ABSTRACT The design of a complete system level modeling and simulation tool for optical micro-systems is the focus of our research . We use a rigorous optical modeling technique based on the rigorous Scalar Rayleigh-Sommerfeld formulation, which is efficiently solved with an angular spectrum approach. Our current research involves a semi-vector analysis which is applied in cases where the boundary conditions have to be explicitly modeled . In a related area of research, we are using our optical modeling technique to support the challenge of automated alignment and packaging of complex optical micro-systems.

+ + Optical Microsystems OPTICS ELECTRONICS MICROMECHANICS SENSING TELECOMMUNICATIONS http://www.usitt.ecs.soton.ac.uk Switches, Attenuators, Modulators Thick-Film PZT Sensing Element BELL-Labs LUCENT IMAGING Dmd..digital micro device dimensions 150X140um. 1 million projection mirrors on a side of 16um.typcial distance between components is between 10-1000um. Micromachined Silicon Accelerometer with Thick-Film PZT Sensing Elements .. AT THE HEART OF LUCENT TECHNOLOGIES' WAVESTAR(tm) LAMBDA ROUTER, a breakthrough all-optical lightwave-routing device invented at Bell Labs, is an array of microscopic mirrors, each able to tilt in various directions, to steer light. The micro-mirrors route information in the form of photons, or light pulses, to and from any of 256 input/output optical fibers.all optical router.free space optical dsip picku up head consists of a semiconductor laser, a collimating lens, a beamsplitter, a focussing lens, a 45 degree reflecting mirror, and a 45 degree upward reflecting mirror, the reflecting signal is collected by the focusing lens and directed by the beamsplitter and the downward mirror to a photodetector on a silicon substrate. Optical disk pickup head-optical sensing, multistorage media,,dmd-scanning ,imaging,display.640-480 dmd array OPTICAL COMPUTING UCLA –Integrated Free-Space Optical Disk Pickup Head Texas Instruments-DMD

System-Level Simulation Ensemble of component behavioral models. Fast solvers at component/behavior level. Domain specific signal propagation Global discrete event dataflow. Ensemble performance measures: BER Optical/electrical crosstalk. Packaging/alignment tolerances. Thermal effects. System Modeling System Performance Behavioral Level Circuit Modeling Reduced Order-ODE System level tools include multiple domains and model components with their functionality rather than their physical construction .device based models are solved using 3D vector solutions.components are accurately modeled, however complexity makes simulations prohibitive.second level is modeling abstraction and are used using reduced order models, typically ode.eg.spice,vhdl-ams.as components and domain increase, computaitonally inefficient.highest abstract modeling is system level.uses component behavior models and uses fast solvers .and supports domain specific signal propagation models.using this, ber,crosstalk etc are simulated. Device Level Device Modeling 3D/EM

Optical Propagation Models Ray Propagation - Direction, position and angles Gaussian Propagation - 9 scalar parameters(z0,x,y,z,etc..) - Fast simulation (no integration) - Limited diffraction modeling Scalar Optics - 2D complex wave front - Propagation by summation of wave fronts Vector Analysis - Intensive computation, Boundary Element Rays obeying a set of rules.. Size of objects are much greater than the wavelength.,,ray optics is the limit of wave optics when wavelength is infifntesimaly small..classical or quantum optics provides the complete treatment of highher optical phenomena.

Validity of Scalar Models Rayleigh-Sommerfeld & Fresnel-Kirchoff Fresnel (Near Field) Fraunhofer (Far field) Full Wave Solutions Z >> Z >> λ Z >> Scalar Approximations Vector Solutions Wave front -Spherical Wave front -Parabolic Wave front -Planar Micro-Systems Wavefront remains spherical in rs region, becomes parabolic in fresnel and plane in fraunhofer region. z 850nm 966um 4.66mm Example: 50 um Aperture, 200 um Observation, λ=850 nm

Rayleigh-Sommerfeld Formulation SCALAR DIFFRACTION-RAYLEIGH SOMMERFELD FORMULATION: Diffractive component >>λ Distance to observation plane >>λ  x U1(,) U2(x,y) r z  y IMPLEMENTATION: Huygens- Fresnel Principle Direct Integration - Computation Order: O(N4) Angular Spectrum Approach - Computation Order: O(N2LogN) Supports diffraction,order is n2m2 using brute force integration method...with angular spectrum approach we get n2logn. Efficiency.

