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An optically-controlled terahertz (THz) modulator based on nonlinear photonic crystals (PCs) is proposed, which has the merits of high speed, compactness and easy integration. The PC structure consists of point and line defects. High speed modulation of THz wave can be realized by filling one of the point defects with organic polymer polyaniline which has rapid nonlinear response time. Simulation results show that the modulation rate, modulation depth and insertion loss of the modulator achieve 2.5 GHz, 20.3 dB and 1.02 dB, respectively.
©2011 Optical Society of America
1. Introduction
The Terahertz (THz) region of the electromagnetic spectrum, with wavelength between the millimeter wave and far infrared wave, is the last empty frequency band. Compared with the current wireless communication band, THz band occupies wider frequency resource, has great potential in broadband wireless communication. As one of the most important components in a THz communication system, the THz wave modulator is becoming a research focus [1–3].
With the properties of photonic band gap (PBG) and photon localization, photonic crystals (PCs), especially tunable PCs, have the ability to provide extra degree of freedom in manipulating the light transmission [4,5]. The PBG and defect mode frequency of the PCs vary dynamically with the field excitation, e.g., electric field, light field, magnetic field and temperature filed. This phenomenon is widely used in optical communication components, such as optical switch, optical resonator and optical modulator. THz modulator based on PCs can be obtained by applying tunable PCs in the THz band and modulating the PBG and defect mode frequency of the PCs under external field to achieve the ‘on’ and ‘off’ states of THz wave. Li [6] and Koch [7] reported electrically-controlled liquid crystal PC THz modulators by this theory respectively. However, the modulation rate is limited by the slow electro-optical response time of liquid crystal, which confines its applications in high-speed THz communication systems.
In this paper, we proposed a novel optically-controlled THz modulator based on a nonlinear PC consisting of line and point defects, as well as an organic polymer with fast nonlinear response, polyaniline, is introduced into the point defects. According to the Kerr effect, the refractive index of polyaniline changes rapidly under the control of the applied pump intensity. Then the mode frequency in the point defect shifts dynamically, and the on/off modulation of THz wave is realized. Simulation results show that this kind of THz modulator has the modulation rates of up to 2.5 GHz, modulation depth of 20.3 dB, and insertion loss of 1.02 dB.
2. Structure model and modulation mechanism
2.1 Structure of the modulator
The modulator we propose is formed by a two-dimensional PC with a triangular array of air holes in silicon substrate, with parameters as following: the lattice constant a = 129.6 µm, the radius of circular air holes r = 0.45a. The substrate material is high-purity silicon with negligible loss and the refractive index n = 3.4 in THz region [8]. The schematic diagram of the modulator is shown in Fig. 1 . The center point defect (in grey) is filled with polyaniline (PEMB state) to form a microcavity. Two line defects are introduced on each side along the z-axis. Three air holes lie between the center point defect and the line defect, and the radius of the air hole adjacent to the line defect is R = 0.1a. The two air holes with smaller radius are used as two connective point defects to enhance the energy coupling between point and line defects.
Fig. 1 The structure model of THz wave modulator with (a) the schematic diagram of the modulator and (b) the structure parameters.
2.2 The modulation mechanism
Line defects are introduced as waveguides for transmitting THz wave whose frequencies locate within the PBG, while the point defects are used as resonant cavity, in which only THz frequencies that accord with the resonant frequency (or defect mode frequency) can be selected. This is the unique characteristics of the structure combining both point and line defects. When the pump intensity is zero, the linear refractive index of polyaniline is 1.5 (0.1~3 THz) [9] and the defect mode frequency is 1.01 THz, thus the frequency of 1THz cannot resonate in the microcavity and the modulator is at the “off” state. However, if the pump intensity is 30 GW/cm2, the refractive index of polyaniline is rapidly changed owing to the third-order nonlinear polarization because of the Kerr effect. The variation of refractive index with the pump intensity can be expressed as
where I is the pump intensity, n0 and n2 are the linear and nonlinear refractive indices respectively. Based on the third-order nonlinear polarizability of polyaniline, χ (3) = 9.0 × 10−11 esu, n 2 = 1.58 × 10−14 cm2/W can be obtained. Therefore, if I = 30 GW/cm2, the refractive index of polyaniline is 1.55 and the defect mode frequency moves to 1 THz, so the modulator is at the “on” state. The input THz wave with f = 1 THz can be coupled from the first line defect into the microcavity and resonates in it, then this wave couples into the second line defect and is output. That means that the modulation of THz wave is realized by controlling the pump intensity and sequent dynamic shift of defect mode frequency of the nonlinear PC.3. Simulation results and discussions
The properties of the THz modulator are simulated with the two-dimensional finite difference time domain (2D-FDTD) method. The PC used in the modulator contains 21 × 21 air holes with lattice constant a = 129.6 µm, as shown in Fig. 1. The perfectly matched layer boundary condition is set around the modulator. The space step both in horizontal and vertical directions are set to be 8 μm. The time step t satisfies the stability condition. A continuous wave THz source is considered with the frequency of f = 1 THz and a monitor is placed at the exit of the modulator.
