1. Introduction

Recently, considerable research efforts have been devoted to realizing photonic structures in high-index-contrast silicon-on-insulator (SOI) platform owing to its compatibility with standard complementary metal-oxide-semiconductor (CMOS) manufacturing technology and its potential ability to realize chip-scale integrated compact optical devices [1]. Wavelength filtering optical devices are fundamental components for applications in switching,wavelength division multiplexing (WDM), and sensing, and have been extensively developed for the SOI platform with structures such as ring resonators [1,2], Bragg gratings [3–5], arrayed waveguide gratings (AWGs) [6], and planar waveguide echelle gratings [7]. Compared to ring resonators, Bragg gratings are flexible in designs, free spectral range (FSR) free, and have been widely used in optical communication applications. Bragg grating devices work on the basis of light coupling between two contradirectional propagating modes and they can be implemented by physically corrugating the surface [3,8,9] or the side wall of the silicon waveguides [4,5,10–12]. To achieve precise and wide dynamic range control of the grating coupling strength, cladding-modulated Bragg grating using periodic placements of cylinders along a waveguide have also been proposed and demonstrated [13]. Due to the high-refractive contrast between silicon and oxide, the grating pitch satisfying Bragg condition for coupling wavelength within the telecom wavelength range is short and its fabrication usually requires electron beam lithography [3, 4, 9–11, 13] or focused ion beam lithography [14], which is very slow and thus could be very expensive. Using a third-order grating instead of a first-order grating allows use of long grating pitch patternable with the 248 nm deep UV photolithography, however, the grating efficiency becomes low and a long grating length or a deep corrugation grating is needed to keep the same grating performance [8]. Such Bragg gratings have been made in spiral-shaped waveguides in order to increase their grating lengths while making them more compact [15, 16].

Long-period grating filter is another type of filter which is based on light coupling between two co-propagating guided modes [17–20]. Compared to Bragg grating filters, its grating pitch is much longer (several to hundred micrometers) and its spectrum bandwidth is broad in nature (several to tens of nanometers). It is easy to fabricate and operates in transmission mode with low insertion loss. However, one major limitation of long-period grating filter is its requirement for relatively long grating length to achieve desired characteristics. Its device length can be reduced by employing high-index-contrast silicon waveguides. For example, a long-period grating filter with a 260-μm long anti-symmetric sidewall grating has been formed in a two-mode silicon waveguide and a rejection band with an attenuation contrast as large as ~13 dB has been demonstrated [20]. Through this anti-symmetric sidewall grating, light coupling occurs between the two co-propagating modes at the coupling wavelength and results in a rejection band at the output [20]. However, due to large index contrast, the required corrugated grating depth for achieving maximum attenuation is only ~5 nm and several angstroms deviation from the ideal designed corrugation depth changes the attenuation contrast significantly [20]. Therefore, the fabrication of such fine features requires electron beam lithography and its fabrication tolerance is very tight.

In this paper, we demonstrate a long-period grating filter based on the same working principle as that in [20]. Instead of using a sidewall grating, a cladding modulated grating is used. The anti-symmetric cladding modulated grating is formed by placing two periodic arrays of silicon squares offset by half of a grating pitch along the two-mode waveguide. By using cladding modulated gratings, the grating strength can be widely controlled by the two-mode waveguide width or separation distance between the grating and the waveguide. The fabrication tolerance is large and patternable with the conventional 248 deep UV photolithography which is CMOS compatible and suitable for high volume manufacturing. The paper is organized as follows: in Section 2, we describe the working principle of the filter and the grating pitch, coupling coefficient, transmission spectrum, and 3-dB bandwidth are analyzed with the coupled-mode theory. In Section 3, the filter fabrication is introduced first. Grating filters in two-mode waveguides with different widths are fabricated and characterized. Discussion and concluding remarks are given in Section 4.

