Abstract

A compact (4.49 μm × 4.54 μm) and ultra-broadband circular Bragg grating mirror with relaxed fabrication requirements is proposed and demonstrated based on the 220 nm silicon-on-insulator (SOI) platform. Based on FDTD-simulations, the proposed grating mirror can achieve a reflectivity of >90% over a ultrabroad bandwidth of 500 nm (1263 - 1763 nm), and a high reflectivity of >95% over a broad bandwidth of 397 nm (1340 - 1737 nm), which covers the entire E- to U-bands. The circular grating is fabricated, and the experimental measurement results exhibit a high reflectivity of 93% - 98% within the measured band of 1530 to 1610 nm, which agrees well with simulations. Based on the proposed broadband and high-efficiency circular Bragg mirror, a compact notch filter with high rejection ratio (>10 dB) and low transmission loss (<0.5 dB) is also fabricated and presented, and the proposed filter could find various potential applications in optical communications and sensing applications. With its ultrabroad bandwidth, high reflectivity and compact size, the proposed circular Bragg mirror is expected to be a promising element for large-scale photonic integrated circuits and applications which require ultra-broadband and high-efficiency on-chip reflections.

© 2017 Optical Society of America

1. Introduction

High-index-contrast Bragg gratings (HBGs) with high reflectivity have been widely utilized to provide broad and flat reflection spectra in a wide variety of applications, such as filters, resonators and semiconductor lasers [1–6]. Typically, HBGs on the silicon integration platform are built using a relatively thick silicon layer (normally >1 μm thickness) with deeply- or fully-etched grating trenches to achieve the high index contrast [5,6]. However, this approach becomes problematic when implemented on the popular silicon photonics integration platform based on silicon-on-insulator (SOI) wafers with a thin silicon layer of 220 nm, where waveguides typically with a dimension of 460 × 220 nm for single-mode transmission are utilized. In this photonic integration platform, the grating index contrast is normally very limited due to the shallow etch, and a large number of periods are employed. Otherwise, the grating suffers from severe mode diffraction loss due to the small size of the waveguide. As a result, it is challenging to realize both broad bandwidth and high reflectivity simultaneously for a Bragg grating based on this popular thin SOI platform.

To overcome this difficulty, we presented a novel circular Bragg grating mirror in [7] [the structure is reproduced in Fig. 1(a)], where the diffraction loss was eliminated by recollecting the diffracted light back to the waveguide, and a high index contrast of >1.4 was realized based on the circular grating blades. However, the proposed circular grating has very stringent fabrication requirements, which limit its practical applications. For instance, to match with the circular wavefront diffraction from the strip waveguide end, grating blades were bended around the end of the strip waveguide to form a circular shape, and their inner-radiuses (r) were selected as rp=wt+(p1)Λ, where wt is the grating trench width (170 nm), Λ is the grating period (360 nm), and p is the blade number. Consequently, circular blades with very small radiuses are needed, which is difficult to realize based on standard fabrication lines. Particularly, from the equation above, the first blade has a critical radius (r1) of only 170 nm, which significantly increases the fabrication challenge, and in practice, extremely high-resolution lithography (a sub-10-nm EBL was used in [7]) is required to realize a smooth circle with such a tiny radius. Furthermore, a small gap is needed between the waveguide end and the first blade in the previous design, and the gap needs to be ≤30 nm to ensure satisfying grating performance, which further increases fabrication challenges.

 figure: Fig. 1

Fig. 1 (a): The lateral schematic of the circular Bragg grating proposed in [7]. (b): The lateral schematic of the new circular Bragg grating design proposed in this paper (size scaled).

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In this paper, to resolve these fabrication issues, we propose another circular Bragg grating mirror design with significantly relaxed fabrication requirements and a better grating performance in terms of a much broader high-reflectivity (>95%) grating bandwidth. The minimum radius of the grating blade in the current design can be increased by more than tenfold to >2 µm, while overall the circular grating still has a very compact size of only 4.49 μm × 4.54 μm. In addition, the minimum device feature size is increased substantially to 100 nm, which allows a much larger fabrication tolerance and greatly relieves fabrication challenges. The proposed circular grating is studied via numerical simulations, and results show an ultrabroad operation band of 500 nm with a reflectivity of >90%, and a broad 397-nm band with a high reflectivity of >95% covering the entire E- and U-bands. The device is also fabricated and measurement results show that a high reflectivity of 93% to 98% is achieved within the measured wavelength range of 1530 to 1610 nm. Based on the proposed ultra-broadband, compact and high-reflectivity circular grating mirror, an integrated notch filter with a large notch depth (>10 dB) and a low transmission loss (<0.5 dB) is also experimentally demonstrated. The proposed notch filter could be utilized in various optical applications such as optical monitoring, sideband suppression, optical modulation, etc., as well as sensing applications such as thermal and biochemical sensors [8–10].

