Design and Numerical Analysis of Ultra-High Negative Dispersion, Highly Birefringent Nonlinear Single Mode Core-Tune Photonic Crystal Fiber (CT-PCF) over Communication Bands

This paper presents the development of a highly efficient CT-PCF (Core-Tune Photonic Crystal Fiber) with substantial birefringence, tailored for applications in high-bit-rate communication and sensing while minimizing signal loss. The design incorporates a modified broadband dispersion compensating structure, optimized for operation across the E, S, C, and L communication bands within a wavelength range spanning 1360 nm to 1625 nm. Notably, the CT-PCF demonstrates a remarkable birefringence of 2.372 × 10-2 at 1550 nm, surpassing traditional PCF structures. Single-mode performance is evaluated using the Higher Order Mode Extinction Ratio (HOMER) method, revealing a peak HOMER value of 104 at 1550 nm. Furthermore, at 1550 nm, the CT-PCF exhibits exceptional nonlinear characteristics, featuring a high nonlinearity of 50.74 W-1⋅Km-1 for y polarization. In comparison to existing designs, the proposed CT-PCF exhibits superior performance metrics and optical characteristics. Additionally, the y polarization dispersion coefficient of the CT-PCF at 1550 nm is measured at -3534 ps/(nm⋅km). Overall, the CT-PCF represents a significant advancement, outperforming established systems in terms of performance metrics and optical properties.

Effect of initial linear chirp on collision characteristics of two solitons in the birefringent fibre

The collision characteristics of the orthogonally polarized solitons with initial linear frequency chirp in the linear birefringent fibre for β2 〈 0 are numerically studied. It is found that initial chirp changes the threshold value of solitons to form the bound-state in the birefringent fibre. The effect of initial positive chirp on the threshold value is more obvious than that of negative chirp. In the case of （δ= 0.7 and initial interval 2τ0 = 1.25, the two solitons are mutually bound for 0.2 ≤ C ≤ 1, and they do not form the bound-state for -1 ≤ C 〈 0.2. Frequency shifts increase with the increase of chirp parameter C for -1 ≤ C 〈 0.2, and have the oscillatory structure for C ≥ 0.2. The effect of positive chirp on temporal FWHM is greater than that of negative chirp. The peak of temporal waveform oscillates with the propagation distance. The period and amplitude of the oscillation for the chirped case are greater than those for the unchirped case, and they vary with the increase of ｜C｜. The peak of output temporal waveform can be controlled by changing the initial chirp.

Dual Visual Cryptography Using the Interference Color of Birefringent Material

Visual cryptography is a method of encrypting an image into several encrypted images. Conventional visual cryptography can display only monochrome images. We previously proposed a color visual cryptography method that uses the interference color of high-order retarder films and encrypts one secret image into two encrypted images. In other words, this method can only encrypt one image at a time. In this paper, we propose a new method that encrypts two color images using interference color.

Optical feedback characteristics in a helium neon laser with a birefringent internal cavity

The output characteristics of optical feedback in a helium neon laser with a birefringent internal cavity are studied systematically in five different regions of the gain curve for the two orthogonally polarized modes. When the laser operates in the two end regions of the laser gain curve, one of the two orthogonally polarized modes will be a leading one in optical feedback. Strong mode competition can be observed. However, when the laser operates in the middle region of the laser gain curve, the two modes can oscillate equally with optical feedback. Besides the intensity of the two polarized lights, the total light intensity is also studied at the same time. M-shaped optical feedback curves are found. Particularly, when the average intensities of the two lights are comparable, the intensity modulation curve of the total light is doubled, which can be used to improve the resolution of an optical feedback system.

