Phase Modal Birefringence Research Articles

Measurement of birefringence and ellipticity of polarization eigenmodes in spun highly birefringent fibers using spectral interferometry and lateral point-force method

We show that the spectral interferometry method and the lateral point-force method used up to now to measure spectral dependence of the group and the phase modal birefringence in highly birefringent fibers with linearly polarized eigenmodes, can be after some modifications extended for the class of spun highly birefringent fibers with elliptically polarized modes. By combining the two methods, it is possible to determine spectral dependence of the group and phase elliptical birefringence in spun highly birefringent fibers. Moreover, if the fiber spin pitch is independently measured, the spectral dependence of ellipticity angle of polarization eigenmodes as well as the built-in linear phase and group birefringence, can be also obtained using the analytical relations between the parameters of spun and non-spun fibers. We demonstrate the effectiveness of the proposed approach in spectral measurements (700-1600 nm) of the spun side-hole and microstructured highly birefringent fibers with different birefringence dispersion and spin pitches ranging from 4.1 to 200 mm.

Spectral-domain measurement of the strain sensitivity of phase modal birefringence of polarization-maintaining optical fibers

The paper presents a new and simple method of measuring the strain sensitivity of phase modal birefringence (dΔn/dε) of polarization maintaining fibers (PMFs). The method is based on measuring the spectral strain sensitivity of a strain sensor in the configuration of a Sagnac interferometer with a PMF. The measured spectral strain sensitivity of the sensor is used to determine the strain sensitivity of phase modal birefringence and the polarimetric strain sensitivity of the PMF. In addition, a new procedure for determining the sign of the strain sensitivity of phase and group modal birefringence of a PMF. Using this method, measurements of the strain sensitivity of modal birefringence of PMFs were performed: a PM-PCF and a Bow-Tie fiber, in the wavelength range 1460–1600nm. A comparison of the results of these measurements with results obtained using other methods for the same types of fibers is presented.

Measurement of the Temperature Sensitivity of Modal Birefringence of Polarization Maintaining Fibers Using a Sagnac Interferometer

This paper presents a significantly improved method for measuring the temperature sensitivity of phase modal birefringence of polarization-maintaining optical fibers (PMFs) based on the Sagnac interferometer. In this method, a measurement of the spectral temperature sensitivity of a PMF-based Sagnac interferometer temperature sensor is performed. The measured spectral temperature sensitivity of the sensor is used to determine the polarimetric temperature sensitivity of the PMF, and with the additionally measured phase modal birefringence, to determine its temperature sensitivity of phase modal birefringence based on the derived equations relating these quantities to the spectral temperature sensitivity of the sensor. The temperature sensitivity of group modal birefringence of the fiber was calculated on the basis of its already determined temperature sensitivity of phase modal birefringence. In addition, a new procedure for determining the sign of the group modal birefringence was given, and new procedures for determining the signs of the temperature sensitivities of phase modal birefrigence and group modal birefringence of a PMF were also given. Using the proposed method, the measurements of PMFs were performed: a polarization maintaining photonic crystal fiber (PM-PCF) and a PANDA PMF, in the temperature range 20 °C–70 °C, for the wavelength range 1500–1600 nm. A comparison of the results of these measurements with results obtained by other methods for the same types of fibers is presented.

Polarimetric sensitivity to hydrostatic pressure and temperature in a side-hole fiber with squeezed microstructure

We report on sensing characteristics of an endlessly single mode silica fiber with microstructure squeezed by very large side-holes. An elliptical shape of the cladding holes results in high phase and group modal birefringence, equal respectively to B = 3.33 × 10−4 and G = −6.62 × 10−4 at 1.55 μm. Thanks to a large diameter of the side-holes located in the solid part of the cladding, the fiber polarimetric sensitivity to hydrostatic pressure was increased two times compared to earlier reports and equals Kp = −25.6 rad MPa−1 m−1 at 1.55 μm. Moreover, the fiber has a very low polarimetric sensitivity to temperature KT = −9.18 × 10−3 rad K−1 m−1 at 1.55 μm, thus allowing for hydrostatic pressure measurements with little cross-sensitivity to temperature. All measured parameters are in good agreement with the results of numerical simulations conducted using the finite element method.

