Higher-order Transverse Modes Research Articles

Single-Mode Vertical Cavity Surface Emitting Laser via Oxide-Aperture-Engineering of Leakage of High-Order Transverse Modes

Properly designed oxide-confined vertical cavity surface emitting laser (VCSEL) allows leakage of the optical modes from the all-semiconductor core region to the selectively oxidized periphery if the orthogonality between the core mode and the modes on the periphery is broken by the oxidation-induced optical field redistribution. The leakage losses are stronger for high-order transverse modes, which have a higher field intensity close to the oxidized region. Single mode lasing in the fundamental mode can thus proceed up to large aperture diameters. The 850-nm GaAlAs thick oxide aperture VCSEL based on this concept is designed, modeled, and fabricated, showing single-mode lasing with the aperture diameters up to 5 μm. Side mode suppression ratio >20 dB is realized at the current density of ~10KA/Cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in devices with the series resistance of 90 Ω.

Very large mode area optical fiber with complex ring cores

A novel kind of single-mode large-mode-area optical fiber is presented in this paper. The proposed fiber core is composed of high-index central rod and the surrounding multilayer rings. The mode characteristics are discussed considering the fiber structure parameters. The calculation results show that the proposed fiber possesses extreme large mode area of 2975μm2 with single mode operation at the wavelength of 1.08μm. Even larger mode area of the complex ring core fiber with single mode output can be achieved by coiling the fiber, due to the significant difference of bending loss between the fundamental mode and the higher-order transverse modes. Such fibers are expected to find applications in the field of fiber lasers and amplifiers.

Mode characteristics for unidirectional-emission microring resonator lasers

Mode characteristics are investigated numerically and experimentally for microring resonator lasers directly connected to an output waveguide. Optimized structural parameters are proposed for the microring resonators for realizing single-mode and unidirectional-emission operation. Finite-difference time-domain simulations indicate that the inner wall of the microring resonators introduces additional radiation loss and scattering loss, and so suppresses the higher-order transverse modes with higher field distributions in the internal region of the microrings. However, the mode Q factors can be enhanced several times for some modes with suitable inner-wall radii. AlGaInAs/InP microring lasers with inner-wall radii of 0, 5, and 7 μm and an outer-wall radius of 10 μm connected to a 2-μm-wide output waveguide are fabricated by planar techniques. Lasing spectra with longitudinal mode wavelength intervals of 11–12 nm and side-mode suppression ratios of 28–36 dB are observed, and suppression of higher-order transverse modes is achieved as the prediction of the simulation results.

Rigorous analysis of the transverse acoustic modes in optical waveguides by exploiting their structural symmetry.

A full-vectorial finite-element-based approach has been developed to find accurate modal solutions of acoustic modes in Ge-doped planar silica waveguides. The structural symmetry is exploited, and Aitken's extrapolation is also used to improve the accuracy of the solution. The spatial dependences of the dominant and nondominant displacement vectors are shown for the fundamental and higher-order transverse modes. The modal hybridness and modal birefringence between the two fundamental transverse modes are also presented.

Observation of self-mode-locking assisted by high-order transverse modes in optically pumped semiconductor lasers

The criterion for achieving the self-mode-locking (SML) in an optically pumped semiconductor laser (OPSL) with a linear cavity is systematically explored. Experimental results reveal that the occurrence of SML can be assisted by the existence of high-order transverse modes. Numerical analysis is performed to confirm that the critical pump power for obtaining the SML operation agrees very well with the pump threshold for exciting TEM1,0 mode. The present finding offers an important insight into laser physics and a useful indication for obtaining the SML operation in OPSLs.

Combination of Transverse Mode Selection and Active Longitudinal Mode-Locking of Broad Area Semiconductor Lasers

Experimental results of the combination of transverse mode selection and active mode-locking with anti-reflection-coated broad area lasers (BALs) are presented. The BALs are subject to feedback from a free-space external Fourier-optical 4f-setup with a reflective spatial frequency filter in the Fourier-plane for transverse mode selection. Driving the BALs with a high frequency modulated pump current above threshold active longitudinal mode-locking is achieved. Pulse durations as low as 88 ps are obtained, while the Gaussian-like fundamental or a higher order transverse mode up to mode number 5 is selected on purpose. Pulse duration and shape are nearly independent of the selected transverse mode.

