receiver sensitivity. >

Polarization rotation in nonlinear bimodal optical fibers

The effect of nonlinear interactions on second-order modes in circular cross-section optical fibers is considered. In the linear case, analysis using the proper modes reveals that the fiber is a natural polarization rotator. An initial linearly polarized (LP) mode is actually a mixture of proper modes and recurs only periodically as the field propagates; at half-periods the input polarization and field pattern are rotated by 90 degrees . Complete analytical expressions and numerical examples describing the modification of this phenomenon by nonlinearity are presented. For lower powers, the phenomenon persists with period increasing toward infinity at a transition point, beyond which complete polarization rotation is suppressed. At very high powers, the Kerr effect dominates: polarization is fixed in one direction and an LP mode does become a real mode of the system. >

Measurement of microwave backscatter from a cypress with and without leaves

Radar backscatter from Japanese Cypress has been mea­ sured for S, C, and X bands from two canopy states: With and without leaves. Measurements have been made indoors, forming an extended target of the cypress. The measurements indicate that, after leaf re­ moval, the scattering coefficient aO at X band decreased 4-6 dB in the like (HH and VV) polarizations, although less in the cross (HV and VH) polarizations. At C band, aO decreased 1-2 dB in the like polari­ zation, but no decrease was noted for cross polarization. Similarly, aO at S band decreased slightly in the like case, but not in the cross. The relative contributions of leaves and branches to backscatter are dis­ cussed, based on the changes of the scattering coefficients. A measure­ ment in circular polarization of the backscatter at C band is also de­ scribed. HH, VV, HV, and VH, and the second measurement was made in 1987 using a C-band scatterometer which oper­ ates in circular as well as linear polarization modes. We shall discuss the relative contributions of leaves and branches (including thin vertical trunks) to backscatters in these bands by using the observed changes in the scat­ tering coefficients of the cypress before and after leaf re­ moval. The contribution of thick trunks to radar back­ scatter is not treated in this study.

A single-polarization fiber

We report an oPtical fiber which guides only one polarization. This fiber polarizer utilizes high modal birefringence ( 4.7 \times 10^{-4} ) to split the two polarizations of the fundamental mode and an ellipitcal depressed-index cladding to provide a steep wavelength-dependent tunneling loss to the fast axis mode. The stress-induced birefringence is created by an elliptical SiO 2 -B 2 O 2 inner cladding. A 4.7-m length of polarizer fiber exhibits an extinction ratio of 34 dB at a wavelength of 633 nm, with polarizing behavior over a bandwidth of 50 nm. Insertion loss of less than 1 dB has been observed for the guided linear-polarization mode. The polarizing band may be shifted from 620 to 525 nm by bending the fiber to a radius of 0.67 cm. Such fiber polarizers should find a variety of applications in fiber sensors, attenuators, isolators, wavelength filters, and tuners.

Instability of the Linearly Polarized Mode in Counterstreaming Electron-Ion Plasmas

The instability of the linearly polarized mode propagating perpendicular to the magnetic field, considered previously for counterstreaming electron plasmas, is here studied for plasmas with ion streaming using the cold-plasma equations. For two ion beams with velocities +ui and −ui in a neutralizing background of electrons, it is found that instability occurs when ui>cΩi/ωpi, with maximum growth rate (ui2ωpi2/c2 − Ωi2)1/2, when Ωi and ωpi are, respectively, the ion cyclotron and plasma frequencies; c is the velocity of light. The case of two counterstreaming plasmas with both electron and ion streaming is also discussed.