Three-mode coupling in a passive dielectric waveguide with index modulation

The characteristics of a three-mode coupling in a passive dielectric waveguide are investigated for the case of even TE modes. The index is assumed to have a doubly periodic harmonic variation in the propagation direction. By a singular perturbation procedure using multiple space scales, the coupled-mode equations governing the Bragg interactions are systematically deduced. The three-mode coupling causes a stop band in frequency and the characteristics of the resulting evanescent mode are analyzed. For a periodic dielectric waveguide of finite length, the three coupled-mode equations are solved subject to suitable boundary conditions to obtain the reflection and the transmission coefficients. The frequency response of the reflection and the transmission coefficients are investigated and compared with the results of the pair of corresponding two-mode couplings. Representative numerical results are presented to illustrate the characteristics of the interaction of the three modes.     

Stability of higher-order bragg interactions in active periodic media

The stability of waves in unbounded, longitudinally periodic media is studied for index and gain coupling. Time-independent periodic media are found to support both stable and absolutely unstable waves. The wave characteristics depend upon average gain or loss, coupling type, and Bragg order. The extended coupled waves (ECW) equations provide explicit values of threshold, frequency, and temporal growth rate for instabilities at all Bragg resonances through the dispersion relation. The first and second Bragg resonances are studied in detail since they are the archetypes for all odd and even resonances. Applications to multiharmonic periodicities and complex couplings are briefly discussed with particular not taken of possible reductions of the stability thresholds and removal of threshold degeneracies. Comparisons are made to the longitudinally bounded case of distributed feedback (DFB) lasers.     

Modal analysis of a super-elliptical Bragg waveguide with a small number of periodic cladding layers based on a very simple analytical technology

Using a simple matrix method and replacing the boundary condition by a matrix equation, the characteristic equation of an unconventional Bragg waveguide, namely a super-elliptical Bragg waveguide, has been obtained analytically. Computed results are shown in the form of dispersion curves and are compared with the dispersion curves of a standard step index fiber and a standard Bragg fiber having circular core [V. Singh, B. Prasad, S.P. Ojha. Analysis of the modal characteristics of a Bragg fiber with a small number of claddings using a very simple analytical approach, Microw. Opt. Technol. Lett. 46 (2005) 271-275 [1]]. It is seen that the correspondence between the cutoff values for the standard step index fiber and the new super-elliptical Bragg fiber is quite close for the lowest mode under the weak guidance condition.     

硅基拉曼放大器增益的理论分析

提出了硅波导中受激拉曼散射信号光获得正增益的理论分析方法,并对关键参量自由载流子寿命和抽运光功率做了分析,得到了可以获得正增益的自由载流子寿命阈值公式,抽运光功率阈值.研究了抽运方式对于硅基拉曼放大器增益的影响,并指出采用双向抽运方式可以使拉曼增益大大提高. 关键词： 硅基放大器 拉曼放大器 抽运方式     

Low threshold gain metal coated laser nanoresonators

We introduce a low refractive index layer between the metal and the gain medium in metal-coated laser resonators and demonstrate that it can significantly reduce the dissipation losses. Analysis of a gain medium waveguide shows that for a given waveguide radius, the low index layer has an optimal thickness for which the lasing threshold gain is minimal. The waveguide analysis is used for the design of a novel three-dimensional cylindrical resonator that is smaller than the vacuum wavelength in all three dimensions and exhibits a low enough threshold gain to lase at room temperature.     

Modulational instability in one-dimensional saturable waveguide arrays: Comparison with Kerr nonlinearity

Discrete modulational instability within the first band of uniform one-dimensional waveguide arrays possessing a saturable self-defocusing nonlinearity is investigated in detail within the coupled mode approach. Explicit analytical results for both the threshold and the maximal gain of instability are compared with the corresponding data from waveguide arrays exhibiting Kerr nonlinearity. We find that saturation bounds the interval of existence of discrete modulational instability, stabilizes the frequency region of perturbations around ±π/2 and decreases both gain and critical spatial frequency of perturbations.     

