Modeling of the dynamic transmission properties of chalcogenide ring resonators in the presence of fast and slow nonlinearities.

We propose a simple iterative method for calculating the dynamic behavior of ring resonators with fast and slow (cumulative) optical nonlinearities when an optical pulse with an arbitrary-shaped envelope is incident into them. In the case of a slow nonlinearity, the nonlinear phase shift and nonlinear absorption are temporally-integrated over the incident pulse. In this paper, we consider two types of single-ring resonators made out of As2Se3 chalcogenide glass with high nonlinearity and investigate the dynamic properties (especially the effect of the cumulative nonlinearity on optical bistability) using known nonlinear material parameters. It is found that the cumulative nonlinearity suppresses overshoot and ringing after switching, decreases the width of the hysteresis loop between the input and output powers, and shifts its center corresponding to the operating point. The obtained results are useful in developing chalcogenide-based bistable optical devices and the proposed approach is applicable to modeling of a variety of nonlinear optical devices.

Optical nonlinearities in As2Se3 chalcogenide glasses doped with Cu and Ag for pulse durations on the order of nanoseconds.

We investigate the dependence of the nonlinear optical properties of Cu-doped and Ag-doped As(2)Se(3) glasses on the incident pulse-width at 1.064 microm using the Z-scan technique. In this work, 11.5-ns optical pulses from a Nd:YAG laser were compressed up to 1.6 ns by using stimulated Brillouin scattering in heavy fluorocarbon liquid. The measurement of the pulse-width dependence of the optical nonlinearities leads to the separation of an ultrafast Kerr nonlinearity and a slow (cumulative) nonlinearity such as a thermal nonlinearity. The measured values of the nonlinear refractive index and the nonlinear absorption coefficient of 4 at.% Cu-doped As(2)Se(3) glass (where the normal photodarkening effect is sufficiently suppressed) and 4 at.% Ag-doped As(2)Se(3) glass were proportional to the pulse width, showing that the cumulative nonlinearity is present in these two glasses. The cumulative nonlinearity of these doped glasses is larger than one of the undoped glass. The origin of such slow nonlinearity is presumably attributed to the photostructural changes inherent in chalcogenide glasses and is directly independent of one of photodarkening.

Pulse-width dependence of optical nonlinearities in As2Se3 chalcogenide glass in the picosecond-to-nanosecond region.

We study the dependence of optical nonlinearities in As(2)Se(3) glass on the incident pulse-width using the Z-scan technique. In this work, 11.5-ns optical pulses from a Nd:YAG laser operating at 1.064 mum were compressed up to 1.6 ns by using stimulated Brillouin scattering in heavy fluorocarbon liquid, where the duration of the compressed pulses depends on the pump energy. Moreover picosecond optical pulses with a 1.053-mum wavelength were utilized for the Z-scan experiments. To investigate the pulse-width dependence of the optical nonlinearities leads to the separation of an ultrafast Kerr nonlinearity and a slow (cumulative) nonlinearity such as a thermal nonlinearity because the magnitude of the cumulative nonlinearity should be proportional to the pulse duration. The experimental results clearly show that both the nonlinear refractive index and the nonlinear absorption coefficient increase linearly with pulse width. The origin of such pulse-width dependence is presumably attributed to photostructural changes inherent in chalcogenide glasses, which are induced not by nonlinear absorption such as two-photon absorption or two-step absorption, but by linear absorption in the weak-absorption region.

Optical nonlinearities in silicon for pulse durations of the order of nanoseconds at 1.06 microm.

We study free-carrier nonlinearities in crystalline silicon at 1.064 microm using the Z-scan technique, with special emphasis on the dependence of their nonlinearities on the width of incident pulses. In the Z-scan experiment, the pulse duration was changed from 11.5 ns to 1.6 ns by the pulse compression using stimulated Brillouin scattering in a liquid. At this excitation wavelength, linear absorption is dominant for the creation of electron-hole pairs and the photoexcited carriers can modify the refractive index and absorption coefficient just as a third-order nonlinear effect. The effective nonlinear refractive index n(2eff) and nonlinear absorption coefficient beta(eff) are proportional to the pulse duration and optical intensity, i.e. the fluence when the pulse duration is shorter than the carrier recombination lifetime. We can determine the variation of refractive index per unit of photoexcited carrier density sigma(r) and the total carrier absorption cross section sigma(ab) from the dependence of n(2eff) and beta(eff) on the pulse width, respectively. In this work we had sigma(r) =-1.0 x 10(-21) cm(3) and sigma(ab)=8.4 x 10(-18) cm(2), which agree well with previous data. We also observed the decrease in the magnitude of n(2eff) and beta(eff) at high incident fluence, which is presumably attributed to band filling. This new measurement approach has an advantage of being able to separate an ultrafast Kerr nonlinearity and a cumulative nonlinearity such as the free-carrier nonlinearity treated in this paper and can be utilized to evaluate the optical nonlinearities of other materials.

