Athermal and flat-topped silicon Mach-Zehnder filters

Qingzhong Deng; Lu Liu; Rui Zhang; Xinbai Li; Jurgen Michel; Zhiping Zhou

doi:10.1364/OE.24.029577

1. Introduction

Silicon photonic wavelength division multiplexing (WDM) is widely anticipated to solve the bandwidth bottleneck problem in nowadays high-performance computing systems [1,2]. One main requirement of a WDM filter is the flat-topped transmission pass-bands and almost all kinds of silicon WDM filters have been modified to satisfy this requirement, such as cascade for ring resonators [3–6], multimode interference (MMI) assisted aperture for Arrayed Waveguide Gratings (AWGs) [7–10], multi-stage interference for Mach-Zehnder (MZ) filters [11–14]. All of these methods are efficient in flatting the pass-bands. For a silicon WDM filter, another main requirement is the athermal transmission spectrum since the large positive thermo-optic coefficient of silicon material (TOC ∼1.86 × 10⁻⁴ K⁻¹) will cause considerable temperature dependent wavelength shift (~80 pm/K). Aiming at athermal filters, several methods have been reported, such as cladding with negative TOC materials [15–17], coupling with multiple structures [18, 19], and combination of multiple types of waveguide [20–25]. Constructing the arms of a MZ filter with the combination of multiple types of waveguide is the most promising athermal scheme, as summarized in [2], due to the merits of CMOS-compatible fabrication process and zero extra energy consumption. Therefore, MZ filters are the leading candidate to simultaneously satisfy the two main requirements. However, an athermal and flat-topped silicon MZ filter has not been experimentally demonstrated since the flat-top scheme is proposed only for the MZ with the same loss in the two arms while the athermal scheme makes the two arms hold significantly different losses.

In this paper, we expand the flat-top theory to the MZ with different losses in the two arms firstly. Then, an athermal and flat-topped MZ filter is experimentally demonstrated. We have presented some preliminary results in the 13th International Conference on Group IV Photonics [26], while the complete simulation and measurement results are analyzed here.

2. Flat-topped Mach-Zehnder filter

Two-stage interference [Fig. 1(a)] is utilized to flatten the pass-bands of a MZ filter. It consists of 3 directional couplers (DCs) and 2 phase shifters (PSs). κ_i denotes the cross-coupling coefficient of DC_i (i = 1, 2, 3), and the self-coupling coefficient (r_i) can be expressed as $r_{i} = \sqrt{1 - κ_{i}^{2}}$ if the coupling loss is negligible. $Δ O L_{e f f}$ denotes the optical path length difference of the two arms in PS₁ while the value is $2 Δ O L_{e f f}$ for PS₂. a₁ denotes the optical field attenuation factor in the shorter arm of PS₁, which means incident light with electric field amplitude of E will attenuate to a₁E after transmission through this waveguide, and a₂ corresponds to the longer arm. We define the relative attenuation factor of PS₁ as a = a₂/a₁, and the value of PS₂ will be a². Then, the transmission spectrum of Ch.1 (Tr₁) and Ch.2 (Tr₂) can be expressed as truncated Fourier series.

Fig. 1 (a) Schematic and (b) theoretically calculated transmission spectra of the two-stage MZ filter.

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{\begin{cases} T r_{1} = a_{1}^{6} \cdot {| κ_{1} κ_{2} r_{3} - r_{1} r_{2} r_{3} a e^{- j ϕ} + κ_{1} r_{2} κ_{3} a^{2} e^{- j 2 ϕ} + r_{1} κ_{2} κ_{3} a^{3} e^{- j 3 ϕ} |}^{2} \\ T r_{2} = a_{1}^{6} \cdot {| κ_{1} κ_{2} κ_{3} - r_{1} r_{2} κ_{3} a e^{- j ϕ} - κ_{1} r_{2} r_{3} a^{2} e^{- j 2 ϕ} - r_{1} κ_{2} r_{3} a^{3} e^{- j 3 ϕ} |}^{2} \\ ϕ = Δ O L_{e f f} \cdot \frac{2 π}{λ}; r_{i} = \sqrt{1 - κ_{i}^{2}} (i =1, 2, 3) \end{cases}

In the form of Eq. (1), a₁ contributes to the insertion loss only. Therefore, we fix a₁ = 1 in the following theoretical analysis for the flat-top performance. If the loss difference in the arms are neglected (a = 1), designing the coupling coefficients to satisfy $κ_{1}^{2} = 0.50$ , $κ_{2}^{2} = 0.29$ , and $κ_{3}^{2} = 0.08$ will simultaneously make Ch.1 and Ch.2 flat-topped [Fig. 1(b)] [11]. We mark the value of κ_i under this condition as Κ_i (i = 1, 2, 3) for the convenience of statement.

