Theoretical analysis of output statistics of Er3+:Ti:LiNbO3 M-mode straight waveguide amplifiers

In this paper we present a theoretical analysis of some statistical parameters which characterize the Er³⁺-doped Ti:LiNbO₃ M-mode straight waveguides. The derivation and the evaluation of the spectral optical gain, the spectral noise figure, the Fano factor, the statistical fluctuation and the spontaneous emission factor are performed under the small gain approximation. The simulations show the evolution of these parameters under various pump regimes and waveguide lengths. The obtained results can be used for the design of complex rare earth doped integrated circuits.     

Variational analysis of Er:Ti:LiNbO3 waveguide lasers based on Gaussian/two-half Gaussian mode field distribution

Starting with two dimensional, scalar wave equation, a variational equation was established for the fundamental TE and TM modes guided in Ti:LiNbO₃ waveguides on the basis of assuming a symmetric Gaussian mode field function in the width direction and two-half Gaussian trial functions in the depth direction. The controllable waveguide fabrication parameters, including channel width, diffusion temperature, initial Ti-strip thickness and diffusion time, dependent of fundamental mode size, effective pump area, coupling efficiency between pump and laser modes, and the coupling loss between a Ti:LiNbO₃ waveguide and a fiber were numerically calculated for Z-cut Er:Ti:LiNbO₃ channel waveguide lasers at three possible emission wavelengths 1532,1563 and 1576 nm and two possible pump wavelengths 1480 and 980 nm. The calculated results were compared with those of Gaussian/Hermite–Gaussian mode field distribution in detail.     

Theoretical Study of the Statistical Properties of Single- and Double-Pass M-Mode Er3+-Ti:LiNbO3 Straight Waveguide Amplifiers

Abstract

In this article, we report a theoretical study concerning some statistical parameters which characterize the single- and double-pass Er³⁺-doped Ti:LiNbO₃ M-mode straight waveguides. For the derivation and the evaluation of the Fano factor, the statistical fluctuation and the spontaneous emission factor we used a quasi two-level model in the small gain approximation and the unsaturated regime. The simulation results show the evolution of these parameters under various pump regimes and waveguide lengths. The obtained results can be used for the design of complex rare earth-doped integrated circuits.     

掺铒铌酸锂波导放大器增益特性的理论分析

对掺铒铌酸锂（Ｅｒ３＋：ＬｉＮｂＯ３）波导放大器在１４８０ｎｍ泵浦光单向和双向泵浦下的增益特性作了计算机模拟理论分析,采用二能级速率方程,忽略ＥＳＡ的影响,应用数值法得出方程解,优化设计放大器参数     

Spectral line intensities of Yb3+ ion in LiNbO3 crystals

Optical spectra of absorption and luminescence of LiNbO₃:Yb³⁺ crystals are investigated experimentally and theoretically. Within the framework of the point charge approximation of crystal field, the Stark problem is solved: crystal field parameters and wave functions of Stark states are determined. Line strengths due to indirect electric-dipole and magnetic-dipole inter-Stark transitions are calculated and values of the Judd-Ofelt parameters are determined. Values of the branching ratios of luminescence. Einstein coefficients and, lifetime of the excited sublevel are calculated. A satisfactory agreement of calculated results with experimental data is obtained.     

Exact analysis of cascaded second-order nonlinearity in rotated Ti:LiNbO3 Couplers

The effects of anisotropic coupling on the nonlinear behavior of different LiNbO₃ waveguides and couplers employing cascaded second-order nonlinearity are analyzed and the importance of leaky mode effect is shown. A set of practical coupling structures made of both symmetric and asymmetric waveguides is investigated and their performance is compared. The home-made computer-code, based on coupled wave theory and anisotropic mode propagation in the complex domain, allows an exact electromagnetic investigation of devices, taking into account both guided and leaky propagation in structures which exhibit losses, the generated second harmonic wave having leaky nature. As an example, for the well-investigated slab three layer waveguide, by taking into account the leaky nature of the generated second harmonic, the modal mismatch = 333 m^–1 is obtained at the azimuthal angle _m 61.9 (between the crystal optical c-axis and the propagation direction) while the angle found via the conventional approach is _m 63.5. Moreover, the calculated second harmonic wave exhibits an attenuation equal to 7.44 × 10^–1dB/cm that strongly influences the whole cascaded second-order phenomenon. The simulation results, for those structures in which it is possible to neglect the hybrid and leaky nature of the propagation modes, are compared with the literature data and an excellent agreement is found.     

