Analysis of mode characteristics for equilateral triangle semiconductor microlasers with imperfect boundaries

The influence of imperfect boundaries on the mode quality factor is investigated for equilateral-triangle-resonator (ETR) semiconductor microlasers by the finite difference time domain technique and the Pade approximation with Baker's algorithm. For 2-D ETR with a refractive index of 3.2 and side length of 5 mum, the confined modes can still have a quality factor of about 1000 as small triangles with side length of 1 mum are cut from the vertices of the ETR. For a deformed 5 mum ETR with round vertices and curve sides, the simulated mode quality factors are comparable to the measured results.

Symmetry analysis and numerical simulation of mode characteristics for equilateral-polygonal optical microresonators

Mode characteristics for two-dimensional equilateral-polygonal microresonators are investigated based on symmetry analysis and finite-difference time-domain numerical simulation. The symmetries of the resonators can be described by the point group C-Nv, accordingly, the confined modes in these resonators can be classified into irreducible representations of the point group C-Nv. Compared with circular resonators, the modes in equilateral-polygonal resonators have different characteristics due to the break of symmetries, such as the split of double-degenerate modes, high field intensity in the center region, and anomalous traveling-wave modes, which should be considered in the designs of the polygonal resonator microlasers or optical add-drop filters.

Mode analysis and Q-factor enhancement due to mode coupling in rectangular resonators

Modes in rectangular resonators are analyzed and classified according to symmetry properties, and quality factor (Q-factor) enhancement due to mode coupling is observed. In the analysis, mode numbers p and q are used to denote the number of wave nodes in the direction of two orthogonal sides. The even and odd mode numbers correspond to symmetric and antisymmetric field distribution relative to the midlines of sides, respectively. Thus, the modes in a rectangle resonator can be divided into four classes according to the parity of p and q. Mode coupling between modes of different classes is forbidden; however, anti-crossing mode coupling between the modes in the same class exists and results in new modes due to the combination of the coupled modes. One of the combined modes has very low power loss and high Q-factor based on far-field emission of the analytical field distribution, which agrees well with the numerical results of the finite-difference time-domain (FDTD) simulation. Both the analytical and FDTD results show that the Q-factors of the high Q-factor combined modes are over one order larger than those of the original modes. Furthermore, the general condition required to achieve high-Q modes in the rectangular resonator is given based on the analytical solution.

Analysis of mode characteristics for deformed square resonators by FDTD technique

The mode frequencies and quality factors (Q-factors) in two-dimensional (2-D) deformed square resonators are analyzed by finite-difference time-domain (FDTD) technique. The results show that the deformed square cavities with circular and cut corners have larger Q-factors than the perfect ones at certain conditions. For a square cavity with side length of 2 mu m and refractive index of 3.2, the mode Q-factor can increase 13 times as the perfect corners are replaced by a quarter of circle with radius of 0.3 pm. Furthermore the blue shift with the increasing deformations is found as a result of the reduction in effective resonator area. In square cavities with periodic roughness at sidewalls which maintains the symmetry of the square, the Q-factors of the whisperin gallery (WG)-like modes are still one order of magnitude larger that those of non-WG-like modes. However, the Q-tactors of these two types of modes are of the same order in the square cavity with random roughness. We also find that the rectangular and rhombic deformation largely reduce the Q-factors with the increasing offset and cause the splitting of the doubly degenerate modes due to the breaking of certain symmetry properties.

Analysis of mode quality factors and mode reflectivities for nanowire cavity by FDTD technique

The mode frequency and the quality factor of nanowire cavities are calculated from the intensity spectrum obtained by the finite-difference time-domain (FDTD) technique and the Pade approximation. In a free-standing nanowire cavity with dielectric constant epsilon = 6.0 and a length of 5 mu m, quality factors of 130, 159, and 151 are obtained for the HE11 modes with a wavelength around 375 nm, at cavity radius of 60, 75, and 90 nm, respectively. The corresponding quality factors reduce to 78, 94, and 86 for a nanowire cavity standing on a sapphire substrate with a refractive index of 1.8. The mode quality factors are also calculated for the TE01 and TM01 modes, and the mode reflectivities are calculated from the mode quality factors.

Analysis of mode quality factors for equilateral triangle semiconductor microlasers with rough sidewalls

The eigenmode characteristics for equilateral triangle resonator (ETR) semiconductor microlasers are analysed by the finite-difference time-domain technique and the Pade approximation. The random Gaussian correlation function and sinusoidal function are used to model the side roughness of the ETR. The numerical results show that the roughness can cause the split of the degenerative modes, but the confined modes can still have a high quality factor. For the ETR with a 3 mum side length and the sinusoidal fluctuation, we can have a quality factor of 800 for the fundamental mode in the wavelength of 1500 nm, as the amplitude of roughness is 75 mn.

Analysis of semiconductor microlasers with an equilateral triangle resonator by rate equations

Semiconductor microlasers with an equilateral triangle resonator (ETR) are analyzed by rate equations with the mode lifetimes calculated by the finite-difference time-domain technique and the Pade approximation. A gain spectrum based on the relation of the gain spectrum and the spontaneous emission spectrum is proposed for considering the mode selection in a wide wavelength span. For an ETR microlaser with the side length of about 5 mum, we find that single fundamental mode operation at about 1.55 mum can be obtained as the side length increases from 4.75 to 5.05 mum. The corresponding wavelength tuning range is 93 nm, and the threshold current is about 0.1 to 0.4 mA.

