1. Introduction

A rapid growth of optical communication systems has attracted great interest in optical waveguide devices. Optical waveguide switches have been the key devices in optical communications because of their ability in routing and switching optical signals along different paths. During the past decades, a variety of switching devices based on different physical mechanisms, such as plasma dispersion effect [1–3], thermo-optic effect [4–5], acousto-optic effect [6–7] and magneto-optic effect [8–9], have been reported. As the density of channels keeps increasing in optical communications, it is very crucial to develop multi-port optical waveguide switches. So more and more modulation regions and control signals are introduced in optical waveguide switching design [1–2, 10]. To optimize index modulation regions and simplify the multi-port switches, in this work, a decoder switch is proposed.

Decoder switch is a multiple-input, multiple-output electro-optical logic switch, which can switch input optical signals into different output ports according to logic states of control signals. As a decoder switch, both input and output signals should be optical ones. Its control signals can be some kind of modulations applied to the index modulation regions, such as forward bias voltages applied to p-n junctions of the index-modulation regions. Compared with other kinds of multi-port switches, the decoder switch generally possesses fewer control signals and modulation regions. This is because the output signals can be controlled by control signals and their logic states. n control signals are sufficient to control 2ⁿ output ports.

The aim of this work is to propose a 2-to-4 decoder switch based on multimode interference principle and plasma dispersion effect. In the 2-to-4 decoder switch, four different output states can be realized, controlled by binary logic states of the two forward bias voltages applied to the two modulation regions.

2. Basic theory

2.1 Multimode interference principle

Multimode interference (MMI) couplers based on self-imaging multimode waveguide can perform different functions [10–14]. In the MMI coupler, a multimode waveguide is designed to support a large number of modes. According to the self-imaging theory [11], when an input light beam is coupled into the multimode waveguide from a single-mode input waveguide, the interfered optical fields will be reproduced in single or multiple images at periodic intervals along the propagation direction. In general, taking the Goos-Hähnchen shifts into account, an effective width W _e of the multimode waveguide can be expressed as:

where σ = 0 for TE mode and σ = 1 for the TM mode, λ₀ is a free-space wavelength, n _r and n _c are effective refractive indices of ridge waveguide and cladding layer, respectively, W _M is the width of the multimode waveguide.

By defining L _π as the beat length of the two lowest-order modes:

where ° ₀ and ° ₁ are the propagation constants of the fundamental and the first-order lateral modes, respectively. When the width W _M and length L of the multimode waveguide satisfy the following condition:

the input light field will be repeated and single image can be obtained.

For the multimode waveguide with a length of z = 3L _π, according to the partial index-modulation principle for the multimode waveguide [10], when a π phase shift around the position z = 3L _π/2 is introduced, a transformation between the even and odd modes will take place. Thus after a further propagation of z = 3L _σ/2, the input optical signal will be outputted from another corresponding output waveguide.

2.2 Free-carrier plasma dispersion effect

It is known that the refractive index of Si material is related with its carrier concentration [15]. When a forward bias voltage is applied to the p-n junction of Si, an increment of carrier concentration and a decrease of its refractive index will be caused. For SiGe material, there is a similar behavior when a component of Ge is less than 20%, and it can be expressed as [1]

where e is electron charge, ε₀ is permittivity of free space, n is refractive index of the SiGe, λ₀ is wavelength, c is light velocity, ∆N _e and ∆N _h are concentration changes of electrons and holes, respectively, and $m_{\text{ce}}^{*}$ and $m_{\text{ch}}^{*}$ are conductivity effective masses of electrons and holes of SiGe, respectively. For λ= 1.55 μm, equation (4) can be expressed as [3]:

