A technique for modelling the performance of birefringent wave plates

By considering the phase delay introduced by a birefringent wave plate to each frequency component of a finite bandwidth light source we establish the polarisation state of the transmitted light. Realisable designs of achromatic, zero-order and high-order quarter wave and half wave plates are analysed for use with a variety of light sources with different bandwidths.     

Retardation calculation for achromatic and apochromatic quarter and half wave plates of gypsum based birefringent crystal

This paper presents retardation calculations for achromatic and apochromatic half and quarter wave retarders of gypsum based birefringent crystal. The calculations indicate that an achromatic wave plates can be obtained by combining gypsum crystal with KDP, ADP, MgF₂, sapphire and calcite birefringent crystals. The residual variation percentages of retardations as a function of wavelength for gypsum/KDP, gypsum/ADP, gypsum/MgF₂, gypsum/sapphire and gypsum/calcite were found to be ± 1.7%, ± 3%, ± 12.2%, ± 12.0% and ± 7.2%, respectively. To reduce the spectral variation of retardations, a third layer (apochromatic) of birefringet material is added to the aforementioned achromatic wave plates. The proposed apochromatic wave plates are gypsum/KDP/quartz, gypsum/ADP/quartz, MgF₂/ADP/gypsum, MgF₂/KDP/gypsum and gypsum/sapphire/MgF₂. The addition of a third layer has reduced spectral residual variation percentages of retardations of the aforementioned apochromatic designs to ± 0.27, ± 0.33, ± 0.3, ± 0.17 and ± 0.45, respectively.     

New formulas for phase retardance measurements of birefringent plates

Two simple formulas are introduced that allow for simultaneous determination of the phase retardances of two birefringent plates from a single pair of readings of the polarizer and the analyzer at extinction. These formulas are of great importance since they furnish the basis of a model for a simple, timesaving and accurate method for calibrating phase plates in the Senarmont compensator arrangement without requiring an exact λ/4 plate and with almost direct results. The Poincaré sphere representation of polarization states is used to illustrate the model.     

Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber

Spectral interference of white-light beams propagating through a tandem configuration of birefringent crystal and sensing birefringent fiber is analyzed theoretically and experimentally. The spectral interference law is expressed analytically under the condition of a Gaussian response function of a spectrometer taking into account the dispersion of birefringence in the crystal and in the fiber. Two types of spectral interferograms are modeled knowing dispersion characteristics of the sensing fiber and using a quartz crystal of the positive or a calcite crystal of the negative birefringence. The theoretical analysis is accompanied by two experiments employing a highly birefringent fiber and a birefringent quartz crystal of two suitable thicknesses. Within both experiments the spectral interference fringes are resolved in accordance with the theory with phases dependent on the fiber length.     

消色散光变图像的二元光学设计与制作方法

提出了一种实现消色散光变图像的二元光学方法.以不同取向的狭缝光阑作为目标物光场,采用迭代傅里叶变换算法计算得到具有定向衍射特性的二元位相结构,并作为光变图像的微结构.面向不同图形结构的光变图像,给出了两种不同的数据方案.利用自行研制的激光直写系统以逐图形方式和矢量化直写工作方式分别光刻不同结构的光变图像,位相结构的线宽为2 μm.实验结果表明,定向衍射二元光学位相结构具有消色散特征,且适合于热压复制工艺,为制造消色散光变图像提供了一种新方法.     

Field-compensated birefringent Fourier transform spectrometer

A field-compensation method applied for Savart birefringent Fourier transform spectrometer is presented. By using a combination of Savart plates fabricated from positive and negative birefringent materials, the useful solid angle of field of view can be increased by a large amount in broad spectral coverage. Compared to the conventional Fourier transform spectrometers, the compensated field angle has optical throughput higher by one order in magnitude. To demonstrate the effectiveness, a design example operating at 400-1100 nm with a large solid angle exceeding ± 40° is presented in detail.     

Transmission properties of microcoils based on twisted birefringent fibre

We model the linear transmission properties of birefringent optical microcoil resonators (OMRs) by numerically solving polarisation dependent coupled mode equations. When the fibre is twisted, results show spectral bands where strong coupling between the different polarisations occur. The extinction ratio of certain resonances is also found to be enhanced by the exchange of power into another polarisation. Compared to the standard OMR, the choice of fibre twist and level of birefringence provide additional flexibility in tailoring the OMR spectral properties as needed for applications such as filtering, signal processing and sensing.     

