Majid Sodagar

Vertical integration of high-Q silicon nitride microresonators into silicon-on-insulator platform

We demonstrate a vertical integration of high-Q silicon nitride microresonators into the silicon-on-insulator platform for applications at the telecommunication wavelengths. Low-loss silicon nitride films with a thickness of 400 nm are successfully grown, enabling compact silicon nitride microresonators with ultra-high intrinsic Qs (~ 6 × 10(6) for 60 μm radius and ~ 2 × 10(7) for 240 μm radius). The coupling between the silicon nitride microresonator and the underneath silicon waveguide is based on evanescent coupling with silicon dioxide as buffer. Selective coupling to a desired radial mode of the silicon nitride microresonator is also achievable using a pulley coupling scheme. In this work, a 60-μm-radius silicon nitride microresonator has been successfully integrated into the silicon-on-insulator platform, showing a single-mode operation with an intrinsic Q of 2 × 10(6).

High-efficiency and wideband interlayer grating couplers in multilayer Si/SiO 2 /SiN platform for 3D integration of optical functionalities

We have designed interlayer grating couplers with single/double metallic reflectors for Si/SiO(2)/SiN multilayer material platform. Out-of-plane diffractive grating couplers separated by 1.6 μm thick buffer SiO(2) layer are vertically stacked against each other in Si and SiN layers. Geometrical optimization using genetic algorithm coupled with electromagnetic simulations using two-dimensional (2D) finite element method (FEM) results in coupler designs with high peak coupling efficiency of up to 89% for double- mirror and 64% for single-mirror structures at telecom wavelength. Also, 3-dB bandwidths of 40 nm and 50 nm are theoretically predicted for the two designs, respectively. We have fabricated the grating coupler structure with single mirror. Measured values for insertion loss and 3-dB bandwidth in the fabricated single-mirror coupler confirms the theoretical results. This opens up the possibility of low-loss 3D dense integration of optical functionalities in hybrid material platforms.

Design of a GaN White Light-Emitting Diode Through Envelope Function Analysis

In this paper, we present an envelope function analysis technique for the design of the emission spectra of a white quantum-well light-emitting diode (QWLED). The nanometric heterostructure that we are dealing with is a multiple QW, consisting of periods of three single QWs with various well thicknesses. With the aid of 6 × 6 Luttinger Hamiltonian, we employ the combination of two methods, k·p perturbation and the transfer matrix method, to acquire the electron and hole wave functions numerically. The envelope function approximation was considered to obtain these wave functions for a special basis set. While adjacent valence sub-bands have been determined approximately, the conduction bands are approximated as parabolic. The effect of Stokes shift has also been taken into account. The dipole moment matrix elements for interband atomic transitions are evaluated via the correlation between the electron and hole envelope functions, for both orthogonal polarizations, thus simplifying the calculation of the photoluminescence intensity. Spatial variations in the hole/electron wave functions have been examined with the introduction of piezoelectric and spontaneous polarization internal fields. We theoretically establish the possibility of a highly efficient InGaN red emitter, resulting in a uniform luminescence in red, green, and blue emissions from a white light emitting diode by adjusting the material composition, internal field, and well thickness.In this paper, we present an envelope function analysis in order to design the emission spectra of a white quantum well light emitting diode. The nanometric heterostructure that we are dealing with is a multiple quantum well, consisting periods of three single quantum wells with various well thicknesses. With the aid of 6x6 Luttinger Hamiltonian, we employ the combination of two methods, k.p perturbation and transfer matrix method, to acquire electron and hole wavefunctions analytically. The envelope function approximation was considered to obtain these wavefunctions for a special basis set. While adjacent valence subbands have been studied exactly, the conduction bands are approximated as parabolic. The effect of Stokes shift has been also taken into account. The dipole moment matrix elements for interband atomic transitions are evaluated via correlation between electron and hole envelope functions, for both orthogonal polarizations. This has simplified the calculation of photoluminescence intensity. Spatial variations in hole/electron wavefunctions have been examined with the introduction of piezoelectric and spontaneous polarizations internal field. We theoretically establish the possibility of a highly efficient InGaN red emitter, resulting in a uniform luminescence in red, green and blue emissions from the while light emitting diode, through adjusting material composition, potential slope, and thickness.

Design and Fabrication of Photonic Crystal Nano-Beam Resonator: Transmission Line Model

We present a new method for modeling and design of photonic crystal nano-beam resonators (PCNBRs) based on cascaded transmission lines. The proposed model provides an accurate estimate of the PCNBRs properties such as resonance wavelength and quality factor (Q) with much smaller computation cost as compared to the brute-force numerical methods. Furthermore, we have developed a straightforward technique for the design of high-Q PCNBRs based on resonance modes with Gaussian electromagnetic field profiles. The results obtained by using the proposed transmission line model are compared against numerical and experimental results and the accuracy of the model is verified. The proposed model provides an insight to silicon cavity design and significantly reduces computational burden.

