Optical MEM

1. Introduction
Recently, optical MEM (micro-electrical-mechanical) components have been used in a number of optical
interconnect designs. Typically, these systems are based on micro-mirror components used to switch, steer, and
direct optical beams through the system. Lucent Technologies and Optical Micro Machines (OMM) have
commercialized small switching systems using these optical MEM mirrors and plan on scaling these designs to
larger switching networks. For successful development of optical MEM systems, CAD tools are needed to simulate
and reduce the high cost of prototyping and testing. CAD tools can greatly reduce the time it takes to develop a
marketable product.
Currently, a complete mixed-technology CAD tool is not available, as simulations of these systems are
commonly performed using a variety of single domain tools, such as SPICE for the electronics, Code V [1] for the
optics, and ANSYS [2] for the mechanics, with very little or no interaction between the tools. We have developed a
free-space opto-electronic CAD tool, called Chatoyant, for system-level modeling of optical interconnects [3]. With
the addition of mechanical models and determining the appropriate optical propagation technique for micro-systems,
we have extended Chatoyant to support the modeling and simulation of optical MEM systems. In this paper, we
briefly describe our modeling methodology for micro-optics and mechanics, and present the dynamic simulation of a
2x2 optical MEM switch.
2. Models
For the quickest simulations, Chatoyant performs Gaussian propagation for its optical models. However, this
propagation method does not support diffraction or propagation through diffractive components. At OC'99, we
presented Chatoyant's addition of the Fresnel approximation to simulate diffractive effects in interconnect and
switching systems. However, when system and component sizes shrink to the scale of microns, as found in optical
MEM systems, the validity of the Fresnel approximation is questioned and a more rigorous technique must be
performed. Chatoyant currently supports the Rayleigh-Sommerfeld formulation for optical propagation [4]. This
technique is limited only by the requirement that the aperture sizes and propagation distances are greater than the
light's wavelength, which is valid for most optical MEM systems.
Our mechanical models extend our piece-wise linear (PWL) technique that is used to model Chatoyant's
electrical signals. We employ a modified nodal representation for the component, piece-wise linear modeling of
non-linear devices, and piece-wise characterization of signals to accomplish the simulation of these mixed
technology systems. The details can be found in [5]. This PWL technique results in a decrease in computational
time and allows for a user-determined trade-off between accuracy and computation speed. The model for a
mechanical device can be summarized in a set of differential equations that define its dynamics as a reaction to
external forces and given to the PWL solver for evaluation. In Chatoyant, a MEM device is characterized by its
basic components, such as beams, plate-masses, joints, and electrostatic gaps, and the local interactions between
these components.
3. Simulations
In this paper, we concentrate on the modeling and simulation of a 2x2 optical MEM switch. This architecture
consists of a set of four optical fibers in the shape of a "+" sign, with the input and output fibers facing each other
through a free-space gap. The switching system is in the "cross" state when the light is passed straight across the
free-space gap. However, to switch to the "bar" state, a micro-mirror is inserted between the fibers at a 45-degree
angle, and the light is reflected to the alternate output. Systems built with these switches have numerous advantages
over typical waveguide or fiber switching systems, including a reduction of coupling loss and crosstalk, as well as
being independent of wavelength, polarization, and data format [6]. The switches have been reported to be 10 times
smaller and faster than typical fiber-based switches, while requiring only 1/100th of the operating power [7]. We
use RSoft's BeamPROP [8] to simulate the light through the fiber, and have developed an interface between the
fiber propagation (BeamPROP) and free-space (Chatoyant) through a data file.
For simplicity, we simulate only a single input switching to either the cross or bar state throughout this paper.
Both output states are seen in Figure 1, represented by the solid and dashed arrows, respectively. The mirror
fabrication and positioning can be achieved in a variety of ways. For example, in a Bell-labs design [9], a "see-saw"
pivoting mirror is inserted into the optical path. UCLA [6] and AT&T [10] both have systems using scratch drive
actuators (SDA) to assemble and position the mirror between the fibers, and the University of Neuchael, Switzerland
[11] uses a combdrive actuator design to slide the mirror into the free-space gap. However, for the simulations
presented in this paper, we use a system loosely based on an experimental system designed and tested at UCLA [12].