光学介质薄膜优化的宽带消色差λ/4相位延迟器

根据全反射相变理论设计了菲涅耳菱体型相位延迟器延迟量对入射角变化不敏感的结构角。根据薄膜的偏振效应,从薄膜的特征矩阵出发,通过在菱体的两个全反射面蒸镀光学介质膜的方法拓宽了菲涅耳菱体型相位延迟的消色差宽度。在ML_EB900型镀膜机上适当控制沉积条件制备了消色差相位延迟膜,实验测试结果表明:在530~700 nm的波长范围内,可以获得90°的相位延迟量,且最大偏差小于0.7°。     

Non-linear polarization and chiral effects in birefringent solitons

Novel effects resulting from joint action of chirality and non-linearity are discussed using a basic equation describing the temporal evolution of fields in a chiral medium with Kerr non-linearity. The spatial chirality effect is characterized through the Born-Fedorov formalism. Our simulations are based on the split-step Fourier method and the solution of the Stokes parameters. The numerical results show the chiral effect on solitons with circular polarization and mixed polarization spatial solitons.     

A flat-top birefringent interleaver based on ring-cavity architecture

We propose and demonstrate a flat-top 25-GHz birefringent interleaver using a novel ring-cavity architecture. The ring-cavity provides the phase shifts needed to achieve a flat-top spectral passband at the output. Fresnel reflectivities (for s- and p-polarization states) at the prism-air interface of the ring cavity are employed so that highly accurate thin-film coatings are not needed for the phase shifts. By choosing the appropriate incident angle near the Brewster angle, the optimum interface reflectivities for flat passbands and low crosstalk can be obtained. The ring cavity based interleaver in a 25-GHz channel spacing application exhibits a 0.5-dB passband larger than 0.14 nm, a 25-dB stopband greater than 0.14 nm, and a channel isolation higher than 28 dB over the entire C-band.     

双菱体λ/4消色差相位延迟器的设计

根据菲涅尔全内反射相变理论,给出了双菱体λ/4消色差器的结构设计、性能分析和测量方法.由有效通光孔径和光线追迹设计出BK7玻璃在波长532 nm时相位延迟λ/4的双菱体的结构,用作532 nm至1 064 nm波长范围的标准λ/4相位延迟器.理论分析了入射角变化和波长变化对双菱体相位延迟的影响,当入射角变化限制在±4.3°以内时,其影响得到补偿;波长从532 nm到1 064 nm产生的误差为－0.65°.采用椭偏法中的消光技术,分别实测了双菱体在532 nm和1 064 nm波长下的相位延迟为：90.08±0.14°和88.99±0.1°,可知两不同波长产生的相位延迟误差为－1.09°.     

Polarization modulational instability in a birefringent optical fiber with fourth order dispersion

We obtain conditions for the occurrence of polarization modulational instability in the anomalous and normal dispersion regimes for the coupled nonlinear Schrödinger equation modelling fourth order dispersion effects when the linearly polarized pump is oriented at arbitrary angles with respect to the slow and fast axes of the birefringent fiber.     

高精度消色差相位延迟器的新设计

消色差相位延迟器是在某一宽度光谱范围内使用的光相位延迟器件。从相位延迟的全反射相变理论出发,对斜入射消色差相位延迟原理进行阐述,参考菲涅耳棱镜的具体设计形式,对引起相位延迟变化的参量进行分析,通过选择合适的材料新设计出了特殊角度入射的高精度相位延迟器,其理论曲线显示,在365~1150nm的光谱区域内延迟偏差小于0.4°,是常规相位延迟器在相同条件下的五分之一,是一种宽广谱范围内、负延迟偏差小、精度高的消色差相位延迟器。     

Analysis of retroreflector-introduced spectrum distortion in birefringent crystal-based interleaver filters

Spectrum distortion in a birefringent crystal-based interleaver filter introduced by the right-angle total internal reflection retroreflector is studied. The phase shift between two perpendicularly polarized components of the polarized light incident onto the retroreflector is calculated. The sensitivity of the phase shift to the incident angle for different materials from which the retroreflector is made is also considered. This study indicates that the phase shift is less sensitive to the incident angle for retroreflectors having a higher index of refraction, suggesting a fixed-phase compensator that can be used to cancel out the phase shift introduced by the retroreflector to recover the interleaver filter's spectrum. The fold-back 50 GHz channel spacing birefringent crystal interleaver filter is fabricated to demonstrate that the spectrum distortion due to the phase shift introduced by retroreflector can be eliminated by a phase compensator.     