Exciton?photon interaction in a quantum dot embedded in a photonic microcavity

We present a detailed analysis of exciton–photon interaction in a microcavity made out of a photonic crystal slab. Here we have analysed a disc-like quantum dot where an exciton is formed. Excitonic eigen functions in addition to their eigen energies are found through direct matrix diagonalization, while wavefunctions corresponding to unbound electron and hole are chosen as the basis set for this procedure. In order to evaluate these wavefunctions precisely, we have used the 6 × 6 Luttinger Hamiltonian in the case of hole while ignoring bands adjacent to the conduction band for electron states. After analysing excitonic states, a photonic crystal-based microcavity with a relatively high quality factor mode has been proposed and its lattice constant has been adjusted to obtain the prescribed resonant frequency. We use a finite-difference time-domain method in order to simulate our cavity with sufficient precision. Finally, we formulate the coupling constants for the exciton–photon interaction both where intra-band and inter-band transitions occur. By evaluating a sample coupling constant, it has been shown that the system can be in a strong-coupling regime and Rabi oscillations can occur.

Optical bistability in a one-dimensional photonic crystal resonator using a reverse-biased pn-junction

Optical bistability provides a simple way to control light with light. We demonstrate low-power thermo-optical bistability caused by the Joule heating mechanism in a one-dimensional photonic crystal (PC) nanobeam resonator with a moderate quality factor (Q ~8900) with an embedded reverse-biased pn-junction. We show that the photocurrent induced by the linear absorption in this compact resonator considerably reduces the threshold optical power. The proposed approach substantially relaxes the requirements on the input optical power for achieving optical bistability and provides a reliable way to stabilize the bistable features of the device.

Compact, 15 Gb/s electro-optic modulator through carrier accumulation in a hybrid Si/SiO(2)/Si microdisk.

High-speed electro-optic modulators are among the key elements in any optical interconnect system. In this work we design and demonstrate an electro-optic modulator based on carrier accumulation on a multilayer integrated photonic platform comprising a stack of high quality Si, SiO(2), and Si layers. The device consists of a 3-μm radius microdisk with an embedded capacitor. Characterization results reveal an operation bandwidth of exceeding 10 GHz. The device is capable of transmitting 15 Gb/s with the on/off keying format in a single polarization. The proposed structure can be self-trimmed by up to 1 nm in wavelength by applying a dc bias voltage without any power consumption. This feature eliminates the need for power-hungry thermal-based compensation methods to address the resonance wavelength mismatch due to fabrication imperfections.

Revised guided mode expansion on dispersive photonic media

A novel plane-wave-based approach for analytical treatment of dispersive relation is developed and applied to analyze the behavior of electromagnetic waves in plasmonic-photonic-crystal slabs. Here Drude model is used for describing frequency dependent permittivity of plasma rods in host dielectric medium. In the present work, dispersion relation below and above the light line is calculated approximately by means of Maxwell-Garnett effective medium and Revised Plane Wave Method (RPWM). The eigen-functions are then used in Revised Guided Mode Expansion (RGME) as the set of orthonormal bases. Following this procedure, the accurate band structure is obtained. In these kind of methods there are two main sources of error: stair-casing error due to discretization and numerical dispersion due to calculation of frequency domain dielectric matrix elements with finite number of bases. Sub-cell averaging and harmonic inversion methods are suggested to overcome these errors. For investigation purpose we apply this approach for calculating photonic dispersion of dispersive and non-dispersive photonic crystal slabs. Resulted band structures are verified by conventional FDTD method as well.

Field-programmable optical devices based on resonance elimination

Optical switches are among the essential building blocks in optical networks due to their unique role in routing data. In this Letter, for the first time to our knowledge, we have exploited a high-quality factor (Q) optical microresonator combined with the well-known irreversible dielectric breakdown phenomenon to introduce a simple field-programmable on/off optical switch. This simple unit can be thought of as a building block for more complex optical systems with different functionalities. By using this simple unit we have demonstrated an optical field-programmable 2×2 switch. After the device is programmed by the user, no external electrical signal is needed to maintain the state of the device. The same approach can readily be adopted to design a field-programmable arbitrary N×N optical switch.

Analytical study of dissipative solitary waves

In this paper, the analytical solution to a new class of nonlinear solitons is presented with cubic nonlinearity, subject to a dissipation term arising as a result of a first-order derivative with respect to time, in the weakly nonlinear regime. Exact solutions are found using the combination of the perturbation and Greens function methods up to the third order. We present an example and discuss the asymptotic behavior of the Greens function. The dissipative solitary equation is also studied in the phase space in the non-dissipative and dissipative forms. Bounded and unbounded solutions of this equation are characterized, yielding an energy conversation law for non-dissipative waves. Applications of the model include weakly nonlinear solutions of terahertz Josephson plasma waves in layered superconductors and ablative Rayleigh–Taylor instability.