3. Device structure and design considerations

Figure 1 shows a schematic structure of the proposed 2-to-4 decoder switch. Figure 1(a) is the top view of the decoder switch while Figs. 1(b) and (c) are cross-section views of the index-modulation regions I and II, respectively. As shown in Fig. 1(a), the decoder switch consists of three sections: an input section, a central section and an output section. The input section consists of two input waveguides A and B, while the output section consists of four output waveguides 1, 2, 3, and 4. All the input and output waveguides are single-mode waveguides. The central section consists of a multimode waveguide with two electronically controlled index-modulation regions (I, II) and a rectangular air groove. Index-modulation regions I and II are designed as p-n junctions as shown in Figs. 1(b) and (c), respectively. In this design, the optical signals are input from the two input waveguides A and B, and are outputted from the four output waveguides 1, 2, 3 and 4. The control signals V_CI and V_CII are the forward bias voltages applied to the p-n junctions of the two index-modulation regions I and II, respectively. When a control signal, i.e. a forward bias voltage is applied to any one of the two p-n junctions, a decrease of refractive index in the index-modulation regions I and II will be caused due to the plasma dispersion effect by injected minority carriers. This decrease in the refractive index will lead to a change in propagation of the input optical signals. This will divert the input optical signals to any one of the four output waveguides and the device functions as a 2-to-4 decoder switch.

In design, physical parameters of the decoder switch are determined by the following considerations. In order to be compatible with single-mode fiber operation in 1.55 μm, all the input waveguides and output waveguides are set to be 6 μm in width and 2.5 μm in thickness. Based on a large cross-section single-mode operation principle, an etching depth of 1.0 μm is chosen for all waveguides corresponding to a Ge component of 4% [13]. Considering proper spacing between the single-mode waveguides, the width of the multimode waveguide is set to be 36 μm. To achieve decoder switch function, the length of the multimode waveguide is set to a little larger than 3L _π, and a rectangular air groove is introduced at the end side of the multimode waveguide as shown in Fig. 1(a). The purpose will be discussed in the following paragraph.

 

Fig. 1. Schematic structure of the proposed 2-to-4 decoder switch: (a) top view, (b) cross-section view of the index-modulation region I and (c) cross-section view of the index-modulation region II.

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In order to make the design considerations well understood, we would like to discuss the case that the optical signal is input from the input waveguide A for instance, as shown in Fig. 2. When no control signals are applied to the two p-n junctions of the index-modulation regions I and II, the input signal will enter the MMI region at the position z = 0. The single image obtained at the position z = 3L _π will be reflected by the boundaries of the multimode waveguide and the air groove. As a result, single optical image will be obtained in the output waveguide 3, as shown in Fig. 2(a). On the other hand, when a control signal V_CI applied to the p-n junction of the index-modulation region I, minority carriers will be injected into the multimode waveguide and the refractive index in region I will decrease. Thus, the input signal will be restricted by the boundary of the multimode waveguide and the region I. As a result, the length of the MMI region for the input signal is turned to 3L _π, and the single image will be obtained in the output waveguide 4, as shown in Fig. 2(b). In order to switch the output signals to the other two output waveguides, the index-modulation region II is placed at the position where it basically functions as a partial index-modulation region. As a result, when a control signal V_CII is applied to the p-n junction of the index-modulation region II, a phase shift π could be introduced, and the optical signals from waveguide 3 and 4 will be switched to output waveguide 2 and 1, as shown in Figs. 2(c) and (d), respectively.

In the simulation, the decrease of the refractive index is chosen to be ∆n = 0.3%. According to Eq. (5) and the calculation method presented by S. M. Sze [16], the calculated forward bias voltages V_A and the current density J applied to the p-n junction in the regions I and II are 0.95 V and 27.7 kA/cm², respectively. The optimal widths of the two regions (I, II) and air groove are 24, 18 and 6 μm, respectively, while the optimal lengths of them are 700, 258 and 400 μm, respectively. The optimal length of the multimode waveguide is 14,150 μm. Thus, two control signals V_CI, V_CII are sufficient to control the four different output ports.

4. Operation characteristics

Fundamental characteristics of the 2-to-4 decoder switch are demonstrated theoretically by the beam propagation method. Because the switch will work if and only if the inputs are phase coherent, all the input light beams are assumed to be of same wavelength, i.e. of 1.55 μm and with original phase, amplitude. For simplification, we use “0” and “1” to indicate without forward bias voltages and with forward bias voltages V_A, respectively. So the four different binary logic states of the two control signals (V_CII, V_CI) are (0, 0), (0, 1), (1, 0) and (1, 1), respectively.

