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A thermo-optical variable optical attenuator (VOA), consisting of three cascaded three-waveguide directional couplers, was designed on Silicon-On-Insulator (SOI) wafer. Thermo-optical dynamic, static analysis and optical propagation characteristic simulation at the wavelength of 1550 nm were presented. The dynamic attenuation range from 0.14 dB to 50 dB was achieved by a refractive index (RI) variation: 0 to 5.55×10-3, (the corresponding temperature variation: 0 to 30 °C). The response time was about 5 µs, which was attributed to Si/Al2O3/Si structure. The device could be easily used to fabricate multi-channel VOA as the basic unit and integrated in silicon optoelectronic circuits.
©2008 Optical Society of America
1. Introduction
Wavelength Division Multiplexing (WDM) has become the mainstream system in solving the higher levels of traffic in optical communications networks. Variable Optical Attenuators (VOAs) is an indispensable component of WDM systems, which plays an important role in providing dynamically flexible gain level adjustment and flatting gain profile over a wide band range [1–3]. There have been various approaches for fabricating the VOA, including opto-mechanical systems, micro-electromechanical systems (MEMS), and planar light-wave circuits (PLC). In MEMS, electronically driven mirrors are placed along the optical path to control the power attenuation by changing the mirror reflection angles and directions. The main drawback of this method is the slow time response and the difficulty of integration with other optical device [4, 5]. In PLC, the typical structure is straight channel waveguides, bend waveguides and Mach-Zehnder interferometer based on electro-optic materials, such as LiNbO3. These devices are attractive due to their fast time response (~ns). However, they suffer from the high fabrication cost and the difficulty of monolithic integration [6–8].
Electro-optics integration has attracted more and more attention in recent years. The success of Raman silicon laser and high speed (30 Gb/s) modulator in a Silicon-On-Insulator (SOI) waveguide made by Intel research group further stimulates the development of electro-optics integration [9, 10]. A silicon waveguide fabricated on a silicon substrate becomes one of the most popular ways to fabricate PLC devices in order to achieve low cost, good performance, high reliability and high integration with electronic circuits [11]. Also, SOI becomes a promising material applied in electronics and optic-electronics devices [12–14]. Free carrier plasma dispersion effect and thermo-optic effect play important roles in designing silicon optical devices. For thermo-optical device based on general SOI (Si/SiO2/Si), the response time is in the order of 10 µs [15]. The slow time response is ascribed to the low conductivity of buried silicon oxide of general SOI. In order to solve heat accumulation in device layer and improve time response, some special SOI materials with high conductivity insulator layer, such as Al2O3, are investigated [16, 17].
In this paper, we propose a Thermo-Optic Variable Optical Attenuator (TO-VOA) using three directional coupling units. A special SOI (Si/Al2O3/Si) is used as the waveguide material in order to achieve good performance in terms of integration, high attenuation range, and fast time response.
2. Device structure and the basic working principle
The VOA is essentially a three-waveguide directional coupler device consisting of three almost identical parts A, B and C. Their coupling region lengths are LC1, LC2 and LC3, respectively. Each coupling region consists of a center waveguide and two bypassing waveguides. The three waveguides, which are identical in geometry and Refractive Index (RI) distribution, are designed to support the fundamental mode only. In order to avoid the crosstalk between the center waveguide and the bypassing waveguides in non-coupling region, we design the straight bypassing waveguides with cosine bend (See Fig. 1).
For theoretical analysis, the coupled mode theory, which has been applied successfully in dealing with weakly coupled directional couplers, is used to analyze the device. Here, we extend the basic idea of the complete light transfer between two waveguides to discuss the three-waveguide coupling system. Then, these results are used to design our VOA.
We assume the optical field of waveguide 1 (bypassing), 2 (center), 3 (bypassing) is An 0(z)(n=1, 2, 3), respectively. The relationships between the three optical fields can be expressed by the following differential equations [18]:
Here, the three identical waveguides are separated by the same distance. Therefore, according to the symmetry of the structure, coupling coefficients can be simplified as the following:
Therefore, the general solutions of the simplified equations (1) are:
a,b,C10,C20 are undetermined coefficients. Assuming that the initial input amplitudes of the optical field are: A 10(0)=S 10,A 20(0)=R 20,A 30(0)=S 30, the coefficients can be expressed as:
We assume that optical power is initially launched into the center waveguide. (i.e., R 20≠0, S 10=0, S 30=0). Formula (6) can be written as Keff1≈Keff 2=Keff=√2K 0 because K 2 is much smaller than K 0 in general (See Eqs. (2) and (3)). The coupling length of the three-waveguide coupler is Ltri0=π/(2Keff)=π/(2√2K 0). Compared with that of two-waveguide Lbi0=π/(2K 0), a conclusion can be deduced: if we can symmetrically increase the number of bypassing waveguide around the centre waveguide under the condition that there is no coupling between bypassing waveguides (i.e.,K 0≫K 2), for n bypassing waveguides coupling system, the effective coupling coefficient can be expressed as Keffn=√nK 0, and its coupling length is L (n+1)0=π/(2Keffn)=π/(2√nK 0). The advantage of multi-waveguide coupling system is that it increases the effective coupling coefficient, and shortens the coupling length. Because the optical field is relative to the refractive index (RI) of waveguide material (See Eqs. (2), (3), (5), and (6)), the power attenuation can be achieved by continuously changing RI by thermo-optic effect.