2. Circular Bragg grating structure and simulation results

The schematic of proposed new circular Bragg grating design is shown in Fig. 1(b), which mainly consists of three parts: a single-mode strip waveguide (460 × 220 nm), a pie-shaped taper which is spread from the end of the waveguide, and several circular blades following the taper with the same arc angle to serve as the grating teeth. The arc angle of the taper and the blades is denoted as θ, and the length of the taper is denoted as L (measured from the end of the strip waveguide). In the proposed new grating design, the grating blades are also bended around the waveguide end to form the circular shape, which is similar to the previous design shown in Fig. 1(a). However, the insertion of the taper significantly expands their radiuses, now the minimum radius of the circles is increased to >L (the center O of the circumference that defines the taper is located slightly left to the waveguide end, as indicated in the figure), which greatly relieves fabrication challenges associated with the tiny radius in the previous design. In addition, as the waveguide is gradually spread to the circular shape which is directly aligned with the following grating blades, a small gap (wg ≤30 nm) between the waveguide end and the first grating blade is no longer required, and it further reduces fabrication challenges.

In the new device design, the pie-shaped taper is intentionally used to create a circular wave diffraction to match with the subsequent circular grating blades. In this case, the taper functions like a free propagation region (FPR), and the wave diffraction through the strip waveguide to the taper is similar to a Huygens-Fresnel diffraction, according to which the transversely confined light transmitting to an aperture (a) which is small enough relative to its wavelength (aλ) will be diffracted to circular waves [11]. The taper angle θ is a critical parameter which affects the shape of diffracted wavefront with a specific wave evolution length. Figures 2(a)-2(d) show the simulated diffraction field distribution within the tapers with different taper angles, where the taper length (L) is fixed at 2 µm. In principle, to perform like an FPR, θ should be ≥180° so that the diffracted wave is not obstructed along the y-direction, and fast circular wave evolution can be realized. Figure 2(a) shows the simulated field distribution with a taper angle of 270°. In this case, although circular waves form quickly within the taper, the reflected mode transmitting back towards the waveguide will be split by the sharp V-shaped branching corners formed by the non-vertical taper boundary and the waveguide, and results in the additional propagation routes inside the taper, as shown in the figure. These unwanted fields will experience multiple resonance routes inside the grating, which could seriously interfere with the intended Bragg reflection and destruct the Bragg spectrum. The sharp branches can be avoided by setting θ to 180°, as shown in Fig. 2(b), and perfect circular waves are observed in the taper. But in this case, the effective index contrast at the interface of the waveguide and the taper is relatively large (2.37 and 2.85 respectively, calculated by a commercial eigenmode solver [12]), which could result a considerable amount of power to be reflected again at this interface, and the disturbing resonant effect can be generated. To avoid this problem, we set θ to a smaller value of 60°, and the field distribution within the taper is shown in Fig. 2(c). The taper here can still cover the main lobe of the diffraction observed in an 180° taper, while in the meantime, the index contrast at the interface is reduced (2.37 and 2.47 for the waveguide and near the taper end, respectively). Such design also enables a much smaller device size. Further reducing θ will result in a slower wave diffraction, and circular wavefront is difficult to achieve within the 2 µm short taper length, as illustrated in Fig. 2(d) where θ is set to a relatively small value of 20°.

 figure: Fig. 2

Fig. 2 The field distribution (1550 nm) within the 2 µm long taper simulated with angles (θ) of (a) 270°, (b) 180°, (c) 60°, and (d) 20°. Note that the above field distributions were captured to illustrate the wave diffraction from strip waveguide to taper, and no grating blades were set in the simulation. The reflection observed was due to the refractive index contrast between taper and cladding, rather than Bragg reflection. The red circles in (a) and (b) indicate the branches formed in the 270° taper and the index-contrast interface in the 180° taper, respectively. The dashed line in (b) shows the 60° boundary. The tapers were all covered by 2 µm thick SiO2.