Highly birefringent polymer side-hole fiber for hydrostatic pressure sensing.

We report on the fabrication of a birefringent side-hole polymer optical fiber with an elliptical core made of polymethyl metacrylate-polystyrene (PMMA/PS) copolymer and pure PMMA cladding. The fiber core is located in a narrow PMMA bridge separating the holes. Two fibers with different bridge thickness were fabricated and characterized. We demonstrate, experimentally and numerically, that, by narrowing the bridge between the holes, one can increase simultaneously the fiber birefringence and the polarimetric sensitivity to hydrostatic pressure. In the fiber with the bridge as narrow as 5 μm, we achieved a record-high polarimetric sensitivity to hydrostatic pressure ranging between 175 and 140 rad/MPa/m in the spectral range of 600-830 nm. The phase modal birefringence in this fiber is also high and exceeds 3×10(-5) at 600 nm, which results in small polarization cross talk.

Distributed group birefringence measurement in a polarization-maintaining fiber using optical frequency-domain reflectometry

We propose to use optical frequency-domain reflectometry to measure distributed group birefringence along a section of polarization-maintaining fiber. Frequency dependence of the propagation constant difference along the fiber between the fast and slow modes can be determined. The scanning frequency bandwidth has influences on the measurement of the phase modal birefringence and beat length. Besides phase modal birefringence and beat length can be measured, distributed group birefringence along the fiber is obtained with a spatial resolution of 7.8cm.

Fabrication, Characterization, and Sensing Applications of a High-Birefringence Suspended-Core Fiber

In this paper, we report on the fabrication, characterization, and sensing applications of a high-birefringence suspended-core fiber (HB-SCF) using the stack-and-draw technique. Capillaries in two sizes were used for stacking, forming an elliptical core, giving rise to geometric modal birefringence of the HB-SCF. Through a finite-element method, the theoretical values of the phase and group modal birefringence of the HB-SCF were found to be $2.59 \times 10^{-4}$ and $4.75 \times 10^{-4}$ , respectively. Based on a Sagnac interferometer (SI), the group modal birefringence of the HB-SCF was measured to be $4.84 \times 10^{-4}$ , which agrees well with the theoretical result. The sensing characteristics of the HB-SCF SI for pressure, strain, and torsion measurements were analyzed theoretically and investigated experimentally. It exhibits sensitivities of 2.82 nm/MPa for hydrostatic pressure, 0.43 pm/μϵ for strain, and 0.0157/° for torsion measurements. The HB-SCF is made entirely of pure silica without stress-applying parts, thus its modal birefringence is thermally insensitive, resulting in a low temperature sensitivity of ∼1 pm/°C.

Higher-order rocking filters induced mechanically in fibers with different birefringence dispersion

We studied the transmission characteristics of higher-order rocking filters induced mechanically in birefringent microstructured fibers and standard elliptical core fibers with varying spectral dependence of phase modal birefringence. We demonstrated the effect of birefringence dispersion on polarization mode coupling induced by a point-like force. We also investigated the spectral dependence of the resonance depth and force-induced resonance wavelength shift in mechanical rocking filters. The observed phenomena were explained by a numerical model linking the spectral dependence of the polarization mode coupling coefficient with the dispersion of intrinsic fiber birefringence and applied force.

Spectral-Domain Measurements of Birefringence and Sensing Characteristics of a Side-Hole Microstructured Fiber

We experimentally characterized a birefringent side-hole microstructured fiber in the visible wavelength region. The spectral dependence of the group and phase modal birefringence was measured using the methods of spectral interferometry. The phase modal birefringence of the investigated fiber increases with wavelength, but its positive sign is opposite to the sign of the group modal birefringence. We also measured the sensing characteristics of the fiber using a method of tandem spectral interferometry. Spectral interferograms corresponding to different values of a physical parameter were processed to retrieve the spectral phase functions and to determine the spectral dependence of polarimetric sensitivity to strain, temperature and hydrostatic pressure. A negative sign of the polarimetric sensitivity was deduced from the simulation results utilizing the known modal birefringence dispersion of the fiber. Our experimental results show that the investigated fiber has a very high polarimetric sensitivity to hydrostatic pressure, reaching −200 rad × MPa−1× m−1 at 750 nm.