Simulative demonstration of soliton pulse stability over the nonlinear regime in a birefringent optical fiber

In this paper, the results of numerical analysis are demonstrated for sech pulse (soliton) propagation in a birefringent optical fiber using computer modeling and simulation. Here, the initial pulse is polarized linearly and guided into the fiber at an angle of 45° to its polarization axes. The birefringence-induced time delay of 200 and 440 ps between X and Y polarization components has been reported at a fiber length of 631.72 km (10 soliton periods) by considering linear and nonlinear regimes, respectively. The Kerr nonlinearity, which stabilizes solitons against spreading due to GVD, also stabilizes them against splitting due to birefringence. A similar fact is true for the birefringent walk-off. Above a certain soliton order (N_th), the evolution scenario is qualitatively different and two orthogonally polarized components of the soliton move with a common group velocity despite their different modal indices or polarization mode dispersion (PMD) at a fiber length of 631.72 km (10 soliton periods) and 1264.344 km (20 soliton periods) over a nonlinear regime at θ≠45°. The physical effect responsible for this type of behavior is the cross-phase modulation (XPM) between the two polarization components.     

Theoretical and experimental study of differential group delay and polarization dependent loss of Bragg gratings written in birefringent fiber

In this paper, we completely study the wavelength dependency of differential group delay (DGD) and polarization dependent loss (PDL) for Bragg gratings written in birefringent fibers. Based on the coupled mode theory, we present analytical expressions for the evolution with wavelength of the transmission coefficient, the DGD and the PDL. The wavelength dependencies of these evolutions on the birefringence are then discussed. Experimental results are finally presented for an apodized FBG written in a bow-tie fiber. A very good agreement between theory and experience is reported, confirming the validity of the theoretical analysis.     

Soliton coupling in birefringent optical fiber with third-order dispersion

Nonlinear coupling of polarized solitons in birefringent optical fiber in the presence of third-order dispersion is considered in the framework of the coupled nonlinear Schrödinger equations. The influence of third-order dispersion on the interaction between solitons is investigated. For sufficiently strong third-order dispersion the interaction may even become repulsive. The stable conditions for solitons of partial pulses are analyzed and amplitude threshold, which decreases with third-order dispersion coefficient decreasing, for the capture of solitons of partial pulses into a coupled two-component pulse is obtained.     

菱体型消色差相位延迟器延迟相位的方位效应

菱体型相位延迟器是高度消色差的λ/4相位延迟器.由于材料折射率色散的影响,在可见光范围内,仍存在2°的延迟偏差.为满足精确应用和测量的需求,从相位延迟的全反射相变理论出发,阐述了斜入射相位延迟原理,以菲涅耳菱体为例,分析了菱体型相位延迟器相位延迟随其入射角变化的规律性,结果表明:当光线非严格准直时,光的入射角对相位延迟量有明显的影响,延迟量不但对入射角变化敏感,而且还与入射光线的入射方位密切相关,呈不对称形式.当入射光的波长改变时,只需改变菱体延迟器的方位,让光线在菱体的前端面上斜入射,适当选取入射角,就可以补偿相位延迟的色散偏差,使同一菱体达到对不同波长都满足λ/4相位延迟.当角度调整精度Δi=±0.01°时,引入的延迟偏差不超过±0.009°,这一精度是其它石英波片或云母波片所不能比的.     

Temperature sensing using the spectral interference of polarization modes in a highly birefringent fiber

The spectral interference of polarization modes in a highly birefringent (HB) fiber to measure temperature is analyzed theoretically and experimentally. A tandem configuration of a birefringent delay line and a sensing HB fiber is considered and the spectral interferograms are modelled for the known birefringence dispersion of the HB fiber under test. As the delay line, a birefringent quartz crystal of a suitable thickness is employed to resolve a channeled spectrum. The channeled spectra are recorded for different temperatures and the polarimetric sensitivity to temperature, determined in the spectral range from 500 to 850 nm, is decreasing with wavelength. It is demonstrated that the temperature sensing is possible using the wavelength interrogation, i.e., the position of a given interference maximum is temperature dependent. The temperature sensitivity of the HB fiber under test is −0.25 nm/K and the resolution is better than 0.5 K.