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.

+ +ELECTRONICS OPTICS MICROMECHANICS

TELECOMMUNICATIONS SENSING

BELL-Labs LUCENTThick-Film PZT Sensing Element

http://www.usitt.ecs.soton.ac.uk

OPTICAL COMPUTING

UCLA –Integrated Free-Space Optical Disk Pickup Head Texas Instruments-DMD

IMAGING

Switches, Attenuators, Modulators

System Level

System Modeling

System Performance

Behavioral Level

Circuit Modeling

Reduced Order-ODE

Device Level

Device Modeling

3D/EM

• Ensemble of component behavioral

models.

• Fast solvers at component/behavior

level.

• Domain specific signal propagation

models.

• Global discrete event dataflow.

Ensemble performance measures:

• BER

• Optical/electrical crosstalk.

• Packaging/alignment tolerances.

• Thermal effects.

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

Vector

Solutions

Scalar Approximations

Full Wave Solutions

Rayleigh-Sommerfeld & Fresnel-Kirchoff

Fresnel (Near Field)

Fraunhofer (Far field)

Z >> λ Z >> Z >>

z

850nm 966um 4.66mm

Micro-Systems

Example: 50 um Aperture, 200 um Observation, λ=850 nm

Wave front -Spherical

Wave front -Parabolic

Wave front -Planar

x

U1(,) U2(x,y)

r

z

y

2),(1),(2r

eU

j

zyxU

jkr

• Diffractive component >>λ

• Distance to observation plane >>λ

SCALAR DIFFRACTION-RAYLEIGH SOMMERFELD FORMULATION:

IMPLEMENTATION:

• Huygens- Fresnel Principle

• Direct Integration

- Computation Order: O(N4)

•Angular Spectrum Approach

- Computation Order: O(N2LogN)

Input Complex Wave front Free Space Propagation Output Complex

Wave front

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

Example: 100X100 points, λ=850nm, spot size=20um, z=300um

Aperture Plane Observation Plane

Tilt in x

Offset in Y

Example: 100X100 points, λ=850nm, spot size=20um, z=300um

VCSEL THIN REFRACTIVE LENS DETECTOR

f 2f f

King et al. 1996

Input Output

Example: 100X100 points, λ=850nm, spot size=20um, z=300um, focal length=100um

Z=300um

REFRACTIVE LENS

FRESNEL LENS

UCLA- Fresnel Lensf f2f

Input Output

Example: 100X100 points, λ=850nm, spot size=20um, z=300um, focal length=100um

Z=300um

An Optical System that alters the Polarization of a plane wave

Example: Reflection and Refraction of a TEM wave

Transition of Scalar Wave theory to Semi-Vector theory in cases where boundary conditions have to be taken into consideration.

T1

T2

T3

R1

R2

R3

n1

n2

n3

Multi Thin-film stack

Incident

ReflectedRefracted

A Complex wave incident at a planar interface with n1=1, n2=1.5,z1=300um,z2=300um,z3=300um.

In a related area of research, we propose:

OPTICAL MODELING:

Efficient Rayleigh- Sommerfeld Scalarand Semi-Vector Modeling.

CONTROL ALGORITHM:

Model Predictive control.

EMPLOY:

Off -the-shelf semiconductor and otherautomation assembly equipment.

BENEFITS:

High Performance, Low cost, Increased Productivity.

A Planar Light wave Structure

www.bonders.com

•Determine errors between expected maximum power and measured•Fine tune position forfabrication misalignments

•Detect Power

•Set initial position(i.e., feed forward)

•Enable Input Sourcefor power testing

•Simulation performed using system level optical CAD tool•Uses Rayleigh-Sommerfeld scalar modeling

Feed-forward Controller

FeedbackController Motor

Power EfficiencyVs.

Displacement

Power Sensing Element

Output+

-Reference Input

www.bonders.com

Current Solution:

Compares optical power with neighboring optical power, until maximum is reached. In this example, takes 50 time steps.

Proposed Solution:

Simulate system to find initial position, then fine tune result. Alignment reached quickly. In this example, takes 3 time steps.

Optical Intensity Profile

Current Solution:

Hill climbing method gets caughtin a local minimum of intensity distribution.

Proposed Solution:

With simulation, we feed forward our control algorithm to the ideal initial placement.

Fiber-Array Coupling

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.