Fiber Bragg grating inscription in few-mode highly birefringent microstructured fiber

In this Letter, we present the technology of fiber Bragg grating (FBG) inscription in highly birefringent (HB) few-mode microstructured fibers (MSFs) with two different (nanosecond and femtosecond) lasers in a Talbot interferometer setup. The spectral characteristics of FBGs written in the core region of the investigated fiber, with particular modes represented by dual peaks, are presented and discussed. Furthermore, we calculate the fundamental fiber parameters (mode effective refractive index and phase modal birefringence) from the spectral characteristics and show very good agreement with the performed numerical fiber characterization. We expect the results of our experiments to be very useful in future development of FBG sensors based on novel HB MSFs, with enhanced strain sensitivity of higher-order modes.

Highly birefringent microstructured polymer fibers optimized for a preform drilling fabrication method

We propose two designs of birefringent microstructured fibers assuring high geometrical birefringence in the visible range and low confinement losses. An increased birefringence level in the visible range is achieved by breaking the hexagonal symmetry of the structure and shifting selected holes with respect to the nodes of the hexagonal lattice. Such geometry of the microstructured cladding is feasible for polymer fibers fabricated using a preform drilling method. In the first optimized design, two large air-holes adjacent to the core are shifted towards each other to increase modal birefringence. In the second design, high birefringence is achieved by approaching two regions with large holes separated by a row of smaller holes. The simulation results show that in the first fiber with a pitch distance of 3.0 μm, it is possible to obtain a phase birefringence of the fundamental mode greater than 1 × 10−4, while the confinement losses do not exceed 0.06 dB m−1 in the visible range. In the second fiber with the same pitch distance, the confinement losses are smaller than 0.3 dB m−1 in the spectral range of 500–1100 nm, while the phase modal birefringence exceeds 1 × 10−4 in the visible range and reaches 4.0 × 10−4 at 633 nm. We also present the fiber fabricated according to the second design and compare the calculated and the measured spectral dependence of birefringence.

Measurements of polarimetric sensitivity to hydrostatic pressure, strain and temperature in birefringent dual-core microstructured polymer fiber

We experimentally characterized a birefringent microstructured polymer fiber of specific construction, which allows for single mode propagation in two cores separated by a pair of large holes. The fiber exhibits high birefringence in each of the cores as well as relatively weak coupling between the cores. Spectral dependence of the group and the phase modal birefringence was measured using an interferometric method. We have also measured the sensing characteristics of the fiber such as polarimetric sensitivity to hydrostatic pressure, strain and temperature. Moreover, we have studied the effect of hydrostatic pressure and strain on coupling between the cores.

Broad spectral range measurements and modelling of birefringence dispersion in two-modeelliptical-core fibres

We present the results of measurement and modelling of the birefringence dispersion inelliptical-core fibres (ECFs). The measurement is performed over a broad wavelength range(e.g. 450–1450 nm) by two spectral interferometric techniques. First, a technique employinga tandem configuration of a Michelson interferometer and an ECF under test is used for abroad spectral range measurement of the group modal birefringence for two spatial modessupported by the fibre. Second, a method with a lateral point-like force acting on thefibre and based on spectral interferometry is used for measuring the phase modalbirefringence at one wavelength for the fundamental mode only. The measured value iscombined with the dispersion of the group modal birefringence to obtain thephase modal birefringence over a broad wavelength range. We also modelled thedispersion characteristics taking into account contributions of both the ellipticalshape of the core and the residual thermal stress. The dispersion characteristicsmeasured for the three ECFs show very good agreement with the results of numericalmodelling.

Lateral stress-induced propagation characteristics in photonic crystal fibres

Using the finite element method, this paper investigates lateral stress-induced propagation characteristics in a photonic crystal fibre of hexagonal symmetry. The results of simulation show the strong stress dependence of effective index of the fundamental guided mode, phase modal birefringence and confinement loss. It also finds that the contribution of the geometrical effect that is related only to deformation of the photonic crystal fibre and the stress-related contribution to phase modal birefringence and confinement loss are entirely different. Furthermore, polarization-dependent stress sensitivity of confinement loss is proposed in this paper.