3. Design consideration
The proposed device consists of three rib waveguides based on a special SOI material (i.e., Si/Al2O3/Si, see Fig. 2(a)). In our design, we first convert the 3-D rib waveguide into 2-D planar waveguide by Effective Index Method (EIM) [19]. See Fig. 2(b). Then, we use the coupled mode theory discussed in section 2 to optimize the parameters of the device. In addition, the single mode transmission in rib waveguides is insured by the following single mode condition [20, 21]:
Where, t = W/He, r = he/He = (h + σ0)/(H + σ0) > 0.5, k0 is the vacuum wave vector. c j=1 for TE mode, and c j=n 2 j/n 2 1 for TM mode, j=2, 3. H and h are the height of the inner rib and outer rib, respectively. W is the width of the rib waveguide. n 1, n 2, and n 3 are the refractive indices of core layer, cladding layer, and buried oxide layer, respectively.
Fig. 2. (a) Cross section of three-rib waveguide; (b) Equivalent three layer planar waveguide using EIM; (c) The designed value(red point) of rib waveguide far away from the critical line allows greater fabrication tolerance
The following parameters are obtained at the wavelength of 1550 nm to design the VOA: the three silicon-waveguides have the same rib width W=3 µm and a core layer thickness H=5 µm, the rib waveguides are defined by a lateral etch (H-h)=1 µm. The rib waveguides with these parameters support the fundamental mode only. Figure 2(c) shows the single mode area and the position of designed value (red point). The buried Al2O3 layer is 2 µm, which is thick enough to avoid the optical field leaking into the substrate since this thickness is much greater than the penetration depth (about 80 nm) of optical field. The deposited Al2O3 is 0.2-µm-thick, serving as upper cladding on the top of the core. The main effect of the upper cladding is to separate the core effectively from the metallic heater, which can induce absorption loss and Polarization Dependent Loss (PDL) [22]. The big refraction index difference between Si and Al2O3 insures the infrared radiation to be confined effectively in the core. The metallic stripe on the top of the upper cladding is 0.5-µm-thick and 3-µm-wide, serving as a good heater. The distance between neighboring waveguides is d=8 µm for two reasons: First, it insures the effective coupling between neighboring waveguides, and the effective separation between the two bypassing waveguides (i.e., K 0≫K 2). Second, it can effectively control the impact of temperature’s horizontal diffusion. The substrate is standard crystalline silicon (c-Si) wafer. C-Si is used as substrate due to its high thermal conductivity. It can be treated as an almost perfect heat sink.
The operation of the device is based on the effective refractive index (RI) variation induced by thermo-optical effect. Heating can be obtained by applying voltage on the deposited metallic film which is used as thermal resistors on the top of the rib waveguides.
4. Numerical analysis
In this section, four subsections (including coupling region length design, fabrication tolerance analysis, thermal analysis, and BPM analysis) are taken to analyze and optimize the device. Material parameters used in this section are listed in table 1:
Table 1. Optical and thermal parameters used in BPM and FEM analysis
4.1 design of coupling region length
According to the different coupling region length LC, the VOA can work in two states: (a) “off state”: the length of coupling region is odd times of one coupling length. i.e., L eff=(2m-1)L tri0=(2m-1)π/(2K eff)(m=1, 2, 3…). In this state, optical power is completely exported from the bypassing waveguides if there is no external modulation. VOA is in “off-state”. (b) “on-state”: the length of coupling region is even times of one coupling length. i.e., L on=2m L tri0=mπ/K eff(m=1, 2, 3…). In this state, optical power is completely exported from the center waveguides if there is no external modulation. VOA is in “on-state”. The continuous power attenuation of the VOA is realized through RI variation induced by thermo-optic effect, however, the realization of RI variation is not easy, especially high RI variation. Therefore, the key of our design is to optimize parameters as far as possible to realize the power attenuation by a suitable RI variation or temperature variation. Figure 3 distinctly indicates that “on-state” attenuation unit is more effective than that of “off-state” in decreasing RI variation range. That is, for the same optical power attenuation, e.g., 0~40 dB, the corresponding RI variation range is 0 to 5.5×10-3 for “on-state” and 0 to 16×10-3 for “off-state”. In this paper, attenuation unit with Lc=2L tri0=7500 µm is used to design the “on-state” VOA. Considering that actual device may not achieve the same performance as numerical analysis, a solution to achieve big attenuation is to integrate more attenuation units.