Similar to that system, a mirror is placed on top of a long anchored cantilever beam. In our system, the bar state is
achieved in the steady-state of the system, with the mirror positioned between the fibers in the free-space gap. The
cross state is achieved by the cantilever beam bending towards the substrate, moving the attached mirror out of the
optical path. The beam movement is a result of electrostatic attraction between a voltage applied below the
cantilever and the beam itself. This attraction results in a force being applied to the beam. The simulated system is
also represented by Figure 1. The mirror is 100 x 100 mm, and is positioned at the end of a 700 mm cantilever beam.
Both beam and mirror are fabricated with polysilicon, with the ideal mirror having a 100% reflectivity. The beam is
2 mm wide and 100 mm thick, while the mirror is 4 mm thick, to ensure the mirror remains rigid. The collimating
lenses (f = 50 mm) are placed 50 mm from the fiber ends, and there is a free-space gap of 100 mm between the lenses.

We first use Chatoyant to analyze the mechanical movement of the beam and mirror. The more significant mode
frequencies of the beam, including the mirror mass, are determined to be 3.7 and 27.1 kHz, resulting in a period of
about 270 msec. These results have been verified through the finite element (FE) solver, ANSYS, with the results
within 5% of each other. For a switching speed of 400 msec, the response of the beam, in terms of the center
position of the mirror from the original steady-state value, is shown in Figure 2. The switching force applied to the
cantilever beam is also included in Figure 2, represented by the dashed line. We next examine the optical power that
is detected on the bar state's fiber end (10 mm diameter) for the same 400 mm switching case. Chatoyant intensity
distributions at an observation plane on the bar fiber end are included for three points on the response curve, labeled
A, B, and C. A is when the mirror is inserted in the optical path, achieving the bar state in the system.
B is at the point where the mirror is totally out of the optical path, achieving the cross state. As seen in the intensity
distribution, no power hits the bar detector,. C is somewhere in the middle, as the response of the mirror has caused
some power to be detected at the bar state. The power on the bar fiber is shown in Figure 3 in terms of dB lost.
Notice that the power detected corresponds to the mirror position movement in Figure 2. Therefore, as the mirror
bounces, like at point C, optical power is detected in the bar fiber, even though the input force is trying to drive the
light into the cross state. This allows for the possibility of crosstalk or the detection of a false "1". Also included in
Figure 3, is the optical power detected with a slower switching speed (600 msec). With this mirror response, the
power detected in the bar state, while the mirror is switched to the cross state is always less than -45 dB.
We next further examine the mirror position, where the light strikes it, and the effect that this has on the power
detected on the observation plane at the bar state fiber end. To help us in our explanations, we look at the intensity
contour for each of the three cases we previously examined. The three intensity contours are seen in Figure 4, along
with a circle drawn to representing the fiber. For case A, the light strikes the mirror in the center and reflects
directly into the bar fiber. As seen in the figure, the contour for A is directly on the fiber, and we consider this full
detected power (0 dB loss). For case B, the mirror is moved totally out of the optical path, resulting in virtually no
power being detected on the fiber (123 dB of loss). However, it is interesting to note that even though almost all the
power is missing the detector plane, there is still a diffractive effect, with very low power, striking the observation
plane, approximately 28 mm away from the fiber center. In this system, it is not destructive, however, an effect like
this could introduce crosstalk in larger scaled systems. With case C, the mirror is positioned such that half of the
light is reflected off the mirror to the bar detector, and the other half propagates through to the cross detector. With
the light striking the edge, the power is still concentrated, however, it is centered 3 mm from the fiber center. For C,
a 6 dB loss in power is experienced on the bar fiber.