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Regarding the taper length L, it needs to be sufficiently larger than the wavelength (λ) and the aperture size (a) to create circular wavefronts [11,13] (λ here is the wavelength inside the silicon taper). Due to the sub-wavelength size of the silicon strip waveguide and the high material refractive index, circular waves can be obtained even with a short taper. As shown in Fig. 2, a short taper length of 2 μm is sufficient to create circular waves, if a relatively large taper angle is used. It should be noted that theoretically, the longer the wave evolution length, the closer for the diffracted wave to become circular [11]. Therefore, the diffracted wave can match better with the circular grating blades by using a longer taper, at the cost of a larger device size. On the other hand, in the previous design, the wave evolution length from the strip waveguide to the grating blade cannot be made large, because the lack of confinement between waveguide and grating leads to high diffraction losses if a large gap is used [7].

Different from the previous work where a 53% duty cycle (dc) was chosen to balance the grating performance in bandwidth and reflectivity [7], in this paper, the grating bandwidth and reflectivity are optimized separately to achieve the optimal results. Theoretically, the grating bandwidth increases with the grating strength. To achieve the optimal bandwidth, a 50% dc (defined as the ratio of the blade width to the grating period) based on the first-order Bragg reflection condition was selected as the starting point for device optimization, as in principle it provides the optimum grating strength [14,15]. The Bragg condition is expressed as follows:

ntWt+nbWb=λ02
where Wt and Wb are the width of the grating trenches and the blades, respectively, nt and nb are the effective refractive index for the grating trenches and the blades, respectively, and λ0 is the Bragg wavelength.

The performance of proposed circular grating was investigated using a commercial three-dimensional finite difference time domain (3D-FDTD) simulator [16]. In the simulation, Wt and Wb were set to 181 nm based on the following parameters: λ0 = 1.55 μm, nt = 1.44, nb = 2.85. Here, nt was selected as the refractive index of SiO2, and nb was approximated as the effective index of a 220 nm thick slab silicon waveguide as it is difficult to calculate the accurate effective index of a circular-shaped blade. The number of grating blades was set to 6. The simulated reflection spectrum is shown by the red dotted line in Fig. 3(a). As can be seen, the grating has an ultrabroad spectrum ranging approximately from 1260 to 1760 nm benefited from its strong index contrast. However, the reflection has a gradually declining tendency towards the shorter wavelengths, resulting in a non-flat top for the spectrum. This is mainly caused by the extra mode diffraction loss in the vertical direction inside grating trenches, due to strong vertical confinement within the thin silicon layer. This effect is shown in Figs. 3(b) and 3(c), where the vertical diffraction is clearly stronger for smaller wavelength, due to its tighter confinement within the taper (equivalently, a larger neff). Therefore, the vertical diffraction loss needs to be reduced to achieve a flat-top reflection spectrum.

 figure: Fig. 3

Fig. 3 (a): The grating reflection spectra simulated with different sets of W1, Wt, Wb, and the reflection spectrum of the optimized grating when TM-polarized light is launched. (b - e): The vertical field intensity distributions of the proposed grating captured at y = 0 plane, based on different input wavelengths (1.3 µm and 1.75 µm). The width of the first grating trench (W1) is adjusted while the widths of all other grating trenches and blades are fixed at 181 nm.

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Theoretically, the diffraction loss in a fully-etched waveguide grating can be reduced by using narrower grating trenches [17,18]. This can be illustrated by the simulated grating spectra with Wt reduced to 140 and 100 nm, respectively in Fig. 3(a) [correspondingly, based on Eq. (1), Wb was increased to 201 and 221 nm, respectively, to maintain the Bragg condition at 1550 nm]. It is clear that a smaller Wt enables a smaller grating loss within the bandwidth. Particularly, a flat top spectrum can be realized for the grating with a trench width of 100 nm. However, based on this method, the grating duty cycle is shifted away from 50% (dc was shifted to 59% and 69% respectively for the two cases above), which results in weaker grating strength and non-optimal grating bandwidth, as demonstrated in Fig. 3(a).

