Modelization of the whispering gallery mode in microgear resonators using the Floquet-Bloch formalism

In this paper, a two-dimensional (2-D) method describing the whispering gallery mode in a microgear resonator is presented. The microgear is a microdisk surrounded by a circular grating. The method, which is based on the Floquet-Bloch formalism, analytically describes the field within the disk and outside the grating. On the other hand, the field within the grating is calculated using a finite-difference scheme in polar coordinates. Matching the boundary conditions, it is possible to work in a forced oscillation regime or in a free oscillation regime (laser mode). The resonant wavelength and quality factor can then be deduced. Compared to the coupled mode theory and to 2-D finite-difference time-domain computations, the method is faster and more accurate. Moreover, a polarization effect of the microgear is demonstrated. The TE polarization experiences a Q-factor improvement contrary to TM polarization. Finally, microgear structures prove to be more efficient than micro flowers.     

Tunneling injection quantum-dot lasers with polarization-dependent photon-mediated carrier redistribution and gain narrowing

A theoretical and experimental study of a particular transverse-electric (TE) mode lasing mechanism of a tunneling injection InP quantum-dot (QD) laser is reported. In the experiment, the TE mode lasing action takes place at the first excited state of InP biaxially compressively strained QDs. This QD state is coupled to the ground state of two tensile-strained InGaP quantum wells (QWs) although the tensile-strained QW structure favors the transverse-magnetic (TM) polarization light emission. The measured TE and TM modal gain spectra show a typical QW gain evolution behavior at low injection currents, which can be theoretically modeled by the quasi-equilibrium of carrier distribution. When the injection current is increased near threshold, a TE gain narrowing and a simultaneous TM gain pinning are observed in the measured modal gain spectra, which cannot be explained via the quasi-equilibrium model. We propose a polarization-dependent photon-mediated carrier redistribution in the QD-coupled-QW structure to explain this TE and TM gain evolution behavior. When the injection current is just below threshold, the strong carrier depletion via stimulated emission due to coupling between the InP QD and InGaP QW states plays an important role in carrier redistribution, which depends on the optical transition energy and polarization. This concept of the polarization-dependent photon-mediated carrier redistribution explains the TE gain narrowing and TM gain pinning behavior. In addition, a coupled rate equation model is established, and the calculated polarization power ratio based on the coupled rate equations explains the experimental observation.     

基于两次衰减全反射结构的激光偏振控制器

为了实现激光偏振态的控制和提高两偏振态消光比,用由各向异性材料加工而成的耦合棱镜并采用两次衰减全反射方法,使具有相同入射角的TE和TM偏振态的共振激发条件不同,即当TE偏振态满足共振激发条件能量耦合进波导时,TM偏振态却不满足共振激发条件而被反射来实现其在空间上的分离.同时将电光系数较大、光学性能和热稳定性好的聚合物材料作为波导层,利用其电光效应来改变共振条件来实现输出光束偏振态的调谐.结果表明,反射型结构插入损耗小于0.2dB,器件的消光比高达27dB,驱动电压为19V.该方案预计在光信息存储、光路由、光开光以及图像处理等光学系统里有着极其广泛的应用.     

杂质吸收对光子晶体缺陷模偏振态的影响

引入复折射率并利用特征矩阵法,研究了杂质的吸收对TE波和TM波缺陷模透射峰的影响.得出:杂质的消光系数对TE波和TM波的缺陷模透射峰都有显著的影响,但对TE波缺陷模的影响比对TM波缺陷模的影响更为明显.当消光系数一定时,TE波的缺陷模透射峰随入射角的增大而迅速减小,而TM波的缺陷模透射峰随入射角的增大而增大.利用这一特性可以设计光子晶体偏振滤波器.     

