1. 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.

2. + + Optical Microsystems OPTICS ELECTRONICS MICROMECHANICS SENSING
TELECOMMUNICATIONS
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 um. 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 dmd array
OPTICAL COMPUTING
UCLA –Integrated Free-Space Optical Disk Pickup Head
Texas Instruments-DMD

3. 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

4. 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.

5. 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

6. 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.

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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.

15. 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

16. Simple Uni-Modal Distribution Case
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.

17. 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.

18. 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.