Resolution enhancement of confocal microscopy by subtraction method with vector beams.

We proposed a subtraction method using vector beams for resolution enhancement in confocal microscopy. The imaging simulation revealed that the negative side lobe due to the excess subtraction resulted in the degradation of the object image. The subtraction imaging using vector beams demonstrated high spatial resolution with avoiding the negative side lobe. Further resolution enhancement beyond 100nm was predicted by using a flat-top beam obtained by the combination of beams with radial and azimuthal polarizations and a higher-order transverse mode azimuthally polarized beam without significant negative side lobe.

Temperature dependent polarization switch of 850-nm VCSELs with different apertures

Temperature greatly affects the polarization properties of VCSELs. In this paper, these polarization properties of top-emitting 850-nm VCSELs are simulated by numerical calculation and then they are verified by experimental measurement. For a 4-μm aperture VCSEL, polarization switch current reduces from 1.4 mA to 0.4 mA as the temperature increases from 273 K to 323 K, which is caused by the change of the reflectivity of DBR and differential gain for LP01 transverse-mode. For VCSELs with 8-μm aperture, the first polarization switch current reduces from 2.1 mA to 0.8 mA as temperature increases from 273 K to 313 K. However, the second polarization switch current increases from 3.8 mA to 6.3 mA for the same increase in temperature because of the competition and polarization selection among several higher-order transverse modes. When the device aperture is further increased to 12 μ mo r 16μm, there are several high-order transverse modes emitting even at small injection current, resulting in a serious competition and selection among themselves. This is why the polarization characteristics of VCSELs with 12 μm or larger aperture are irregular and different from those of smaller aperture devices. Our research results provide useful guidelines for the application of VCSELs operating at different ambient temperatures.

Inverted-relief cavity used in VCSELs to suppress higher-order transverse modes

One of the most acute VCSEL disadvantages is an excitation of higher-order transverse modes in devices emitting more intense radiation. The paper presents results of simulation of VCSEL performance with the aid of the inverted-relief cavity used to suppress those modes. This suppression method is very efficient and relatively simple from technological point of view, so it is worth to be recommended. Full Text: PDF References C. Jung, R. J&auml;ger, M. Grabherr, P. Schnitzer, R. Michalzik, B. Weigl, S. M&uuml;ller, K.J. Ebeling, "4.8 mW singlemode oxide confined top-surface emitting vertical-cavity laser diodes", Electron. Lett. 33, 1790 (1997). CrossRef W. Nakwaski, "VCSEL structures used to suppress higher-order transverse modes", Opto-Electr. Rev. 19, 119 (2011). CrossRef R. Sarzała, T. Czyszanowski, M. Wasiak, M. Dems, Ł. Piskorski, W. Nakwaski, K. Panajotov, "Numerical Self-Consistent Analysis of VCSELs", Adv. in Opt. Techn. (2012). CrossRef H. Martinsson, J.A. Vuku&scaron;ič, A. Larsson, "Single-mode power dependence on surface relief size for mode-stabilized oxide-confined vertical-cavity surface-emitting lasers", IEEE Photon. Technol. Lett. 12, 1129 (2000). CrossRef H.J. Unold, S.W.Z. Mahmoud, R. J&auml;ger, M. Grabherr, R. Michalzik, K.J. Ebeling, "Large-area single-mode VCSELs and the self-aligned surface relief", IEEE J. Sel. Top. Quantum Electron. 7, 386 (2001). CrossRef D. Supper, J. Pfeiffer, M. Ilzh&ouml;fer, Ch. Giuliani, Ch. Degen, A.P. Lima, A. Ramakrishnan, G. Ebbinghaus, G. Steinle, "Long-wavelength VCSEL with integrated relief for control of singlemode emission", Opt. Comm. 267, 447 (2006). CrossRef

Klystron Output Circuit of High Order Transverse Magnetic Mode in Coaxial Cavity Loaded with Waveguide Filter

