A precise data processing method for extracting χ from Z-scan technique

We present a precise data processing method, in the Z-scan experiments using a Gaussian beam and trimmed Airy beam, for directly extracting nonlinear refraction from the closed aperture Z-scan trace with the aid of the open aperture Z-scan trace when the materials exhibit nonlinear refraction and nonlinear absorption simultaneously. This method is still applicable when the nonlinear absorption is dominant and the closed aperture Z-scan curve degenerates into a single valley configuration, which is a salient advantage over other methods. In addition, we give gracefully empirical formulas with very high precision, which have good practicability for characterizing the optical nonlinearities of materials by use of the Gaussian beam and trimmed Airy beam Z-scan technique, respectively.     

Compensation for Radio-over-Fibre Uplink Based on Hybrid Neural Networks

The radio-over-fibre （ROF） uplink, which combines the merit of optical fibre with that of microwave technology, can supply the high capacity of communication. However, there are two major issues： nonlinear distortion of the optical link and the multipath dispersion of the wireless channel, affecting the performance of the system. We propose an equalizer based on hybrid neural networks. The compensation needs no estimation of the channel. The simulated result shows that the ROF uplink can be adequately compensated and the performance of the equalizer depends on the channel noise.     

Optimization of phase objects in 4f coherent imaging system for nonlinear refraction measurements

We numerically analyze the effects of radius and phase shift of phase objects on the diffraction image of the 4f coherent imaging system, a system used for measuring the third-order nonlinear refractive index. The selection of the aperture radius is discussed. We prove that when the phase object radius is 0.1 time of the aperture radius and the phase change of the phase object is 0.57π, one can get the highest sensitivity for nonlinear refraction measurement.     

Theory of thin-film, narrowband, linear-polarization rejection filters with superlattice structure

A device to be obtained by depositing a columnar thin-film on a transparent substrate decorated periodically by an array of rectangular grooves is proposed as a narrowband, linear-polarization rejection filter. The rigorous coupled-wave approach is harnessed to calculate the reflectances and transmittances. High-quality filters of chosen materials and with less than 2 nm bandwidths can be designed with a vapor flux angle for deposition of the columnar thin-film as the controlling parameter.     

Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

We show that the two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values for both the electric permittivity ? and the magnetic permeability μ in some frequency range. This follows from a recently proven general theorem. The negative values of ? and μ are found by a numerical simulation. Using values |?| and |μ| for the medium surrounding the PC slab we simulate the Veselago lens, a unique optical device predicted by Veselago. An approximate analytical theory is proposed to calculate the values of ? and μ from the PC band structure. It gives the results that are close to those obtained by the numerical simulation. The theory explains how a non-zero magnetization arises in a non-magnetic PC.     

A numerical parameter study of chiral metamaterial based on complementary U-shaped structure in infrared region

In this paper, the optical properties of the chiral metamaterial (CMM) with complementary U-shaped structure assembly have been investigated numerically in infrared frequencies. Here, we systematically study the dependence of CMM's optical properties to the structural parameters. The giant optical activity, circular dichroism (CD), and high negative refraction can be obtained by properly selecting the parameters, respectively. CMMs will also lead to many applications in photonic devices due to their strong polarization effect and CD effect.     

Negative refractive behavior of a two-dimensional negative-index photonic crystals using a wave vector diagram method

We have theoretically studied the negative refractive behavior and the focusing effect in a two-dimensional square-lattice photonic crystal made of air rods in a dielectric background. Detailed explanations are given for the effect of the negative refraction, and the imaging of the plano-concave lens is shown by the use of a wave vector diagram formalism. The typical negative refractive behavior is demonstrated by considering the Bloch mode with the wave vector inside the first Brillouin zone, because only those wave vectors inside the first Brillouin zone of multiple Brillouin zones have a definite meaning. The single propagating beam is analyzed by the use of the wave vector diagram formalism following the folding of the wave vectors. Good-quality focusing of a plane wave can be realized by using a photonic crystal plano-concave lens, while a plane wave is formed by a point source placed at the focal point. Our results are in good agreement with the experimental ones shown for a negative-index plano-concave lens by Vodo et al. [Appl. Phys. Lett. 86 (2005) 201108]. Finally, we also have shown the focusing behavior of a plane wave and a Gaussian pulse by a plano-concave lens structure with high-index modulation instead of air in the concave region.     

