Influence of the cladding layer field of fiber on beam parameters

Beam parameters, including mode-field radius, divergence half-angle and beam propagation factor are studied and relations among them are derived under the condition of paraxial approximation. Several formulas of the beam parameters for end diffraction-limited from the fundamental mode of fiber are given based on the normalized standing wave parameter, normalized evanescent wave parameter and radii of core layer and circular aperture. Moreover, influence of change of the near-field on beam parameters is researched and the results show that the cladding layer field has determinant effect and cannot be neglect. These conclusions may provide theoretical foundation for further researching the beam parameters.     

Beam parameters for end diffraction of slab waveguide

Beam parameters including mode-field half-width, divergence half-angle and beam propagation factor are investigated and their relations are derived. Moreover, the beam parameters of end diffraction-limited beam from TE₀ propagating mode are given and influence of change of the near-field distribution on them is researched too.     

Theory of the partially coherent temporal Talbot effect

The behaviour of the temporal Talbot effect under carrier partial coherence is analysed. This effect finds application as a passive method for multiplying the repetition rate of the intensity of pulse trains in first-order dispersive media. The study is based on the representation of the average intensity of partially coherent modulated light after first order dispersion as a coherence-dependent low pass filter acting on the intensity distribution obtained with a monochromatic carrier. The resulting coherence limitations are more restrictive in Talbot devices with high indices, due to the necessity of highly coherent carriers to produce a faithful reconstruction of trains by multiple pulse-to-pulse interference. Coherence limitations for architectures composed of externally modulated cw sources are analysed. Generalizations of the theory to several spectral lines, and its relation with the Collett-Wolf theorem are also reported.     

Generation of Efficient Dispersive Waves in Photonic Crystal Fibers

Based on the generalized nonlinear Schroedinger equation, we investigate efficient dispersive wave （DW） generation in a photonic crystal fiber （POF） by numerical simulation and discuss a way to control DW generation by using an initial input pulse chirp. It is shown that efficient red-shifted DW generation can be obtained in a PCF with negative dispersion slopes. The energy contained in the DWs is considerably decreased for both positively and negatively chirped pulses at the fiber output. This provides us with an opportunity to conveniently and efficiently manipulate the DW generation by controlling the pre-chirp of the soliton. Moreover, we also show that forth- and higher-order dispersion terms play Iittle part in deciding the evolution of DWs.     

Transverse Multimode Evolution in Non-Adiabatic Optical Micro/Nanofiber Tapers

The multimode evolution, optical losses and wavelength response of non-adiabatic micro/nano-fiber （MNF） tapers are numerically simulated using a three-dimensional finite-difference beam propagation method. For a non-adiabatic MNF taper, it is illustrated that optical losses vary with the transition region length and the optical wavelength. We explain how the complicated multimode evolutions result in the complicated optical loss and wavelength response properties, especially when the waist diameters are large enough to allow much higher-order modes. These results may offer valuable references for trapping and guiding cold atoms in atom optics and practical application of micro/nano-devices.     

Dynamics of Incoherent Photovoltaic Spatial Solitons

Propagation properties of bright and dark incoherent beams are numerically studied in photovoltaic-photorefractive crystal by using coherent density approach for the first time. Numerical simulations not only exhibit that bright incoherent photovoltaic quasi-soliton, grey-like incoherent photovoltaic soliton, incoherent soliton doublet and triplet can be established under proper conditions, but also display that the spatial coherence properties of these incoherent beams can be significantly affected during propagation by the photovoltaic field.     

Long Optical Delay Lines Enhanced by Ring Configuration in Optical Fibres

A long optically controlled delay line enhanced by ring configuration is demonstrated by using the group-velocity control of signal pulses based on stimulated Brillouin scattering. In experiment, two optical fibre ring cavities are used： one is used as the Brillouin laser, providing single-mode Stokes wave as probe wave; the other is used as the Brillouin amplifier, working as slow light medium. We achieve a maximum time delay of 215ns using the ring Brillouin amplifier, five times larger than the input probe pulse width of 40ns. In the meantime, a considerable pulse broadening is observed, which agrees well with the theoretical prediction based on linear theory.     

