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All-Optical Gyroscope Based on Sagnac Effect in Photonic Crystal Coupled Cavity Waveguides and Slow Light Structures. Work published in: B.Z. Steinberg, ‘’ Rotating photonic crystals: a medium for compact optical gyroscopes ” , Phys. Rev. E, vol 71, pp. 056621-7, May 31 2005.

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slide1
All-Optical Gyroscope Based on Sagnac Effect in Photonic Crystal Coupled Cavity Waveguides and Slow Light Structures

Work published in:

B.Z. Steinberg, ‘’Rotating photonic crystals: a medium for compact optical gyroscopes”,

Phys. Rev. E, vol 71, pp. 056621-7, May 31 2005

basic principles

Micro-cavities

Basic Principles

A CCW folded back upon itself in a fashion that preserves symmetry

Stationary

Rotating at angular velocity

  • C - wise and counter C - wise propag are identical.
  • “Conventional” self-adjoint formulation.
  • Dispersion is the same as that of a regular CCW except for additional requirement of periodicity:
  • Co-Rotation and Counter - Rotation propag DIFFER.
  • E-D in accelerating systems; non self-adjoint
  • Dispersion differ for Co-R and Counter-R:

Two different directions

formulation
Formulation
  • E-D in the rotating system frame of reference:
    • We have the same form of Maxwell’s equations:
    • But constitutive relations differ:
    • The resulting wave equation is (first order in velocity):
solution

At rest

Rotating

w

|W0Q|

w (km ; W0)

Dw

w (-km ; W0)

w0

w (km ; W0 = 0 )

k

-km

km

W0Q

Solution
  • Procedure:
    • Tight binding theory
    • Non self-adjoint formulation (Galerkin)
  • Results:
    • Dispersion:

Depends on system design

the gyro application
The Gyro application
  • Measure beats between Co-Rot and Counter-Rot modes:
  • Rough estimate:
  • For Gyro operating at optical frequency and CCW with :