四层不对称波导的一些近似关系式

本文在四层不对称波导的归一化电场方程和本征方程基础上,导出了归一化有效折射b表达式和限制因子Γ_x等的近似关系式,并提出了不对称近场和远场高斯分布的近似表达式。应用上述分析,研究了四层不对称波导的动态特性。文中导出了注入载流子分布,增益分布的解析表达式,可方便地计算模增益,阈值电流密度,最佳有源区厚度和最佳阈值电流密度。并进一步研究了结构参数对器件的影响。 关键词：     

Second-order bragg interaction in double grating couplers: TM mode

An analytical treatment of the second-order Bragg interaction is presented for the transverse magnetic mode of a dielectric film waveguide having gratings on both the film-cover and the film-substrate interfaces. Four canonical equations that describe the interactions of two guided waves propagating in the opposite directions in the film and the normally incident and radiated free waves in the cover and the substrate are deduced.     

Stable high-power TE01 gyro-TWT amplifiers

The stability of high power gyro-TWT amplifiers operating in the low-loss TE₀₁ mode of cylindrical waveguide has been studied, Linear theory has been used to determine the threshold start-oscillation beam current for absolute instability in the operating mode and the critical section lengths for the dominant gyro-BWO interactions occurring at various cyclotron harmonics in other waveguide modes. The performance of the amplifier was evaluated with a nonlinear, self-consistent slow-timescale simulation code. Utilizing interaction sections whose lengths are less than the threshold start-oscillation length and are separated by attenuating severs for isolation, two stable three-section devices have been designed which are predicted to yield: (1) a peak output power of 230 kW at 35 GHz with an efficiency of 23%, a saturated gain of 46 dB and a constant-drive bandwidth of 6% for a 100 kV, 10 A electron beam with an α=ν_⊥ /ν_z =1.0 and an axial velocity spread Δν_z/ν_z=5% and (2) 105 kW at 94 GHz with 21% efficiency, 45 dB saturated gain and 5% constant-drive bandwidth for a similar 5 A electron beam. In addition, the design of the 0 dB input/output couplers and the MIG electron gun are given. Due to the low loss of the TE₀₁ mode, both of these amplifiers can be operated continuously     

Self-aligned Coupled Waveguide Distributed Bragg Reflector Lasers

A novel self-aligned coupled waveguide (SACW) multi-quantum-well (MQW) distributed Bragg reflector (DBR) laser is proposed and demonstrated for the first time. By selectively removing the MQW layer and leaving the low SCH/SACW layer the Bragg grating is partially formed on this layer. By optimizing the thickness of the low SCH/SACW layer, a～80% coupling efficiency between the MQW gain region and the passive region are obtained. The typical threshold current of the SACW DBR laser is 39 mA, the slope efficiency can reach to 0.2 mW/mA and the output power is more than 20 mW with a more than 30dB side mode suppression ratio.     

Self-aligned Coupled Waveguide Distributed Bragg Reflector Lasers

A novel self-aligned coupled waveguide (SACW) multi-quantum-well (MQW) distributed Bragg reflector (DBR) laser is proposed and demonstrated for the first time. By selectively removing the MQW layer and leaving the low SCH/SACW layer the Bragg grating is partially formed on this layer. By optimizing the thickness of the low SCH/SACW layer, a-80% coupling efficiency between the MQW gain region and the passive region are obtained. The typical threshold current of the SACW DBR laser is 39 mA, the slope efficiency can reach to 0.2 mW/mA and the output power is more than 20 mW with a more than 30dB side mode suppression ratio.     

窄带高反射光纤布拉格反射滤波器

利用改进的非对称六层波导模型，分析了光纤布拉格反射滤波器的特性。讨论了波导结构参数－主要是高折射率层的厚度对器件特性的影响，指出了在制作过程中控制器件反射率的途径。     

Effect of plasma on modal dispersion characteristics of elliptical Bragg waveguide

In this paper, the dispersion characteristics of a plasma filled elliptical Bragg waveguide is investigated. The modal characteristic equations of the proposed Bragg waveguide for both ω > ω_p and ω < ω_p are derived. The effects of plasma frequency, numbers of cladding layers and the eccentricity of elliptical Bragg waveguide on the dispersion characteristics are studied. The analysis shows that the introduction of plasma in the proposed waveguide allows to control the propagation of modes.     

Instability of wave packets in nonlinear inhomogeneous waveguides

Conditions for modulation instability of a wave packet to occur in cubically nonlinear single- and double-mode waveguides with various distributions of dispersion parameters over the waveguide length are investigated. Analytical expressions are obtained for the integral gain increment and other characteristics governing the modulation instability dynamics. Features of the dynamics are revealed using numerical simulation.     