Polarization properties of a fiber to planar waveguide couplerincorporating a thin metal layer

A fiber to planar waveguide coupling structure incorporating a thin metal layer is described. The resonant wavelengths for the TM polarization were found to be highly sensitive to the refractive index of the superstrate material while those for the TE polarization were unaffected. A theoretical model for the multilayer structure was developed on the basis of a matrix method approach and a preliminary analysis of the resonance shift phenomena for the TM mode shows good agreement with experiment     

Non-polarization and high-coupling-efficiency coupler using multilevel grating structure

A multilevel grating coupler based on silicon-on-insulator (SOI) material structure is proposed to realize the coupling between waveguide and waveguide or waveguide and fiber. This coupler is compatible with the current fabrication facilities for complementary metal oxide semiconductor (CMOS) technology with vertical coupling. This structure can realize coupling when the beams with transverse electric (TE) polarization and transverse magnetic (TM) polarization are incident at the same time. The influences of the grating coupler parameters including wavelength, the thickness of waveguide layer, the thickness of SiO₂ layer and the number of steps on the TE mode and TM mode coupling efficiencies are discussed. Theory researches and simulation results indicate that the wavelength range is from 1533 nm to 1580 nm when the TE mode and TM mode coupling efficiencies are both more than 40% as the grating period is 0.99 μm. The coupling efficiencies of the incident TE and TM modes are 49.9% and 49.5% at the wavelength of 1565 nm, respectively, and the difference between them is only 0.4%.     

含负折射率光子晶体缺陷模偏振态的吸收特性

为了研究含负折射率掺杂光子晶体各缺陷模偏振态的吸收特性,引入复折射率并利用光学特征矩阵法进行分析,结果表明：杂质的消光系数对TE波和TM波的缺陷模均有影响,但对TE波的影响更为明显;当消光系数一定时,对TE波而言,中心波长相对较大的两个缺陷模透射峰值均随入射角的增加而迅速减小,而TM波的三个缺陷模透射峰均随入射角的增加而增加。利用这一特性可以设计双（多）通道光子晶体偏振滤波器。     

An analysis of intersecting diffused channel waveguides

The coupling characteristics of intersecting diffused channel waveguides are computed for realistic three-dimensional diffusion profiles by means of the propagating beam method (PBM). Both TE and TM polarizations are treated for waveguides formed onz-cut LiNbO3. Good agreement between computed and previously reported measured results is found for the TE polarization. Agreement between computed and measured results is not as good for the TM polarization. This is explained by the fact that the applicable2Deltan-waveguide supports four modes, which should make coupling characteristics very sensitive to input conditions.     

Push-pull polarization conversion using novel asymmetric coupled quantum-well structures

A novel type of polarization conversion modulator, employing multiple repetitions of two novel InGaAlAs-InAlAs asymmetric coupled quantum-well structures, is proposed. The novelty of the proposed design is that, via the electrorefraction effect, it allows for a change in the TM mode's effective refractive index, which is opposite in sign to the change in the TE mode's effective refractive index. Numerical simulations based on the effective-mass envelope-function approximation show that the modulator provides not only an electrorefractive response similar to other quantum-well modulators but can also provide a low-chirp push-pull polarization modulation.     

High-power TE11 and TM11 circular polarizers in oversized waveguides at 70 GHz

Elliptical deformation of oversized, smooth-wall circular waveguides can produce choosable elliptical or circular polarization from a linearly polarized TE11 or TM11 mode used as intermediate linearly polarized modes in TEO1 to HE11 mode conversion sequences in electron cyclotron resonance heating (ECRH) of magnetically confined thermonuclear fusion plasmas with high-power gyrotrons. Mode coupling in elliptically distorted overmoded circular waveguides has been studied theoretically and experimentally in order to optimize TE11 (and TM11) polarizers (I.D.=27.79 mm) for the 1 MW/70 GHz long-pulse (3s) ECRH system on the Garching Stellarator W VII-AS. Coupling coefficients for ellipticity coupling of non-degenerate modes are given (coupled-mode differential equations formalism). The polarization converters essentially consist of smooth-wall circular waveguides which are gradually squeezed. A sine-squared function of the length coordinate is used to get an almost elliptical crosssection in the middle and circular cross sections at both ends. Arbitrary elliptical polarization states can be generated introducing an extremely low level (<<1%) of undesired spurious modes. Well defined differential phase characteristics have been achieved.     

