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High-speed low-voltage electro-optic modulator with a polymer-infiltrated silicon photonic crystal waveguide

Jan-Michael Brosi, Christian Koos, Lucio Claudio Andreani, Michael Waldow, Juerg Leuthold, and Wolfgang Freude

Open Access Open Access

Abstract

A novel electro-optic silicon-based modulator with a bandwidth of 78GHz, a drive voltage amplitude of 1V and a length of only 80µm is proposed. Such record data allow 100Gbit/s transmission and can be achieved by exploiting a combination of several physical effects. First, we rely on the fast and strong nonlinearities of polymers infiltrated into silicon, rather than on the slower free-carrier effect in silicon. Second, we use a Mach-Zehnder interferometer with slotted slow-light waveguides for minimizing the modulator length, but nonetheless providing a long interaction time for modulation field and optical mode. Third, with this short modulator length we avoid bandwidth limitations by RC time constants. The slow-light waveguides are based on a photonic crystal. A polymer-filled narrow slot in the waveguide center forms the interaction region, where both the optical mode and the microwave modulation field are strongly confined to. The waveguides are designed to have a low optical group velocity and negligible dispersion over a 1THz bandwidth. With an adiabatic taper we significantly enhance the coupling to the slow light mode. The feasibility of broadband slow-light transmission and efficient taper coupling has been previously demonstrated by us with calculations and microwave model experiments, where fabrication-induced disorder of the photonic crystal was taken into account.

©2008 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. Mach-Zehnder modulator schematic. The input WG carries a quasi-TE mode, the dominant electric field component of which (Ex ) is oriented along the x-direction. A Y-branch (in reality an MMI coupler) splits the input into two arms where PC phase modulators are inserted. A coplanar transmission line provides electric bias and a modulation field driving the phase modulators in push-pull mode. The optical signals in both arms experience phase shifts +ΔΦ and -ΔΦ.

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Fig. 2.
Fig. 2. Phase modulator (a) schematic and (b) dominant electric field component Ex . A slot filled with an electro-optic polymer (EO) of width W gap is cut in a silicon photonic crystal line-defect waveguide of width W 1. The silicon slabs of height h and width w are doped for electrical conductivity and contacted with aluminum layers. Ex is strongly confined to the slot. The phase ΔΦ of the propagating optical wave is tuned by applying a voltage to the polymer. The triangular-lattice period is a.

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Fig. 3.
Fig. 3. Band diagram of W1.4 PC slot waveguide. The desired mode exhibits a low group velocity below the light line of the polymer cladding. PC slab height h=220nm, polymer gap width W gap=150nm, PC lattice period a=408nm, hole radii r/a=0.3, line defect width W 1=1.4√3a. The polymer refractive index is n poly=1.6, f, k, c denote frequency, propagation constant and vacuum speed of light, respectively.

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Fig. 4.
Fig. 4. W1.25 PC slot waveguide with slab height h=220nm, polymer gap width W gap=150nm, PC lattice period a=408nm. (a) Structure parameters and (b) group velocity as a function of frequency with varying hole radii r 2. With r 2/a=0.36, the group velocity amounts to 4% of the vacuum speed of light c, and the group velocity dispersion is negligible in a bandwidth of 1THz. For comparison, the group velocity of the conventional W1.4-WG of Fig. 2 is plotted as a dashed line (W 1=1.4√3a, W 2=W 3=0.5√3a, r 1=r 2=r 3=r=0.3a). Parameters of the W1.25-WG are W 1=1.25√3a,W 2=0.65√3a, W 3=0.45√3a, r 1=0.25a, r 3=r=0.3a.

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Fig. 5.
Fig. 5. Schematic of the coupling structure. (a) Transition from strip-WG to slot-WG (b) Coupling to PC WG. The transmission is significantly increased by introducing a PC taper, where the width W 1 of the PC-WG is slightly decreased from 1.45√3a to 1.25√3a over some lattice periods, indicated by the overlaid tilted (green) lines, and the width W2 is increased from 0.55√3a to 0.65√3a. The width of the strip-WG is 440nm, and the gap width of both the slot-WG and the PC-WG is 150nm.