4.1 Optical signal input from input A

When an optical signal is input from the input waveguide A, it will be outputted from the four different output waveguides according to binary logic states of the two control signals (V_CII, V_CI), as shown in Fig. 2. (1) When (V_CII, V_CI) = (0, 0), the input optical signal will be outputted from the output waveguide 3 (Fig. 2(a)). The normalized output power in the output waveguide 3 is P ₃ = 95.2% while the normalized output powers in the output waveguides 1, 2 and 4 are P ₁ = 0.03%, P ₂ = 0.03%, and P ₄ = 1%, respectively. The calculated insertion loss is -10log (P _total-out/P _in) = 0.17 dB while the calculated crosstalks are 10log (P ₁/P ₃) = -35.0 dB, 10log (P ₂/P ₃) = -35.0 dB and 10log (P ₄/P ₃) = -19.8 dB for the output waveguides 1, 2 and 4, respectively. (2) When (V_CII, V_CI) = (0, 1), the optical signal will be outputted from output waveguide 4 (Fig. 2(b)). The normalized output power in the output waveguide 4 is P ₄ = 93.2% while the normalized output powers in the output waveguides 1, 2 and 3 are P ₁ = 0.06%, P ₂ = 0.03% and P ₃ = 0.5%, respectively. The calculated insertion loss is 0.28 dB while the calculated crosstalks are -31.9 dB, -34.9 dB and -22.7 dB for the waveguides 1, 2 and 3, respectively. (3) When (V_CII, V_CI) = (1, 0), the optical signal will be outputted from output waveguide 2 (Fig. 2(c)). The normalized output power in the output waveguide 2 is 95.0% while the normalized output powers in the output waveguides 1, 3 and 4 are 1%, 0.03% and 0.06%, respectively. The calculated insertion loss is 0.17 dB while the calculated crosstalks are -19.8 dB, -35.0 dB and -32.0 dB for the waveguides 1, 3 and 4, respectively. (4) When (V_CII, V_CI) = (1, 1), optical signal will be outputted from output waveguide 1 (Fig. 2(d)). The normalized output power in the output waveguide 1 is 92.3% while the normalized output powers in the output waveguides 2, 3 and 4 are 0.6%, 0.03% and 0.03%, respectively. The calculated insertion loss is 0.32 dB while the calculated crosstalks are -21.9 dB, -34.9 dB and -34.9 dB for the waveguides 2, 3 and 4, respectively. Table 1 is the output states of the 2-to-4 decoder switch when optical signal is input from input waveguide A. It should be pointed out that in the “Input” column of the table, 1 indicates the optical signal coupled from the input waveguide A, while 0 and 1 in the “Outputs” columns indicate without output signal and with output signal in the output waveguides, respectively.

 

Fig. 2. Simulated output results of the 2-to-4 decoder switch when optical signal is input from input A: (a) (V_CII, V_CI) = (0, 0), (b) (V_CII, V_CI) = (0, 1), (c) (V_CII, V_CI) = (1, 0) and (d) (V_CII, V_CI) = (1, 1).

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Table 1. Output stated of the decoder switch when optical signal input from input A

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4.2 Optical signal input from input B

Similarly, when optical signal is input from input waveguide B, it will be outputted from the four different output waveguides according to the binary logic states of the two control signals (V_CII, V_CI), as shown in Fig. 3. (1) When (V_CII, V_CI) = (0, 0), the input optical signal will be outputted from the output waveguide 2 (Fig. 3(a)). The normalized output power in the output waveguide 2 is P ₂ = 95.0% while the normalized output powers in the output waveguides 1, 3 and 4 are P ₁ = 1%, P ₃ = 0.03%, and P ₄ = 0.03%, respectively. The calculated insertion loss is -10log (P _total-out/P _in) = 0.17 dB while the calculated crosstalks are 10log (P ₁/P ₂) = -19.8 dB, 10log (P ₃/P ₂) = -35.0 dB and 10log (P ₄/P ₂) = -35.0 dB for the waveguides 1, 3 and 4, respectively. (2) When (V_CII, V_CI) = (0, 1), the optical signal will be outputted from output waveguide 1 (Fig. 3(b)). The normalized output power in the output waveguide 1 is P ₁ = 92.3% while the normalized output powers in the output waveguides 2, 3 and 4 are P ₂ = 0.6%, P ₃ = 0.03% and P ₄ = 0.06%, respectively. The calculated insertion loss is 0.32 dB while the calculated crosstalks are -21.9 dB, -34.9 dB and -31.9 dB for the waveguides 2, 3 and 4, respectively. (3) When (V_CII, V_CI) = (1, 0), the optical signal will be outputted from output waveguide 3 (Fig. 3(c)). The normalized output power in the output waveguide 3 is 95.2% while the normalized output powers in the output waveguides 1, 2 and 4 are 0.03%, 0.02% and 1%, respectively. The calculated insertion loss is 0.17 dB while the calculated crosstalks are -35.0 dB, -36.8 dB and -19.8 dB for the waveguides 1, 2 and 4, respectively. (4) When (V_CII, V_CI) = (1, 1), optical signal will be outputted from output waveguide 4 (Fig. 3(d)). The normalized output power in the output waveguide 4 is 93.2% while the normalized output powers in the output waveguides 1, 2 and 3 are 0.03%, 0.03% and 0.6%, respectively. The calculated insertion loss is 0.28 dB while the calculated crosstalks are -34.9 dB, -34.9 dB and -21.9 dB for the waveguides 1, 2 and 3, respectively. Table 2 is the output states of the 2-to-4 decoder switch when optical signal input from input waveguide B.