A polarization independent GaAs-AlGaAs electrooptic modulator

Two designs for polarization independent GaAs-AlGaAs interferometric electrooptic modulators are described. One design uses the linear electrooptic effect to couple degenerate TE/TM eigenmodes of a single-mode waveguide. In the other design the eigenmodes need only be near degenerate. The design using the coupling between near degenerate TE/TM modes utilizes a novel biasing scheme. A novel polarization independent GaAs-AlGaAs interferometric optical modulator based on this design has been fabricated and characterized at 1.3 μm. This modulator is fabricated as a traveling wave modulator incorporating 50 Ω, phase velocity matched, low microwave loss electrodes for maximum electrical bandwidth     

Gain saturation properties of a semiconductor gain medium withtensile and compressive strain quantum wells

Gain saturation properties of a multiple-quantum-well structure with both tensile and compressively strained quantum wells are investigated analytically. This type of structure has recently been experimentally demonstrated to serve as a basis for the implementation of a two-polarization/two-frequency laser and polarization insensitive travelling wave(TW) amplifier. The performance of these devices strongly depends on the interaction between the TE and TM gains of the structure. The gain medium model appropriate for this type of structure is developed and the rate equation approach is used to describe the saturation properties of TE/TM gains and the coupling between the TE and TM gains due to gain saturation. The minimum amount of coupling between the two is governed by the basic symmetry of the light-hole wavefunction which interacts with photons of both polarization: photon cross-coupling. The finite rate of carrier escape from the quantum wells provides for carrier induced coupling between the populations of the two well types and therefore also couples TE and TM gains: carrier cross-coupling. The performance of a polarization insensitive amplifier, laser, and polarization control element is evaluated as a function of the amount of carrier cross-coupling, which is a structure dependent parameter. A structure with high degree of cross-coupling is desirable for polarization insensitive TW amplifier, while two-polarization lasers and polarization control elements require minimum cross-coupling     

多量子阱有效折射率偏振相关性研究

分析了多量子阱材料各参数对其TE模和TM模有效折射率的影响。结果表明:阱数增多,多量子阱有效折射率降低,当量子阱数目大于3时,其有效折射率的变化不明显。垒厚增加,有效折射率略有降低。存在合适的张应变量使TE模和TM模有效折射率峰值波长接近的同时,折射率差值整体最小,偏振相关性最小。据此提出多量子阱材料有效折射率低偏振相关设计方法,并设计出C波段内(1530~1565 nm)折射率低偏振相关的InGaAs/InGaAsP多量子阱材料。研究结果有助于设计实用化的有效折射率低偏振相关量子阱材料。     

Radiation loss coefficients of asymmetric dielectric waveguides with shallow sinusoidal corrugations

Kiselev [10] has solved the boundary equations for an asymmetric slab waveguide with a shallow sinusoidal corrugation, and derived explicit, closed expressions for the TE radiation loss coefficients of various waveguide geometries. For many practical applications in integrated optics, the Rayleigh assumption justifying the boundary-matching procedure and the approximations of linear perturbation analysis employed in this derivation are both satisfied. We have extended this procedure to TM modes and found that the expressions for both TE and TM modes in all of the geometries so treated agree identically with those derived by coupled-mode theory. The dependence of the TM radiation loss coefficient in each waveguide geometry on the grating period, radiation angle, refractive index profile, and mode polarization is illustrated graphically, and compared with its TE counterpart.     

Impedance boundary method of moments for accurate and efficientanalysis of planar graded-index optical waveguides

An impedance boundary method of moments (IBMOM) is proposed to accurately and efficiently compute the propagation characteristics including the number of guided modes of general graded-index dielectric slab waveguide structures. The method is based on Galerkin's procedure in the method of moments and employs the exact impedance boundary condition at the interfaces between the graded-index region and constant-index cladding. Legendre polynomials are utilized in the field expansion. Computational results are shown for waveguides with various inhomogeneous refractive index profiles. The results indicate that typically five Legendre polynomials are sufficient for accurate solutions of the dominant TE and TM modes in optical waveguides having a finite region of inhomogeneous refractive index. Diffused optical waveguides with untruncated index profiles as well as coupled dielectric waveguides can be accurately analyzed using ten Legendre polynomials     