2. Working principle and grating analysis

The schematic diagram and top view of the silicon waveguide filter are shown in Figs. 1(a) and 1(b). The input and output single-mode waveguides of width W₁ are connected to the two-mode waveguide of width W₂ with two linear tapers. An anti-symmetric grating is formed by two periodic arrays of silicon squares of width W_g offset by half of a grating pitch Λ. The grating is placed at distance d from the two-mode silicon waveguide. Both grating and waveguides have the same height. Only transverse-electric (TE) polarization is considered here and the transverse-magnetic (TM) polarization works similarly. The two-mode waveguide supports both $E_{11}^x$ mode and $E_{12}^x$ mode and their electric field intensity profiles and field distributions are shown in Fig. 1(c). The electric field distributions of these two modes are symmetric and anti-symmetric with respect to the center of the two-mode waveguide in the x-direction. As the $E_{11}^x$ mode is launched into the single-mode waveguide, it gradually evolves into the $E_{11}^x$ mode of the two-mode waveguide through the input taper. The taper length is chosen to be long enough that all the light is converted into the $E_{11}^x$ mode of the two-mode waveguide and no $E_{12}^x$ mode or radiation mode is excited in the taper. When a grating period Λ is appropriately chosen, the light will be coupled from $E_{11}^x$ mode to the co-propagating $E_{12}^x$ mode and the strongest coupling occurs at a particular wavelength λ₀ (coupling wavelength) where the phase-matching condition [17–20]

 

Fig. 1 (a) Schematic diagram and (b) top view of the cladding-modulated anti-symmetric long-period grating filter. (c) Electric field intensity profiles and field distributions for $E_{11}^x$ mode and $E_{12}^x$ mode.

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For the numerical analysis given below, unless stated otherwise, the following waveguide parameters are used: refractive index of silicon n_core = 3.476, refractive indices of silica lower cladding and upper cladding n_clad = 1.444, and waveguide thickness 220 nm. These values are typical of a silicon waveguide fabricated from commercially available silicon-on-insulator (SOI) wafers. Two-mode waveguide width W₂, grating separation distance d, and silicon grating width W_g are allowed to vary. The two-mode waveguide is analyzed with a full-vectorial finite difference mode solver (Lumerical Mode Solutions). For the sake of simplicity, material dispersion is ignored and only TE polarization is considered in the analysis.

Equation (1) governs the dependence of the coupling wavelength on the grating pitch and, therefore, plays an important role in the study of long-period grating filters. The variation of the coupling wavelength with the grating period is shown in Fig. 2 for two-mode waveguides with four different values of width: W₂ = 1 μm, 0.9 μm, 0.8 μm, and 0.7 μm. The curves shown in Fig. 2 help us choose a grating pitch to filter out a certain wavelength from the transmission spectrum of the waveguide. Each curve characterizes the coupling between the $E_{11}^x$ mode and $E_{12}^x$ mode. Thanks to the large refractive index contrast of silicon waveguides, the grating pitches required for different widths are smaller than 5 μm for coupling wavelength within 1500-1600 nm, which are one or two orders of magnitude smaller those of long-period grating filters formed in low-index-contrast waveguides or fibers [17, 18]. It is also interesting to note that the coupling wavelength shifts to shorter wavelength as the grating pitch increases, i.e., the sign of the slope of the curve is negative. The slope of the curve is given by $d{\lambda }_0/d\Lambda =\Delta N_{\text{eff}}/(1-\Lambda \partial \Delta N_{\text{eff}}/\partial \lambda )$. For low-index-contrast waveguide, the item $\partial \Delta N_{\text{eff}}/\partial \lambda$ is small and $d{\lambda }_0/d\Lambda \approx \Delta N_{\text{eff}}$, and the sign of the slope of the curve is positive. For high-index-contrast waveguide, $\partial \Delta N_{\text{eff}}/\partial \lambda$varies widely and can be even sufficiently large that the denominator becomes negative. Thus, the coupling wavelength shifts to short wavelength as the grating pitch increases. In addition, the magnitude of the slope for W₂ = 0.7 μm is the largest among four curves, indicating that its coupling wavelength is more sensitive to the grating pitch than others.

