Silicon-Based Asymmetric Add-Drop Microring Resonators with Ultra-Large Through-Port Extinctions

We theoretically simulate and experimentally demonstrate ultra-large through-port extinctions in silicon-based asymmetrically-coupled add-drop microring resonators (MRs). Through-port responses in an add-drop MR are analyzed by simulations and large extinctions are found when the MR is near-critically coupled. Accurate fabrication techniques are applied in producing a series of 20 mu m-radii add-drop microrings with drop-side gap-widths in slight differences. A through-port extinction of about 42.7 dB is measured in an MR with through-and drop-side gap-width to be respectively 280 nm and 295 nm. The large extinction suggests about a 20.5 dB improvement from the symmetrical add-drop MR of the same size and the through-side gap-width. The experimental results are finally compared with the post-fabrication simulations, which show a gap-width tolerance of > 30 nm for the through-port extinction enhancement.

Investigation of mode radiation loss for microdisk resonators with pedestals by FDTD technique

Mode radiation loss for microdisk resonators with pedestals is investigated by three-dimensional (3D) finite-difference time-domain (FDTD) technique. For the microdisk with a radius of 1 mu m, a thickness of 0.2 mu m, and a refractive index of 3.4, on a pedestal with a refractive index of 3.17, the mode quality (Q) factor of the whispering-gallery mode (WGM) quasi-TE7,1 first increases with the increase of the radius of the pedestal, and then quickly decreases as the radius is larger than 0.75 mu m. The mode radiation loss is mainly the vertical radiation loss induced by the mode coupling between the WGM and vertical radiation mode in the pedestal, instead of the scattering loss around the perimeter of the round pedestal. The WG M can keep the high Q factor when the mode coupling is forbidden.

Enhancement of quality factor for TE whispering-gallery modes in microcylinder resonators

The enhancement of quality factor for TE whispering-gallery modes is analyzed for three-dimensional microcylinder resonators based on the destructive interference between vertical leakage modes. In the microcylinder resonator, the TE whispering-gallery modes can couple with vertical propagation modes, which results in vertical radiation loss and low quality factors. However, the vertical loss can be canceled by choosing appropriate thickness of the upper cladding layer or radius of the microcylinder. A mode quality factor increase by three orders of magnitude is predicted by finite-difference time-domain simulation. Furthermore, the condition of vertical leakage cancellation is analyzed.

Analysis of coupled microcircular resonators coupled to a bus waveguide with high output efficiency

Coupled microcircular resonators tangentially coupled to a bus waveguide, which is between the resonators, are numerically investigated by the finite-difference time-domain technique. For symmetrically coupled microcircular resonators with refractive index of 3.2, radius of 2 mu m, and width of the bus waveguide of 0.4 mu m, a mode Q factor of the order of 105 is obtained for a mode at the frequency of 243 THz. An output coupling efficiency of as high as 0.99 is calculated for a mode with a Q factor ranging from 10(3) to 10(4). The mode Q factor is 2 orders larger than that of the modes confined in a single circular resonator tangentially coupled to the same bus waveguide. Furthermore, the high Q traveling modes in the coupled microcircular resonators are suitable for optical single processing.

Experimental investigation on submicron rib waveguide microring/racetrack resonators in silicon-on-insulator

in experiment, characteristics of silicon microring/racetrack resonators in submicron rib waveguides have been systematically investigated. It is demonstrated that only a transverse-electric mode is guided for a ratio of slab height to rib height h/H = 0.5. Thus, these microring/racetrack resonators can only function for quasi-transverse-electric mode, while they get rid of transverse-magnetic polarization. Electron beam lithography and inductively coupled plasma etching were employed and improved to reduce side-wall roughness for low propagation loss and high performance resonators. Then, the effects of waveguide dimensions, coupling region design, waveguide roughness, and oxide cladding for the resonators have been considered and analyzed. (C) 2008 Elsevier B.V. All rights reserved.