基于表面等离子波耦合的流体波导光栅耦合器

提出了一种由金属光栅和流体光波导结构组成的,基于表面等离子波耦合的光栅耦合器。利用光栅的衍射效应,将金属光栅与介质分界面之间产生的表面等离子波耦合到流体光波导中,并且能够沿着流体光波导稳定地向前传播。通过采用基于有限时域差分算法的FDTD Solutions软件对光栅耦合器进行了参数优化及特性分析,通过优化使该结构在650 nm波长下的耦合效率达到56%。此外,由于该结构对TE偏振光和TM偏振光的选择比达到70∶1,因此具有偏振器的功能。同时由于TE偏振光耦合频谱的频带宽度仅为20 nm,该结构还具有窄带滤波的作用。此外,还研究了光栅结构参数、入射角以及流体折射率对耦合频谱的影响。     

Polarization optical bistability induced by TM mode injection to aDFB laser with complex coupled coefficient

A novel method is proposed to produce an optical bistability by using a dynamically stable complex coupled DFB (CC-DFB) laser with TM mode injection. In this paper polarization optical bistabilities are analyzed in detail using coupled mode equations and rate equations for the CC-DFB lasers considering the longitudinal hole burning and carrier dependent complex coupling coefficients. Several parameters reflecting the physical features of a complex coupled DFB laser are discussed. It is shown that for a CC-DFB laser the polarization bistability induced by the TM mode injection is much stronger for the antiphase of complex coupling than that for the in-phase. In addition, the influences of initial coupling condition for gain grating structure on the optical bistability are also investigated considering both cases of the antiphase and in-phase     

Guided modes of a width-reduced photonic-crystal slab line-defect waveguide with asymmetric cladding

The authors fabricated GaAs-based width-reduced photonic-crystal (PC) slab line-defect waveguides with asymmetric cladding, characterized optically by broadband transmission spectral results. These waveguides were vertically sandwiched between air and oxide claddings. Transmission peaks originating from the guided mode located within the bandgap were observed, thereby showing the presence of a bandgap effect for the transverse-electric (TE)-like guided mode even with the coexistence of a fundamental transverse-magnetic (TM)-like mode. Propagation loss spectra were derived from transmission spectra for both TE and TM polarization inputs. Comparing the obtained spectra to band diagrams, the authors detected a mini-stopband effect in the transmission spectra arising from a folding of the fundamental TM-like mode at the Brillouin zone boundary. The coupling coefficient was then estimated to be /spl sim/0.01 [a/sup -1/] (with a being a lattice constant). Dips in spectral intensity were also observed and were attributed to TE-TM mode conversion based on a comparison to the band diagram.     

Accurate analysis and modeling of laminated multilayered 3-D optical waveguides

The theoretical investigation of waveguides having nonuniform cross-sections is an attractive and challenging problem which deserves serious interest. In this paper, we present a novel analysis of laminated multilayered three-dimensional waveguide, based on two modes: 1) a new coupled transmission line approach that considers the sloping of the layers along the longitudinal direction and 2) a transmission line matrix integral equation (TLMIE) modeling that complete and extends the investigation of the field propagation. In method 1), we neglect radiation modes and their EM coupling. All physical effects instead are accounted for by the full-wave TLMIE method. By using TLMIE, we validate the EM analysis and calculate TE/TM losses, arising from radiation modes.     

多孔硅/聚合物复合膜等效折射率的研究

用多孔Si（PS）圆柱空腔二维结构模型,理论研究了TE模式情况下PS／聚合物复合膜的等效折射率,给出了PS等效折射率与孔隙率和嵌入率的关系。实验采用波导耦合m线法分别研究了TE模和TM模入射情况下（633nm波长处）,孔隙率为73%的PS膜嵌入聚合物聚合基丙烯酸甲酯（PMMA）材料后的等效折射率与聚合物嵌入率的关系。理论分析与实验结果基本符合。