Application of the Beam Mode Expansion to the Analysis of Noise Reduction Structure (Short Papers)

The beam mode expansion method used to discuss the distraction problem by an aperture is applied to the analysis of the noise reduction structure consisting of two aperture stops. The incident field is a fundamental wave beam whose amplitude distribution is Gaussian. The transmitted field through the structure can be represented as a sum of beam mode functions and is regarded as a signal. The noise which is originated from the spontaneous emission is added to the incident Gaussian wave beam. The signal-to-noise ratio (SNR) in the output is discussed and optimum conditions are obtained numerically.     

A Complete Solution of the Inductive Iris with TE/sub k0/ Incidence in Rectangular Waveguide

A TE/sub k0/ wave incident on an inductive metal iris in a rectangular waveguide excites a reflected and a transmitted wave in the TE/sub k0/ mode. The reflection and transmission coefficients describing these waves are computed. In addition to the incident mode, a number of other modes are excited by the discontinuity. The amount of coupIing to these other modes, given by coupling coefficients, is determined using the variational technique. The method developed makes it possible to find the coupling to any desired mode without first finding the coupling to any other mode or group of modes. The analysis shows under what conditions certain modes can be suppressed or eliminated. The method should be applicable to other problems of interest where modes other than the incident one are excited. Since the reflection, transmission, and coupling coefficients are known, the total field at any point in the waveguide can be computed. As an example, the total field at the discontinuity when the TE/sub 10/ mode is incident is calculated. The result closely resembles the expected result (of zero electric field over the metal iris).     

Output coupling for closely confined Pb1-xSnxTe double-heterostructure lasers

The output coupling of an idealized, symmetric model of a double-heterostructure (DH) laser is analyzed theoretically using parameters suitable to Pb1-xSnxTe. For the TEOmode incident at the laser mirror and for thin optical guiding regions such that only the TEO, TE1, TMO, and TM1modes may propagate, an exact formulation of the coupling problem is obtained including mode coupling at the mirror into the continuum of unguided radiation modes. Using this formulation, the power reflection and transmission coefficients, the fraction of incident power coupled into the radiation modes, the mirror illumination, and the far-field pattern are calculated for typical parameters. Significant mode coupling can occur, limiting the maximum external efficiency of such lasers. This and other potentially undesirable characteristics resulting from close optical confinement, such as large output beam divergence, must be considered in design criteria for DH structures in this alloy system.     

Transmission of an Optical Wave Beam Through a System of Two Aperture Stops

The beam-mode expansion method used in the discussions of the diffraction of a Gaussian wave beam through an aperture is applied to a system of two circular or square aperture stops, and the analytical expressions of the power transmission and conversion coefficients of a fundamental mode through the system are obtained. By using these expressions, the optimum incidence conditions that maximize the power transmission coefficient of the fundamental mode can be known. These conditions coincide formally with those obtained by Kogelnik and Yariv for an incident wave having a prolate spheroidal-wave function distribution. Both circular and square geometries can be analyzed in the same way.     

Walk-Off Effects in Fabry-Perot Diplexers

Fabry-Perot (FP) resonators working under oblique incidence can be used in the millimeter and far infrared bands as diplexers or channel dropping filters. The response of two-grid Fabry-Perot resonators under Gaussian beam excitation is evaluated by adding the fields of the successive passes of the beam. The results coincide with those obtained from a plane wave expansion of the incident field. Closed form expressions are obtained for the losses due to diffraction walk-off, geometrical walk-off, and mismatch. Excellent agreement is obtained with experiments in the 70-80-GHz band. For a 1-GHz-bandwidth filter, working at an incidence angle of 15 degrees, and an incident beam waist radius of 40 mm, the transmission loss at resonance does not exceed 1 dB. The reflection loss off-resonance is about 0.1 dB. This type of diplexer is particularly useful when used in conjunction with quasioptical guiding systems.     

An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction

In this paper the geometrical theory of diffraction is extended to treat the radiation from apertures or slots in convex perfectly conducting surfaces. It is assumed that the tangential electric field in the aperture is known so that an equivalent infinitesimal source can be defined at each point in the aperture. Surface rays emanate from this source which is a caustic of the ray system. A launching coefficient is introduced to describe the excitation of the surface ray modes. If the field radiated from the surface is desired, the ordinary diffraction coefficients are used to determine the field of the rays shed tangentially from the surface rays. The field of the surface ray modes is not the field on the surface; hence if the mutual coupling between slots is of interest, a second coefficient related to the launching coefficient must be employed. In the region adjacent to the shadow boundary, the component of the field directly radiated from the source is represented by Fock-type functions. In the illuminated region the incident radiation from the source (this does not include the diffracted field components) is treated by geometrical optics. This extension of the geometrical theory of diffraction is applied to calculate the radiation from slots on elliptic cylinders, spheres, and spheroids.     

