22 February 2017 (Version 1.1) – Cem Bonfil
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OptiSPICE applications:
Ring Resonator Gyroscope

Fiber Optic Gyroscope Building Blocks

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Phase Modulator
Phase ModulationThe first splitter is used to create clockwise (CW) andcounter clockwise (CCW) propagating waves in the ring
resonator using a single laser source
In OptiSPICE phase delay elements can be used tochange the phase of an optical signal using a voltage nodeIn this Ring Resonator Gyroscope design, phase delay
elements are used to introduce a linear increase in phaseover time to shift the carrier frequency of the CW and CCW
propagating waves
This frequency shift is used to keep the carrier frequency of
the CW and CCW propagating waves at resonanceLinear Phase Increase
The simulation results show the effect of the linear
increase in phaseAt time=0 the carrier frequency is equal to theresonant frequency of the ring resonator

The introduction of the linear increase in phaseover time shifts the carrier frequency of the waves
travelling inside the ring resonatorOver time, because the carrier frequencies shift
towards off-resonance, the output at the drop port
decreases and reaches a new steady stateOptiSPICE Ring Resonator Model

Ring Resonator parametersCircumference of the ring, L = 3.14 m

Refractive index of the waveguide, n = 1.5

Propagation loss, a = 1

Coupling coefficients, r1 = 0.045, r2 = 0.045

Change in length (L1 = L + alphaL*V) , alphaL = 1

Basic Equations*, m = 1,2 3 ...





*Bogaerts, Wim, et al. "Silicon microring resonators." Laser & Photonics Reviews 6.1 (2012): 47-73.
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Ring Resonator/Sagnac Effect

Building blocks

2 Cross Couplers



4 Waveguides



4 Optical Isolators



4 Waveguides

CWCCW

OptiSPICE Model

Explicit multilayer filter model is set up with a single layerThe length change in the waveguide can be controlled by avoltage source

The relationship between the length change in the waveguide andthe voltage can be made linear or non-linearOptical Forks and Isolators are used to separate clockwise (CW)
and counter clockwise (CCW) traveling signals so a different
length change (due to Sagnac effect) can be applied to eachsignal

Sagnac Effect*
Number of turns, NSpeed of light, cSpeed of light in dielectric medium,

Area of the ring resonator, A

Rotational Speed,

The change in distance seen by CW and CCW signals,

The relationship between rotational speed and change inresonant frequency is given by,

CCW DropPortCW Drop Port

*VAWTER, GREGORY A., et al. Developments in pursuit of a micro-optic gyroscope. No. SAND2003-0665. Sandia National Labs.,
Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US), 2003.

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Resonance Detection
Keeping the carrier at resonant frequency

2 separate resonance detectors are used for CW and CCW
propagating optical signals
The output of the balanced detectors are used to drive the controllerthat generates the signal for phase modulation
The RC filter following the output of the balanced detectors is usedto filter out sudden changes at the output which may destabilize thecircuit and cause divergence during simulation

Length vs. Detector Output


The simulation results show the balanced
detector output vs. the change in thecircumference of the ring resonatorThe carrier frequency is equal to theresonant frequency of the ring resonatorwhen dL = 0, the drop port output is at its
peak and the balanced detectors are at 0 V

The output of the balanced detectors
increase/decrease as the circumference ofthe ring resonator increases/decreasesThe output at the drop port also decreases
as the size of the circumference changes

Balanced Detectors
Drop PortOutput
Laser
OutputRC Filter

PID CONTROLLER
PhaseModulator
Control Signal

Generating Phase Modulation Signal
When there is a shift in resonant frequency the outputof the balanced detectors shift away from 0 V

The proportional-integral (PI) controller calculates ashift in frequency proportional the balanced detector
output

The integrator following the PI controller generates thephase modulator signal that shifts the carrier frequency
going into the ring resonator

The RC filter following the output of the PI controller isused to filter out sudden changes at the output which
may destabilize the circuit and cause divergenceduring simulation

PI CONTROLLER
BalancedDetectorOutput

RC FilterIntegrator

Simulation Results
Calculating the rotation speedIn this example rotation speed of 3500
deg/h (0.01697 rad/s) was applied to thering resonator by varying its
circumference using the following
equation,

The simulation results from OptiSPICE
shows the output of the drop port moving
back to resonance (max output) overtimeAs the output of the drop portapproaches resonance the balanced
detector output reaches 0 due to theapplication of the linear phase increaseby the phase modulator



Finally the rotation speed can becalculated from the difference in resonant
frequencies of CW and CCW signals
using the following equation,