Mathematical analysis of the lasing eigenvalue problem for the optical modes in a layered dielectric cavity with a quantum well and distributed Bragg reflectors

Optical modes and associated linear threshold values of material gain bringing them to lasing are investigated for a VCSEL-type cavity with a quantum well, sandwiched between two distributed Bragg reflectors. They are found as solutions to a specific novel eigenvalue problem with the “active” imaginary part of the quantum well refractive index. For the calculation of the Bragg mirror reflection coefficients, well-established method of the transfer matrices is used. The presented results accurately quantify intuitively predictable lowering of the modal thresholds for the modes whose lasing frequencies lay inside the reflectors rejection bands. Besides, they demonstrate that this approach automatically incorporates the account of overlapping between the active region and the modal E-field patterns and its effect on the thresholds.     

Computing Eigen value equation and modal dispersion characteristics of an elliptical Bragg waveguide

Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a new type of Bragg waveguide having elliptical core cross section with multilayered cladding is derived. The eigen equation is written in the form of Mathieu and the modified Mathieu functions and a dispersion relation is obtained for various modes supported by the proposed Bragg waveguide. The cutoff frequencies for several lower order even-odd modes have been calculated and their propagation characteristics are plotted. The results show that the dispersion curves are discontinuous and modes can exist only in particular wavelength bands. The effects of elliptical eccentricity on the mode cutoff values and mode transmission are addressed. Finally, the modal birefringence in the said waveguide is also estimated.     

Collisions between discrete spatiotemporal Ginzburg-Landau solitons

We report systematic results of collisions between discrete spatiotemporal Ginzburg-Landau solitons in waveguide arrays. Depending on the value of the kick parameter (collision momentum), four generic outcomes are identified in the case of collision of two identical solitons located at equal distances from the edge of the waveguide array: (a) merger of the solitons into a single one, at small values of the kick parameter, (b) creation of an extra soliton at intermediate values of the collision momentum, (c) quasi-elastic interactions at both intermediate values of the kick parameter (for relatively small values of the cubic gain) and at large values of the kick parameter (for relatively high values of cubic gain), and (d) soliton spreading at relatively large values of the collision momentum but only in the case of relatively small values of the cubic gain. In the case of collision of two non-identical solitons located at different distances from the edge of the waveguide array four generic outcomes were identified too: (e) soliton bouncing, accompanied by a sharp modification of soliton velocities during the interaction process, for relatively small values of the collision momentum, (f) soliton creation at intermediate values of the kick parameter and for relatively low values of the cubic gain, (g) soliton spreading (in time) at intermediate values of the collision momentum and for relatively high values of the cubic gain, and (h) quasi-elastic interactions at large values of the the kick parameter.     

Femtosecond laser direct writing of multiwavelength Bragg grating waveguides in glass

Novel Bragg grating waveguide structures have been fabricated in bulk borosilicate glass through a type II photosensitivity mechanism driven by single femtosecond laser pulses. Low-loss single-mode waveguides and narrow-linewidth Bragg gratings were generated simultaneously by forming an array of refractive index voxels in a single laser scan. Laser pulse duration is shown to significantly affect the grating strength and waveguide loss. Bragg wavelengths, defined by the periodicity of laser-modified volumes, were fully controlled by the sample scan speed to provide resonances anywhere in the 1200-1620 nm telecommunication bands. Four linear Bragg filters with distinct resonant wavelengths are presented that define the first demonstration of laser writing of multiple-wavelength and cascaded Bragg grating waveguides in a single process step.     

Tamm States in Bragg Heterostructures on Waveguide Slot Lines

Tamm surface states are experimentally studied and calculated for a Bragg heterostructure consisting of two groups of periodic fragments of waveguide slot transmission line with finite sizes. The Tamm surface states are not observed in a perfect Bragg heterostructure. The Tamm surface states emerge in the presence of an interface element at the interface of two Bragg structures when the characteristics of the element differ from the characteristics of both Bragg structures.     

Fundamental losses in planar Bragg waveguides

This paper considers a planar Bragg waveguide. The guided modes and their dissipation due to the fundamental absorption are described. In the interacting-wave approximation, an analytical relation between the characteristics of the modes and parameters of the Bragg-waveguide geometry was established. Absorption losses in hollow Bragg waveguides were shown to be significantly lower than in a regular waveguide fabricated from the same material. Quantitative estimates of the fundamental and radiation losses in Bragg waveguides are given for materials used at wavelengths of 1.55, 10.6, and 0.245 μm.