Higher-order core mode resonances in a mechanically induced long-period holey fiber grating

We present the spectral analysis of higher-order core mode resonances in a long period holey fiber grating induced mechanically in an asymmetric holey fiber. Calculations based on a fast-Fourier transform mode solver shows that the mode resonances obtained experimentally correspond to the odd- and even-LP_1,1 core modes. Additionally, we analyze the twist and polarization response of these mode resonances in the long period holey fiber grating. The results obtained in this work are of great importance in the design of new all-fiber optical devices that involve couplings of higher order core modes in asymmetric holey fibers.     

Twist phase-induced polarization changes in electromagnetic Gaussian Schell-model beams

Electromagnetic Gaussian Schell-model (EGSM) beam with twist phase (i.e., twisted EGSM beam) is introduced as an extension of its scalar version based on the unified theory of coherence and polarization. We show how analytical paraxial propagation formulae of isotropic and anisotropic EGSM beams passing through a general astigmatic ABCD optical system can be modified in the presence of the twist phase. Numerical examples demonstrate that the twist phase affects the spectral density, the state of coherence, and the degree of polarization of EGSM beams on propagation.     

Effective Non-Hermitian Hamiltonians for Studying Resonance Statistics in Open Disordered Systems

We briefly discuss construction of energy-dependent effective non-hermitian hamiltonians for studying resonances in open disordered systems.     

衍射扭曲高斯-谢尔模型光束在远场的光谱移动和光谱开关

从部分相干光的传输理论出发,研究了被光阑衍射扭曲高斯-谢尔模型光束远场的光谱变化规律。结果表明,扭曲高斯-谢尔模型光束在远场也会出现光谱移动和光谱开关效应。与衍射高斯-谢尔模型光束情况相比,光谱移动和光谱开关效应不仅与光束空间相关性、截断参量和源光谱谱宽有关,光束的扭曲因子也会对衍射扭曲高斯-谢尔模型光束远场的光谱移动和光谱开关效应产生影响。通过数值计算结果详细讨论了光束扭曲因子影响衍射扭曲高斯-谢尔模型远场光谱的规律。     

A Non-unitary Mapping from Cooper Pairs to Bosons

We derive a non-hermitian boson-fermion Hamiltonian, that is equivalent to the entirely fermionic Richardson Hamiltonian which describes the dynamics of conduction electrons in a superconductor. This is done using a generalized Dyson mapping, that replaces Cooper pairs with bosons. We show that the calculation of some physical quantities is simpler when one uses the boson-fermion Hamiltonian rather than the original Richardson Hamiltonian.     

Compact vector twist sensor using a small period long period fiber grating inscribed with femtosecond laser

We propose and demonstrate a sensitive vector twist sensor based on a small period long period fiber grating(SP-LPFG)fabricated with a femtosecond(fs) laser. The fabricated SP-LPFG is compact in size(2.8 mm) and shows strong polarization dependent peaks in its transmission spectrum due to the vectorial behavior of high-order cladding modes. Twist sensing is realized by monitoring the polarization dependent peaks, since the polarization of input light changes with fiber twist. The proposed sensor can be interrogated by the peak intensity and wavelength, with high twist sensitivity that reaches0.257 d B/deg and 0.115 nm/deg, respectively.     

Stability of minimal periodic orbits

Symplectic twist maps are obtained from a Lagrangian variational principle. It is well known that nondegenerate minima of the action correspond to hyperbolic orbits of the map when the twist is negative definite and the map is two-dimensional. We show that for more than two dimensions, periodic orbits with minimal action in symplectic twist maps with negative definite twist are not necessarily hyperbolic. In the proof we show that in the neighborhood of a minimal periodic orbit of period n, the nth iterate of the map is again a twist map. This is true even though in general the composition of twist maps is not a twist map.     