This leads to a trade-off between the quantity of attenuation units and the total size of the device. Here three cascaded attenuation units are used to control the optical power. This measure insures the big attenuation and a suitable size.
Fig. 3. Simulated relation between optical power and RI variation with different coupling region length. “on-state” is better than “off-state” in reducing RI variation. (One attenuation unit)
4.2 Fabrication tolerance analysis
Actually, the default “on-state” may not fully open because of fabrication errors, since the performance of the VOA is very sensitive to W, h, the errors of W, h must be considered. However, L c is so long that its errors could be neglected. Here, for the fabrication error δ=±100 nm, nine kinds of error need to be considered: 1. W+δ, h+δ; 2. W+δ, h; 3. W+δ, h-δ; 4. W-δ, h+δ; 5. W-δ, h; 6. W-δ, h-δ; 7. W, h+δ; 8. W, h (designed values); 9. W, h-δ. At the same time, the error of W will change the distance d between two neighboring waveguides. The impact on VOA’s performance induced by the variation of d should also be taken into account in worst-case analysis.
The horizontal diffusion of temperature field will induce RI variation in outer rib region (See Fig. 2(a)). In order to express the horizontal diffusion quantitatively, the average temperature variation between ΔT outer of outer rib region and ΔT inner of inner rib region could be connected by a scale factor α: ΔT outer=αΔT inner, where, α is determined only by the materials and its structure. Then, Δn outer of outer rib region and Δn inner of inner rib region could also be described as Δn outer=αΔn inner for RI variation is proportional to the temperature variation. i.e., Δn=C TO ΔT, where, C TO=1.86×10-4/°C is the thermo-optical coefficient of silicon. Here, we analyzed the attenuation characteristics at different α based on the worst-case discussed above. Figure 4 shows the results of different values of α for one attenuation unit.
The tolerance analysis of “on-state” shows that all the curves with positive fabrication errors (green lines) were moved to the right side of its ideal position (red lines) and those with negative fabrication errors (black lines) were moved to the left (See Fig. 4(a)). In other words, the default on-state can not be fully opened in the case of errors. Figure 4(b) shows that more optical power loss was brought by the fabrication errors. The loss of moving to the right side (about 0.1 dB) could be compensated by increasing the index of silicon by thermo-optic effect, but that moving to the left could not be compensated because the index of silicon can not be reduce by thermo-optical effect. Fortunately, this loss is very small (about 0.15 dB) at the fabrication error δ=-100 nm. In addition, because of the nonlinear relationship between attenuation and RI variation (See Eqs. (2), (3), (5), and (6)), the attenuation response will become sharp with the increase of RI variation, in other words, the temperature tolerance will become poor in sharpness region. To improve the temperature tolerance, we can appropriately increase the RI variation to achieve the same attenuation, namely, a bigger α or a stronger horizontal diffusion of temperature is needed (See Fig. 4(a)). In terms of structure design, the distance between neighboring waveguides should not be quite large. The optimized value of 8 µm is used to design the VOA here.
Fig. 4. (a) Relations between power attenuation and RI variation under design value (W=3 µm, h=4 µm, d=8 µm) (red lines), positive fabrication errors (W=3.1 µm, h=4.1 µm, d=7.8 µm) (green lines) and negative fabrication errors (W=2.9 µm, h=3.9 µm, d=8.2 µm) (black lines). (b) The zoom-in Figure of Fig. 4(a), which shows that the fabrication errors can bring more optical power loss in the case of no RI modulation.
4.3 Thermal analysis
In this section, our target is to achieve a needed average temperature variation ΔT to realize the needed optical power attenuation. We established the 2-D finite element model (FEM) in x − y plane (z is the light propagation direction) according to the symmetry of the device’s structure. Then, dynamic and steady state temperature response of the device can be obtained by solving Fourier’s heat transfer equation:
Where, ρ is the material density, c is the specific heat, k is the thermal conductivity, and Q(x,y,z,t) is the heat generation density induced by heating the thermal-resistor. The boundary conditions used for solving this equation are a heat sink at the bottom and perfect isolators at the top, right, and left boundaries of the calculation window. We simulated the temperature profile with Q(x,y,z,t)=3 mw/µm3. Fig. 5 - Fig. 7 show the detailed steady-state temperature distribution in x-y plane.