Er：YLF晶体中Er^3＋离子的光谱特征

利用居地－奥非脱（Ｊｕｄｄ－Ｏｆｅｌｔ）理论计算了Ｅｒ＾３＋离了在氟化钇锂（ＬｉＹＦ４简写为ＹＬＦ）晶体中的辐射跃迁几率Ａｊｊ无辐射跃迁几率ωＪＪ及激发态荧光寿命τ，并根据荧光动力学方程计算出各激发态布居数ＮＪ与掺杂浓度ｘ的关系，对２．７μｍ激光（＾４Ｉ１１／２→＾４Ｉ１３／２）来说，掺杂浓度要大于～３ａｔ％，才能实现布居数反转，对波长为１．７３μｍ的＾４Ｉ１３／２→＾４Ｉ１５／２跃迁，存在荧光强     

Wavelength conversion in a Ti:PPSMgLN channel waveguide

A periodically poled titanium (Ti)-diffusion waveguide in near-stoichiometric MgO:LiNbO₃ (SMgLN) was fabricated that exhibits a second harmonic generation (SHG) efficiency of 63%. The device shows very high resistance to photorefractive damage at room temperature. All optical wavelength conversion by difference frequency generation (DFG) has been demonstrated in a periodically poled SMgLN (PPSMgLN) with Ti-diffusion channel waveguides. The wavelength conversion efficiency was measured to be −7.3 dB with the pump power of 150 mW and the signal power of 50 mW at room temperature.     

Refined modeling of traveling-wave Ti:LiNbO3 channel waveguide modulator

A refined computation model for traveling-wave operation of external electro-optical phase modulators made of a single titanium in-diffused lithium niobate channel waveguide (Ti:LiNbO₃WG) is described. The modulator circuit model outlined as two traveling-wave coupled microstrips includes microwave losses and dispersion. In the optimization procedure, we consider different circuit load conditions. The influence of a dielectric overlay covering the electrodes is examined. The consolidated techniques of conformal mapping, multiple image, and finite element are used to investigate the microwave characteristics of the structure, and the refractive effective index method is used in calculating the characteristics of the diffused anisotropic optical channel. The performances of Y-cut and Z-cut substrate configurations are compared. We have verified that the Y-cut substrate modulator gives the best overall performance, and that the overlay presence causes significant improvements in the evaluated modulation efficiency and in the bandwidth. A model of the modulator that takes electrode thickness into account permits one to obtain a wider bandwidth.     

Near-stoichiometric Ti:LiNbO3 strip waveguide with varied substrate refractive index in waveguide layer

We report the near-stoichiometric Ti:LiNbO3 strip waveguides fabricated by vapour transport equilibration (VTE) at 1060 C for 12 h and co-diffusion of 4-8 μm wide, 115-nm thick Ti-strips. Optical studies show that these waveguides are monomode at 1.5 μm and have losses of 1.3 and 1.1 dB/cm for the TM and TE modes, respectively. In the waveguide width/depth direction, the mode field follows a Gauss/Hermite-Gauss profile. A secondary ion mass spectrometry study reveals that the Ti profile follows a sum of two error functions along the width direction and a complementary error function in the depth direction. Micro-Raman analysis shows that the Li-composition in the depth direction also follows a complementary error function. The mean Li/Nb ratio in the waveguide layer is about 0.98. The inhomogeneous Li-composition profile results in a varied substrate index in the guiding layer, and the refractive index profile in the guiding layer is given.     

Surface acoustic wave distribution and acousto-optic interaction in proton exchanged LiNbO3 waveguides

The efficiency of acoustooptic (AO) interaction in YZ-cut proton exchanged (PE) LiNbO₃ waveguides is theoretically analysed by determining the overlap between the optical and acoustic field distributions. The present analysis takes into account the perturbed SAW field distribution due to the presence of the PE layer on the LiNbO₃ substrate determined by the rigorous layered medium approach. The overlap is found to be significant upto very high acoustic frequencies of the order of 5 GHz, whereas in the earlier analysis by vonHelmolt and Schaffer [6] for diffused waveguides, it was shown that the overlap integral rolls down to nearly zero at this high frequency range.     

Bent waveguide with a high index reflector on LiNbO3

An abrupt bend structure with a corner reflector on LiNbO₃ is proposed. In the proposed structure, a region whose refractive index is higher than that of the substrate is placed at the corner of the bend. The interface between the substrate and the high index region is used as a reflector for the guided wave. The calculated normalized transmission power is about 94% even when the bend angle is 10.     

Upconversion in Highly Doped Er3+-Yb3+ Fiber Pumped by Ti:Sapphire Laser at 800 nm

The up-conversion processes were investigated in highly doped Er3+-Yb3+ silica fiber pumped by CW or mode-locked Ti:Sapphire laser at 800 nm band. The mechanism is different from that at 980 nm pumped band. The pumping wavelength and power dependences of green, blue and red fluorescence emission were obtained. The up-conversion efficiencies of different doped concentration were investigated. The strong infrared emissions, which limit the efficiency of up-conversion were observed.     