In order to achieve a flat spectrum with both high reflectivity and broad device bandwidth simultaneously, instead of changing the grating duty cycle for all periods, here we propose a new solution of only reducing the width of the first grating trench [denoted as W1 in Fig. 1(b)] while keeping the widths of all other trenches/blades unchanged at 181 nm to maintain the 50% dc. The vertical field distributions based on different W1 values and input wavelengths are shown in Figs. 3(b)-3(e), where the widths of other grating trenches/blades are fixed at 181 nm. As shown in Fig. 3(b), due to the strong index contrast of the grating, light is reflected within only a few grating periods, and the mode intensity decreases sharply along the propagation direction due to the strong reflection at each blade. Consequently, since the mode intensity is strongest within the taper, the diffraction occurring at the first trench is much stronger than others. Therefore, the diffraction loss can be suppressed considerably as long as W1 is reduced. Figure 3(d) shows the field distribution when W1 is reduced to 100 nm for the wavelength of 1.3 μm. It is clear that the diffraction at the first trench has been significantly weakened, and the diffraction at other trenches still remains weak. In addition, as the dc of most periods is unchanged (50%), the reduction of W1 imposes a negligible impact on the grating strength. Figure 4(a) shows the simulated grating reflection spectra with W1 adjusted from 181 to 100 nm and other trench/blade widths fixed at 181 nm. It is clear that the grating reflectivity is gradually improved with decreasing W1. Meanwhile, the reflectivity improvement gradually becomes insignificant for longer wavelengths. This is mainly because the mode diffraction becomes weaker, as can be illustrated by Figs. 3(c) and 3(e), where the reduction of W1 from 181 to 100 nm shows a negligible impact on the diffraction at the wavelength of 1.75 µm. With W1 chosen at 100 nm, the simulated circular grating reflection spectrum is shown by the blue solid line in Fig. 3(a), which presents a flat reflectivity of >90% over an ultrabroad band of 500 nm (1263 - 1763 nm) with a high Δλ/λ of 32.3%, and a high reflectivity of >95% over a broadband of 397 nm (1340 - 1737 nm) with a Δλ/λ of 25.6% which covers the entire E- to U- bands. At 1550 nm, the reflectivity is 97.6%. Compared to the previous design which has a high-efficiency (>95%) bandwidth of only 171 nm (1410 - 1581 nm), the high-efficiency band of the proposed new circular grating has been improved significantly. In addition, as shown by Fig. 4(a), even for W1 = 120 nm, the grating still shows a comparably good performance, which has a 498-nm band with a reflectivity of >90% and a 298-nm band with a high reflectivity of >95%, indicating an even larger fabrication tolerance.

 figure: Fig. 4

Fig. 4 (a): The grating spectra simulated with different W1 values. (b): The change of the grating reflectivity (1550 nm) and ∆λ with dc. (c): The grating spectra simulated with different angles (θ). (d): The change of the reflectivity (1550 nm) and ∆λ with the taper length (L) for gratings with a 20° and 60° angle. (e): The change of the grating reflectivity (1550 nm) and ∆λ with the number of blade (N). (f): The grating spectra simulated with 6, 8, and 10 periods.

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With W1 fixed at 100 nm to maintain a low vertical diffraction loss, the impact of dc on the grating operation bandwidth Δλ (defined as the bandwidth with reflectivity >90%) and the reflectivity (at 1550 nm) was investigated and results are shown in Fig. 4(b), where the dc was adjusted over a wide range from 30% to 70%. As shown in figure, ultrabroad bandwidth of ≥500 nm can be achieved within the dc region of 45% - 50%, where the difference in Δλ is very small (<10 nm). In addition, with 50% dc the reflectivity is the highest. Therefore, 50% dc is an optimum choice for the proposed grating to achieve the optimal performance.