 

Fig. 3. Simulated output results of the 2-to-4 decoder switch when optical signal is input from input B: (a) (V_CII, V_CI) = (0, 0), (b) (V_CII, V_CI) = (0, 1), (c) (V_CII, V_CI) = (1, 0) and (d) (V_CII, V_CI) = (1, 1).

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Table 2. Output states of the decoder switch when optical signal input from input B

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4.3 Optical signals input from inputs A and B simultaneously

The 2-to-4 decoder switch can also operate when optical signals input from input A and input B simultaneously, as shown in Fig. 4. (1) When (V_CII, V_CI) = (0, 0), optical signal A will be outputted from output waveguide 3 while optical signal B will be outputted from output waveguide 2 (Fig. 4(a)). The normalized output powers in the output waveguides 1, 2, 3 and 4 are 0.5%, 46.8%, 46.8%, and 0.5%, respectively. The calculated insertion loss and average crosstalk are 0.24 dB and -19.7 dB, respectively. (2) When (V_CII, V_CI) = (0, 1), optical signal A will be outputted from output waveguide 4 while optical signal B will be outputted from output waveguide 1 (Fig. 4(b)). The normalized output powers in the output waveguides 1, 2, 3 and 4 are 45.9%, 0.3%, 0.3%, and 45.9%, respectively. The calculated insertion loss and average crosstalk are 0.34 dB and -21.8 dB, respectively. (3) When (V_CII, V_CI) = (1, 0), optical signal A will be outputted from output waveguide 2 while optical signal B will be outputted from output waveguide 3 (Fig. 4(c)). The normalized output powers in the output waveguides 1, 2, 3 and 4 are 0.5%, 47.3%, 45.2%, and 0.3%, respectively. The calculated insertion loss and average crosstalk are 0.30 dB and -20.8 dB, respectively. (4) When (V_CII, V_CI) = (1, 1), optical signal A will be outputted from output waveguide 1 while optical signal B will be outputted from output waveguide 4 (Fig. 4(d)). The normalized output powers in the output waveguides 1, 2, 3 and 4 are 46.5%, 0.3%, 0.3%, and 45.0%, respectively. The calculated insertion loss and average crosstalk are 0.36 dB and -21.8 dB, respectively. Table 3 is the truth table of the 2-to-4 decoder switch when optical signals input from input A and input B simultaneously. It should be pointed out that in the column “Outputs” columns of Table 3, 1(A) and 1(B) indicate that the output signals in the output waveguide are optical signal A and optical signal B, respectively.

 

Fig. 4. Simulated output results of the 2-to-4 decoder switch when optical signals are input from input A and B simultaneously: (a) (V_CII, V_CI) = (0, 0), (b) (V_CII, V_CI) = (0, 1), (c) (V_CII, V_CI) = (1, 0) and (d) (V_CII, V_CI) = (1, 1).

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Table 3. Output states of the decoder switch when optical signal input from input A and B simultaneously

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5. Conclusion

A multimode interference 2-to-4 decoder switch has been proposed and simulated based on the MMI principle and free-carrier plasma dispersion effect in SiGe/Si material for 1.55 μm window operation. The performance of the decoder switch has been analyzed by the beam propagation method. The calculated insertion loss and crosstalk are less than 0.36 dB and -19.7 dB, respectively. It may find some applications in optical communication systems or optical computer.