Analysis of the temperature-induced transition to current self-oscillations in doped GaAs/AlAs superlattices

We observed the decrease of the hysteresis effect and the transition from the stable to the dynamic domain regime in doped superlattices with increasing temperature. The current-voltage characteristics and the behaviours of the domain boundary are dominated by the temperature-dependent lineshape of the electric field dependence of the drift velocity (V(F)), As the peak-valley ratio in the V(F) curve decreases with increasing temperature, the hysteresis will diminish and temporal current self-oscillations will occur. The simulated calculation, which takes the difference in V(F) curves into consideration, gives a good agreement with the experimental results.

Analysis and numerical simulation of eigenmode characteristics for semiconductor lasers with an equilateral triangle micro-resonator

The eigenmodes confined in the equilateral triangle resonator (ETR) are analyzed by deriving the eigenvalues and the mode field distributions and by the finite difference time domain (FDTD) technique. The analytical results show that the one-period-length for the mode light rays inside the ETR is the perimeter of the ETR, and the number of transverse modes is limited by the condition of total internal reflection. In addition, the sum of the longitudinal mode index and the transverse mode index should be an even number, which limits the number of confined modes again. Based on the FDTD technique and the Pade approximation, we calculate the mode resonant frequencies and the quality factors from the local maximum and the width of the spectral distribution of the intensity The numerical results of mode frequencies agree very well with the analytical results, and the quality factor of the fundamental mode is usually higher than that of the higher order transverse modes. The results show that the ETR is suitable to realize single-made operation as semiconductor microcavity lasers.

Static and dynamic electric field domain formation in a doped GaAs/AlAs superlattice

We have observed the transition from static to dynamic electric field domain formation induced by a transverse magnetic field and the sample temperature in a doped GaAs/AlAs superlattice. The observations can be very well explained by a general analysis of instabilities and oscillations of the sequential tunnelling current in superlattices based solely on the magnitude of the negative differential resistance region in the tunnelling characteristic of a single barrier. Both increasing magnetic field and sample temperature change the negative differential resistance and cause the transition between static and dynamic electric field domain formation. (C) 2000 Elsevier Science B.V. All rights reserved.

Dynamic dc voltage band observed within each current branch in the transition from static to dynamic electric-field domain formation in a doped GaAs/AlAs superlattice

A dynamic dc voltage band was found emerging from each sawtooth-like branch of the current-voltage characteristics of a doped GaAs/AlAs superlattice in the transition process from static to dynamic electric-field domain formation caused by increasing the sample temperature. As the temperature increases, these dynamic dc voltage bands expand within each sawtooth-like branch, squeeze out the static regions, and join up together to turn the whole plateau into dynamic electric-field domain formation. These results are well explained by a general analysis of stability of the sequential tunneling current in superlattices. (C) 1999 American Institute of Physics. [S0003-6951(99)04443-5].

Analysis of directional emission in square resonator lasers with an output waveguide

Square microcavity laser with an output waveguide is proposed and analyzed by the finite-difference time-domain (FDTD) technique. For a square resonator with refractive index of 3.2, side length of 4 microns, and output waveguide of 0.4-micron width, we have got the quality factors (Q factors) of 6.7×10~2 and 7.3×10~3 for the fundamental and first-order transverse magnetic (TM) mode near the wavelength of 1.5 microns, respectively. The simulated intensity distribution for the first-order TM mode shows that the coupling efficiency in the waveguide reaches 53%. The numerical simulation shows that the first-order transverse modes have fairly high Q factor and high coupling efficiency to the output waveguide. Therefore the square resonator with an output waveguide is a promising candidate to realize single-mode directional emission microcavity lasers.

Static and dynamic electric field domain formation in a doped GaAs/AlAs superlattice

We have observed the transition from static to dynamic electric field domain formation induced by a transverse magnetic field and the sample temperature in a doped GaAs/AlAs superlattice. The observations can be very well explained by a general analysis of instabilities and oscillations of the sequential tunnelling current in superlattices based solely on the magnitude of the negative differential resistance region in the tunnelling characteristic of a single barrier. Both increasing magnetic field and sample temperature change the negative differential resistance and cause the transition between static and dynamic electric field domain formation. (C) 2000 Elsevier Science B.V. All rights reserved.

Surface transformation and inversion domain boundaries in gallium nitride nanorods

Phase transformation and subdomain structure in [0001]-oriented gallium nitride (GaN) nanorods of different sizes are studied using molecular dynamics simulations. The analysis concerns the structure of GaN nanorods at 300 K without external loading. Calculations show that a transformation from wurtzite to a tetragonal structure occurs along {0110} lateral surfaces, leading to the formation of a six-sided columnar inversion domain boundary (IDB) in the [0001] direction of the nanorods. This structural configuration is similar to the IDB structure observed experimentally in GaN epitaxial layers. The transformation is significantly dependent on the size of the nanorods.

Influence of Inter-Fiber Spacing and Interfacial Adhesion on Failure of Multi-Fiber Model Composites: Experiment and Numerical Analysis

The uniaxial tension experiments on glass-fiber-reinforced epoxy matrix composites reveal that the fragmentations of fibers display vertically aligned fracture, clustered fracture, coordinated fracture, and random fracture with the increase of inter-fiber spacing. The finite element analysis indicates that the fragmentations of fibers displaying different phenomena are due to the stress concentration as well as the inherent randomness of fiber defects, which is the dominant factor. The experimental results show that matrices adjacent to the fiber breakpoints all exhibit birefringent-whitening patterns for the composites with different interfacial adhesion strengths. The larger the extent of the interfacial debonding, the less the domain of the birefringent-whitening patterns. The numerical analysis indicates that the orientation of the matrix adjacent to a fiber breakpoint is caused by the interfacial shear stress, resulting in the birefringent-whitening patterns. The area of shear stress concentrations decides on the domain of the birefringent-whitening patterns.