Abstract

I study theoretically the responsivity of optical modulators. For the case of a linear response, by using perturbation theory I find an upper bound imposed on the responsivity. For the case of a two-mode modulator I find a lower bound imposed on the optical path required for achieving full modulation when the maximum birefringence strength is given.

© 2006 Optical Society of America

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References

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  1. M. Weissbluth, Photon-Atom Interaction (Academic, 1989).
  2. E. Buks, J. Opt. Soc. Am. B 23, 0000 (2006); arXiv: quant-ph/0412198.
    [CrossRef]
  3. M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
    [CrossRef]
  4. A. B. Migdal, Qualitative Methods in Quantum Theory (Benjamin, 1977).

2006 (1)

E. Buks, J. Opt. Soc. Am. B 23, 0000 (2006); arXiv: quant-ph/0412198.
[CrossRef]

1984 (1)

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Berry, M. V.

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Buks, E.

E. Buks, J. Opt. Soc. Am. B 23, 0000 (2006); arXiv: quant-ph/0412198.
[CrossRef]

Migdal, A. B.

A. B. Migdal, Qualitative Methods in Quantum Theory (Benjamin, 1977).

Weissbluth, M.

M. Weissbluth, Photon-Atom Interaction (Academic, 1989).

J. Opt. Soc. Am. B (1)

E. Buks, J. Opt. Soc. Am. B 23, 0000 (2006); arXiv: quant-ph/0412198.
[CrossRef]

Proc. R. Soc. London Ser. A (1)

M. V. Berry, Proc. R. Soc. London Ser. A 392, 45 (1984).
[CrossRef]

Other (2)

A. B. Migdal, Qualitative Methods in Quantum Theory (Benjamin, 1977).

M. Weissbluth, Photon-Atom Interaction (Academic, 1989).

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Figures (2)

Fig. 1
Fig. 1

(Color online) Example of numerical integration of the equation of motion for the case λ = 5 . Left, curve κ ( s ) ; right, evolution of the polarization vector p ( s ) on the Bloch sphere.

Fig. 2
Fig. 2

Calculated and upper bound of responsivity. (a) Numerical calculation of T versus λ. (b) Comparison between the calculated d T d λ and the upper bound given by inequality (22).

Equations (22)

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d d s ψ = i K ψ ,
K ( s ) = K 0 ( s ) + ϵ K 1 ( s ) ,
ψ f = U ( ϵ ) ψ i ,
T ( ϵ ) = ψ p ψ f ( ϵ ) 2 .
ρ ( ϵ ) = ψ f ( ϵ ) ψ f ( ϵ )
Δ ρ = ρ ( ϵ ) ρ ( 0 ) .
d T d ϵ = 1 ϵ ψ p Δ ρ ψ p .
d T d ϵ 1 ϵ [ 1 ψ i U ( 0 ) U ( ϵ ) ψ i 2 ] 1 2 .
ψ i U ( 0 ) U ( ϵ ) ψ i = 1 + i ϵ s 0 s 1 d s K 1 ( s ) ϵ 2 s 0 s 1 d s s 0 s d s K 1 ( s ) K 1 ( s ) ,
A H ( s ) u 0 ( s , s 0 ) A u 0 ( s , s 0 ) ,
ψ i U ( 0 ) U ( ϵ ) ψ i 2 = 1 ϵ 2 s 0 s 1 d s s 0 s 1 d s Δ K 1 ( s ) Δ K 1 ( s ) ,
d T d ϵ 2 s 0 s 1 d s s 0 s 1 d s Δ K 1 ( s ) Δ K 1 ( s ) .
d T d ϵ 2 s 0 s 1 d s { [ Δ K 1 ( s ) ] 2 } 1 2 .
K 1 = κ 1 σ ,
σ 1 = ( 0 1 1 0 ) , σ 2 = ( 0 i i 0 ) , σ 3 = ( 1 0 0 1 ) .
d T d ϵ s 0 s 1 d s κ 1 ( s ) .
θ 2 s 0 s 1 d s ϵ κ 1 ( s ) .
Δ s π 2 κ max .
T ( ϵ ) = sin 2 ( ϵ k 1 s 1 2 π 4 ) .
κ ( s ) = γ ( 0 , [ λ 2 ( γ s ) 2 ] 1 2 , γ s ) ,
T π 2 4 J 0 2 ( 2 λ 2 ) ( for λ 1 ) ,
d T d λ λ γ λ γ d s γ λ [ λ 2 ( γ s ) 2 ] 1 2 = π λ .

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