Application of fast Pade approximation in simulating photonic crystal nanocavities by FDTD technology

The exact calculation of mode quality factor Q is a key problem in the design of high-Q photonic crystal nanocavity. On the basis of further investigation on conventional Pade approximation, FDM and DFT, Pade approximation with Baker's algorithm is enhanced through introducing multiple frequency search and parabola interpolation. Though Pade approximation is a nonlinear signal processing method and only short time sequence is needed, we find the different length of sequence requirements for 2D and 3D FDTD, which is very important to obtain convergent and accurate results. By using the modified Pade approximation method and 3D FDTD, the 2D slab photonic crystal nanocavity is analyzed and high-Q multimode can be solved quickly instead of large range high-resolution scanning. Monitor position has also been investigated. These results are very helpful to the design of photonic crystal nanocavity devices. (C) 2008 Elsevier B.V. All rights reserved.

GaSb based midinfrared equilateral-triangle-resonator semiconductor lasers

Theoretical calculations of the mode characteristics of an equilateral-triangle resonator (ETR) with a 10 mu m cavity side length show that the fundamental mode, with longitudinal mode index of 25, has a wavelength of 2.185 mu m and a longitudinal mode separation of 100 nm. This mode has a quality factor (similar to 2x10(5)) that is much larger than the first (similar to 5x10(4)) and second (similar to 3x10(4)) order modes, indicating that single fundamental mode lasing should be accessible over a broad wavelength tuning range. An electrically injected ETR based on this design is fabricated from an InGaAsSb/AlGaAsSb/GaSb, graded-index separate-confinement heterostructure, laser diode wafer with a 2.1 mu m emission wavelength. This device achieved single mode, continuous wave operation at 77 K with a threshold current of 0.5 mA and a single mode wavelength tuning range of 3.25 nm, which is accomplished by varying the injection current from 0.5 to 6.0 mA. (C) 2008 American Vacuum Society.

Design of high polarization and single-mode photonic crystal laser

The dipole mode in triangular photonic crystal single defect cavity is degenerate. By deforming the lattice in photonic crystal we can obtain non-degenerate dipole modes. Lattice deforming in the whole photonic crystal destroys the characteristic of symmetry, so the distribution of the electromagnetic field is affected and the polarization of the electromagnetic field is also changed. Lattice deforming divides the degenerate dipole mode into the x-dipole mode and the y-dipole mode. It is found that the non-degenerate modes have better properties of polarization. So the high polarization and single dipole mode photonic crystal laser can be achieved by deforming the lattice of photonic crystal. In this paper, we simulated the cavity in photonic crystal slab and mainly calculated the quality factor of x-dipole mode under different deforming conditions and with different filling factors. The properties of polarization of x-dipole and y-dipole modes are also calculated. It is found that the ratio of intensities of E-x to E-y in x-dipole mode and that of E-y to E-x in y-dipole mode are 44 and 27, respectively.

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.

Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Pade approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Pade approximation. The decaying constant beta of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity v(g) as beta = omega/(2Qv(g)). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 10(3) to 10(-4) cm(-1) can be reliably obtained from 8 x 10(3)-item FDTD output with the FDTD computing time of 0.386 ps. And at most 1 ps is required for the mode with the Q-factor of 4 x 10(11) and the decaying rate of 10(-7) cm(-1). In the triangular-lattice photonic crystal slab, a 10(4)-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5 x 10(8) and the decaying rate of 0.05 cm(-1). (c) 2004 Elsevier B.V. All rights reserved.

Design of two-dimensional photonic crystal edge emitting laser for photonic integrated circuits

An edge emitting laser based on two-dimensional photonic crystal slabs is proposed. The device consists of a square lattice microcavity, which is composed of two structures with the same period but different radius of air-holes, and a waveguide. In the cavity, laser resonance in the inner structure benelits from not only the anomalous dispersion characteristic of the first band-edge at the M point in the first Brillouin-zone but also zero photon states in the outer structure. A line defect waveguide is introduced in the outer structure for extracting photons from the inner cavity. Three-dimensional finite-difference time-domain simulations apparently show the in-plane laser output from the waveguide. The microcavity has an effective mode volume of about 3.2(lambda/eta(slab))(3) for oscillation -mode and the quality factor of the device including line defect waveguide is estimated to be as high as 1300.

WG-like modes selectivity in a square cavity with posts

We investigate the characteristics of Whispering-Gallery(WG)-like modes in a square cavity with posts by employing the two-dimentional (2D) finite-difference time-domain (FDTD) technique combined with the effective index method. The results indicate that the posts can result in mode selection in the WG-like modes. The WG-like modes with odd mode numbers are not much sensitive to the sizes of the posts. However, the quality factor (i.e. Q-factor) of the WG-like modes with even mode numbers decreases sharply with the increasing size of the posts. The decreasing Q-factor is attributed to mode leakage and scattering loss due to the presence of the post. The mode selection increases with the mode spacing of square cavity twice in an optimized strucure.