Design of Microstructured Optical Fibres with Elliptical Air Holes for Properties： Single-Polarization Single-Mode and Nearly Zero Ultra-Flattened Dispersion

By using the complex finite element method （FEM） under perfectly matched layer （PML） boundary conditions, dispersion properties of microstructured optical fibres （MOFs） with elliptical air holes are analysed by changing the pitch and sizes of air holes belonging to the inner three rings. Meanwhile, the confinement loss of the fundamental mode is engineered to achieve the single-polarization single-mode transmission. Based on this analysis, a novel design of MOFs for properties of the single-polarization single-mode and the nearly zero ultraflattened dispersion between lpskm^-1 nm^-1 in the wavelength range of 1.2-1.6μm is presented for the first time.     

Heterodyne polarimetry for mapping defects in lithography masks

A new optical technique based on the heterodyne polarimetry is developed for fast inspection of uniformity of lithography masks in semiconductor industry. Sub-wavelength periodical structure of a sample acts as a wire-grid polarizer, making both the amplitude and phase of the reflected laser beam dependent on geometrical dimensions and optical properties of the mask pattern. The heterodyne technology based on the cross-polarized two-frequency Zeeman laser is used to simultaneously measure the amplitude and the phase of the reflected laser beam. A two-dimensional map of spatial variations can be obtained via point-by-point scanning of the sample. The technique is applicable not only to exact periodical structures like diffraction gratings, but also to double-periodical patterns consisting of large number of periodically distributed small areas of sub-wavelength gratings. Theoretical background, simulation, and experimental results are presented.     

Influence of Spectral Filtering and Nonlinear Gain on an Optical Soliton

Using the direct soliton perturbation theory, we investigate the evolution of soliton parameters and the firstorder correction of bright soliton in a system with linear and nonlinear gain （or loss） and spectral filtering in a comprehensive way. The results obtained by means of our analytic method are consistent with numerical simulations. It is also found that the stable soliton propagation which has been investigated in a previous report by others is the limit case of our results.     

Research on the temperature characteristics of optical fiber refractive index

The delay of optical signal is determined by the refractive index and length of optical fiber, and temperature would have an intense influence on the index. To establish the relationship between refractive index and temperature, the temperature characteristics of refractive index was analyzed and the thermo-optical coefficient equation was derived according to the polarization of the induced electric dipole moment in SiO₂ optical fiber. A measuring system based on optical fiber delay was carried out to measure the index within the temperature range of −30 °C to 70 °C and the experimental result was compared with the theoretical result. The final result shows that the relationship between refractive index and temperature is linear in the temperature range of discussion.     

Analysis of propagation characteristics for an octagonal photonic crystal fiber (O-PCF)

An octagonal photonic crystal fiber (O-PCF) structure with eight air-holes on the first ring is proposed based on a unit isosceles triangle. The propagation characteristics and cut-off behaviors of the O-PCF and the standard hexagonal PCF (H-PCF) are numerically investigated by combining the vector boundary method and the effective area method. The phase boundaries for cut-off, single-mode, and multi-mode operations between the O-PCF and H-PCF are calculated and compared. It is found that under the same pitch Λ and air filling fraction (AFF) of the air-holes the O-PCF has significantly wider wavelength range operating in single-mode region, more circular-like field distribution, and less confinement loss than the H-PCF.     

Veselago’s lens consisting of left-handed materials with arbitrary index of refraction

We study Veselago’s lens with arbitrary index of refraction and characteristic impedance. Using a full wave optics calculation, we show that this lens can be considered as an imaging system and we derive the appropriate lens formula. The lens with arbitrary index and impedance retains some of the properties of the matched lens, such as the invariance of its optical axis, three-dimensional imaging and easy manufacturing, but it loses the property of sub-wavelength resolution. We also show that identical results can be obtained for the impedance matched lens in the framework of paraxial geometrical optics, from which it can be inferred that optical systems containing such a lens can be studied and designed using traditional ray-tracing tools.     

Modeling of nanoparticle-induced Rayleigh-Gans scattering for nanofiber optical sensing

Based on Rayleigh-Gans scattering theory of spherical particles and evanescent-wave guiding properties of nanofibers, we calculate the scattered power of nanoparticles in the vicinity of typical waveguiding nanofibers. It shows that, by optimizing the wavelength of the probing light and the diameter of the nanofiber, nanoparticle-induced scattering intensity can reach detectable level with possibilities for single-molecule detection. Results presented in this work suggest a simple approach to high-sensitivity nanofiber optical sensing of nanoparticles in aqueous solutions.     