Optical bistability in photonic crystal microrings with nonlinear dielectric materials.

We study the linear resonance properties of several types of microrings in a two-dimensional photonic crystal (PC) consisting of a square lattice with air holes in dielectric using the plane-wave expansion method and the FDTD method. Moreover we investigate the nonlinear responses, especially optical bistability when an intense optical pulse is incident into the microrings. In this paper, Ag-As-Se chalcogenide glass is assumed as nonlinear dielectric, which has a high third-order nonlinearity. Although line-defect waveguides in an air-hole-type PC are usually multimoded, we can obtain interesting unique properties such as counter rotation of intracavity fields, transmission to all output ports, and unstable nonlinear oscillations in the multimoded PC microring. We can improve the resonance characteristics by partly introducing single-mode waveguides into microrings and can obtain stable optical bistability.

Transmission characteristics of photonic crystal waveguides with stubs and their application to optical filters.

We study the transmission characteristics of a photonic crystal waveguide with a single stub of a finite length and propose a double-stub waveguide structure for its application to optical filters. The proposed device operates as a Fabry-Perot interferometer and can be used as a broad bandstop filter and a narrow bandpass filter. These filters are inherently compact and their center frequency is given by the resonant frequency of the stub.

Simple and accurate measurement of the absorption coefficient of an absorbing plate by use of the Brewster angle.

We propose a simple and accurate method for measuring the refractive index and the absorption coefficient of an absorbing parallel plate. The method is essentially based on transmittance measurement with minimum reflectance at the Brewster angle for p-polarized light, which enables us to measure a low absorption loss of the order of 0.1 dB/cm for a typical plate thickness of 1 mm. The error that is due to the approximation used is practically negligible, and the accuracy of measured results depends mainly on the variations in the flatness and parallelism of the two surfaces of the sample and on instrumental errors.

Optimization of a continuous phase-only sampling for high channel-count fiber Bragg gratings.

A novel continuous phase-only sampling function capable of producing up to 81-channel FBG with excellent channel uniformity and high in-band energy efficiency is presented and optimized by using the simulated annealing algorithm. In order to fabricate this kind of FBG with a conventional side-writing phase-mask technique, both the diffraction effects and fabrication tolerance of the phase-shifted phase mask have also been addressed. Compared with the numerical results, a 45-channel (spacing 100 GHz) and an 81-channel (spacing of 50 GHz) phase-only sampled linearly chirped FBG are successfully demonstrated.

Influence of cladding-mode coupling losses on the spectrum of a linearly chirped multi-channel fiber bragg grating.

Influence of cladding-mode coupling losses on the spectrum of multi-channel fiber Bragg grating (FBG) has been numerically investigated on the basis of the extended coupled-mode equations. It has been shown that there exists a reflection slope in the spectrum of both the intra- and inter-channels due to the existences of the cladding modes. This slope could be larger than 1 dB when the induced index change is about 3x10-3, which makes the channels considerably asymmetric. For comparison, a 39-channel linearly chirped FBG with a channel spacing of 0.8 nm and a chromatic dispersion of -850 ps/nm has been designed and fabricated. The experimental results show good agreement with the numerical ones. Finally, one method to pre-compensate the reflection slope within the intra-channels has been proposed and successfully demonstrated.

Single-mode Ag-As2Se3 strip-loaded waveguides for applications to all-optical devices.

We report the fabrication and characterization of Ag-As2Se3 strip-loaded waveguides fabricated by the standard lift-off method and photodoping, where Ag-As2Se3 (i.e., Agx(As0.4Se0.6)100-x) is a very promising material for all-optical switching devices because of a high third-order optical nonlinearity. Absorption coefficient of the bulk glasses is also presented for different values of the Ag content x. The addition of Ag into an As2Se3 guiding layer increases its nonlinearity and eliminates or weakens a harmful photo-oxidation reaction of As2Se3 films. The measured propagation loss in the single-mode waveguides with the Ag content x=3 at.% was 0.5 dB/cm at a wavelength of 1.053 mum and was attributable to the absorption loss in the waveguide materials.

Linear and nonlinear optical properties of Ag-As-Se chalcogenide glasses for all-optical switching.

We prepared Ag(x)(As0.4Se0.6)(100-x) chalcogenide glasses by a melt-quenching method and measured their linear and nonlinear optical properties to evaluate their potential applications to all-optical ultrafast switching devices. Their nonlinear refraction and absorption were measured by the Z-scan method at 1.05 microm. The addition of Ag to As2Se3 glass led to an increase in the nonlinear refractive index without introducing an increase in the nonlinear absorption coefficient. The glass with a Ag content of x = 20 at. % revealed high nonlinearity ranging from 2000 to 27,000 times that of fused silica, depending on the incident optical intensity.