Polarisation-sensitive four-wave mixing and soliton self-frequency shift effect in the highly birefringent photonic crystal fibre

By adjusting the polarisation state of the pump at 805 nm parallel to slow （x） and fast （y） axes of the highly birefringent photonic crystal fibre with zero dispersion wavelengths 790 nm and 750 nm, this paper demonstrates the efficient polarisation-sensitive four wave mixing involved in pump, anti-Stokes and Stokes signals and soliton self- frequency shift effects induced by the phase-matching between red-shifted solitons and blue-shifted dispersive waves. If the reduction of coupling efficiency to the circular pump laser mode or other circular fibres due to asymmetry of the core is neglected, more than 98% of the total input power is kept in a single linear polarisation. Controlled dispersion characteristic of the doublet of fundamental guided-modes results in achieving light field strongly confined in principal axes of photonic crystal fibre, and enhancing the corresponding nonlinear-optical process through the remarkable nonlinear birefringence.

Orientation dependence in high harmonics of ZnO with polarization corrections to counteract the birefringent effect

We investigate the influence of the birefringence on the high-order harmonics in an a-cut Zn O crystal with midinfrared laser pulses.The high harmonics exhibit strong dependence on the alignment of the crystal with respect to the laser polarization.We introduce the Jones calculus to counteract the birefringent effect and obtain the harmonics with polarization corrections in Zn O.We show that the birefringent effect plays an important role in the orientation dependence of HHG.

Efficient frequency upshift of 10 fs laser pulses propagating in a 5-cm length birefringent photonic crystal fibre

This paper reports that a 5-cm length birefringent photonic crystal fibre is used to tune the output frequency of unamplified 10-fs Ti：sapphire pulses. The zero dispersion of the fibre is at 823 nm and 800 nm for slow and fast fundamental modes, respectively. It is demonstrated that efficient upshift of the output frequency can be achieved when the pumped radiation is polarized along the slow axis of the fibre. When the average input power reaches 320 mW, about 60% of the output energy is located in one peak at 600 nm and is accompanied by depletion of the pulse inside the anomalous dispersion region.

Effect of Third-order Dispersion of Birefringent Fiber on Pulse Transmission

The effect of third order dispersion on pulse transmission is discussed. The coupled nonlinear Schrdinger equations characterizing the birefringent single mode fibers is solved numerically with combined consideration on chromatic dispersion, including second and third order dispersions, polarization mode dispersion (PMD) and nonlinearity. Various simulation results are presented.

Polarization-based range-gated imaging in birefringent medium:Effect of size parameter

We have investigated the effect of size parameter of the scatterer on the image quality obtained with polarization-based range-gated imaging in birefringent turbid medium. Both linearly and circularly polarized light were utilized for imaging.The simulated results indicate that the improvement of visibility is more pronounced using circularly polarized light for the birefringent medium composed of smaller-sized scatterers at lower values of optical thickness and the birefringent medium comprising larger-sized scatterers. In contrast, linearly polarized light provides better image quality for the birefringent medium composed of smaller-sized scatterers at larger values of optical thickness. The evolution of the polarization characteristics of backscattered light and target light under the conditions mentioned above was measured to account for these numerical results.

A Breather in Birefringent Fibers

The propagation properties of the breather in birefringent fibers are investigated. The breather can propagate stably in strongly birefringent fibers. The propagation law can be expected. However, random birefringence makes the propagation of the breather more complex. The breather will partly disappear and partly appear, even may split into two smaller breathers. In addition, the varying range of relative time displacement between two components of the breather becomes narrower with the effect of third-order dispersion. If third order dispersion is too strong, the breather behavior will disappear gradually during the transmission. The breather can exist in random birefringent fiber with dispersion management rather than in strongly birefringent fiber.

Design on a highly birefringent and nonlinear photonic crystal fiber in the C waveband

In this paper, a novel photonic crystal fiber （PCF） with high birefringence and nonlinearity is designed. The charac- teristics of birefringence, dispersion and nonlinearity are studied by using the full-vector finite element method （FVFEM）. The numerical results show that the phase birefringence and nonlinear coefficient of PCF can be up to 4.51× 10-3 and 32.8972 w-l.km-1 at 1.55 μm, respectively. The proposed PCF could be found to have important applications in the polarization-dependent nonlinear optics such as the pulse compress and reshaping in the C waveband.