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Fig. 6.
Fig. 6. Transmission and reflection for the transition from slot-WG to PC-WG and back to slot-WG, Fig. 5(b), with and without a PC taper. The introduction of the PC taper significantly enhances the transmission to a value better than -4dB. The reflection is below -10dB.

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Fig. 7.
Fig. 7. Electrical RC-effects. (a) Generator-determined limitation (b) Parallel-loss determined limitation. In (a), the electrically short PM section is represented by a lumped gap capacitance C gap, and the voltage across the gap U gap is only a fraction of the generator voltage U G because of the generator impedance R G. In (b), a voltage wave with constant amplitude |U| travels in z-direction. The voltage U gap across the gap (capacitance per length C′) is reduced because of the finite resistivity of the doped silicon sections of width w (conductance per length (R′-1).

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Tables (1)

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Table 1. Characteristic data for a PC slot waveguide modulator. Group velocity v g,opt, field interaction factor Γ, modulator length L and modulation bandwidth f 3dB are estimated at different optical carrier frequencies f 0. We assume an electro-optic coefficient of r 33=80pm/V. The modulation voltage amplitude for maximum extinction is fixed to Û=Uπ /4=1V.

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Equations (19)

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f 3 dB ≈ 0.5 t g , opt = 0.5 v g , opt L , U π ∝ W gap r 33 v g , opt L .
f 3 dB ( TW ) = 0.5 ∣ t g , opt − t g , el ∣ = 0.5 v g , opt L 1 ∣ 1 − v g , opt v g , el ∣ .
f 3 dB = 0.5 ∣ t g , opt + t g , el ∣ = 0.5 v g , opt L 1 ∣ 1 + v g , opt v g , el ∣ .
Δ n = − 1 2 r 33 n poly 3 E el , E el = U W gap .
Δ Φ = − Δ β L = − Γ Δ n k 0 L .
Γ = ∫ gap n Z 0 ∣ E ̂ x ∣ 2 d V ∫ a ℜ ( E ̂ × H ̂ * ) · e z d A ∝ 1 v g , opt .
U π = c n poly 3 f 0 W gap r 33 1 L Γ , U π ∝ W gap r 33 1 L Γ ∝ W gap r 33 v g , opt L ∝ W gap r 33 f 3 dB .
∇ × E = − μ ∂ H ∂ t ,
∇ × H = ∂ [ ( ε + Δ ε ) E ] ∂ t .
E ( x , y , z , t ) = A ( z , t ) E ̂ ( x , y , z ) e j ( ω 0 t − β 0 z ) ,
H ( x , y , z , t ) = A ( z , t ) H ̂ ( x , y , z ) e j ( ω 0 t − β 0 z ) .
∫ ( E ̂ q × H ̂ p * − H ̂ q × E ̂ p * ) · e z d A = 4 δ pq P p .
∂ A ∂ z + 1 v g , opt ∂ A ∂ t = j ω 0 Γ KUA , A = ∣ A ∣ e j ( Φ + Δ Φ ) .
∇ × H ̂ − j β 0 e z × H ̂ = j ω 0 ε E ̂ .
− d β 0 ( e z × H ̂ ) = d ω 0 ε E ̂ .
d β 0 ∫ 1 4 ( E ̂ × H ̂ * + E ̂ * × H ̂ ) · e z d V = d ω 0 ∫ 1 2 ε ∣ E ̂ ∣ 2 d V .
1 v g , opt = d β 0 d ω 0 = ∫ 1 2 ε ∣ E ̂ ∣ 2 d V a ∫ ℜ ( 1 2 E ̂ × H ̂ * ) · e z d A .
U gap U G = 1 1 + j ω R G 2 C gap , f 3 dB ( R G C gap ) = 1 4 π R G C gap .
U gap U = 1 1 + j ω 2 R ′ C ′ , f 3 dB ( R ′ C ′ ) = 1 4 π R ′ C ′
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