We present a new numerical method for the analysis of second-harmonic generation (SHG) in one- and two-dimensional (1D, 2D) diffraction gratings containing centrosymmetric quadratically nonlinear materials. Thus, the nonlinear optical properties of a material are determined by its symmetry properties: non-centrosymmetric materials lack inversion symmetry and therefore allow local even-order SHG in the bulk of the material, whereas this process is forbidden in centrosymmetric materials. The inversion symmetry of centrosymmetric materials is broken at their surface whence they allow local surface SHG. Additionally, centrosymmetric materials give rise to nonlocal (bulk) SHG.
Our numerical method extends the linear generalized source method (GSM), which is an efficient numerical method for solving the problem of linear diffraction in periodic structures of arbitrary geometry. The nonlinear GSM is a three-step algorithm: for a given excitation at the fundamental frequency the linear field is computed using the linear GSM. This field gives rise to a nonlinear source polarization at the second harmonic (SH) frequency. This nonlinear polarization comprises surface and bulk polarizations as additional source terms and is subsequently used to compute the nonlinear near- and far-field optical response at the SH.
We study the convergence characteristics of the nonlinear GSM for 1D and 2D periodic structures and emphasize the numerical intricacies caused by the surface SH polarization term specific to centrosymmetric materials. In order to illustrate the practical significance of our numerical method, we apply it to metallic gratings made of Au and Ag as well as dielectric grating structures made of silicon and investigate the relative contribution of the bulk and surface nonlinearity to the nonlinear optical response at the SH. Particular attention is paid to optical effects that have a competing influence to the nonlinear optical response of the grating structures, namely the resonant local field enhancement and optical losses.
In this communication, we report about the design, fabrication, and testing of echelle grating (de-)multiplexers for the
100GBASE-LR4 norm and other passive architectures such as vertical fiber-couplers and slow-wave waveguides in the
O-band (1.31-μm) for Silicon-based photonic integrated circuits (Si-PICs). In detail, two-point stigmatic 20th-order
echelle gratings (TPSGs) on the 300-nm-thick SOI platform designed for 4x800-GHz-spaced wavelength division
multiplexing featuring extremely low crosstalk (< -30 dB), precise channel spacing and optimized average insertion
losses (~ 3 dB) are presented. Distributed Bragg reflectors (DBRs) are used to improve the grating facets reflectivity,
while multi-mode interferometers (MMIs) are used in optimized perfectly-chirped echelle gratings (PCGs) for pass-band
flattening. Moreover, 200-mm CMOS pilot lines processing tools including VISTEC variable-shape e-beam lithography
are employed for the fabrication. In addition, wafer-level statistics of the multiplexers clearly shows the echelle grating
to be inherently fabrication-insensitive to processing drifts, resulting in a minimized dispersion of the multiplexer
performances over the wafer. In particular, the echelle grating spectral response remains stable over the wafer in terms of
crosstalk, channel spacing and bandwidth, with the wavelength dispersion of the filter comb being limited to just 0.8 nm,
thus highlighting the intrinsic robustness of design, fab pathways as well as the reliability of modeling tools.
As well as that, apodized one-dimensional vertical fiber couplers, optimized multi-mode interferometers (MMIs) and
extremely low-losses slow-light waveguides are demonstrated and discussed. The adiabatic apodization of such 1-D
gratings is capable to provide band-edge group indices ng as high as 30 with propagation losses equivalent to the indexlike
propagation regime.
We present a new numerical method for the analysis of second-harmonic generation (SHG) in one- and twodimensional (1D, 2D) diffraction gratings with arbitrary profile made of non-centrosymmetric optical materials. Our method extends the generalized source method (GSM), which is a highly efficient alternative to the conventional Fourier modal method, to quadratically nonlinear diffraction gratings. The proposed method consists of a two-stage algorithm. Initially, the electromagnetic field at the fundamental frequency is computed in order to obtain the second-harmonic polarization using the known second-order nonlinear susceptibility. Then the optical field at the second-harmonic frequency is computed using this polarization as an additional source term in the GSM. We show how to integrate this source term into the GSM framework without changing the structure of the basic algorithm. We use the proposed algorithm to investigate a doubly resonant mechanism that leads to strong enhancement of SHG in a nonlinear 2D circular GaAs grating mounted on top of a GaAs slab waveguide. We design this optical device such that slab waveguide modes at the fundamental and second-harmonic are simultaneously excited and phase matched by the grating. The numerically obtained resonance frequencies show good agreement with analytically computed resonance frequencies of the unperturbed slab waveguide.