Design and fabrication of polarization-independent micro-ring resonators

Origin of polarization sensitivity of photonic wire waveguides (PWWs) is analysed and the effective refractive indices of two different polarization states are calculated by the three-dimensional full-vector beam propagation method. We find that PWWs are polarization insensitive if the distribution of its refractive index is uniform and the cross section is square. An MRR based on such a polarization-insensitive PWW is fabricated on an 8-inch silicon-on-insulator wafer using 248-nm deep ultraviolet lithography and reactive ion etching. The quasi-TE mode is resonant at 1542.25 nm and 1558.90 nm, and the quasi-TM mode is resonant at 1542.12 nm and 1558.94 nm. The corresponding polarization shift is 0.13 nm at the shorter wavelength and 0.04 nm at the longer wavelength. Thus the fabricated device is polarization independent. The extinction ratio is larger than 10 dB. The 3 dB bandwidth is about 2.5 nm and the Qvalue is about 620 at 1558.90 nm.

Analysis of mode characteristics for equilateral-polygonal resonators with a center hole

Mode characteristics for equilateral triangles, squares, and hexagonal resonators with a center hole are numerically simulated by the finite-different time domain (FDTD) technique. The center hole does not break the symmetry behavior of the original resonators and can result in modification of the mode field patterns and mode Q factors. In an equilateral triangle resonator the center hole can suppress the symmetry state of degenerate states with the merit of single mode operation. In a square resonator, the Q factor can be enhanced for some modes with a suitable size of the hole. For a hexagonal resonator with a side length of 1 mu m and a refractive index of 3.2, the mode Q factors first gradually decrease with the increase of the hole diameter for modes at a wavelength of about 1500 nm, then the modes transform to that of a microdisk with a jump of the mode wavelength as the hole diameter approaches 0.7 mu m. Finally, the mode Q factors greatly enhance as the hole diameter reaches about 1 mu m. The results indicate that the center hole can greatly modify mode characteristics, especially that of the mode Q factor. (C) 2009 Optical Society of America

Mode quality factor based on far-field emission for square resonators

The quality factors of modes in square resonators are calculated based on the far-field emission of the analytical field distribution. The obtained quality factors are in reasonable agreement with those calculated by the finite-difference time-domain (FDTD) technique and Pade approximation method. The emission power in the square diagonal directions for whispering-gallery-like modes in square resonators is zero due to the interference cancellation caused by the odd field distributions relative to the diagonal mirror planes, so they have larger quality factors than the modes with even field distribution.

Modes in square resonators

Modes in square resonators are analyzed and classified according to the irreducible representations of the point group C-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 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.

Experimental observation of resonant modes in GaInAsP microsquare resonators

GaInAsP-InP microsquare resonators with InP pedestals are fabricated by two-step chemical etching, and obvious mode peaks are observed in the photoluminescence spectra of the resonators. The mode Q-factors about 500 are obtained for a microsquare resonator with the side length of 7 mu m. The experimental mode interval is in agreement with that predicted by the light ray method based on the cavity length, instead of that of the whispering-gallery (WG)-like modes, which has mode interval twice of that determined by the cavity length. The finite-difference time-domain simulation shows that a little asymmetry may greatly reduce the difference of the Q-factors between the WG-like modes and the other modes.

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.

Investigation of mode characteristics for microdisk resonators by S-matrix and three-dimensional finite-difference time-domain technique

The mode characteristics of a three-dimensional (3D) microdisk with a vertical refractive index distribution of n(2)/3.4/n(2) are investigated by the S-matrix method and 3D finite-difference time-domain (FDTD) technique. For the microdisk with a thickness of 0.2 mu m. and a radius of 1 mu m, the mode wavelengths and quality factors for the HE7,1 mode obtained by 3D FDTD simulation and the S-matrix method are in good agreement as n(2) increases from 1.0 to 2.6. But the Q factor obtained by the 3D FDTD rapidly decreases from 1.12 X 10(4) to 379 as n2 increases from 2.65 to 2.8 owing to the vertical radiation losses, which cannot be predicted by the proposed S-matrix method. The comparisons also show that quality factors obtained from the analytical solution of two-dimensional microdisks under the effective index approximation are five to seven times smaller than those of the 3D FDTD as n(2) = 1 and R = 1 mu m. (c) 2006 Optical Society of America.

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.

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-3v. The results show that doubly degenerate eigenstates can be reduced to the A(1) and A(2) representations of C-3v, if the longitudinal mode number is a multiple of 6; otherwise, they form the E irreducible representation Of C-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 mu m, and the mode wavelength intervals are compared with the analytical results.

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.