Sagnac effect in rotating photonic crystal micro cavities and miniature optical gyroscopes
This presentation is the property of its rightful owner.
Sponsored Links
1 / 14

Sagnac Effect in Rotating Photonic Crystal Micro-Cavities and Miniature Optical Gyroscopes PowerPoint PPT Presentation


  • 112 Views
  • Uploaded on
  • Presentation posted in: General

Tel Aviv University. Sagnac Effect in Rotating Photonic Crystal Micro-Cavities and Miniature Optical Gyroscopes. Ben Z. Steinberg Ady Shamir Amir Boag. No mode degeneracy. Presentation Overview. The PhC CROW – based Gyro New manifestation of Sagnac Effect

Download Presentation

Sagnac Effect in Rotating Photonic Crystal Micro-Cavities and Miniature Optical Gyroscopes

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Tel Aviv University

Sagnac Effect in Rotating Photonic Crystal Micro-Cavities and Miniature Optical Gyroscopes

Ben Z. Steinberg

Ady Shamir

Amir Boag


No mode degeneracy

Presentation Overview

  • The PhC CROW – based Gyro

    • New manifestation of Sagnac Effect

    • Array of weakly coupled “conventional” micro-cavities

      • What happens if the micro-cavities support mode-degeneracy ?

  • Micro-cavities with mode degeneracy

    • Single micro-cavity: the smallest gyroscope in nature.

    • Set of micro-cavities: interesting physics

Steinberg, Scheuer, Boag, Slow and Fast Light topical meeting, Washington DC July 06.


Micro-cavities

[1] Steinberg B.Z., “Rotating Photonic Crystals: A medium for compact optical gyroscopes,” PRE71 056621 (2005).

CROW-based Gyro: Basic Principles

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

Stationary

Rotating at angular velocity

  • C - wise and counter C - wise propag are identical.

  • Dispersion: same as regular CROW except for additional requirement of periodicity:

  • Co-Rotation and Counter - Rotation propag DIFFER.

  • Dispersion differ for Co-R and Counter-R:

Two different directions


Formulation

  • E-D in the rotating system frame of reference:non-inertial

    • We have the same form of Maxwell’s equations:

    • But constitutive relations differ:

    • The resulting wave equation is (first order in velocity):

[2] T. Shiozawa, “Phenomenological and Electron-Theoretical Study of the Electrodynamics of Rotating Systems,” Proc. IEEE61 1694 (1973).


At rest

Rotating

w

|W0Q|

w (km ; W0)

Dw

w (-km ; W0)

w0

w (km ; W0 = 0 )

k

-km

km

W0Q

Solution

[1] Steinberg B.Z., “Rotating Photonic Crystals: A medium for compact optical gyroscopes,” PRE71 056621 (2005).

  • Procedure:

    • Tight binding theory

    • Non self-adjoint formulation (Galerkin)

  • Results:

    • Dispersion:

Depends on system design !

=Stationary micro-cavity mode


Theoretical

Numerical

The Gyro application

  • Measure beats between Co-Rot and Counter-Rot modes:

  • Rough estimate:

  • For Gyros operating at FIR and CROW with :

Theoretical and

Numerical


  • Two waves having the same resonant frequency :

  • Two different standing waves

  • Or: (any linear combination of degenerate modes is a degenerate mode!)

  • CW and CCW propagations

  • Rotationaffects these two waves differently:Sagnac effect

The single micro-cavity with mode degeneracy

  • The most simple and familiar example: A ring resonator

  • Degenerate modes in a Photonic Crystal Micro-Cavity

Local defect:

TM

How rotation affects this system ?


  • The rotating system field satisfies the wave equations:

Reasonable approximation because:

Rotation has a negligible effect on mode shapes.

It essentially affects phases and resonances.

H.J. Arditty and H.C. Lefevre, Optics Letters, 6(8) 401 (1981)

FormulationRotating micro-cavity w M -th order degeneracy

  • M - stationary system degenerate modes resonate at :

  • After standard manipulations (no approximations):

  • Express the rotating system field as a sum of the stationary system degenerate modes (first approximation):


An M x M matrix eigenvalue problem for the frequency shift :

Then, is determined by the eigenvalues of the matrix :

Formulation (Cont.)

where the matrix elements are expressed via the stationary cavity modes,

Frequency splitting due to rotation

Splitting depends on effective rotation radius, extracted byB


But recall:

More on Splitting: Symmetries

  • The matrix C is skew symmetric , thus

    • M even: are real and always come in symmetric pairs around the origin

    • Modd: The rule above still applies, with the addition of a single eigenvalue at 0.

  • For M=2, the coefficients (eigenvector) satisfy:

The eigen-modes in the rotating system rest-frame are rotating fields


Specific results

For the PhC under study:

Full numerical simulation

Using rotating medium Green’s function theory

Extracting the peaks


  • Mechanically Stationary system:

  • Both modes resonate at

  • “Good” coupling

Interaction between micro-cavities

  • The basic principle:

    A CW rotating mode couples only to CCW rotating neighbor

  • Mechanically Rotating system:

  • Resonances split

  • Coupling reduces

A new concept: the miniature Sagnac Switch


  • An -dependent gap in the CROW transmission curve

cascade many of them…

  • Periodic modulation of local resonant frequency

  • Periodic modulation of the CROW difference equation, by

Excitation coefficient of the m-th cavity

Steinberg, Scheuer, Boag, Slow and Fast Light topical meeting, Washington DC July 06.


Conclusions

  • Rotating crystals = Fun !

  • New insights and deeper understanding of Sagnac effect

  • The added flexibility offered by PhC (micro-cavities, slow-light structures, etc) a potential for

    • Increased immunity to environmental conditions (miniature footprint)

    • Increased sensitivity to rotation.

Thank You !


  • Login