Angular Spectrum Algorithm Input Complex Wave front Output Complex Wave front Free Space Propagation Spatial Domain Fourier Domain Spatial Domain Decompose Spherical wave front into angled plane waves using Fast Fourier Transform. Multiply with Free Space Transfer function. Sum Plane waves into Spherical Wave Function with Inverse Fast Fourier Transform. Computational order (N2LogN). Spatial Frequencies

Free Space Propagation Observation Plane Aperture Plane Free Space Propagation Eg a complex waveform with waist 10um and propagation distance 300um wavelength=850nm. Example: 100X100 points, λ=850nm, spot size=20um, z=300um

Optical Propagation in Tilted and Offseted Planes Tilt in x Offset in Y Planes are tilted and offseted by 30 degree and offseted by 20um Example: 100X100 points, λ=850nm, spot size=20um, z=300um

Optical Systems (4 -f imaging System) VCSEL THIN REFRACTIVE LENS DETECTOR REFRACTIVE LENS King et al. 1996 Input Output Refractive lens= focal length=100um..low focal length lens are difficult to fabricate. Refractive lens 300um in diameter. Z=300um Example: 100X100 points, λ=850nm, spot size=20um, z=300um, focal length=100um

Diffractive Optical System UCLA- Fresnel Lens f 2f f FRESNEL LENS Input Output Frenel lens=10% efficienccy.. Major use as a collimator. Z=300um Example: 100X100 points, λ=850nm, spot size=20um, z=300um, focal length=100um

Semi-Vector Analysis Transition of Scalar Wave theory to Semi-Vector theory in cases where boundary conditions have to be taken into consideration. Considering boundary condiotns leads to transition from scalar to vector solutions.. An Optical System that alters the Polarization of a plane wave Example: Reflection and Refraction of a TEM wave

Reflection and Refraction at a planar interface Reflected Refracted Eg reflections from multilayer strcuture… Multi Thin-film stack A Complex wave incident at a planar interface with n1=1, n2=1.5,z1=300um,z2=300um,z3=300um. R3 T3 n3 R2 T2 n2 n1 R1 T1 Incident

Knowledge Based Optoelectronic Packaging In a related area of research, we propose: OPTICAL MODELING: Efficient Rayleigh- Sommerfeld Scalar and Semi-Vector Modeling. CONTROL ALGORITHM: Model Predictive control. EMPLOY: Off -the-shelf semiconductor and other automation assembly equipment. BENEFITS: High Performance, Low cost, Increased Productivity. A Planar Light wave Structure Modeling using a priori knowldege.. Our approach is to build an a priori knowledge model, specific to the assembled package’s optical power propagation characteristics. To gain this a priori knowledge, we must design a model based controller with both feed-forward and feedback components, along with the inclusion of a built in optical power sensor . As can be seen, we first simulate the complete system, and feed-forward the ideal position of the motors to achieve maximum coupling efficiency. The optical power is measured at the specified position, and errors can be determined by comparing the measured result and the expected simulated power value. From this result, the feedback loop continues fine tuning the position of the components to achieve maximum power coupling efficiency. Small misalignment errors are expected when compared to the ideal simulations, as the positions of the photonic chip and input and output fibers can not be guaranteed in automatic grippers/positioners and fiber V-groves. www.bonders.com

Model based Optoelectronic Assembly Simulation performed using system level optical CAD tool Uses Rayleigh-Sommerfeld scalar modeling Set initial position (i.e., feed forward) Enable Input Source for power testing Feed-forward Controller + Feedback Controller Output Motor Power Efficiency Vs. Displacement Reference Input - Feed forward algorithm.. As can be seen, we first simulate the complete system, and feed-forward the ideal position of the motors to achieve maximum coupling efficiency. The optical power is measured at the specified position, and errors can be determined by comparing the measured result and the expected simulated power value. From this result, the feedback loop continues fine tuning the position of the components to achieve maximum power coupling efficiency. Small misalignment errors are expected when compared to the ideal simulations, as the positions of the photonic chip and input and output fibers can not be guaranteed in automatic grippers/positioners and fiber V-groves. Power Sensing Element Determine errors between expected maximum power and measured Fine tune position for fabrication misalignments Detect Power

Simple Uni-Modal Distribution Case www.bonders.com Proposed Solution: Simulate system to find initial position, then fine tune result. Alignment reached quickly. In this example, takes 3 time steps. Current Solution: Compares optical power with neighboring optical power, until maximum is reached. In this example, takes 50 time steps.

Multi-Modal Distribution Grating Coupling Optical Intensity Profile Fiber-Array Coupling Current Solution: Hill climbing method gets caught in a local minimum of intensity distribution. Proposed Solution: With simulation, we feed forward our control algorithm to the ideal initial placement.

Conclusion and Future Work Achievement of speed of Fraunhofer approximation, with the accuracy of Rayleigh-Sommerfeld formulation. A Semi-Vector technique is employed to support boundary conditions. More System Level Simulations and Validations. Advanced Modeling of MEMS and Grating Devices. Error Prediction.