Highly Nonlinear Bending-Insensitive Birefringent Photonic Crystal Fibres

Highly nonlinear birefringent Photonic Crystal Fibre (PCF) that exhibits low losses and small effective mode area across a wide wavelength range has been presented. The effects of angular orientation on bending losses of the proposed PCFs have been thoroughly investigated by employing a full vectorial finite element method (FEM). It has been demonstrated that it is possible to design a bending-insensitive nonlinear PCF with a birefringence in the order of 10-2 and a nonlinear coefficient of 49 W-1km-1 at the wavelength of 1.55 μm. Also, significant improvements on key propagation characteristics of the proposed PCFs have been demonstrated by carefully altering the desired air hole diameters and the hole-to-hole spacing. It is demonstrated that two zero dispersion wavelengths can be achieved by the proposed design.

Modulation instabilities in randomly birefringent two-mode optical fibers

Modulation instabilities in the randomly birefringent two-mode optical fibers （RB-TMFs） are analyzed in detail by accounting the effects of the differential mode group delay （DMGD） and group velocity dispersion （GVD） ratio between the two modes, both of which are absent in the randomly birefringent single-mode optical fibers （RB-SMFs）. New MI characteristics are found in both normal and anomalous dispersion regimes. For the normal dispersion, without DMGD, no MI exists. With DMGD, a completely new MI band is generated as long as the total power is smaller than a critical total power value, named by Per, which increases significantly with the increment of DMGD, and reduces dramatically as GVD ratio and power ratio between the two modes increases. For the anomalous dispersion, there is one MI band without DMGD. In the presence of DMGD, the MI gain is reduced generally. On the other hand, there also exists a critical total power （Per）, which increases （decreases） distinctly with the increment of DMGD （GVD ratio of the two modes） but varies complicatedly with the power ratio between the two modes. Two MI bands are present for total power smaller than Per, and the dominant band can be switched between the low and high frequency bands by adjusting the power ratio between the two modes. The M1 analysis in this paper is verified by numerical simulation.

Bound states in the continuum in metal-dielectric photonic crystal with a birefringent defect

By using the difference of the band structure for the TE and TM waves in the metal-dielectric photonic crystals beyond the light cone and the birefringence of the anisotropic crystal,a one-dimensional photonic system is constructed to realize the bound states in the continuum(BICs).In addition to the BICs arising from the polarization incompatibility,the Friedrich-Wintgen BICs are also achieved when the leaking TM wave is eliminated due to the destructive interference of its ordinary and extraordinary wave components in the anisotropic crystal.A modified scheme favorable for practical application is also proposed.This scheme for BICs may help to suppress the radiation loss in the metal-dielectric photonic crystal systems.

A simple and comprehensive electromagnetic theory uncovering complete picture of light transport in birefringent crystals

Birefringence production of light by natural birefringent crystal has long been studied and well understood.Here,we develop a simple and comprehensive rigorous electromagnetic theory that allows one to build up the complete picture about the optics of crystals in a friendly way.This theory not only yields the well-known refraction angle and index of ellipse for birefringence crystal,but also discloses many relevant physical and optical quantities that are rarely studied and less understood.We obtain the reflection and transmission coefficient for amplitude and intensity of light at the crystal surface under a given incident angle and show the electromagnetic field distribution within the crystal.We derive the wavefront and energy flux refraction angle of light and the corresponding phase and ray refractive index.We find big difference between them,where the phase refractive index satisfies the classical index of ellipse and Snell’s law,while the ray refractive index does not.Moreover,we disclose the explicit expressions for the zero-reflection Brewster angle and the critical angle for total internal reflection.For better concept demonstration,we take a weak birefringent crystal of lithium niobate and a strong birefringent crystal tellurium as examples and perform simple theoretical calculations.In addition,we perform experimental measurement upon z-cut lithium niobate plate and find excellent agreement between theory and experiment in regard to the Brewster angle.Our theoretical and experimental results can help to construct a clear and complete picture about light transport characteristics in birefringent crystals,and may greatly facilitate people to find rigorous solution to many light-matter interaction processes happening within birefringent crystals,e.g.,nonlinear optical interactions,with electromagnetic theory.