The impact of grating angle (θ) and taper length (L) on the device performance were investigated as well, and simulation results are shown in Figs. 4(c) and 4(d). In Fig. 4(c), the taper length was fixed at 2 µm, and the grating spectrum was simulated with θ set to the different values corresponding to Figs. 2(a)-2(d). As shown Fig. 4(c), when θ is chosen at the small value of 20°, neither high grating reflectivity nor the broad bandwidth can be realized, since circular wave is difficult to create with the 2 µm short taper, which is illustrated in Fig. 2(d). A longer taper provides better wave evolution and thus, a better match between the diffracted wave and the circular grating blades, which can improve the grating performance. As shown in Fig. 4(d), both grating reflectivity and bandwidth improve with longer tapers. For the grating with 20° angle, relatively long tapers (≥5 µm) are needed to achieve optimal performances, which scarifies the device footprint. In contrast, when θ is chosen at 60°, the wave diffraction evolution process is similar with that in an 180° taper [Fig. 2(b)], and almost perfect circular wave is formed even within a short taper of 2 µm, which matches well with the circular blades. Therefore, 2 µm long taper length is sufficient for the 60° grating to reach the optimal performance in both reflectivity and bandwidth, and further increasing taper length does not provide substantial improvements. When θ continues to increase above 60°, no notable improvement can be observed either, as both neff and the wavefront shape remain relatively stable [the main lobe of the diffraction in the 180° taper is already fully captured as demonstrated in Figs. 2(b) and 2(c)]. Therefore, as shown in Fig. 4(c), with θ further increased to 180°, the spectrum is only slightly wider than the spectrum with θ = 60°. On the other hand, for θ = 180°, a periodic fluctuation in the spectrum can be seen, which is mainly due to the mode resonance inside the taper explained previously. This problem can be further confirmed by calculating the corresponding resonance cavity length (from the resonance peak spacing), which is about 2.56 μm [19]. The calculated cavity length is slightly larger than the taper length, and this is due to the mode penetration into the grating, as can be illustrated in Figs. 3(d) and 3(e). When θ is further increased to 270°, the Bragg reflection is severely destructed due to strong disturbing fields inside the taper, and the grating reflection becomes unusable. Therefore, θ = 60°/L = 2 µm was chosen as the optimal combination in our design to achieve both the optimal performance and a compact device size.

The impact of the number of grating blades (N) on the grating reflectivity and the operation bandwidth was also investigated, and simulation results are shown in Fig. 4(e). It is clear that both grating operation band and reflectivity improve sharply with a larger N until N reaches 6. For N > 6, the reflectivity and the bandwidth remain almost unchanged, whilst the spectrum shows sharper edges, as shown in Fig. 4(f). To summarize, based on the device optimization, the main design parameters of the proposed circular grating are chosen to be: θ = 60°, L = 2 µm, dc = 50%, W1 = 100 nm, and N = 6, to ensure that a high-efficiency and broadband spectrum with a flat top can be achieved using a very compact device footprint.

Compared with the previously presented structure [7], the proposed grating in this paper shows a comparable performance in polarization selectivity. As shown by the simulation results in Fig. 3(a), when the fundamental TM polarization is launched into the circular grating optimized for TE-polarized light, the grating exhibits very low reflection efficiency within its operation band. Based on the simulation results, the proposed grating could achieve a high polarization extinction ratio (PER) of >16.5 dB over a broad wavelength range of 330 nm (1433 - 1763 nm). The high PER property is very useful in applications such as on-chip lasers to reduce the polarization degeneration and to maintain the polarization stability.

3. Device fabrication and experimental demonstration

The proposed circular Bragg grating was fabricated based on the SOI wafer with a 220 nm thick silicon layer and a 2 μm thick buried oxide (BOX) layer. Spot size converters with a tip width of 180 nm and a length of 200 μm were used for the coupling between the fabricated chip and the lensed single-mode fiber (LSF). The structures were patterned through EBL and reactive-ion etching (RIE) with SF6/C4F8 chemistry, and the chip was covered by 2 μm thick SiO2 as the upper cladding layer deposited by PECVD. The inset of Fig. 5(a) shows the scanning electron microscope (SEM) image of the fabricated device and the schematic of measurement setup. A broadband light source (THORLABS ASE730) with an operation wavelength of 1530 to 1610 nm followed by an in-line polarizer and a polarization controller (PC) was used to provide the TE-polarized light. The input light passed through a circulator (Port 1→2) before being injected to the chip. After being back-reflected by the circular grating, the signal was routed by the circulator (Port 2→3) to an optical spectrum analyzer (OSA) for spectrum characterizations (shown by Setup 1). To measure the insertion loss (IL) of the grating, a reference strip waveguide was measured with the setup indicated by the dotted connection (Setup 2) in Fig. 5(a), and the length of the reference waveguide was chosen as twice the length of the waveguide connecting the circular grating to the spot size converter, considering the round-trip propagation of the light reflected by the circular grating. It should be noted that, during the input light injection in Setup 1, there were chip-facet reflections which could also be collected by Port 3 of the circulator. This facet-reflected power was measured at Port 3 of the circulator using Setup 2, and the measured facet reflection is shown in Fig. 5(b). Although this reflection was relatively weak, it was measured for more reliable performance characterization of the circular grating. Furthermore, the IL of the circulator for Port 2→3 was also measured and compensated to the device characterization results.