 

Fig. 2 Dependence of the coupling wavelength on the grating period for equivalent unperturbed waveguides with four different values of widths W₂. The silicon grating width W_g is fixed at 300 nm.

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According to Eq. (2), the strength of the rejection band of a long-period grating filter is governed by the coupling coefficient. Figure 3 shows the dependence of the coupling coefficient and required grating length for achieving 100% coupling on the waveguide width W₂ for three different values of silicon grating width W_g. The grating separation distance d is 200 nm and the wavelength is 1550 nm. As shown in Fig. 3(a), the coupling coefficient increases from 7.19 × 10² m⁻¹ to 4.96 × 10³ m⁻¹ as the waveguide width W₂ decreases from 1 μm to 0.7 μm for W_g = 300 nm. Since narrow waveguide has more fractional power at the grating perturbed area, larger field overlap and coupling coefficient are obtained. As noted from Eq. (3), the transmission at the coupling wavelength varies periodically with κL, therefore, the results in Fig. 3 help us choose a suitable grating length to achieve a specific contrast for a given waveguide width W₂. For example, with W₂ = 0.8 μm and W_g = 300 nm, the coupling coefficient required for achieving a maximum attenuation is given by 2.23 × 10³ m⁻¹ as shown in Fig. 3(a), which, according to Fig. 3(b), requires a grating length of ~704 μm. It is also seen from Fig. 3 that the coupling coefficient depends weakly on the silicon grating width W_g, especially for the waveguide with large width.

 

Fig. 3 Dependence of the (a) coupling coefficient and (b) required grating length for achieving 100% coupling on the waveguide width W₂ for three different values of silicon grating width W_g. The grating separation distance d is fixed at 200 nm.

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The effect of the grating separation distance d on the coupling coefficient is also studied as shown in Fig. 4 for four different values of waveguide width W₂. The coupling coefficient can vary over a wide range as d changes and it is plotted on a logarithmic scale in Fig. 4(a). Since fields of both modes decay exponentially outside the waveguide towards the grating, the coupling coefficient plotted in log scale is roughly linearly dependent on the separation distance d. In particular, for small value of d, grating becomes a strong perturbation to the fields of both modes which do not decay exponentially in the grating area as d varies. Therefore the relationship between the coupling coefficient plotted in log scale and the separation distance is no longer linear as shown in Fig. 4(a). As seen from Fig. 4(a), the coupling coefficient decreases rapidly as the grating separation increases. For example, as the value of d increases from 50 nm to 300 nm, the coupling coefficient decreases from 1.91 × 10⁴ m⁻¹ to 1.02 × 10² m⁻¹ for W₂ = 1 μm. The required grating length for achieving maximal coupling at the coupling wavelength increases from 82.2 μm to 15400 μm according to Fig. 4(b). Similar to the results shown in Fig. 3, for the same grating separation distance, grating formed in waveguide with smaller width has larger coupling coefficient. As noted from Fig. 4(b), the required grating length is more sensitive to d variation for larger waveguide width W₂. Additionally, it should be pointed out that the grating can no longer be treated as a perturbation for very small values of d, and the CMT assumptions break down and the results obtained from Eq. (2) become less accurate [13, 22].

 

Fig. 4 Dependence of the (a) coupling coefficient and (b) required grating length for achieving 100% coupling on the grating separation distance d for four different values of waveguide widths W₂. The silicon grating width W_g is fixed at 300 nm. Both the coupling coefficient and grating length are plotted in log-scale.

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Figure 5 shows the dependence of the 3-dB bandwidth of filters on the two-mode waveguide width for three different values of grating separation distance. The grating length of each point on the curve is chosen for achieving 100% light coupling by calculating its coupling coefficient first. According to Eq. (4), the 3-dB bandwidth is inversely proportional to the number of the grating periods. As seen from Figs. 3(b) and 4(b), the required grating length for achieving 100% light coupling decreases as grating separation d or two-mode waveguide width W₂ decreases. The 3-dB bandwidth can be larger than 50 nm for filters with d = 170 nm and W₂ = 650 nm as shown in Fig. 5. Therefore, by choosing the grating separation or two-mode waveguide width properly, the bandwidth of the filter is can be widely controlled.