Steady state simulation (See Fig. 6) indicates that the temperature variation ΔT of the inner rib is about 36°C and that of the outer rib is about 25 °C. Therefore, we can estimate that the scale factor described in section 4.2 is about α=0.7. In order to obtain big optical power attenuation at this scale factor, ΔT inner=30 °C is needed for designed values, and ΔT inner=34°C is needed for the worst case. In any case, the needed temperature variation can always be obtained by applying suitable heat flux density. Therefore, the continuous power attenuation can also be obtained.
Transient thermal analysis was carried out by using the steady state temperature profile as the initial condition. Because of the high thermal conductivity and low specific heat of Al2O3 and Si, the heat transfer of special SOI becomes quicker than that of general SOI. The simulated results also indicate that the sum of heating and cooling time is about 5 µs. (See Fig. 8), which makes the proposed device be able to operate in the range of about 200 kHz. To our knowledge, this frequency is the highest value reported for thermo- optical devices.
4.4 BPM analysis
In this section, the average temperature variation ΔT is converted into RI distribution and the attenuation characteristics with designed values and the fabrication errors discussed in section 4.2 are simulated respectively at the wave length of 1550 nm. In order to obtain the power attenuation with different RI of the core layer, Visual Basic Script (VBS) language, which is embedded in BPM software to manipulate the geometric and physical properties of waveguides, is used to control the RI value of silicon layer. For the case with designed values, Figure 9 (green line) shows that the attenuation range from 0.14dB to more than 50 dB is achieved for α=0.7. The corresponding RI variation (Δn), effective index variation (Δn eff) is from 0 to 5.55×10-3, and 0 to 5.54×10-3, respectively. Δn=5.55×10-3 can be easily achieved by increasing temperature to ΔT=30°C. For the case with fabrication errors, the loss induced by fabrication errors is about 0.8 dB and 0.9 dB for positive and negative error, respectively. It can be seen from Fig. 9 that the tendency of these simulated curves coincides well with that of the numerical analysis in subsection 4.2. The attenuation range from 0.9 dB to more than 50 dB can also be achieved for the worst case. Figures 9 and 10 show the relationship between attenuation, RI variation, and temperature variation.
Fig. 9. Power attenuation as a function of the variation of N1. Blue, green, and red lines are the attenuation characteristics with negative error, designed values, and positive error, respectively.
Finally, the simulated optical field propagation characteristic of no external modulation (“A” point in Fig. 9) and that of large attenuation (“B” point in Fig. 9) are given in Fig. 11. The corresponding optical power patterns of “A” and “B” point are shown in Fig. 12(a) and (b), respectively. For Fig. 12(a), the loss with no RI modulation (default open) is about -0.14 dB, and the normalized optical power of bypassing waveguide is about -25.4 dB, which is large enough to neglect the loss. Figure 12(b) shows that more than 50 dB’s attenuation is obtained. Almost all the optical power is exported from the bypassing waveguides.
Fig. 11. The optical field propagation characteristic at ‘A’ point (ΔT=0°C) and ‘B’ point (ΔT=30°C) in Fig. 9
5. Conclusion
In this paper, three measures are taken to design the device and improve its performance. First, the special SOI, i.e., Si/Al2O3/Si, is used as waveguide material. Its high thermo-optical coefficient insures an enough RI variation (about 0 to 5.55×10-3) for large attenuation. Meanwhile, its high thermo conductivity fastens the heat transfer from the top metallic film to the bottom Si-substrate. The response time is about 5 µs. Second, three-waveguide coupling unit was used to achieve relatively short coupling region length (Lc is about 7500 µm). The size of the VOA is 26000-µm-long and 200-µm-wide. Multi-channel VOA could be easily fabricated. Third, three attenuation units was integrated in one SOI wafer. By this measure, dynamic attenuation range from both 0.14 dB to 50 dB and 0.9 dB to 50 dB is obtained for designed values and the worst case, respectively. The device is expected to be widely used in optical communications fields.
Acknowledgments
This work is supported by Chinese National Programs for High Technology Research and Development (NO. 2007AA03Z406), the National Natural Science Foundation of China (NO. 60877041), Jilin province science and technology development plan (Nos. 20070402 and 20080330). The authors thank Shengping Ruan, Liang Shen, Xueshuo Luan, and Fanxu Meng for helpful discussions.
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