According to Eq. (1), we find that the flat-top feature of Ch.1 can be maintained by modifying the coupling coefficients as Eq. (2) for the case of $a \neq 1$ . After such modifications, the whole spectrum will scale down with the decrease of a while the shape of the spectrum are kept unchanged. As shown in Fig. 2(a), the insertion loss increases with the decrease of a while the 1 dB bandwidth is independent with a. Similarly, Eq. (3) can keep the flat-top feature for Ch.2 as shown in Fig. 2(b).

Fig. 2 The flat-top transmission spectra of (a) Ch.1 and (b) Ch.2; (c) the required coupling coefficients; (d) transmission spectra with compromised coupling coefficients as Eq. (4). Solid lines, Ch.1; dashed lines, Ch.2; Gray dots, wavelength boundaries of 1 dB bandwidths.

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For Ch .1: κ_{1}^{2} = \frac{a^{2} Κ_{1}^{2}}{1 - (1 - a^{2}) Κ_{1}^{2}}; κ_{2}^{2} = Κ_{2}^{2}; κ_{3}^{2} = \frac{a^{- 4} Κ_{3}^{2}}{1 - (1 - a^{- 4}) Κ_{3}^{2}}

For Ch .2: κ_{1}^{2} = \frac{a^{2} Κ_{1}^{2}}{1 - (1 - a^{2}) Κ_{1}^{2}}; κ_{2}^{2} = Κ_{2}^{2}; κ_{3}^{2} = \frac{a^{4} Κ_{3}^{2}}{1 - (1 - a^{4}) Κ_{3}^{2}}

Comparing between Eqs. (2) and (3), one can find that the required coupling coefficients of Ch.1 and Ch.2 are different only in $κ_{3}^{2}$ [Fig. 2(c)]. Moreover, the required $κ_{3}^{2}$ of the two output ports differ slightly when a close to 1. Therefore, Eq. (4) is utilized when the two ports need to be considered simultaneously [Fig. 2(d)]. Even though the spectra are not strictly scaled down, the 1 dB bandwidths are not significantly degenerated.

For Ch .1 and Ch .2: κ_{1}^{2} = \frac{a^{2} Κ_{1}^{2}}{1 - (1 - a^{2}) Κ_{1}^{2}}; κ_{2}^{2} = Κ_{2}^{2}; κ_{3}^{2} = Κ_{3}^{2}

3. Athermalization with hybrid strip-slot waveguide

To achieve athermal performance, two types of waveguides are utilized to construct the arms of the phase shifters [Fig. 3(a)]. The effective thermo-optic coefficient ( $\partial n_{e f f} / \partial T$ ) and the waveguide length ( $Δ L$ ) of the two waveguide types are designed to satisfy the athermal condition,

Fig. 3 (a) The schematic of the proposed athermal flat-topped MZ filter; (b) TO_g of the fundamental TE mode in the two waveguide types; The simulated transverse electric field profile of fundamental TE mode in (c) the strip waveguide with W = 450 nm, (d) the hybrid strip-slot waveguide with W = 600 nm and (e) the waveguide mode converter with W_m = 1.25 μm, L_m = 1.40 μm, L = 5 μm; (f) Micrograph of the fabricated filter. All devices presented in this paper are based on a material platform of silicon-on-insulator (SOI) with SiO₂ cladding, and H = 220 nm, Slab = 90 nm, Slot = 200 nm; The slot is located at the center of the waveguide; The simulations are performed with 3D full vector finite element method (FEM) at 1550 nm wavelength while the refractive index of Si and SiO₂ are set to 3.48 and 1.45 respectively.

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\frac{\partial n_{e f f}^{I}}{\partial T} \cdot Δ L^{I} = \frac{\partial n_{e f f}^{I I}}{\partial T} \cdot Δ L^{I I} .