摘要: 该文设计了工作于高阶横磁TM310模式单间隙封闭圆柱同轴腔。在输出矩形波导内设计了横向电感滤波膜片的新型结构。用模拟场分析法计算了腔内6个漂移管中心处间隙阻抗平均值的频率特性。模拟和计算发现，该结构模式输出回路的间隙阻抗平均值随频率的变化出现双峰曲线。这表明，采用滤波膜片波导的输出带宽比采用空波导情形的带宽有明显的增加。 关键词: 多注速调管 / 同轴谐振腔 / 高阶横磁模 / 间隙阻抗 / 输出带宽 / 滤波器加载输出回路

Resonances of three transverse standing-wave modes in a waveguide with periodic wall undulations

Interactions of three transverse modes are investigated in a waveguide with periodic walls. Resonances of two guided wave modes always result in forbidden bands for wave propagations when the wavenumber matching conditions are satisfied. As a third mode is involved due to the selected wall corrugations, we find that a single high-order mode can penetrate through the forbidden band based on the complex interactions. A method for generating a single high-order transverse mode is proposed by manipulating the multimode interactions. The numerical simulations on acoustic waveguides, showing the extreme suppression of the unwanted modes in the Bragg and non-Bragg gaps, demonstrate the validity and the efficiency of the proposed method.

Mode Regulation of Terahertz Waves Based on Periodically Corrugated Metallic Tubes

Here, we propose a special type of wall corrugations of metallic waveguides to realize mode regulation in bandgaps. The selected tube structures result in the transparency of forbidden bands to the high-order transverse mode. Complex interactions between guided wave modes attenuate all undesired modes and enhance the development of the left perfect one. The numerical simulations show that a single high-order mode can be generated efficiently in the stop band and a special terahertz beam can be obtained with wanted transverse distributions of electromagnetic fields. In addition, the proposed mode interactions can offer potential applications to the future terahertz devices.

Cavity length measurement: bias from misalignment and mismatching

SR-POEM, the sounding rocket principle of equivalence measurement, uses a set of six tracking-frequency laser gauges operating in Fabry-Perot cavities to determine the relative acceleration of two test masses (TMs) that are chemically different. One end of each cavity is a flat mirror on a TM; the other end is a concave coupling mirror mounted to a common reference plate. The tracking-frequency laser gauges work by locking a variable frequency laser to the cavity by the method of Pound, Drever, and Hall. Because the TMs are unconstrained, they are expected to rotate slightly during measurement. Although the distance measurements are intended to be based on the TEM₀₀ cavity mode, any misalignment will couple into higher-order transverse modes, particularly the TEM₁₀ and TEM₀₁. Light thus coupled will contribute a spurious signal to the cavity locking servo that causes a bias (i.e., a systematic error) in the length determination. The spurious signal proportional to the misalignment has an antisymmetric distribution at the detector and thus has a zero average, but causes a distance bias because of the inhomogeneity of the detector responsivity. To prevent such bias, SR-POEM includes a servo to keep the incoming laser beam aligned with the cavity. The required performance of that alignment servo is less stringent than has already been achieved by other projects. There is also a spurious signal proportional to the square of the misalignment that produces a symmetric distribution at the detector. This signal is also made unimportant by the operation of an alignment servo, even when operating well above the shot noise limit. We also look at the locking of a laser to a high finesse cavity and conclude that the alignment quality sets a bound on the ratio of measurement accuracy to cavity linewidth.

Transverse mode discrimination in long-wavelength wafer-fused vertical-cavity surface-emitting lasers by intra-cavity patterning

Transverse mode discrimination is demonstrated in long-wavelength wafer-fused vertical-cavity surface-emitting lasers using ring-shaped air gap patterns at the fused interface between the cavity and the top distributed Bragg reflector. A significant number of devices with varying pattern dimensions was investigated by on-wafer mapping, allowing in particular the identification of a design that reproducibly increases the maximal single-mode emitted power by about 30 %. Numerical simulations support these observations and allow specifying optimized ring dimensions for which higher-order transverse modes are localized out of the optical aperture. These simulations predict further enhancement of the single-mode properties of the devices with negligible penalty on threshold current and emitted power.

Spontaneous picosecond pulse generation in a diode-pumped Nd:YAP laser

We present the first observation, to the best of our knowledge, the spontaneous generation of picoseconds pulse trains in a diode-pumped Nd:YAP laser with gigahertz repetition rate. Spatially dependent temporal dynamics were experimentally observed. After theoretically reconstruct the experimental temporal-resolved patterns, we verify that the complicated spatially-dependent temporal dynamics were originated from simultaneous coherent locking combination of fundamental and several additional higher-order transverse modes.

