Refractive index and material dispersion interpolation of dopedsilica in the 0.6-1.8 μm wavelength region

An extension of the Claussius-Mossotti interpolation scheme is proposed so that the refractive index and material dispersion of GeO₂- and F-doped silica glasses (with doping concentrations different than those of published data) can be predicted in the 0.6-1.8-μm wavelength region. The new interpolation expression provides a well-behaved functional relationship for use in computer models which analyse propagation in single-mode fibers. The technique proposed is particularly powerful because it can be applied to any glass, whether single or multicomponent, having any other single dopant     

Universal conditions for estimating the nonlinear refractive indexn2 of dispersion-compensating fibers by the CW-SPMmethod

We investigated universal conditions for measuring the nonlinear refractive index n₂ of dispersion-compensating fibers by the continuous wave self-phase modulation (CW-SPM) method both theoretically and experimentally. We showed that the required fiber length and the minimum power for n₂ estimation can be expressed as simple functions in terms of chromatic dispersion D. Moreover, we confirmed experimentally that the present conditions for n₂ estimation are reasonable     

SBS threshold of a fiber with a Brillouin frequency shiftdistribution

The SBS threshold of a fiber with Brillouin frequency shift distribution along its length is investigated theoretically and experimentally. We obtain a simple equation for estimating the SBS threshold from the effective gain coefficient, which is calculated by using the Brillouin frequency distribution along its length. The dopant concentration dependence of the Brillouin frequency shift are measured for fibers with an F and GeO₂ codoped silica core. The evaluated frequency shift per unit of dopant concentration is 277 MHz/wt% and 45 MHz/wt% for F and GeO₂, respectively, at 1.55 μm. The SBS threshold of a fiber with a nonuniform Brillouin frequency shift distribution prepared by the VAD method is investigated experimentally. The fiber exhibits 7 dB improvement in its SBS threshold. This value is in good agreement with one estimated by calculating the effective gain coefficient. This simple equation will be useful for estimating the SBS threshold of various fibers     

Nondegenerate optical Kerr effect in semiconductors

We calculate the nondegenerate bound electronic nonlinear refractive index n₂(ω₁;ω₂) (i.e., an index change at frequency ω₁ due to the presence of a beam at frequency ω₂) in semiconductors. We calculate this nonlinearity and its dispersion using a Kramers-Kronig transformation on the calculated nondegenerate nonlinear absorption spectrum due to two-photon absorption, electronic Raman and optical Stark effects. The calculated n₂ values and their dispersion are compared to new experimental values for ZnSe and ZnS obtained using a 2-color Z-scan     

Ultrafast two-photon nonlinearities in CdSe near 1.5 μm studiedby interferometric autocorrelation

We have used interferometric autocorrelation measurements to study the femtosecond nonlinear optical properties of bulk CdSe crystals in the wavelength region just above the half gap wavelength of 1.42 μm. Between 1.42 and 1.55 μm, we measured an ultrafast third-order nonlinearity with nonlinear refractive index n₂=1.3×10 ^-13 cm²/W^-1. Detailed modeling of the autocorrelations revealed the influence of higher order effects due to free carriers generated by nonlinear absorption. We find that CdSe is an interesting alternative material to AlGaAs for applications in this technologically important wavelength region     

Viscosity of GeO2-doped silica glasses

The viscosity of GeO₂-doped silica glasses is experimentally evaluated and found to be expressed as a function of the monoexponential form η₀ exp(-AΔe), where η₀ is the viscosity of pure silica glass, A is a positive constant, and Δe is an equivalent relative-index difference that is introduced for a silica glass with nonuniform dopant distribution in its cross section. The constant A for GeO₂-doped silica glasses is found to be about 0.5, which is much smaller than that for fluorine-doped silica glasses and has almost no temperature dependence between 1400°C and 2200°C     

Measuring the longitudinal distribution of four-wave mixingefficiency in dispersion-shifted fibers

We measured and analysed four-wave mixing (FWM) efficiency and fluctuation along the actual dispersion-shifted fibers (DSF's). In the short, 1.1-km DSF, our results agreed with theory, and we also obtained zero-dispersion wavelength λ₀, zero-dispersion slope dD/dλ, and nonlinear refractive index n₂ simultaneously. In the long, 23-km, DSF, a high FWM efficiency was observed in the wide wavelength region, due to the longitudinal zero-dispersion wavelength distribution. The fluctuation range was about 3.5 nm and the maximum slope about 1.1 km/nm     