Under athermal condition, the free spectral range (FSR) of this filter can be expressed as

{\begin{cases} F S R = \frac{λ^{2}}{Δ O L_{g}} \\ Δ O L_{g} = n_{g}^{I} Δ L^{I} \cdot | 1 - \frac{T O_{g}^{I}}{T O_{g}^{I I}} |; T O_{g}^{i} = \frac{\partial n_{e f f}^{i} / \partial T}{n_{g}^{i}} (i = I, I I) \end{cases}

where

n_{g} = n_{e f f} - λ \cdot \partial n_{e f f} / \partial λ

is the group refractive index. Equation (6) indicates that larger difference in

T O_{g}

of the two waveguide types will produce shorter phase shifters for a certain FSR, which means more compact device. Due to the large difference with the strip waveguide in TO_g, shown in Fig. 3(b), the hybrid strip-slot waveguide is introduced to combine with normal single-mode waveguide (strip waveguide with W = 450 nm) for athermal performance. To ease the fabrication process, the total width of the hybrid strip-slot waveguide is chosen to be W = 600 nm so that the minimum feature size of the filter can be kept as large as 200 nm. The optical mode profiles of the two waveguides are displayed in Figs. 3(c) and 3(d) where mode mismatch can be observed. To overcome this mode mismatch, a multimode interference (MMI) based waveguide mode converter [Fig. 3(e)] is utilized to connect the waveguides [27, 28]. The device fabricated by Singapore A*STAR Institute of Microelectronics (IME) Multi-Project Wafers (MPW) is shown in Fig. 3(f) where ΔL^I = 400 μm, ΔL^II = 553 μm and the coupling length of the three DCs are 10.5 μm, 7.0 μm and 2.4 μm respectively.

Designing the filter in Fig. 3(a) to have flat-top pass-bands, characterization for the relative attenuation factor (a) is essential according to the analysis in the previous section. The mode converter is cascaded for measurement as described in [28] while the hybrid strip-slot waveguide and strip waveguide are constructed into rings to measure the attenuation factor with the method in [29]. The measured optical field attenuation factors are listed in Table 1. Based on the measured a, the required coupling coefficients for top-flat performance can be calculated with Eq. (4), shown in Table 2. Moreover, the coupling coefficients of the DCs in the fabricated filter are characterized and listed in Table 2 also. Comparing the two sets of values, one can find that the fabricated one satisfy the requirements roughly. Therefore, this filter is expected to have athermal and flat-topped transmission spectra. The measured transmission spectra under different temperature are plotted in Fig. 4: (i) the temperature-dependent wavelength shift is only ~-5 pm/K around 1550 nm wavelength which has been prominently improved when compared with traditional MZ filters (~80 pm/K); (ii) the device has flat pass-bands with 1 dB-bandwidths of 5.5 nm for Ch.1 and 5.0 nm for Ch.2 while the FSR is 14.7 nm; (iii) the cross talk between the two channels is ~-13.6 dB; and (iv) the insertion loss is 0.4 dB (Ch.1) and 1.4 dB (Ch.2). It is worth to mention that even though the athermal performance is characterized in the temperature range of 25~45 °C, the proposed filter is expected to hold the athermal performance in a wider temperature range since the athermal condition [Eq. (5)] is not sensitive to temperature fluctuations.

Table 1. The measured optical field attenuation factors.

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Table 2. The required and the fabricated DC coupling coefficients.

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Fig. 4 The measured transmission spectra of the fabricated athermal flat-topped MZ filter.

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4. Conclusion

In this work, a MZ filter which simultaneously satisfies the two main requirements for a silicon WDM filter, athermal and flat-topped transmission, has been experimentally demonstrated. Combination of strip waveguide and hybrid strip-slot waveguide is introduced for athermalization, and two-stage interference is utilized for flat-topped transmission. The designing theory for flat-topped filter is expanded to the MZ with different losses in the two arms so that it can be applied to an athermal MZ filter. The athermal performance is measured to be ~-5 pm/K while the 1 dB bandwidth is 5.5 nm for Ch.1 and 5.0 nm for Ch.2 (@ 14.7 nm FSR). The measured minimum insertion loss is 0.4 dB with a device dimension of 170 μm × 580 μm. Such a MZ filter can be easily fabricated with the state-of-art CMOS-fabrication process since its minimum feature size is as large as 200 nm. Furthermore, the device can be scaled up to multi-channel WDM filters by taking the proposed filter as the fundamental building block and cascading like a binary tree [11].

Funding

National Natural Science Foundation of China (NSFC) (61120106012).

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	κ₁²	κ₂²	κ₃²
Required	0.41 ± 0.02	0.29	0.08
Fabricated	0.38 ± 0.02	0.25 ± 0.02	0.08 ± 0.01

	κ₁²	κ₂²	κ₃²
Required	0.41 ± 0.02	0.29	0.08
Fabricated	0.38 ± 0.02	0.25 ± 0.02	0.08 ± 0.01

Athermal and flat-topped silicon Mach-Zehnder filters

Abstract

1. Introduction

2. Flat-topped Mach-Zehnder filter

3. Athermalization with hybrid strip-slot waveguide

4. Conclusion

Funding

References and links

Cited By

Figures (4)

Tables (2)

Equations (6)

Optics Express