Spectroscopic analysis of Er transition in Mg/Er-codoped LiNbO3 crystal

We present a Judd-Ofelt spectroscopic analysis on the Mg/Er-codoped congruent lithium niobate (LiNbO₃) crystals. The Judd-Ofelt model is applied to the room temperature unpolarized absorption intensities of Er³⁺ ions on eleven transition bands to determine their intensity parameters: Ω₂=2.36×10⁻²⁰ cm², Ω₄=0.76×10⁻²⁰ cm², Ω₆=0.30×10⁻²⁰ cm² in Er:LiNbO₃ crystal heavily codoped with MgO. The radiative lifetime of ²H_9/2 becomes longer when MgO is added into Er:LiNbO₃ crystal. The experimental lifetimes are obtained using microsecond time-resolved spectra at 400 nm femtosecond pulse excitation to predict radiative quantum efficiency. Combining higher radiative quantum efficiency with longer radiative lifetime, we conclude that Mg/Er-codoped LiNbO₃ crystals are more suitable than Er: LiNbO₃ ones in laser materials.     

Ti:LiNbO3 Integrated Optic Electric-Field Sensors based on Electro-Optic Effect

The need for electric-field sensing technology has widely increased, playing a critical role in various scientific and technical areas. This article comprehensively reviews and compares Ti:LiNbO₃ integrated optic electric-field sensors, including the asymmetric Mach-Zehnder interferometer (MZI), 1 × 2 directional coupler (DC), and Y-fed balanced-bridge Mach-Zehnder interferometer (YBB-MZI), based on the operating principles, the electrical and optical performance, and measurements of each fabricated device. We also discuss future works to improve the sensitivity, operating stability, response speed, and bandwidth.     

Spectral line broadening mechanism of Er3+ transitions in Er:Ti:LiNbO3 channel waveguides

In order to elucidate the interaction effects among the various defects present in a LiNbO₃-based integrated optical device, we investigated the change of the optical properties of Er³⁺ ions under the application of an external electric field and hydrostatic pressure. We obtained for stoichiometric bulk material a complete picture of the field-induced spectral shifts as a function of transition and site. As a first important application of these results we were able to clarify the mechanism of spectral broadening of the Er³⁺ transitions in Ti:Er:LiNbO₃ channel waveguides. By selecting different waveguide modes for excitation and using highly selective double-resonance excitation with two lasers, we found that the [Ti⁴⁺] concentration gradient caused by the indiffusion results in an internal E-field gradient. This translates, due to the averaging within the guided mode, into mode-dependent spectral line broadening. Received: 24 May 2001 / Published online: 23 October 2001     

钛扩散铌酸锂矩形波导中的双折射耦合对传播常数的影响

 从亥姆霍兹方程出发，得到了各向异性光波导在弱导近似下的耦合模理论。耦合系数包括偏振耦合项和双折射耦合项。并用马卡提里近似下的模式作为零级近似。用一级微扰法计算了折射率渐变分布的钛扩散铌酸锂矩形波导的传播常数。在给定参数的情况下，得到双折射项引起的传播常数的改变约为主微扰项的3%，因此双折射耦合对钛扩散铌酸锂矩形波导的性能影响不可忽略，这对设计和分析与它相关的光波导器件具有指导意义。     

Er^3＋：YAG晶体Er^3＋离子的浓度对电磁感应光透明的影响

在一个三能级模型中展示了Er^3 :YAG晶体中的Er^3 浓度对电磁感应光透明（EIT）的影响。没有耦合场时,Er^3 离子浓度在15％左右时吸收达到最大;存在共振耦合场时,Er^3 离子浓度在3％左右时透射有一个最优值。     

Method of all-optical frequency-encoded binary adder system using nonlinear waveguide and reflecting semiconductor optical amplifiers

Arithmetic and algebraic operations are the most important part of optical computation and data processing. To implement the optical logic operations, different data encoding/decoding techniques have been reported. Frequency variant encoding/decoding technique is now performing a very faithful role in this regard. Frequency is the fundamental character of any signal and it remains unaltered in reflection, refraction, absorption, etc. during propagation and transmission of the signal. This is the most potential advantage of the frequency encoding technique over any other conventional encoding techniques. Here, in our proposed scheme of addition of binary bits made of two encoded frequencies in C-band (1535-1560 nm), the conjugate beam is generated in LiNbO₃ waveguide using cascaded sum and difference frequency generation by the nonlinear interaction with a third frequency, exploiting the nonlinear response character of periodically poled LiNbO₃ waveguide. The cross-gain modulation property of reflecting semiconductor optical amplifier (RSOA) has also been exploited here for frequency conversion purposes.     

Design of tunable asymmetric directional coupler filter using periodically segmented Ti:LiNbO3 waveguides

A tunable wavelength filter is designed using Ti:LiNbO₃ asymmetric directional coupler. One arm of the directional coupler is made of continuous waveguide while the other arm is periodic segmented. This segmentation reduces the lithographic steps and hence the fabrication cost required for such asymmetric coupler based filter. The propagation constant of periodical segmented and continuous waveguides are analysed using Effective-Index-based Matrix Method. The tunability is achieved using electro-optic property of LiNbO₃.