 

Fig. 5 Dependence of 3-dB bandwidth of grating filters on the waveguide width W₂ for three different values of grating separation distance d. The silicon grating width W_g is fixed at 300 nm. The grating length of each point on the curve is chosen for achieving 100% light coupling by calculating its coupling coefficient.

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3. Filter fabrication and characterization

The fabrication of the silicon waveguide filter starts with a 200 mm SOI wafer with 220 nm-thick top silicon layer and 2 μm-thick buried oxide (BOX) layers. First, the waveguide and grating structures was patterned by 248 nm deep UV lithography and etched to BOX by reactive ion etching (RIE) process. Next, the input and output vertical grating couplers (used to couple TE polarized light into and out of the filter) with etch-depth of 70 nm and grating period of 630 nm were patterned and etched. Finally a 2.9-μm SiO₂ upper cladding layer was deposited on the etched structure using plasma enhanced chemical vapor deposition (PECVD). Figure 6 shows the scanning electron microscope (SEM) images of the fabricated cladding-modulated anti-symmetric long-period grating filter in silicon waveguides before SiO₂ deposition. To study the effect of the two-mode waveguide width W₂ on the grating performance, filters with W₂ = 1 μm, 0.8 μm and 0.7 μm and different grating pitches were fabricated. The grating width W_g and distance from the two-mode silicon waveguide d were fixed at 300 nm and 200 nm, respectively. The width W₁ of both input and output single-mode waveguides was 450 nm and the length of the linear tapers was 200 μm.

 

Fig. 6 SEM images of fabricated cladding-modulated anti-symmetric long-period grating filter.

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The transmission spectra of the filters were measured with an amplified spontaneous emission (ASE) broadband light source and an optical spectrum analyzer (OSA). We first compared the transmission spectrum of an identical waveguide structure without grating (with tapers and two-mode waveguide) with that of a straight single-mode waveguide. No additional loss was found, indicating the taper induced insertion loss was negligible. In addition, no coupling peak was observed in this identical waveguide structure without grating. To remove any wavelength-dependent effect in the transmission spectra that are from the vertical grating couplers, tapers and two-mode waveguide, the measured spectra were normalized with the transmission spectra of the identical waveguide structure without grating. The normalized spectra for filters with W₂ = 1 μm for three grating pitches (Λ = 4.50 μm, 4.60 μm, and 4.64 μm) are shown in Fig. 7(a). The measured coupling wavelengths for different grating pitches and linearly fitted result are shown in Fig. 7(b) (solid squares: measurement; solid red line: linear fitting). The simulation result for W₂ = 1 μm is also shown for comparison (solid blue line). As shown in Fig. 7(b), the coupling wavelength corresponding to W₂ = 1 μm and Λ = 4.60 μm should be ~1590 nm. However the measured coupling wavelength was 1544 nm. This 46-nm blue-shift of the coupling wavelength corresponds to 0.18 μm deviation of the grating pitch (~4% fabrication error). The grating length L_g was 1040 μm, which is expected to give ~50% (3 dB) coupling according to the theoretical results shown in Fig. 4. However, as shown in Fig. 7(a), all filters have maximum attenuation as large as ~15 dB (~96.84% coupling efficiency) at the coupling wavelengths. According to the results shown in Section 2, the separation distance d is a parameter which most significantly affects the coupling coefficient. Therefore, this large discrepancy is most probably due to the fabrication error in the separation distance d. The fabricated separation d is smaller than the nominal design value (200 nm), which greatly increases the coupling coefficient as shown in Fig. 4. By assuming W₂ = 1 μm, the separation distance required for achieving 15-dB attenuation is ~170 nm (~15% fabrication error). The average 3-dB bandwidth for the three rejection bands shown in Fig. 7(a) is ~4.3 nm which is close to the calculated value (4.0 nm) shown in Fig. 5 for d = 170 nm.