We present a tool for the simulation of active and passive photonic integrated circuits (PIC) based on EME (eigenmode
expansion) for modelling the details of circuit elements plus the travelling wave time domain (TWTD) technique for
connecting the circuit together and modelling non-linear elements such as SOAs. We show how the two algorithms can
be linked together using FIR filters to create a highly efficient PIC simulator. We discuss the strengths and weaknesses
of the approach and illustrate it with the simulation of a variety of active and passive examples.
We present a numerical framework for the simulation of lasers in the time domain. The algorithm is based on the finite-difference time-domain method, which has been extended to include material gain by using auxiliary differential equations for a frequency dependent conductivity. The algorithm is applied to the simulation of micro-disk lasers based on an erbium doped SiO2 material system in order to obtain a CMOS compatible fabrication process. Lasing behavior and lasing threshold is studied in two and three dimensions for single and multi-disk systems.
A numerical optimization technique coupled with a finite element frequency domain solver was applied to a variety of
Si nanowire photonic devices in an attempt to improve transmissions or matching to predefined criteria. The
optimisation procedures are iterative in nature, in that they approach the optimal solution by exploring a sequence of
carefully selected points in the parameter space. For any optimisation procedure to be effective, a good optimiser needs
to be coupled with an efficient solver capable of modeling correctly all device configurations allowed by the parameter
space. In the case of electromagnetic problems, it is particularly important that the divergence free condition is obeyed.
The solver used here satisfies this condition and therefore greatly reduces the chances of the optimiser finding artificial
optimal solutions with incorrect field distributions. This FEFD is used by a deterministic global optimisation method,
which systematically subdivides the parameter space to split more quickly in regions most likely to contain an optimum.
Since the entire parameter space is eventually explored, this optimisation technique is not only guaranteed to
(eventually) find the globally optimal solution, but can also show other interesting local optima. As no gradient
information is required, the method works well even in the presence of the random errors typically occurring when
using Finite Element solvers where a unique optimised mesh is generated for each calculation.
This paper reviews the time-domain travelling wave (TDTW) model for the simulation of active semiconductor waveguides. We outline the theory, present a discussion of its advantages and limitations and show how it can be applied to the design and simulation of a tunable 4-section sampled-grating DBR laser.
We present structures obtained with numerical optimization techniques capable of efficiently channeling light at a fraction of the length of a conventional taper. These results could open the way to novel designs in ultra-short light injection devices. We also consider the rather different problem of how to optimise the transmission through a photonic crystal bend. We show how, using a deterministic global optimisation algorithm, novel optimal geometries can be obtained leading to considerable performance improvements.
With the rapid growth of the telecommunications industry over the last 5 to 10 years has come the need to solve ever more complex electromagnetic problems and to solve them more precisely than ever before. The basic EME (EigenMode Expansion) technique is a powerful method for calculation of electromagnetic propagation which has been well known amongst academic environments and also in microwave fields, representing the electromagnetic fields everywhere in terms of a basis set of local modes. It is at the same time a rigorous solution of Maxwell's Equations and is able to deal with very long structures. We discuss here progress that the authors and others have made recently in applying and extending it to integrated, fibre, and diffractive optics - including development of efficient ways of modelling tapers and other smoothly varying structures, new more efficient boundary conditions and improved mode finders. We outline the advantages it has over other techniques and also its limitations. We illustrate its application with a variety of real life examples, including diffractive elements, directional couplers, tapers, MMI's, bend modelling, periodic structures and others.
A GaAs/AlxGa1-xAs multiple quantum well laser with a 3 dB electrical modulation bandwidth of 16 GHz has been developed. Optimized design of the waveguide, including implementation of high average Al mole fraction (xeff equals 0.8) GaAs/AlAs binary short-period superlattice cladding layers, together with a coplanar electrode geometry, has resulted in a vertically compact laser structure suitable for integration.
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