Following-wave amplification mode of a clinotron

The following-wave amplification mode of a model of the clinotron with linear electron trajectories is studied in the framework of linear and nonlinear theories. It is demonstrated that the clinotron effect is absent in the linear mode, since the amplification factor is maximized at zero angle between the beam and the surface of the slow-wave structure. In the large-amplitude mode, an obliquely incident beam, on the contrary, enhances the interaction efficiency. This is associated not only with the fact that partial layers of an obliquely incident beam propagate through the region where the HF field of the surface wave is largely localized, but also with weakening of nonlinear effects of bunching and energy exchange between the beam and the HF field. Comparative analysis of the efficiency of the clinotron effect in the modes of backward-wave oscillation and forward-wave amplification is performed.     

亚波长光栅的模态特性与衍射效率及其应用

采用模态理论研究了TE偏振与TM偏振入射光在一维亚波长光栅区域的模式特性,分析了不同传播模态的有效折射率及其差值与入射条件、光栅周期、光栅深度及光栅填充比之间的关系,使用干涉法得到了在考虑光栅凹槽深度的情况下两种模态的光栅衍射效率。应用亚波长光栅的模式特性与光栅衍射效率设计了一种偏振分束器,其特性是在利特罗入射的条件下,单色光波在0级衍射处为TM偏振,在-1级处为TE偏振。     

Diffraction from an abruptly terminated dielectric slab waveguide in the presence of a cylindrical scatterer

The efficiency of using an adaptor lens in front of an abruptly terminated symmetric slab optical waveguide is examined analytically in this paper. The adaptor lens is assumed to be of cylindrical shape with a constant refractive index. The coupling of the modes propagating inside the slab guide into radiation waves in the presence of the lens is treated by integral equation methods. In the first step an integral equation is derived for the Green's functionG(r/r')of an abruptly terminated slab waveguide. The integral equation is solved approximately by an iterative procedure giving accurate results when the difference of the refractive indices between the slab waveguide and substrate-cover regions is small. The Green's function is then used to formulate another integral equation for the unknown field inside the adaptor lens. The latter integral equation for the cylindrical lens cross section area is solved by adopting a cylindrical partial wave expansion for the unknown interior field. After determining this field, the reflection-coupling coefficients for the guided modes propagating in the opposite direction of the incident wave, are computed by using the Green's functionG(r/r'). Radiation patterns are also derived in the far field region for an incident slab guided mode. Numerical results are computed and presented for several guide dimensions, lens radii, and refractive indices.     

受光阑限制光束衍射场的高阶修正

为了模拟受光阑限制光束衍射场的分布,利用泰勒展开得到了一系列的高阶修正场.随着传输距离z的减少,只需增大到合适的阶数M即可模拟衍射场分布.对于不同的传输距离z,可根据不等式来选择合适的阶数M.以超高斯光束为例,用数值计算例说明理论公式的应用.所得结果对于研究通过光阑衍射光束的传输是有用的.     

Increase of Gyrotron Output Power at High-Order Axial Mode Through an After-Cavity Excitation of the Next Transverse Mode

In the experimental study on the frequency tuning of a double-beam gyrotron, an unexpected abrupt increase of the output power was observed for some magnetic field values corresponding to the excitation of high-order axial modes (HOAM). This effect can be explained through an after-cavity interaction of the spent but bunched electron beam with the neighboring transverse mode which has the same azimuthal but the next (i.e., greater by one) radial index with respect to the operating mode. The calculations show that under certain conditions the cyclotron synchronism between the electron beam and the next radial mode occurs in the extended region of an output cone, while the bunching of the spent electron beam is responsible for the excitation of this mode. The influence of some additional factors such as reflections of both modes from the output window, electron velocity spread, and magnetic field profile was studied numerically. It was shown that reflections, mode transformation, and velocity spread can enhance the effect of an abrupt power increase and reduce the starting current of the operating mode. The discovered after-cavity interaction can be either useful for a power increase at the HOAM operation of the frequency-tunable gyrotron or harmful for high cyclotron harmonic operation due to an expansion of the zone of fundamental cyclotron resonance mode excitation.

     

Three-dimensional analysis of an FEL amplifier operating with acontinuous e beam

The authors discuss a three-dimensional theory of an FEL operating with a continuous e beam. The theory is based on a generalized method of solution of the FEL Helmholtz equation in the high-gain small-signal regime. The method consists basically of expanding the optical field in terms of Hermite-Gaussian modes, taken at the entrance to the undulator. The coefficients of that expansion are expressed in the form of a superposition of plane waves with complex frequencies. As a result, one gets a set of recursive relations, partly reproducing those obtained within the context of the single-mode evolution and partly displaying the effect (revealed by a coupling among the modes) of both the diffraction and the interaction with the e-beam     

Reflection matrix for Gaussian light beams in FEL oscillators

The transformations of Gaussian radiation beams caused by reflection off mirrors is an important issue for the operation of free-electron lasers as oscillators. The reflected radiation from a single incident Gaussian mode will contain other modes due to the finite size, the deflection of the beam, and mismatches in the curvature. A method for analytic computation of the reflection matrix is developed. The mirror surface that reflects spherical incoming wavefronts into spherical outgoing is determined analytically. The cross coupling among vector components of the radiation field, caused by the curvature of the mirror surface, is included     