Non-hermitian random matrix models

We introduce an extension of the diagrammatic rules in random matrix theory and apply it to non-hermitian random matrix models using the 1/N approximation. A number of one-and two-point functions are evaluated on their holomorphic and non-holomorphic supports to leading order in 1/N. The one-point functions describe the distribution of eigenvalues, while the two-point functions characterize their macroscopic cotrelations. The generic form for the two-point functions is obtained, generalizing the concept of macroscopic universality to non-hermitian random matrices. We show that the holomorphic and non-holomorphic one- and two-point functions condition the behavior of pertinent partition functions to order O(1/N). We derive explicit conditions for the location and distribution of their singularities. Most of our analytical results are found to be in good agreement with numerical calculations using large ensembles of complex matrices.     

On Twisting Real Spectral Triples by Algebra Automorphisms

We systematically investigate ways to twist a real spectral triple via an algebra automorphism and in particular, we naturally define a twisted partner for any real graded spectral triple. Among other things, we investigate consequences of the twisting on the fluctuations of the metric and possible applications to the spectral approach to the Standard Model of particle physics.     

Spectral properties of stochastic electromagnetic twist anisotropic Gaussian-Schell model beam truncated by a slit aperture propagating in turbulent atmosphere

With the help of the tensor method, the cross-spectral density matrix for the stochastic electromagnetic twist anisotropic Gaussian-Schell model (ETAGSM) beam truncated by a slit aperture propagating in turbulent atmosphere are derived. The spectral properties of this kind of beam are investigated in detail. It is shown by numerical results and analysis that the affection of the slit aperture on the spectral properties of the stochastic ETAGSM beam is obvious in the near field; while in the far field, the atmospheric turbulence plays an important role; the source beam's coherence can weaken the affection of the slit aperture and the atmospheric turbulence on the spectral properties of the stochastic ETAGSM beam truncated by a slit aperture propagating in turbulent atmosphere, while the twist properties of the source beam can strong the affection of the slit aperture on the spectral properties in the near field. Also, the spectral degree of polarization and normalized spectral density distributions and corresponding contour graphs of the stochastic ETAGSM beam truncated by a slit aperture propagating in turbulent atmosphere and free space at different propagation distances are investigated 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.     

Propagation properties of a partially polarized electromagnetic twist anisotropic Gaussian Schell-model beam in turbulent atmosphere

Based on the extended Huygens-Fresnel integral formula, analytical formulae for the elements of cross-spectral density matrix of partially polarized electromagnetic twist anisotropic Gaussian Schell-model (TAGSM) beam propagating in turbulent atmosphere can been derived by a tensor method. Our main attention was focus on the effect of the atmospheric turbulence, twist parameters and partial coherence on the spectral degree of polarization, the spectral degree of coherence and the spectral density. Numerical calculation results and analysis are given.     

Generalized high-order twisted partially coherent beams and their propagation characteristics

Twist phase is a nontrivial statistical phase that only exists in partially coherent fields, which makes the beam carry orbital angular momentum (OAM). In this paper, we introduce a new kind of partially coherent beams carrying high-order twist phase, named generalized high-order twisted partially coherent beams (GHTPCBs). The propagation dynamics such as the spectral density and OAM flux density propagating in free space are investigated numerically with the help of mode superposition and fast Fourier transform (FFT) algorithm. Our results show that the GHTPCBs are capable of self-focusing, and the beam spot during propagation exhibits teardrop-like or the diamond-like shape in some certain cases. Moreover, the influences of the twist order and the twist factor on the OAM flux density during propagation are also illustrated in detail. Finally, we experimentally synthesize the GHTPCBs with controllable twist phase by means of pseudo-mode superposition and measure their spectral density during propagation. The experimental results agree well with the theoretical predictions. Our studies may find applications in nonlinear optics and particle trapping.     