Publisher's Note: “Precision measurement of single atoms strongly coupled to the higher-order transverse modes of a high-finesse optical cavity” [Appl. Phys. Lett. 103, 083117 (2013)

First Page

Precision measurement of single atoms strongly coupled to the higher-order transverse modes of a high-finesse optical cavity

We have experimentally demonstrated the strong coupling between single atoms and the higher-order Hermite-Gaussian transverse modes in a high-finesse optical microcavity. Compared to the usual low-order symmetric transverse modes, multiple lobes and the asymmetric spatial pattern of the titled modes provide more information about the motion of single atoms in the cavity. The motional information can be extracted from the measured transmission spectra, which includes the velocities and the positions of the atoms in vertical and off-axis directions. The scheme has great potential in time-resolved atom-cavity microscopy and in tracking the three-dimensional single atom trajectory in real time.

Mode Analysis for Unidirectional Emission AlGaInAs/InP Octagonal Resonator Microlasers

We investigate mode characteristics for octagonal resonator microlasers directly connecting an output waveguide. The threshold current of 8 mA at 286 K and single-transverse-mode operation are realized for an octagonal resonator microlaser with a side length of 10.8 μm and a 2-μm-wide vertex output waveguide. The laser spectra of multiple longitudinal modes with mode wavelength intervals of 7-8 nm are observed accompanied with three weak, higher order transverse modes. Furthermore, blueshift of mode wavelength versus the injection current around the threshold current and the far-field patterns are measured and discussed. In addition, the mode characteristics of the octagonal microresonators are simulated by the two-dimensional finite-difference time-domain technique. Two sets of high- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> longitudinal modes are observed experimentally and numerically, for the octagonal resonators with the output waveguide connected to the vertex and the midpoint of one side of the resonators, respectively.

Natural Frequencies and Mode Shapes of Laminated Composite Skew Hypar Shells with Complicated Boundary Conditions Using Finite Element Method

In the present investigation, free vibration behaviour is studied for the laminated composite skew hypar shells having twist radius of curvature. A higher-order shear deformation theory is employed in the C0 finite element formulation. Higher-order terms in the Taylor’s series expansion are used to represent the higher-order transverse cross sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effect of transverse shear. The structural system is considered to be undamped. The correctness of the formulation is established by comparing the present results of problems with those available in the published literature. The effects of different parameters are studied on the free vibration aspects of laminated composite skew hypar shells. Effect of cross curvature is included in the formulation. The C0 finite element formulation has been done quite efficiently to overcome the problem of C1 continuity associated with the HSDT. The isoparametric FE used in the present model consists of nine nodes with seven nodal unknowns per node. Since there is no result available in the literature based on HSDT on the problem of free vibration of laminated composite skew hypar shells, new results are presented by varying geometry, boundary conditions, ply orientations and skew angles which will serve as benchmark for future researchers.

Photonic generation of high-frequency microwave signals utilizing a multi-transverse-mode vertical-cavity surface-emitting laser subject to two-frequency orthogonaloptical injection

We study photonic microwave signal generation obtained when single- and multi-transverse-mode vertical-cavity surface-emitting lasers (VCSELs) are subject to two-frequency orthogonal optical injection. Our calculations show that broadly tunable microwave signals can be obtained in these systems. The response of the multi-transverse-mode VCSEL is enhanced with respect to that obtained with a similar single-transverse-mode VCSEL subject to the same two-frequency orthogonal optical injection. The extra degree of freedom given by the multi-transverse-mode operation of the VCSEL under two-frequency orthogonal optical injection enhances the performance of the photonic microwave generation system, because the higher-order transverse mode is excited with a much larger amplitude than that of the fundamental transverse mode. Periodic oscillations are obtained for a very wide range of frequency detunings between the optical injections and transverse modes. A relative maximum of the microwave signal amplitude is obtained when the frequency of one of the optical injections is very close to the frequency of the orthogonally polarized fundamental mode of the VCSEL. Periodic oscillations are demonstrated for symmetric and asymmetric values of the injection strengths. Wide tuning ranges, extended into the THz band, are obtained in our system. Our results show that the proposed microwave signal generation mechanism is independent of the polarization of the master lasers.