Femtosecond Z-scan measurement of third-order optical nonlinearities in anatase TiO2 thin films

Anatase phase TiO₂ films have been grown on fused silica substrate by pulsed laser deposition technique at substrate temperature of 750 °C under the oxygen pressure of 5 Pa. From the transmission spectra, the optical band gap and linear refractive index of the TiO₂ films were determined. The third-order optical nonlinearities of the films were measured by Z-scan method using a femtosecond laser (50 fs) at the wavelength of 800 nm. The real and imaginary parts of third-order nonlinear susceptibility χ⁽³⁾ were determined to be −7.1 × 10⁻¹¹esu and −4.42 × 10⁻¹²esu, respectively. The figure of merit, T, defined by T=βλ/n₂, was calculated to be 0.8, which meets the requirement of all-optical switching devices. The results show that the anatase TiO₂ films have great potential applications for nonlinear optical devices.     

Theoretical study of saturable Kerr nonlinearity using top-hat beam Z-scan technique

Saturable Kerr nonlinearity is theoretically investigated by use of the top-hat beam Z-scan technique. The saturation intensity changes the nonlinear refractive profile and decreases the sensitivity of the Z-scan measurements, which were quantitatively analyzed. An empirical formula for the saturable Kerr nonlinearity, which gave the relationship between the light intensity and the peak-valley transmittance difference, was accomplished. A high-accuracy method to determine the nonlinear refractive index and the characteristic saturation intensity was proposed.     

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.     

Photorefraction in the ultraviolet: Materials and effects

Doped as well as nominally pure crystals of Lithium Niobate (LiNbO₃), -Arginine Phosphate (LAP), Lithium Iodate (LiIO₃), Potassium Dihydrogen Phosphate (KDP), Lithium Formate (LFM), Beta-Barium Borate (BBO), and lithium tetra borate were grown and investigated for photorefractive effects at ultraviolet wavelengths down to 333 nm. In nominally undoped LiNbO₃ crystals strong beam coupling effects were observed. In contrast to the visible we revealed a diffusion-dominated charge transport mechanism based on holes, and a low photovoltaic field in the order of 550 V/cm. With such a crystal we investigated the modulation transfer function of a lensless image projection system based on a phase conjugation scheme. A spatial frequency response beyond 2800 line pairs per millimeter was observed. Photorefractive beam coupling was also obtained in LiIO₃. Light-induced scattering was detected in iron-doped LiIO₃ whereas as-grown LAP material did not exhibit any observable photorefractive effects. However, 100 kV X-ray irradiation seems to induce material defects which can lead to weak light-induced scattering at 351 nm. In all other above-mentioned materials, doped as well as undoped, light-induced scattering could not be observed. On the other hand, this is appreciated in all the applications where the crystals are used as nonlinear material for optical frequency conversion.     

Numerical aperture invariant focus shaping using spirally polarized beams

The concept of spiral polarization is proposed as an extension of the generalized cylindrical vector beam. The focusing properties of this spatially variant polarization under high NA are studied. It can be shown that with one such polarization, the focus maintains a flat-top intensity shape independent of NA from NA = 0.82 up to NA = 0.95.     

Efficient ultraviolet photorefraction in LiNbO3

A nominally undoped LiNbO₃ crystal with a slightly broadened absorption edge is used to study beam coupling effects in the UV at 351 nm. At this wavelength the crystal exhibits a diffusion-dominated charge transport mechanism, which allows steady state beam amplification of up to 700 times, comparable to BaTiO₃ in the visible. The used crystal material was characterized by an absorption coefficient =2.68 cm^–1 at 351 nm and a maximal gain coefficient =13.94 cm^–1. This high gain value in the UV can be attributed to a hole diffusion-dominated charge transport mechanism together with a low bulk photovoltaic effect. We measured photovoltaic fields of the order of 550 V/cm.     