Mathematical modeling of random coupling between polarization modes in single-mode optical fibers: VI. Evolution in the degree of polarization of nonmonochromatic radiation traveling in a twisted optical waveguide

An analysis is made of the evolution of polarization of nonmonochromatic radiation travelling through single-mode optical fibers in the presence of random coupling between orthogonally polarized modes, which is caused by the random twist of axes of natural linear birefringence of an SMF, and in the presence of a regular axis twist. It is shown that the depolarization length of nonmonochromatic radiation in an SMF increases with increasing regular SMF twist, regardless of the presence of a random axis twist. Using the Monte Carlo method, the dependences of the mathematical expectation and the mean-square deviation of the degree of polarization of nonmonochromatic radiation on the fiber length for SMFs with different linear birefringences and regular axis twists are calculated. It is shown that the fiber length on which the degree of polarization of nonmonochromatic radiation reaches its limiting value increases and the limiting value itself decreases with an increasing regular twist. It is also shown that an induced SMF twist is able to improve parameters of a fiber interferometer, in particular, to decrease random phase changes and intensity fadings of the interference signal, which are caused by random coupling between polarization modes.     

Simple non-hermitian choices for the standardization operator in projected perturbation theory

We suggest simple non-hermitian choices for the Peierls standardization operator and test them in a simplified one-dimensional model of H⁺₂.     

基于低双折射光子晶体光纤Sagnac干涉仪的超低温度系数扭曲传感器

研究了低双折射光子晶体光纤中由光纤扭曲造成的圆双折射效应,并应用Sagnac干涉仪结构设计了扭曲传感器.在Sagnac环中的光子晶体光纤上施加机械压力引入初始线双折射并产生正弦干涉光谱,再扭曲光纤产生圆双折射使干涉光谱随扭曲角度移动.光谱峰值波长随扭曲角度变化符合Sinc函数关系,理论分析与实验相符.传感器灵敏度为1....     

Spectral properties of apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model beam propagating in turbulent atmosphere

Based on the extended Huygens-Fresnel principle, analytical formulas are derived for the cross-spectral density matrix of an apertured stochastic electromagnetic twist anisotropic Gaussian Schell-model (ETAGSM) beam propagating in a turbulent atmosphere by use of a tensor method. Spectral properties of apertured ETAGSM beam are closely related with the strength of atmospheric turbulence, the aperture widths and the beam's parameters, etc. Our main attention was focused on the influence of the aperture widths, atmospheric turbulence, twist parameters and partial coherence on the spectral properties (including spectral degree of polarization, the spectral degree of coherence and the spectral density) of apertured ETAGSM beam propagating in turbulent atmosphere. Numerical calculation results and analysis are given.     

Non-hermitian dynamical matrices in phenomenological lattice dynamics

It is shown that in phenomenological calculations, non-hermitian dynamical matrices can be formulated to be consistent with translational and other symmetry requirements. Such a formulation is proposed and discussed.     

基于低双折射光子晶体光纤Sagnac干涉仪的超低温度系数扭曲传感器

研究了低双折射光子晶体光纤中由光纤扭曲造成的圆双折射效应,并应用Sagnac干涉仪结构设计了扭曲传感器.在Sagnac环中的光子晶体光纤上施加机械压力引入初始线双折射并产生正弦干涉光谱,再扭曲光纤产生圆双折射使干涉光谱随扭曲角度移动.光谱峰值波长随扭曲角度变化符合Sinc函数关系,理论分析与实验相符.传感器灵敏度为1.00 nm/°,分比率为0.01°,并具有超低的温度系数-0.5 pm/℃.     

Ordered growth of germanium dots induced by the strain field of tilt dislocations in molecular bonded silicon (0 0 1) thin films

Germanium dots have been grown on high twist angle (twist angle as high as 20°) molecular bonded silicon (0 0 1) substrates. We show that, depending on the thickness of the silicon film, the strain field generated by an ordered array of mixed edge interfacial tilt (miss-cut) dislocations may induce an ordered growth of germanium dots. We also show that in order to observe an influence of the mixed edge interfacial dislocations on the growth of germanium dots, the thickness of the film has to be much lower that the period of the mixed edge dislocations array. Germanium dots grown by molecular beam epitaxy on 10-15 nm thick silicon films with the period of tilt dislocation array of 43 nm show a high degree of self-ordering.