Cellotape Birefringent Filter: Some New Demonstrations

An easy method is put forward to estimate the optical bandwidth and the wavelength of maximum transmission of Lyot optical filter by measuring the change in phase retardation of birefringent plates as function of thickness. The objective is to demonstrate the experiment with common undergraduate laboratory equipment and thereby provide with an educational aid. The filter is fabricated with cellotape using its birefringence property. The accuracy of measurement is cross-checked with precision spectroradiometric measurements. Some simplification is suggested in the theoretical derivation of the transmitted intensity and a possibility of realizing tunable filter by changing the angle of incidence is indicated.

Clamping effect driven design and fabrication of new infrared birefringent materials with large optical anisotropy

Infrared(IR)birefringent materials with large optical anisotropy and wide transparency range are important for efficient light manipulation in various IR optical devices.Herein,two new IR birefringent materials AMgGeSe_(3)(A=Li,Na)with large optical anisotropy were rationally designed by a rigid octahedron and flexible dimer combined strategy and fabricated in experiment.The introduction of rigid[LiSe_(6)]/[NaSe_(6)]and[MgSe_(6)]octahedra effectively regulates the geometry and arrangement of the flexible[Ge2Se6]dimers,resulting in the birefringence as large as 0.334@1,064 nm in LiMgGeSe_(3) and 0.445@1,064 nm(the largest one in the reported[Ge_(2)Se_(6)]dimer-contained selenides)in NaMgGeSe_(3).Density functional theory(DFT)calculations and statistical analyses highlight the influence of polarizability anisotropy,density,arrangement of units,as well as layer distance on birefringence.The results indicate that AMgGeSe_(3)(A=Li,Na)crystals are the promising IR birefringent materials and it gives an insight into the exploration of new IR birefringent materials with large birefringence based on the clamping effect from rigid groups.

Analysis of electromagnetic propagation in birefringent thin film

In general, the propagating behavior of extraordinary wave in anisotropic materials is different from that in isotropic materials. With the tangential continuity of Maxwell’s equations, the electromagnetic propagating behaviors have been investigated at the incident and exit interfaces of the uniaxial anisotropic thin film. The emphasis was placed on two interesting optical phenomena such as homolateral refraction behavior and wide-angle Brewster’s phenomenon, which occurred at the interfaces of uniaxial anisotropic thin film.

Generation and controlling of the dispersive wave by femtosecond pulses propagating in the normal dispersion regimes of the birefringent photonic crystal fiber

This paper studies the generation of the dispersive wave (DW) in the normal dispersion regimes of the birefringent photonic crystal fiber (BPCF) fabricated in this work. The remarkable blue-shifted radiation is found to be generated when 30 fs pulses are input in the normal dispersion regime of the BPCF for the first time. The characteristics of the blue-shifted DW strongly depend on the polarization of the input pulse. As a result, two peaks appear in the blue-shifted region of the spectrum when the input pulses polarize along the slow axis of the BPCF. With the increase of the center wavelength of the initial input pulse, the difference between the wavelengths of the two peaks widens. The peak location in the spectrum can be explained by the phase matching condition between the DW and the input pulse. In addition, when the input polarization is set to an angle of 45° with respect to the principal axes of the BPCF, the cross-phase modulation and coherent coupling between two orthogonally polarized modes would result in pulse trapping in the BPCF. Accordingly, the DW shift toward short wavelength is restrained. The DW generation in the normal-dispersion regimes of BPCF can be controlled by the phase matching condition and polarization of the input pulse.