Analysis of dual-microring-resonator cross-connect switches and modulators

Stephen J. Emelett; Richard A. Soref

doi:10.1364/OPEX.13.007840

Optics Express
Vol. 13,
Issue 20,
pp. 7840-7853
(2005)
•https://doi.org/10.1364/OPEX.13.007840

Analysis of dual-microring-resonator cross-connect switches and modulators

Stephen J. Emelett and Richard A. Soref

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Stephen J. Emelett and Richard A. Soref, "Analysis of dual-microring-resonator cross-connect switches and modulators," Opt. Express 13, 7840-7853 (2005)

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Abstract

Modeling and simulation results on new, resonant, waveguided 2 × 2 switches and 1 × 1 modulators are presented here. The devices employ two coupled microrings: one fixed and one floating. The fixed ring is coupled to bus waveguides that are crossed or are locally parallel. Electrooptic and thermooptic switching at λ = 1.55 μm are investigated. A novel peaks-and-valley spectral response allows low-power switching with low crosstalk and low insertion loss. Complete switching is attained when the complex index of both rings is perturbed by Δn ~ 4 × 10^-4. The modulator’s optical output power is a linear function of Δn over three to five decades of Δn.

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Fig. 1. Top view of our proposed 2 × 2 waveguided, floating-ring cross-connect switch-and-modulator. In this planar version, the bus waveguides intersect, whereas in a 3D version, they would cross. It is assumed that the complex index of both rings can be changed simultaneously.

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Fig. 2. Alternative arrangement for cross-grid system. This orientation generates the same response as the cross-grid and also adheres to the synthesis. Special attention must be given to insure that only R₁ interacts with R₂ , and not either of the bus guides.

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Fig. 3. The triangular response. The normalized output drop and through port optical power response of the dual microring cross-connect system displays the needed bilateral and local symmetries. These characteristics are generated by following the synthesis and the constraints of Eq. (21).

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Fig. 4. The spike, or elongated triangular, response. The normalized outputs drop and through port optical power response of the dual microring cross-connect system displays the needed bilateral symmetry and a breaking of the local symmetry . These characteristics are generated by following the synthesis and the constraints of Eq. (22).

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Fig. 5 Fig. 6, and Fig. 7. Description and comparison of the maximally flat, left, triangular and spike responses. Superimposed on each plot are a series of index bias positions, A – Resonant, and B − Mid-range, which will serve as a starting locations, or index biases, for the rings’ index perturbation.

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Fig 8. Index perturbation characteristics of the triangular response device at three different initial bias points. Utilizing the prescribed nomenclature, the six depicted diagrams present the drop and through ports as a function of index perturbation. The center column break refers to a zero disruption and the alteration increases in both directions.

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Fig 9. Index perturbation characteristics of the spike response device at three different initial bias points. Utilizing the prescribed nomenclature, the six depicted diagrams present the drop and through ports as a function of index perturbation. The center column break refers to a zero disruption and the alteration increases in both directions.

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Tables (4)

Table 1(a). Displacement parameters of the triangular response system

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Table 1(b). Design parameters and constants of the triangular response system at λ₀ =1.55 μm A_m =6.0 and Δλ = 0.16 nm.

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Table 2(a). Displacement parameters of the spike response system

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Table 2(b). Design parameters and constants of the triangular response system at λ₀ =1.55 μm A_m =6.0 and Δλ = 0.16 nm.

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Equations (30)

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{∣ \frac{E_{T}}{E_{I}} ∣}^{2} = {∣ \frac{A_{α} τ_{a} + A_{Φ} Γ_{a} Γ_{b} τ_{aa} - A (τ_{a} + κ_{a}^{2} τ_{aa} + τ_{a}^{2} τ_{aa}) τ_{b}}{A_{α} - A (1 + τ_{a} τ_{aa}) τ_{b} + A_{Φ} τ_{a} τ_{aa} Γ_{b}} ∣}^{2}

{∣ \frac{E_{D}}{E_{I}} ∣}^{2} = {∣ \frac{A′ κ_{a} κ_{aa} (A_{Φ}^{'} Γ_{b} - A_{α}^{'} τ_{b}^{2})}{A_{α} - A (1 + τ_{a} τ_{aa}) τ_{b} + A_{Φ} τ_{a} τ_{aa} Γ_{b}} ∣}^{2}

A = \exp (\frac{α_{r} L}{2} + j ω T_{r})

A′ = \exp (\frac{α_{r} L}{4} + \frac{j ω T_{r}}{2})

A_{α} = \exp (α_{r} L)

A_{α}^{'} = \exp (\frac{α_{r} L}{2})

A_{Φ}^{'} = \exp ({jωT}_{r})

A_{Φ} = \exp (2 {jωT}_{r})

Γ_{a, b} = (κ_{a, b}^{2} + τ_{a, b}^{2})

g_{1}^{D} = 2 a_{1}^{D} ε

g_{2}^{F} = \frac{1}{4} \frac{a_{2}^{S} a_{1}^{D}}{c_{1}^{S} g_{1}^{D}} ε^{\frac{3}{2}}

g_{3}^{F} = \infty

g_{2}^{D} = 2 a_{2}^{D} ε

a_{q}^{D} = \sin \frac{π}{2} \frac{(2 q - 1)}{N}

a_{q}^{S} = \sin \frac{π}{2} \frac{(2 q - 1)}{N}

C_{q}^{S} = \cos^{2} (\frac{π q}{2 N}) .

K_{1}^{D} = \sqrt{\frac{πB}{2 g_{1}^{D} FS R_{1}}}

K_{2}^{F} = \frac{πB}{2 \sqrt{g_{2}^{F} g_{1}^{D} FS R_{2} FS R_{1}}},

κ_{q} = \frac{2 K_{q}}{K_{q}^{2} + 1}

M_{q} λ_{m} = 2 π R_{1,2} n .

κ_{1} (M_{1})

κ_{2} (\frac{1}{4} M_{2})

κ_{1} (2 M_{1})

κ_{2} (\frac{1}{4} M_{2}) .

N_{Rings} = n + δn + Δ n + i \bar{κ} + iδ \bar{κ} + i Δ \bar{κ}

r_{Δ} = \frac{Δ \bar{κ}}{Δ n}

r_{δ} = \frac{δ \bar{κ}}{δn}

N_{Rings} = n + δn + Δ n + i \bar{κ} + i r_{δ} δn + i r_{Δ} Δ n

n_{δ} = \frac{M_{q}}{2 πR} (λ_{δ} - λ_{0}) + n

Q = \frac{ω_{0} T}{α_{d} L} \approx \frac{λ_{B}}{Δ λ_{B}}

Type	λ_δ (nm)	δn (1×10^-4)
A	0	0
B	0.0618	~2.0125

n	3.5
M_q	36
κ ₁	0.1541
κ ₂	0.0130
r = r_δ =r_Δ	0.053
Q	9751

Type	λ_δ (nm)	δn (1×10^-4)
A	0	0
B	0.0891	~2.0125

n	3.5
M_q	36
κ ₁	0.2129
κ ₂	0.0130
r = r_δ =r_Δ	0.053
Q	4875

Type	λ_δ (nm)	δn (1×10^-4)
A	0	0
B	0.0618	~2.0125

Abstract

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Figures (7)

Tables (4)

Equations (30)

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