Yong-Zhen Huang

Modes in square resonators

Modes in square resonators are analyzed and classified according to the irreducible representations of the point group C/sub 4v/. If the mode numbers p and q that denote the number of wave nodes in the directions of two orthogonal square sides are unequal and have the same even-odd characteristics, the corresponding double modes are accidentally degenerate and can be combined into two new distributions with definite parities relative to the square diagonal mirror planes. The distributions with odd parities belong to the whispering-gallery-like modes in square resonators. The mode frequencies and quality factors are also calculated by the finite-difference time-domain technique and Pade/spl acute/ approximation method. The numerically calculated mode frequencies agree with the theoretical ones very well and the whispering-gallery-like modes have quality factors much higher than other modes, including their accidentally degenerate counterparts in square resonators.

Investigation of mode coupling in a microdisk resonator for realizing directional emission

Mode coupling between the whispering-gallery modes (WGMs) is numerically investigated for a two-dimensional microdisk resonator with an output waveguide. The equilateral-polygonal shaped mode patterns can be constructed by mode coupling in the microdisk, and the coupled modes can still keep high quality factors (Q factors). For a microdisk with a diameter of 4.5 microm and a refractive index of 3.2 connected to a 0.6-microm-wide output waveguide, the coupled mode at the wavelength of 1490 nm has a Q factor in the order of 10(4), which is ten times larger than those of the uncoupled WGMs, and the output efficiency defined as the ratio of the energy flux confined in the output waveguide to the total radiation energy flux is about 0.65. The mode coupling can be used to realize high efficiency directional-emission microdisk lasers.

Directional emission InP/GaInAsP square-resonator microlasers

InP/GaInAsP square-resonator microlasers with an output waveguide connected to the midpoint of one side of the square are fabricated by standard photolithography and inductively-coupled-plasma etching technique. For a 20-mum-side square microlaser with a 2-mum-wide output waveguide, cw threshold current is 11 mA at room temperature, and the highest mode Q factor is 1.0x10(4) measured from the mode linewidth at the injection current of 10 mA. Multimode oscillation is observed with the lasing mode wavelength 1546 nm and the side-mode suppression ratio of 20 dB at the injection current of 15 mA.

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-mode operation as semiconductor microcavity lasers.

Room-Temperature Continuous-Wave Electrically Injected InP–GaInAsP Equilateral-Triangle-Resonator Lasers

Equilateral-triangle-resonator (ETR) microlasers with an output waveguide connected to one of the vertices of the ETR are suitable to be a light source for photonic integrated circuits. InP-GaInAsP ETR lasers with side length from 10 to 30 mum and the output-waveguide width of 1 or 2 mum are fabricated using standard photolithography and inductively coupled-plasma etching techniques. Continuous-wave electrically injected 1520-nm ETR laser with 20-m sides is realized with the maximum output power 0.17 and 0.067 mW and the threshold current 34 and 43 mA at 290 K and 295 K, respectively.

Silicon nitride three-mode division multiplexing and wavelength-division multiplexing using asymmetrical directional couplers and microring resonators

We demonstrate silicon nitride mode-division multiplexing (MDM) and wavelength-division multiplexing (WDM) using asymmetrical directional couplers and microring resonators. Our experiments reveal three-mode multiplexing and demultiplexing. We demonstrate 30Gb/s open eye diagrams with an extinction ratio of ~9 dB for each of the three modes. We observe the worst-case modal crosstalk of ~-10 dB. Our analysis of the measured transmission spectra suggests three contributions to the observed crosstalks, with the dominant cause being a compromised input-coupling at the directional couplers in the multiplexer.

Numerical Analysis of Gain Saturation, Noise Figure, and Carrier Distribution for Quantum-Dot Semiconductor-Optical Amplifiers

The gain saturation behaviors and noise figure are numerically analyzed for quantum-dot semiconductor optical amplifiers (QD-SOAs). The carrier and photon distributions in the longitudinal direction as well as the photon energy dependent facet reflectivity are accounted in the rate equations, which are solved with output amplified spontaneous emission spectrum as iterative variables. The longitudinal distributions of the occupation probabilities and spectral-hole burning are presented for electrons in the excited and ground states of quantum dots. The saturation output power 19.7 dBm and device gain 20.6 dB are obtained for a QD-SOA with the cavity length of 6 mm at the bias current of 500 mA. The influences of the electron intradot relaxation time and the QD capture time on the gain spectrum are simulated with the relaxation time of 1, 30, and 60 ps and capture time of 1, 5, and 10 ps. The noise figure as low as 3.5 dB is expected due to the strong polarization sensitive spontaneous emission. The characteristics of gain saturation and noise figure versus input signal power for QD-SOAs are similar to that of semiconductor linear optical amplifiers with gain clamping by vertical laser fields.

Whispering-gallery-like modes in square resonators

The mode frequencies and field distributions of whispering-gallery (WG)-like modes of square resonators are obtained analytically, which agree very well with the numerical results calculated by the FDTD technique and Pade approximation method. In the analysis, a perfect electric wall for the transverse magnetic mode or perfect magnetic wall for the transverse electric mode is assumed at the diagonals of the square resonators, which not only provides the transverse mode confinement, but also requires the longitudinal mode number to be an even integer. The WG-like modes of square resonators are nondegenerate modes with high-quality factors, which make them suitable for fabricating single-mode low-threshold semiconductor microcavity lasers.

AlGaInAs–InP Microcylinder Lasers Connected With an Output Waveguide

AlGaInAs-InP microcylinder lasers connected with an output waveguide are fabricated by planar technology. Room-temperature continuous-wave operation with a threshold current of 8 mA is realized for a microcylinder laser with the radius of 10 μm and the output waveguide width of 2 μm. The mode Q-factor of 1.2 x 104 is measured from the laser spectrum at the threshold. Coupled mode characteristics are analyzed by 2-D finite-difference time-domain simulation and the analytical solution of whispering-gallery modes. The calculated mode Q-factors of coupled modes are in the same order as the measured value.

Mode characteristics for equilateral triangle optical resonators

Mode characteristics of equilateral triangle resonators (ETRs) are analyzed based on the symmetry operation of the point group C/sub 3v/. The results show that doubly degenerate eigenstates can be reduced to the A/sub 1/ and A/sub 2/ representations of C/sub 3v/, if the longitudinal mode number is a multiple of 6; otherwise, they form the E irreducible representation of C/sub 3v/. And the one-period length for the mode light ray is half of the perimeter of the ETR. Mode Q-factors are calculated by the finite-difference time-domain (FDTD) technique and compared with those calculated from far-field emission based on the analytical near-field pattern for TE and TM modes. The results show that the far-field emission based on the analytical field distribution can be used to estimate the mode Q-factor, especially for TM modes. FDTD numerical results also show that Q-factor of TE modes reaches maximum value as the longitudinal mode number is a multiple of 7. In addition, photoluminescence spectra and measured Q-factors are presented for fabricated ETR with side lengths of 20 and 30 /spl mu/m, and the mode wavelength intervals are compared with the analytical results.