Abstract

In this paper, we analyze the performance of an electro-optic modulator based on a single quantum dot strongly coupled to a nano-resonator, where electrical control of the quantum dot frequency is achieved via quantum confined Stark effect. Using realistic system parameters, we show that modulation speeds of a few tens of GHz are achievable with this system, while the energy per switching operation can be as small as 0.5 fJ. In addition, we study the non-linear distortion, and the effect of pure quantum dot dephasing on the performance of the modulator.

© 2010 Optical Society of America

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Figures (8)

Fig. 1.
Fig. 1.

(a) Transmission spectra of coupled cavity-QD system for two different detunings. The blue arrow shows the wavelength of the laser whose transmission is being modified. (b) Normalized steady state transmission with different QD detunings. The laser is resonant with the cavity. We used the following parameters:g/2π = κ/2π = 20 GHz; γ = κ/80; the pure dephasing rate is assumed to be zero for this analysis (γd /2π = 0).

Fig. 2.
Fig. 2.

The frequency response of the switch for different (a) κ. (g/2π) is kept constant at 20 GHz and (b) g. (κ/2π) is kept constant at 20 GHz. For both simulations Ω = 1 GHz; Δω 0/2π = 10 GHz; γd /2π = γ/2π = 0.1 GHz.

Fig. 3.
Fig. 3.

(a) Cut-off frequency of the modulator as a function of g and κ. In the color scheme, the maximum cutoff frequency of ~ 90 GHz is red and the minimum cut-off frequency of ~ 10 GHz is blue; (b) On-off ratio of the modulator at a modulating frequency of ωe /2π = 5 GHz as a function of g and κ. For both plots Δω 0/2π = 5 GHz; γd /2π = 0.1 GHz; Ω = 1 GHz.

Fig. 4.
Fig. 4.

Normalized output signal for two different maximal QD detunings Δω 0. (a) Δω 0/2π = 2 GHz. (b) Δω 0/2π = 40 GHz. For both simulations the frequency of the electrical signal is Δωe /2π = 20 GHz, κ/2π = g/2π = 20 GHz and Ω = 1 GHz.

Fig. 5.
Fig. 5.

Ratio of the second and third harmonic to the first harmonic of the modulated signal, as a function of the maximum frequency shift of the QD, scaled by a factor of g 2/κ. The first harmonic is proportional to the actual signal. For the simulation we assumed that the modulation is working in the passband (ωe /2π = 20 GHz); κ∣/2π = g/2π = 20 GHz and the dephasing rate γd /2π = 0.

Fig. 6.
Fig. 6.

Step response of the single QD electro-optic modulator. The parameters used for the simulation are: κ/2π = 5 GHz; g/2π = 20 GHz; Δω 0/2π = 20 GHz; Ω = 1 GHz.

Fig. 7.
Fig. 7.

Ratio between the third and first harmonic of the modulated signal for different QD-cavity coupling g and maximum QD detuning Δω 0. The cavity decay rate κ/2π = 20 GHz and the modulation frequency ωe /2π = 5 GHz.

Fig. 8.
Fig. 8.

(a) Normalized steady state transmission of the laser resonant with the dot (i.e., Δωa = 0) with pure dephasing rate γd /2π. Parameters used are: g/2π = κ/2π = 20 GHz; γ = κ/80; (b) On-off ratio of the modulated signal as a function of the dephasing rate, for κ/2π = g/2π = 20 GHz. The modulation frequency ωe /2π = 5 GHz and the amplitude of the change in resonance frequency Δω0/2π =10 GHz.

Equations (19)

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dt = i [ H , ρ ] + κℒ [ a ] + γℒ [ σ ] + γd 2 ( σ z ρ σ z ρ )
[ D ] = 2 D D ρ D D
H = Δ ω c a a + Δ ω a σ σ + ig ( a σ a σ ) + Ω ( a + a )
d X dt = A X + i Ω B
d Y dt = C Y + i Ω D X
X = [ a σ a σ ] T
Y = [ a a σ σ a σ a σ ] T
A = [ κ g 0 0 g Γ 0 0 0 0 κ g 0 0 g Γ * ]
B = [ 1 0 1 0 ] T
C = [ 2 κ 0 g g 0 2 γ g g g g Γ κ 0 g g 0 Γ * κ ]
D = [ 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 ]
a ( t ) Δ ω 0 0 = r ( 0 ) e α ( 0 ) t cos ( β ( 0 ) t + ϕ ( 0 ) ) + SS ( 0 )
a ( t ) 0 →Δ ω 0 = r ( Δ ω 0 ) e α ( Δ ω 0 ) t cos ( β ( Δ ω 0 ) t + ϕ ( Δ ω 0 ) ) + SS ( Δ ω 0 )
α ( ω ) = κ + γ + 2
β ( ω ) = 4 g 2 ( κ γ ) 2 2
SS ( ω ) = i Ω ( γ + ) g 2 + κ ( γ + )
ϕ ( ω ) = tan 1 ( α ( ω ) β ( ω ) )
r ( 0 ) = SS ( Δ ω 0 ) SS ( 0 ) cos ( ϕ ( 0 ) )
r ( Δ ω 0 ) = SS ( 0 ) SS ( Δ ω 0 ) cos ( ϕ ( Δ ω 0 ) )

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