3.1 The simulation of defect mode shift
We firstly analyze the operating process of the defect mode shift of the THz modulator. Considering a THz wave of TE mode with the frequency of 1 THz is incident into the line defect.
When the pump intensity I = 0 is applied, the linear refractive index of polyaniline is 1.50. The defect mode frequency is 1.01THz (), and the quality factor Q is 426, as shown in Fig. 2a . Therefore, THz wave with f = 1 THz cannot pass through the modulator and the modulator is in the “off” state.
When the pump intensity I = 30 GW/cm2 is applied, the refractive index of polyaniline in the point defect is rapidly changed to be n = 1.55, owning to the Kerr effect. The defect mode frequency shifts to be 1THz (), and the quality factor Q is 400, as shown in Fig. 2b. It should be noted that the intensity of THz wave in the modulator is much weaker than the pump intensity and has no nonlinear effect in the point defect, so that the refractive index of polyaniline only changes with the variation of the pulse pump light. Consequently, the THz wave with f = 1THz resonates in the microcavity, and then it couples into the second line defect to be output. Now the modulator is at the “on” state.
It can be seen from the comparison of Fig. 2a and Fig. 2b that the defect mode frequency red shifts from 1.01 THz to 1 THz with the variation of the refractive index of polyaniline from 1.50 to 1.55. As a result, selective pass through of THz wave can be realized by controlling the pulse pump light. The normalized transmission spectrum before and after modulation are shown in Fig. 3 .
Fig. 3 Transmission spectrum of “off” (n = 1.50, solid line) and “on” (n = 1.55, dashed line) states.
3.2 The simulation and analysis of steady-state intensity of the mode field
The steady-state intensity of the mode field is analyzed. When the pump intensity is 30GW/cm2, the modulator is at the “on” state. The corresponding time domain steady-state response is shown in Fig. 4a .
It can be seen from Fig. 4a that the THz wave with the frequency f = 1 THz can pass through the modulator with low loss. 79.86% of the THz wave energy is passed and the insertion loss is 1.02 dB. When the pump intensity is zero and the modulator is at the “off” state, the time domain steady-state response is shown in the Fig. 4b. As we can see, the refractive index of polyaniline is 1.50 and the defect mode frequency is 1.01 THz, so only 0.008% of the THz wave (f = 1 THz) energy can pass through. The modulation depth is an important index to value the capability of digital modulation. If the modulation depth is not large enough, a series of problems will be aroused, such as erroneous judgement. The definition of the modulation depth η is
where I max and I min are the maximum and minimum intensities of the THz wave after modulation, respectively. From Fig. 4 and Eq. (2), we can obtain the modulation depth is 20.3 dB, which is much less than the 30dB [3,10] and 3% passed wave energy [1] reported. We can see from Fig. 4b that the set-up time of steady-state mode field is as short as around 0.4 ns. The modulation rate is related to not only the response time of nonlinear materials, but also the system response time. In our simulation, the nonlinear response time of the third-order nonlinear optical material, polyaniline, is supposed to be about tens of femtoseconds, which is smaller than the system response time. As a result, the modulation rate is mainly determined by the system response time, which means the maximum modulation rate is about 2.5 GHz (1/0.4 ns). The response time is shorter than 0.33 ns reported by Fekete et al. [2]. Figure 5 shows the steady-state THz wave field intensity distribution of E y at n = 1.55 and 1.5 respectively.The simulation results show that this novel nonlinear PC THz modulator can effectively realize the modulation of THz wave with the advantages of high modulation rate, large modulation depth, low insertion loss, small size and easy to integrate.
4. Conclusions
An optically-controlled THz wave modulator based on nonlinear PC is proposed. The refractive index of polyaniline in the point defect can be rapidly changed by the dynamic shift of defect mode frequency under the control of the applied pump intensity. As a result, the modulation of THz wave is realized. Simulation results show that this kind of THz modulator has the modulation rates up to 2.5 GHz, modulation depth up to 20.3 dB, and insertion loss of 1.02 dB. This novel nonlinear optically-controlled THz wave modulator based on nonlinear PC has great potential in future high-speed THz communication systems.
Acknowledgment
This work was supported by the National Natural Science Foundation of China (project No. 61077084).
References and links
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