Christina Manolatou

Coupling of modes analysis of resonant channel add-drop filters

The operation principle of resonant channel add-drop filters based on degenerate symmetric and antisymmetric standing-wave modes has been described elsewhere using group theoretical arguments. In this paper, the analysis is carried out using coupling of modes in time. A possible implementation of such a filter is a four-port system utilizing a pair of identical single-mode standing wave resonators. The analysis allows a simple derivation of the constraints imposed on the design parameters in order to establish degeneracy. Numerical simulations of wave propagation through such a filter are also shown, as idealized by a two-dimensional geometry.

High-density integrated optics

This paper presents two dimensional (2-D) finite difference time domain (FDTD) simulations of low-loss right-angle waveguide bends, T-junctions and crossings, based on high index-contrast waveguides. Such structures are essential for the dense integration of optical components. Excellent performance characteristics are obtained by designing the waveguide intersection regions as low-Q resonant cavities with certain symmetries and small radiation loss. A simple analysis, based on coupled mode theory in time, is used to explain the operation principles and agrees qualitatively with the numerical results.

Elimination of cross talk in waveguide intersections

We present general criteria for crossing perpendicular waveguides with nearly 100% throughput and 0% cross talk. Our design applies even when the waveguide width is of the order of the wavelength. The theoretical basis for this phenomenon is explained in terms of symmetry considerations and resonant tunneling and is then illustrated with numerical simulations for both a two-dimensional photonic crystal and a conventional high-index-contrast waveguide crossing. Cross-talk reduction by up to 8 orders of magnitude is achieved relative to unmodified crossings.

Coupling-induced resonance frequency shifts in coupled dielectric multi-cavity filters.

Coupling-induced resonance frequency shifts (CIFS) are theoretically described, and are found to be an important fundamental source of resonance frequency mismatch between coupled optical cavities that would be degenerate in isolation. Their deleterious effect on high-order resonant filter responses and complete correction by pre-distortion are described. Analysis of the physical effects contributing to CIFS shows that a positive index perturbation may bring about a resonance shift of either sign. Higherorder CIFS effects, the scaling of CIFS-caused impairment with finesse, FSR and index contrast, and the tolerability of frequency mismatch in telecom-grade filters are addressed. The results also suggest possible designs and applications for CIFS-free coupled-resonator systems.

Mode-coupling analysis of multipole symmetric resonant add/drop filters

Time-dependent mode-coupling theory is used to analyze a type of resonant add/drop filter based on the excitation of degenerate symmetric and antisymmetric modes. Flat-top transfer functions are achieved with higher order filters that utilize multiple resonator pairs, designed to satisfy the degeneracy conditions. The resulting analytic expressions lead to an equivalent circuit and the transfer characteristics of the filter are related to standard L-C circuit designs.

Silicon-based highly-efficient fiber-to-waveguide coupler for high index contrast systems

A coupler to efficiently transfer broadband light from a single-mode optical fiber to a single-mode high-index contrast waveguide has been fabricated on a silicon substrate. We utilized a novel coupling scheme, with a vertically asymmetric design consisting of a stepwise parabolic graded index profile combined with a horizontal taper, to simultaneously confine light in both directions. Coupling efficiency has been measured as a function of the device dimensions. The optimal coupling efficiency is achieved for structures whose length equals the focal distance of the graded index and whose input width is close to the mode field diameter of the fiber. The fabricated structure is compact, robust and highly efficient, with an insertion loss of 2.2dB at 1550nm. The coupler exhibits less than 1dB variation in coupling efficiency in the measured spectral range from 1520nmto1620nm. The lowest insertion loss of 1.9dB is measured at 1540nm. The coupler design offers highly efficient coupling for single mode waveguid...

