Abstract

We study the transmission of an optical field through a rotating coupled resonator optical waveguide (CROW) in which the size of the ring resonators changes from one ring to the next. We focus on symmetric integer wavelength chirps of the circumference of the rings relative to the central ring in the array. The transfer matrix method is used to obtain the transmission as a function of the inertial rotation rate Ω resulting from the Sagnac effect. Chirping increases the slope of the oscillations in the transmission as a function of Ω, which can be exploited to further enhance the rotation sensitivity beyond that of a CROW with uniform resonators.

© 2011 Optical Society of America

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References

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  1. J. Scheuer and A. Yariv, Phys. Rev. Lett. 96, 053901 (2006).
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2009 (1)

2007 (2)

2006 (1)

J. Scheuer and A. Yariv, Phys. Rev. Lett. 96, 053901 (2006).
[CrossRef] [PubMed]

2004 (2)

1999 (1)

Boag, A.

Capmany, J.

Digonnet, M. J. F.

Domenech, J. D.

Fan, S.

Huang, Y.

Lee, R. K.

Mookherjea, S.

Munoz, P.

Muriel, M. A.

Paloczi, G. T.

Poon, J. K. S.

Scherer, A.

Scheuer, J.

Steinberg, B. Z.

Terrel, M. A.

Xu, Y.

Yariv, A.

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Figures (3)

Fig. 1
Fig. 1

Plot of CROW transmission T ( ϕ S ) for seven resonators and coupling strength κ = 0.01 . The transmission of the unchirped CROW (blue) is plotted with four transmission regions along a CROW with a chirp parameter γ = 0.0588 , which corresponds to a one wavelength chirp (red) for a center ring of approximately 133 μm . The green plot shows how the peaks stretch in the phase for larger coupling ( κ = 0.05 ). (a) Comparison of the periodic transmission of the unchirped CROW to the nonperiodic transmission with STR due to chirping, (b) central transmission band.

Fig. 2
Fig. 2

Plot of log ( d T / d ϕ s ) max versus number of CROW resonators N for coupling κ = 0.01 . This compares the maximum responsivity in the central transmission band for a single ( n = 1 ), longest lasting in the STR, and two wavelength chirp ( n = 2 ), with largest maximum responsivity, to that of the resonances in the STR and the unchirped CROW.

Fig. 3
Fig. 3

Plot of the wavelength chirp parameter, n, versus maximum responsivity ( d T / d ϕ s ) max for an N = 7 CROW with couplings κ = 0.01 (red), with the largest maximum responsivity, κ = 0.05 (blue), and κ = 0.1 (black). The value of the responsivity for the unchirped ( γ = 0 , κ = 0.1 ) CROW is about 350.

Equations (2)

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U in = ( exp [ i ϕ 1 ] 1 κ exp [ i ϕ 1 ] 1 κ exp [ i ϕ 1 ] exp [ i ϕ 1 ] ) i κ , U out = i κ ( exp [ i ϕ N ] 1 κ exp [ i ϕ N ] 1 κ exp [ i ϕ N ] exp [ i ϕ N ] ) ( i 1 κ κ i κ i κ i 1 κ κ ) , U RHM ( j ) = ( i 1 κ κ exp [ i ϕ j ] i κ exp [ i ϕ j ] i κ exp [ i ϕ j ] i 1 κ κ exp [ i ϕ j ] ) , U LHM ( j ) = ( i 1 κ κ exp [ i ϕ j ] i κ exp [ i ϕ j ] i κ exp [ i ϕ j ] i 1 κ κ exp [ i ϕ j ] )
T CCW = U out l = 1 ( N 3 ) / 2 U LHM ( 2 l + 2 ) U RHM ( 2 l + 1 ) U LHM ( 2 ) U in = ( T 11 T 12 T 21 T 22 ) .

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