Giant and negative bistable shifts for one-dimensional photonic crystal containing a nonlinear metamaterial defect

In this Letter, we investigate giant and negative bistable lateral shifts for a light beam transmitted through a one-dimensional photonic crystal containing a nonlinear metamaterial defect. It is shown that there exists a typical S-shaped curve of the normalized input-output intensity. The hysteresis of lateral shift, resulting from the reshaping effect (constructive and destructive interferences of each plane wave components undergoing different phase shifts) is dependent on the nonlinear defect, the incident intensity and incidence angle. Numerical simulations are also made for the validity of stationary phase approach. All these phenomena lead to potential applications in integrated optics and optical switches.     

Negative refraction of ultra-short electromagnetic pulses

We study pulse propagation across a boundary that separates an ordinary medium from a medium with simultaneously negative dielectric permittivity and magnetic permeability. Solving Maxwell’s equations with two spatial coordinates (one longitudinal, one transverse) and time we find negative refraction as the wave packet undergoes significant and unusual shape distortions. The pulse acquires and maintains a chirp as it traverses the interface, as expected, but with a sign that is opposite to the chirp attained upon traversal into a positive-index material. Both a direct calculation of the spatial derivative of the instantaneous, local phase of the pulse and a Fourier analysis of the signal reveal the same inescapable fact: that inside a negative-index material, a transmitted, forward-moving wave packet is indeed a superposition of purely negative wave vectors. The central findings of this paper are a confirmation that causality is not violated in the short-pulse regime, and that energy and group velocities never exceed the speed of light in vacuum.     

A polarization-dependent wide-angle three-dimensional metamaterial absorber

In this paper, a polarization-dependent wide-angle three-dimensional metamaterial absorber with a near-unity absorbance was presented. The metamaterial absorber structure is composed of coplanar electric and magnetic resonators. By carefully adjusting the structural dimensions, less-than-unity ε and/or μ can be realized. To match the impedance of free space, the structural dimensions were adjusted so that ε=μ, which guarantees minimum reflection. Since the resonance-based structure is made of metallic resonators and lossy substrates, the imaginary part of refractive index is large, which guarantees strong absorption of transmitted waves. Full-wave simulations confirmed the effectiveness of the proposed three-dimensional metamaterial absorber.     

Giant optical activity and circular dichroism in the terahertz region based on bi-layer Y-shaped chiral metamaterial

We present a bi-layer Y-shaped chiral metamaterial (CMM) that can realize a giant optical activity and circular dichroism (CD) effect to the incident linear polarization wave in the terahertz (THz) region. Numerical simulation results exhibit that the pronounced CD effect with a great difference between the transmission coefficients for the circularly polarized waves can be obtained at 5.06 THz, meanwhile the 90°-polarization rotation can be observed at 5.2 THz when a y-polarized wave is incident to this CMM propagating along the −z-axis. The mechanism of the optical activity and giant CD effect is illustrated by simulated surface current distributions. Further, the influences of the structural parameters of the proposed CMM to the optical activity and CD effect have been investigated numerically.     

I-scan thermal lens experiment in the pulse regime for measuring two-photon absorption coefficient

We present a new pump-probe mode-mismatched thermal lens method for pulse excitation aimed to the measurement of nonlinear absorption coefficient in optical materials. We develop a theoretical model based on the Fresnel diffraction approximation and their predictions are verified experimentally with samples of Rhodamine 6G and Rhodamine B in ethanol solution. The principal advantage of this technique is that it does not require any mechanical movement during measurement. Below we perform the new type of thermal lens experiment in the pulse regime for the measurement of nonlinear absorption coefficient in transparent samples and we demonstrate the validity of theoretical predictions using an alternative method to the classical thermal lens technique.     

Chiral planar waveguide for guiding single-mode backward wave

Single-mode backward wave is shown to be guided in a planar dielectric waveguide with a strong chiral core. The significant difference of such a waveguide from the traditional one is the guidance of single-mode backward wave, without using negative permittivity and/or negative permeability. In the design, we generalize the idea of total internal reflection to the chiral medium and make a numerical analysis on the reflection with oblique incidence. We deduce rigorously a general solution of incident wave on the boundary of two arbitrary chiral magneto-electric media. We observe that the impedance matching can eliminate the coupling between two eigenwaves in chiral media. With strong chiral core and the matched impedance with cladding, one eigenwave becomes a backward wave and can be guided without transferring to the other eigenwave. If a single-mode propagation condition is satisfied, we will get single-mode backward guided wave. A special interface has been designed to prevent the forward wave entering the waveguide from the source.