Mode Exciting Properties of Photonic Crystal Fibres with the Optical Field Incident from a Single Mode Fibre

We numerically investigate the mode exciting properties of photonic crystal fibres by using the beam propagation method when the optical field is input from a traditional single mode fibre. The results show that both the excited mode spectrum and the coupling-efficiency of each excited mode depend on the normalized pitch А/λ and the normalized hole-size А/λ. Furthermore, we obtain the boundary profile of the optimizing coupling-efficiency for the excited fundamental mode： the boundary （А/λ）＊ is linear to the boundary （А/λ）. All of these will pave the way for smoothing applications of photonic-crystal fibres, such as splicing and designing photonic-crystal-fibre functional devices.     

Propagation of Single-Mode Fibre Laser Beams through an Optical ABCD System with Circular Aperture at the Fibre Output End

Based on the expansion expression of the fundamental mode of a single-mode fibre in terms of Laguerr-Gauss modes, the propagation of a beam of a weakly guiding fibre laser through an opticM ABCD system with a circular aperture at the fibre end is studied. The results show that there is much difference between the propagation of the laser beam described by the expansion expression and by the Gaussian mode approximation. The depth of focus of the laser beam is longer than that of the Gaussian modes.     

Anti-Stokes Frequency Shift and Evolution in Polarization-Maintaining Photonic Crystal Fiber with Two-Zero Dispersion Wavelengths

Using the tunable pump pulses with about lOO fs pulse duration and 1064 nm central wavelength; the polarization-, wavelength- and power-dependent anti-Stokes lines are generated and modulated simultaneously in a polarization-maintaining photonie crystal fiber （PM-PCF） with two zero-dispersion wavelengths. By accurately controlling the polarization directions, the wavelength and the power of the pump pulse in the fiber anomalous region close to the second zero-dispersion wavelength of the PM-PCF, the output anti-Stokes pulse spectra can be tuned between 563 nm and 603 nm, which is in good agreement with the theoretical simulation. The color conversion of the mode image from yellow to orange is also observed with the different polarization pump pulses. These results can be attributed to the combined interaction between the fiber birefringence （including linear- and nonlinear- birefringence） and dispersion, and are attributed to phase-matching parametric four-wave mixing.     

Fe-Doped Polycrystalline CeO2 as Terahertz Optical Material

Fe-doped CeO2 is synthesized by ceramic method and the effects of Fe doping on the structure and properties are characterized by ordinary methods and terahertz-time domain spectrometer （THz-TDS） technique. Our results show that pure CeO2 only has a small dielectric constant ε of 4, while a smell amount of Fe （0.9 at.%） doping into CeO2 promotes densification and induces a large e of 23. From the THz spectroscopy, it is found that for undoped CeO2 both the power absorption and the index of refraction increase with frequency, while for Fe-doped CeO2 we measure a remarkable transparency together with a fiat index curve. The absorption coefficient of Fe-doped CeO2 at frequency ranging from 0.2 to 1.8 THz is less than 0.35 cm-1, implying that Fe-doped CeO2 is a potential THz optical material.     

Numerical Simulation for Coherent and Partially Coherent Beam Propagation through Atmospheric Turbulence

Propagation properties of coherent and partially coherent beams in atmospheric turbulence are investigated respectively by using numerical simulation It is found that a partially coherent beam has a spreading larger than a coherent beam. However, from the point view of relative beam spreading and intensity scintillation, a partially coherent beam is less affected than the corresponding coherent beam, which may be the most important virtue of partially coherent beams that could be utilized to improve the performance of laser engineering. The beam wandering is almost independent of the degree of the source coherence. More aperture averaging occurs when beam becomes more coherent.     

Beam moments and angular momentum in non-uniformly polarized beams

The angular momentum of non-uniformly totally polarized beams is investigated using methods from the beam characterization approach. The relationship between the elements of the beam matrix for the two components of the field and the angular momentum is given. The unconventional distribution of the polarization across the beam profile could result in contributions to both the spin and orbital terms of the angular momentum. To illustrate this, a particular example with a vortex beam is considered.