腔失调对模耦合的影响

综合分析了腔失配和腔失调对模耦合的影响，分别讨论了模的功率耦合系数与失配参量、失调位移及失调角的相互关系。     

双面金属包覆单轴晶体波导的偏振转换研究

利用转移矩阵方法计算了双面金属包覆单轴晶体波导结构中的色散曲线、反射谱。结果表明,双面金属包覆结构使得波导可以被自由空间光场激发;单轴晶体的光轴取向能对该结构中的波导模式进行调控,使入射光波中的Ey、Ez分量发生相互转换耦合,从而在波导层中形成杂化模。通过调节耦合金属层厚度可以对出射光偏振状态的控制,实现TE线偏振入射光向TM线偏振反射光的转换以及线偏振入射光向圆偏振反射光的转换。     

Frozen-in viscoelasticity for novel beam expanders and high-power connectors

Frozen-in viscoelasticity has a significant, yet previously overlooked, impact on the refractive index profile of optical fibers and can serve as the basis for novel fiber devices. Viscoelastic strains can be frozen into an optical fiber during draw, or by cooling down a drawn fiber from high temperature while under tension. The resulting refractive index perturbation can exceed 0.003, exhibits minimal birefringence, and is concentrated in the highest viscosity region of the fiber. We have developed a quantitative theory for the refractive index perturbation, which is in excellent agreement with measured data. We have harnessed frozen-in viscoelasticity to create novel high-performance all-fiber beam expanders achieving mode field diameters in excess of 40 /spl mu/m. These beam expanders are suitable for low-cost high-volume manufacturing and can serve as the basis for high-power single-mode fiber (SMF) connectors, since their lower power density improves reliability during high-power operation. Because of the significant reduction in free-space diffraction associated with the enlarged mode field diameter, these beam expanders may be suitable for MEMS applications, or for coupling between optical fiber terminations and optical fiber sources or detectors.     

LP01 to LP11 mode convertor based on side-polished small-core single-mode fiber

An all-fiber LP01-LP11 mode convertor based on side-polished small-core single-mode fibers (SMFs) is numerically demonstrated. The linearly polarized incident beam in one arm experiences π shift through a fiber half waveplate, and the side-polished parts merge into an equivalent twin-core fiber (TCF) which spatially shapes the incident LP01 modes to the LP11 mode supported by the step-index few-mode fiber (FMF). Optimum conditions for the highest conversion efficiency are investigated using the beam propagation method (BPM) with an approximate efficiency as high as 96.7%. The proposed scheme can operate within a wide wavelength range from 1.3 μm to1.7 μm with overall conversion efficiency greater than 95%. The effective mode area and coupling loss are also characterized in detail by finite element method (FEM).     

向列相液晶中的耦合自相位调制现象

通过实验研究了C60掺杂的向列相液晶(5CB)在低光强下的自相位调制现象。样品经过二波耦合实验之后液晶分子进行一定的取向,这时在水平和竖直偏振光的照射下可观察到明显的自相位调制现象。改变入射光的偏振方向可以看到自相位调制的衍射图样也随之改变,原因就是液晶折射率变化的各向异性。可见,液晶盒中的分子取向与光束的偏振方向有很强的依赖关系。     

Beam scattering by nonuniform leaky-wave structures

A method is presented for obtaining the scattered field due to a beam incident on a layered structure or on a dielectric grating whose properties vary slowly along a longitudinal direction. The scattered field is expressed in terms of a Green's function whose form is particularly simple for a large class of practical problems involving laser beams incident on structures capable of guiding leaky waves. The incident beam may then strongly couple to the leaky wave, thus producing a scattered field that contains a specularly reflected component and a diffracted component of the leaky-wave type. The presence of the latter component may cause the resulting scattered field to be considerably different from the field of the incident beam. A judicious choice of the leaky-wave structure can be used to produce a scattered field that exhibits any of a wide range of distributions. The method developed herein is illustrated by means of structures whose leakage-properties vary linearly. The results can be utilized either for efficiently coupling a beam into a surface wave, or for splitting the incident beam into two separate but closely similar outgoing beams, both applications being discussed in detail.     

New Results in Dielectric-Loaded Resonators

Analysis of cylindrical dielectric-loaded resonators is reviewed. The fields within the dielectric-loaded region are postulated as the superposition of hybrid, TE, or TM modes of the infinite dielectric-loaded waveguide, while the fields in the end regions of the resonators are described by the superposition of the normal modes of a homogeneously filled waveguide. Numerical results are presented which reveal that accurate representation of the fields in the resonant structure generally require several modes. Hence, the resonant modes cannot be correlated directly with single waveguide modes. A new method for mode identification is proposed. For a wide range of parameters, the resonant frequencies, mode charts, field expansion coefficients, field intensity, and distributions are presented. Excellent agreement of the mode charts with resonant frequency measurement results are obtained.