Rayleigh scattering reduction method for silica-based optical fiber

The effect of the thermal treatment of silica-based glasses and glass fibers on their Rayleigh scattering is investigated experimentally. The Rayleigh scattering coefficients of bulk glasses are found to be increased 5-10% by heating them to 1800 °C because the density fluctuation is in proportion to their fictive temperature. Based on these results, we propose a method for reducing the Rayleigh scattering losses of silica-based optical fibers by drawing them slowly at low temperatures. We used this method to obtain a GeO₂ doped silica core single-mode fiber with a minimum loss of 0.16 dB/km at 1.55 μm. As a result, we confirmed that the reduction in the fictive temperature of silica-based glasses and glass fibers reduces their Rayleigh scattering     

The nonlinear optical properties of AlGaAs at the half band gap

We report experimental values for the nonlinear optical coefficients of AlGaAs, in the half-band-gap spectral region. The dispersion of the nonlinear refractive-index coefficient, n₂, is measured for both TE- and TM-polarized light. We observe n₂(TE)>n₂(TM) and a ratio of cross-phase modulation to self-phase modulation (TE) of ~0.95, as predicted from band structure calculations. The spectral dependence of the two- and three-photon absorption coefficients are also measured. Finally, the implications for all-optical switching and spatial soliton propagation are discussed     

Polarization dependent four-wave-mixing and two-photon coherence insolids

Polarization dependent degenerate-four-wave-mixing experiments on semiconductors (ZnSe, CdS) and dielectrics (NaCl, PbF₂) reveal the essential mechanisms of the bound-electronic χ⁽³⁾ . We show, for the first time, that the observed anomalous dispersion of the polarization dependent phase-conjugate reflectivity can be explained using a simple 3-band model. The near vanishing reflectivity in the two-photon coherence geometry is shown to be a consequence of the interference between transitions originating from heavyand light-hole valence bands. We also present measurements on the polarization dichroism of the nonlinear refractive index (n₂), in good agreement with this simple theory     

Optical loss property of silica-based single-mode fibers

The optical loss property of silica fibers has been investigated theoretically and experimentally based on their Rayleigh scattering and absorption losses. The Rayleigh scattering loss for fibers has been estimated using Rayleigh scattering coefficients and power distribution in the fiber. The Rayleigh scattering coefficients are measured for preforms prepared for fiber fabrication and are discussed for GeO₂ -doped and F-doped glasses. The relationship between the optical loss and fiber parameters is clarified. Moreover, the loss increase due to residual stress which occurs during the drawing process is simulated. The optical loss limitations for GeO₂-doped and pure silica core fibers are shown     

Measurements of the nonlinear coefficient of standard, SMF, DSF,and DCF fibers using a self-aligned interferometer and a Faraday mirror

Using a method based on the detection of the Kerr phase shift by a self-aligned interferometer, we present measurements of the nonlinear coefficient n₂/A_eff for standard single-mode fiber (SMF), dispersion-shifted fibers, and dispersion compensating fibers. The presence of a Faraday mirror in the interferometer makes the setup very robust, and different test fibers can be measured without any further readjustments. Interlaboratory comparisons show that the values found with our method are in good agreement with the other ones. Further, analysis of a SMF fiber with large chromatic dispersion shows a good reproducibility of the n₂/A_eff measurements as a function of fiber length     

Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids

The bound electronic nonlinear refractive index, n₂, and two-photon absorption (2PA) coefficient, β, are measured in a variety of inorganic dielectric solids at the four harmonics of the Nd:YAG laser using Z scan. The specific materials studied are: barium fluoride (BaF₂), calcite (CaCO₃), potassium bromide (KBr), lithium fluoride (LiF), magnesium fluoride (MgF₂ ), sapphire (Al₂O₃), a tellurite glass (75%TeO₂+20%ZnO+5%Na₂O) and fused silica (SiO₂). We also report n₂ and β in three second-order, χ⁽²⁾, nonlinear crystals: potassium titanyl phosphate (KTiOPO₄ or KTP), lithium niobate (LiNbO₃), and β-barium berate (β-BaB₂O ₄ or BBO). Nonlinear absorption or refraction can alter the wavelength conversion efficiency in these materials. The results of this study are compared to a simple two-parabolic band model originally developed to describe zincblende semiconductors. This model gives the bandgap energy (E_g) scaling and spectrum of the change in absorption. The dispersion of nl as obtained from a Kramers-Kronig transformation of this absorption change scales as E_g^-1 . The agreement of this theory to data for semiconductors was excellent. However, as could be expected, the agreement for these wide bandgap materials is not as good, although general trends such as increasing nonlinearity with decreasing bandgap energy can be seen     