Birefringence analysis in photonic crystal fibers with germanium-doped core

We present the results of numerical analysis of birefringence in photonic crystal fibers with germanium-doped inclusions in the core. In such fibers, geometrical birefringence induced by holey cladding interplays with the birefringence induced by shape and composition of doped inclusions. The latter gives rise also to stress birefringence associated with different thermal expansion coefficients in doped and non-doped regions. In our analysis, we consider elliptical and circular inclusions and demonstrate that, by proper selection of the inclusions' geometry, it is possible to increase significantly the phase modal birefringence to a level greater than 10−4 in the short wavelength range. Moreover, it is possible to shape the dispersion of the phase modal birefringence in such a way that the group birefringence crosses zero value at a certain wavelength.

Wide spectral range measurement of modal birefringence in polarization-maintaining fibres

We report on a substantially improved white-light spectral interferometric technique for measurement of the group and phase modal birefringence in polarization-maintaining fibres (PMFs) over a wide wavelength range (e.g. 480–1600 nm). The technique utilizes a tandem configuration of a Michelson interferometer and a PMF placed between Glan–Taylor polarizer and analyzer. Spectral signals are recorded by VIS–NIR and NIR fibre-optic spectrometers to measure the equalization wavelength as a function of the path length difference adjusted in the interferometer, or equivalently, the wavelength dependence of the group modal birefringence in the PMF. Moreover, a new procedure is used to specify the sign of the group modal birefringence. A polynomial fit is applied to the measured data to determine also the wavelength dependence of the phase modal birefringence in the PMF over a wide spectral range.

Birefringence in microstructure fiber with elliptical GeO_2 highly doped inclusion in the core

We studied both numerically and experimentally a birefringence in a microstructure fiber with elliptical inclusion highly doped with GeO(2). We demonstrate that such inclusion increases the phase modal birefringence and modifies its dispersion in the short wavelength range, thus causing that group birefringence crosses zero value at a certain wavelength. Moreover, we numerically analyzed different factors contributing to the overall fiber birefringence, including geometrical birefringence induced by holes distribution and ellipticity of the inclusion as well as stress birefringence associated with thermal shrinkage of the doped glass.

Spectral-domain measurement of phase modal birefringence in polarization-maintaining fiber

We report on a new and simple method for measuring the wavelength dependence of phase modal birefringence in a polarizationmaintaining fiber. The method is based on application of a lateral pointlike force on the fiber that causes strong coupling between polarization modes and utilizes their interference resolved as the channeled spectrum. The change of the phase retrieved from two recorded channeled spectra that are associated with the known displacement of coupling point is used to determine the phase modal birefringence as a function of wavelength. A windowed Fourier transform is applied to reconstruct precisely the phase change and the phase ambiguity is removed provided that we know the phase change of the spectral fringes at one specific wavelength. The measured wavelength dependence of phase modal birefringence is compared with that resulting from the group modal birefringence measurement.

Phase and group modal birefringence of an index-guiding photonic crystal fibre with helical air holes

In this paper, we propose a novel photonic crystal fibre (PCF) with high phase birefringence and very low group birefringence. It is composed of a solid silica core and a cladding with helix-pattern air holes. Using a full-vector finite-element method, we study the phase and group modal birefringence of such PCF at various air-hole sizes, pitches and wavelengths. Owing to this innovative structure of air holes, a high phase to group modal birefringence rate is obtained. Its phase modal birefringence is as large as 10 −4 magnitude; however, the group modal birefringence of this PCF is at 10 −7–10 −6. The phase birefringence is 2 orders of magnitude larger than group birefringence over a broad wavelength span, which means that the light with different polarization and effective index has almost a same group velocity. As a result, the group modal birefringence that closely relates to the polarization modal dispersion is negligible.

Measurement and modelling of dispersion characteristics of a two-mode birefringent holey fibre

Employing several interferometric methods, we measured in a broad spectral range the wavelength dependences of the phase modal birefringence and the polarization mode dispersion for the LP01 and even LP11 spatial modes supported by a birefringent holey fibre. We also determined the wavelength dependence of the intermodal dispersion between the X- and Y-polarized LP01 and even LP11 spatial modes. Furthermore, using a full-vector finite-element method, we modelled all the measured dispersion characteristics and demonstrated good agreement between experimental and theoretical results.