 

Fig. 7 (a) Normalized measured transmission spectra of filters with W₂ = 1 μm and L_g = 1040 μm for three grating pitches. (b) Dependence of the coupling wavelength on the grating pitch (solid squares: measurement; solid red line: linear fitting; solid blue line: simulation result for W₂ = 1 μm).

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The normalized spectra for filters with W₂ = 0.8 μm for two grating pitches (Λ = 2.80 μm and 2.88 μm) are shown in Fig. 8(a). The grating length was 700 μm. The coupling wavelengths corresponding to two grating pitches were 1563.0 nm and 1526.2 nm. Again, a larger grating pitch produces a coupling peak at shorter wavelength. According to Fig. 4(a), the maximal coupling efficiency corresponding to d = 200 nm and W₂ = 0.8 μm is expected to be as large as 41.7 dB (99.99%). The measured attenuation contrasts at two coupling wavelengths were ~19.1 dB (98.77%) and ~15.5 dB (97.18%), respectively, which are close to the calculated results. The bandwidths of both coupling peaks were larger than those filters formed in 1-μm wide waveguides. The normalized spectrum for a filter with W₂ = 0.7 μm, Λ = 2.20 μm and L_g = 340 μm is shown in Fig. 8(b). According to Fig. 4, this grating length gives an attenuation contrast of ~18.7 dB (98.65%) at 1550 nm for d = 200 nm and W₂ = 0.7 μm. As shown in Fig. 8(b), the measured attenuation contrast is ~22.15 dB (99.39%). The agreement between the experimental and simulated results is good.

 

Fig. 8 (a) Normalized measured transmission spectra of filters with W₂ = 0.8 μm and L_g = 700 μm for two grating pitches (Λ = 2.80 μm and 2.88 μm). (b) Normalized measured transmission spectrum of a filter with W₂ = 0.7 μm, Λ = 2.20 μm and L_g = 340 μm.

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4. Discussion and conclusion

As demonstrated by the experimental results, the 3-dB bandwidth for the filters with W₂ = 1 μm is ~4.3 nm. In principle, its bandwidth can be further reduced by simply increasing the grating length while keeping κL an odd multiple of π/2. For example, the bandwidth can be as narrow as 0.4 nm as the grating length is increased to 11.44 mm. Such a long filter structure can be packed into a small area and miniaturized by using both curved gratings and curved two-mode waveguides [15]. Moreover, according to the analysis results shown in Section 2, the grating coupling coefficient is very sensitive to the separation distance d. The 200-nm separation distance is actually a critical dimension to be accurately fabricated by the 248 nm deep UV fabrication system. Therefore, the fabrication error in the separation distance d may result in large discrepancy for achieving desired grating efficiency. To further increase the fabrication tolerance for this kind of cladding modulated grating filter, a larger separation distance (e.g., 300 nm) may be used. The coupling coefficient becomes less sensitive at a larger value of separation distance, and the fabrication tolerance of this larger dimension is also looser for the 248 nm deep UV fabrication system.

In summary, we have designed and characterized optical filters using cladding modulated anti-symmetric long-period gratings in two-mode silicon waveguides. The demonstrated band-rejection filter is FSR free, broadband, and relatively compact in size. The characteristics of the grating filter, including grating pitch, coupling coefficient, transmission spectrum and 3-dB bandwidth are analyzed and investigated with the coupled-mode theory. In contrast to the sidewall grating, the cladding modulated grating is patternable with the conventional 248 deep UV photolithography and its fabrication tolerance is much larger. Its coupling strength can be controlled by the two-mode waveguide width or the separation distance between the grating and the waveguide. Band-rejection filters are experimentally demonstrated in 1-μm, 0.8-μm and 0.7-μm wide two-mode silicon waveguides and rejection bands with different bandwidths and coupling efficiency larger than 97% have been demonstrated.