Parametric analysis of semiconductor-doped glasses for all-opticalswitching

We use the basic physical parameters of semiconductor-doped glasses (SDG's) to compute the dependence of their nonlinear index n₂ due to the bandgap resonant effect on pump intensity and to predict the power and length requirements of an all-optical SDG waveguide switch. The main conclusions are that (1) the pump and signal wavelengths should be in specific and different ranges to minimize the switching power and signal loss, (2) for CdSSe- and CdTe-doped glasses, n₂ is relatively small, (3) their power requirements are consequently quite high (2-100 W), although (4) much lower than in a comparable device operated near the half-bandgap. We provide evidence that this weak nonlinearity, compared to that of semiconductors in bulk, is due to the strong nonradiative recombination of carriers arising from the small size of the semiconductor microcrystallites. Projections indicate a reduction in switching power by up to a factor of 1000 by increasing the microcrystallite size, thus producing a slower (ns) but more power efficient switch     

Large purely refractive nonlinear index of single crystal P-toluenesulphonate (PTS) at 1600 nm

Z-scan measurements at 1600 nm on single-crystal PTS (p-toluene sulfonate) with single, 65 ps pulses gave a complex nonlinear refractive index coefficient of n₂=2.2(±0.3)×10^-12 cm²/W at 1 GW/cm² and α₂<0.5 cm/GW. This is the first highly nonlinear, organic material to satisfy the conditions imposed by the figures of merit     

The optical second-harmonic generation from porous silicon

Second-harmonic generation from porous silicon with a magnitude of two orders greater than that from the original silicon crystalline wafers is discussed. The measured effective second-order nonlinear susceptibility X⁽²⁾_ps.eff for a p-type porous silicon is 1.96×10^-7 esu. The susceptibility is estimated on the base of a bulk property rather than on quantum confinement owing to its large surface to volume ratio     

Achieving Conduction Band-Edge Effective Work Functions by La2O3 Capping of Hafnium Silicates

Conduction band-edge effective work functions (phi_m,eff ) are demonstrated with TaC_x and TiN by means of La₂O₃ capping of HfSiO_x in a gate-first process flow with CMOS-compatible thermal budget. With TaC_x, a 10- Aring-thick La₂O₃ cap results in a phi _m,eff of 3.9 eV with a low equivalent oxide thickness (EOT) increase (1-2 Aring) and unaffected electron mobility. With TiN, non-nitrided La₂O₃ capping results in a smaller phi_m,eff reduction at a larger EOT increase, while with post-cap nitridation, the TiN phi_m,eff is lower at a smaller EOT increase. Results show that the choice of metal and nitridation conditions have significant effects on La₂O₃ capped stacks     

Thermal effects of Brillouin gain spectra in single-mode fibers

Brillouin gain spectra in two 250-m-long single-mode fibers with GeO₂-doped core/pure-silica cladding (fiber A) and pure-silica core/F-doped cladding (fiber B) were measured at temperatures ranging from -40 to +60°C at a wavelength of 1.32 μm. The temperature coefficients of Brillouin frequency shift were found to be 1.17 and 1.33 MHz/°C for fibers A and B, respectively. Temperature coefficients of Brillouin gain bandwidth were found to be -0.12 and -0.10 MHz/°C. These measurements provide useful information for applications of stimulated Brillouin scattering     

Control of Refractive Index Distribution for High-Bandwidth Graded Index Plastic Optical Fiber

The graded index plastic optical fiber (GI-POF) has been proposed as the transmission medium to realize high-speed information transmission. We have succeeded in fabricating a GI-POF by the coextrusion process, a method that allows continuous fabrication of GI-POF. Although it has been indicated that the refractive index distribution of GI-POF fabricated by this process is formed by Fick diffusion with diffusion coefficient dependent on dopant concentration, the method to control it remains unknown. The purpose of this paper is to establish the technology of controlling refractive index distribution in GI-POF fabricated by the coextrusion process. Therefore, we investigate the physical mechanism of the dependency of diffusion coefficient on dopant concentration. It has become clear that the dependency is affected by the decrease of glass transition temperature and the nonlinear increase of melt flow rate. Moreover, through simulation of dopant diffusion by our originally developed program, it has become evident that changing the molecular weight of the core and cladding material allowed control of fabricating a GI-POF with optimal refractive index distribution by this fabrication method.      

Iterative simplex-finite difference method for the characterizationof optical waveguides

A new method is presented for reconstructing smooth refractive index profiles of optical waveguides from measured effective indexes. It is based on the semivectorial finite difference method to solve the polarized wave equation for a given refractive index profile. An iterative simplex algorithm is used to find the best refractive index parameters that give, as a solution, effective indexes close to the measured ones. The method is applied successfully to Ag⁺-Na ⁺ ion-exchanged glass slab waveguides and to diffused Mg/Ti:LiNbO₃ slab waveguides. Dopant concentration profiles are obtained by using secondary ion mass spectrometry. The relationship between the refractive index change and the dopant concentration is determined for both cases. The iterative simplex algorithm-finite difference method (ISA-FDM) is compared to other index profile reconstruction methods, and the advantages with respect to WKB-based methods are pointed out