Passive components for dense optical integration

1 Introduction.- 1.1 Motivation.- 1.2 Outline of the book.- 1.2.1 Theoretical background.- 1.2.2 The FDTD method.- 1.2.3 Resonant channel add/drop filters.- 1.2.4 Low-loss waveguide components.- 1.2.5 Fiber-PIC coupling.- 2 Theoretical Background.- 2.1 Modes in optical waveguides.- 2.1.1 Normal modes.- 2.7.2 General form of guided fields.- 2.1.3 Orthogonality relations.- 2.1.4 Completeness of normal modes.- 2.2 Excitation of modes by localized currents.- 2.3 Scattering matrix.- 2.4 Effective Index Method (EIM).- 2.5 Resonators.- 2.5.1 Coupled resonators.- 2.5.2 Resonator-waveguide coupling.- 2.6 Gaussian Beams.- 2.6.1 Propagation of Gaussian beams.- 2.6.2 ABCD matrices.- 2.6.3 Approximation of effective index and mode profile using Gaussians.- 3 The Finite Difference Time Domain (FDTD) Method.- 3.1 The Yee algorithm.- 3.2 Finite Differencing.- 3.2.1 Three-dimensional algorithm.- 3.2.2 Two-dimensional algorithm.- 3.3 Boundary Conditions.- 3.4 Source Implementation.- 3.5 The use of Discrete Fourier Transform (DFT) in FDTD.- 3.6 Resonator calculations using FDTD.- 4 Resonant Add/Drop Filters.- 4.1 Introduction.- 4.2 Four-port system with single mode resonator.- 4.3 Symmetric standing-wave channel add/drop filters.- 4.3.1 General form of a symmetric channel add/drop filter.- 4.3.2 Symmetric add/drop filter with two identical standing-wave cavities66.- 4.4 FDTD simulations.- 4.4.1 Polygon resonators.- 4.4.2 Single square resonator coupled with two waveguides.- 4.4.3 Channel add/drop filter using a pair of square resonators.- 4.5 High-order symmetric add/drop filters.- 4.6 Phase response and dispersion.- 5 High Density Integrated Optics.- 5.1 Introduction.- 5.2 Sharp 90o bends.- 5.3 3D simulations and measurements on HTC bends.- 5.4 T-splitters.- 5.5 Waveguide crossings.- 6 Fiber-PIC coupling.- 6.1 Introduction.- 6.2 Lateral mode conversion using cascade of square resonators.- 6.3 Mode conversion using dielectric planar lenses.- 6.4 3D mode-conversion scheme.- 7 Conclusions and Future Directions.- 7.1 Summary.- 7.2 Fiber-chip coupling.- 7.3 Polarization dependence.- 7.4 Numerical tools.- References.

OPTICAL RESONATORS AND FILTERS

Dielectric optical resonators of small size are considered for densely-integrated optical components. High-index-contrast microresonators of low Q are shown, using microwave design principles, to permit wavelength-sized, low-loss, reflectionless waveguide bends and low-crosstalk waveguide crossings. The analysis and synthesis of high-Q, high-order microringand racetrack-resonator channel add/drop filters are reviewed, supplemented by simulation examples. Standing-wave, distributed Bragg resonator filters are also described. The study is unified by a coupled-mode theory approach. Rigorous numerical simulations are justified for the design of high-index-contrast optical “circuits”. Integratedoptical components are described within a polarization-diversity scheme that circumvents the inherent polarization dependence of high-index-contrast devices. Filters fabricated in academic and commercial research, and a review of microring resonator technology, advances and applications are presented.

High density optical integration

By proper design of optical waveguides and resonators with high index-contrast one may minimize the radiation loss. Such structures can be used to realize bends, waveguide crossings and filters of small size, leading to dense optical integration.

Compact 3 dB single mode fiber-to-waveguide coupler

On-chip coupler to transform 1550 nm light from single-mode optical fiber to single-mode waveguide index of 1.70 has been fabricated using CMOS processes. A 3-dB insertion loss is recorded for compact structures 18 /spl mu/m long.