Mode-coupling analysis of three-dimensional microdisk resonators by the finite-difference time-domain technique

Quality factor enhancement due to mode coupling is observed in a three-dimensional microdisk resonator. The microdisk, which is vertically sandwiched between air and a substrate, with a radius of 1 mu m, a thickness of 0.2 mu m, and a refractive index of 3.4, is considered in a finite-difference time-domain (FDTD) numerical simulation. The mode quality factor of the fundamental mode HE71 decreases with an increase of the refractive index of the substrate, n(sub), from 2.0 to 3.17. However, the mode quality factor of the first-order mode HE72 reaches a peak value at n(sub) = 2.7 because of the mode coupling between the fundamental and the first-order modes. The variation of mode field distributions due to the mode coupling is also observed. This mechanism may be used to realize high-quality-factor modes in microdisks with high-refractive-index substrates. (c) 2006 Optical Society of America.

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.

High Q microring resonator in silicon-on-insulator rib waveguides - art. no. 68380J

A high quality (Q) factor microring resonator in silicon-on-insulator rib waveguides was fabricated by electron beam lithography, followed by inductively coupled plasma etching. The waveguide dimensions were scaled down to submicron, for a low bending loss and compactness. Experimentally, the resonator has been realized with a quality factor as high as 21,200, as well as a large extinction ratio 12.5dB at telecommunication wavelength near 1550nm. From the measured results, propagation loss in the rib waveguide is determined as low as 6.900/cm. This high Q microring resonator is expected to lead to high speed optical modulators and bio-sensing devices.

Ultra-compact silicon-on-insulator optical filter based on sidewall Bragg grating

Micro-cavity structure composed of silicon wire with 240nm square cross section and two symmetrical sidewall waveguide Bragg gratings is fabricated and studied for the operation under telecommunication wavelengths. Optical filter of quasi-TE mode was realized based on this cavity. In such micro-cavity, optical quality factor (Q) was measured up to 380 with a 4.8nm free spectral range (FSR) and 12dB fringe contrast (FC). The measured group index of silicon waveguide with only 240nm square cross section was between 3.80 and 5.43. It is the first time group delay of silicon wire waveguide with such small core dimension is studied. Larger group delay can be expected after optimizing the design parameters and the fabrication process.

In-situ Boron-doped Low-stress LPCVD Polysilicon for Micromechanical Disk Resonator

Polycrystalline silicon (polysilicon) has been used as an important structural material for microelectro-mechnical systems (MEMS) because of its compatibility with standard integrated circuit (IC) processes. As the structural layer of micromechanical high resonance frequency (high-f) and high quality factor (high-Q) disk resonators, the low residual stress and low resistivity are desired for the polysilicon thin films. In the present work, we investigate the effect of deposition and annealing conditions on the residual stress and resistivity for in-situ deposited low pressure chemical vapor deposition (LPCVD) polysilicon films. Low residual stress (-100 MPa) was achieved in in-situ boron-doped polysilicon films deposited at 570 degrees C and annealed at 1000 degrees C for 4 hr. The as-deposited amorphous polysilicon films were crystallized by the rapid thermal annealing and have the (111)-preferred orientation, the low tensile residual stress is expected for this annealed film, the detailed description on this work will be reported soon. The controllable residual stress and resistivity make these films suitable for high-Q and bigh-f micro-mechanical disk resonators.

Low heat and high efficiency Nd:GdVO4 laser pumped by 913 nm

A Nd:GdVO4 crystal is pumped directly into its emitting level at 913 nm for the first time to the best of our knowledge. 3.35 W output laser emitting at 1063 nm is achieved in a 1.1 at.% Nd-doped Nd:GdVO4. The crystal absorbs pumping light of 4.30 W at 913 nm and produces a very low quantity of heat with the opto-optic conversion efficiency of 77.2%. The average slope efficiency is 81.2% from 0.21 W, at the threshold, to 4.30 W of absorbed pump power. Because of the very weakly thermal effect, the near-diffraction-limit beam is easily obtained with beam quality factor of M-2 approximate to 1.1.

On-Chip All-Optical Passive 3.55 Gbit/s NRZ-to-PRZ Format Conversion Using a High-Q Silicon-Based Microring Resonator

We report the experimental result of all-optical passive 3.55 Gbit/s non-return-to-zero (NRZ) to pseudo-return-to-zero (PRZ) format conversion using a high-quality-factor (Q-factor) silicon-based microring resonator notch filter on chip. The silicon-based microring resonator has 23800 Q-factor and 22 dB extinction ratio (ER), and the PRZ signals has about 108 ps width and 4.98 dB ER.

Stress and resistivity controls on in situ boron doped LPCVD polysilicon films for high-Q MEMS applications

The simultaneous control of residual stress and resistivity of polysilicon thin films by adjusting the deposition parameters and annealing conditions is studied. In situ boron doped polysilicon thin films deposited at 520 ℃ by low pressure chemical vapor deposition (LPCVD) are amorphous with relatively large compressive residual stress and high resistivity. Annealing the amorphous films in a temperature range of 600-800 ℃ gives polysilicon films nearly zero-stress and relatively low resistivity. The low residual stress and low resistivity make the polysilicon films attractive for potential applications in micro-electro-mechanical-systems (MEMS) devices, especially in high resonance frequency (high-f) and high quality factor (high-Q MEMS resonators. In addition, polysilicon thin films deposited at 570 ℃ and those without the post annealing process have low resistivities of 2-5 mΩ·cm. These reported approaches avoid the high temperature annealing process (> 1000℃), and the promising properties of these films make them suitable for high-Q and high-f MEMS devices.