 figure: Fig. 5

Fig. 5 (a): The schematic of the measurement setup and the SEM images of the fabricated grating mirror (right), and a notch filter (left) with the following parameters: Lw = 4 μm, Lc = 0 μm, rb = 5 μm. (b): The measured spectra of the circular grating mirror, reference waveguide, and chip-facet reflections. (c): The measured IL of the circular grating mirror. (d): The transmission spectra of the fabricated notch filters with different cavity and coupling lengths.

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The device measurement results are shown in Fig. 5(b). It can be seen that the measured reflection spectrum of the grating is similar with the transmission spectrum of the reference waveguide, indicating the high reflection efficiency of the device. The measured IL of the grating is shown in Fig. 5(c), which presents small fluctuations that are mainly caused by the imperfect sidewall roughness of the fabricated grating and the reference waveguide. As a result of these small fluctuations as well as the inevitable small measurement/reference errors, at some points the IL spectrum is even slightly above 0 dB. This, on the other hand, also indicates that the mirror has high reflection. To reduce the effect of these small fluctuations and measurement errors, and to obtain more reliable device characterization, a regression line was calculated based on the robust locally weighted regression method [20]. Based on the regression line results, the grating exhibits a low IL of −0.32 to −0.1 dB (corresponding to a reflectivity of ~93% to 98%), which generally matches well with the simulation results.

Based on the proposed circular Bragg mirror, we also fabricated and experimentally characterized a notch filter which we initially proposed in [21]. The notch filter presented in [21] suffered from relatively high transmission loss (2 - 3 dB) and limited notch depth (<2.5 dB), due to the non-optimal performance of the Bragg mirror used in the filter. In this paper, based on the improved performance of the proposed circular Bragg mirror, the fabricated notch filter shows significant improvements which make it much more promising in real applications. The filter consisted of a resonant cavity formed by two circular grating mirrors connected by a strip waveguide. A bending waveguide coupler with a bending radius of rb and a coupling length of Lc was used as the input/output. The SEM image of the fabricated filter is shown in the inset of Fig. 5(a). This filter is equivalent to a 2-port version of a micro-ring based add-drop filter, with its input and output ports corresponding to the drop and pass ports of the micro-ring filter, respectively, and the total cavity length corresponding to half of the round-trip length of a micro-ring filter. The input light was coupled into the resonant cavity through the coupler, and after the cavity the resonant wavelengths were reflected back to the input port (drop port) of the coupler, whilst other wavelengths passed through to the output port (pass port) of the coupler. The total cavity length (T) equals Lw + 2L.

Circular grating based filters with different cavity and coupling lengths were fabricated. The gap between the coupler and the cavity was fixed at 200 nm. The transmission spectrum of the filter is characterized based on Eq. (2) below:

filtertransmission(dB)=filteroutputpower-WGoutputpower
where the output power of the filter and the reference waveguide was extracted based on the Setup 2 shown in Fig. 5(a), and the measured results are shown in Fig. 5(d). Based on the measurement results, the IL of the fabricated filters are all within 0.5 dB, which indicates a low loss of the cavity and thus verifies the high reflectivity of the proposed grating mirror. With a cavity length of 44 μm (corresponding to a micro-ring filter with a radius of ∼14 μm and a footprint of ~616 µm2), the filter shows a free-spectral range (FSR) of about 6.34 nm at around 1550 nm. It can also be seen from the measurement results that for a given cavity length, the notch depth of the filter increases with the coupling strength while the quality factor (Q) decreases with the coupling strength. With a coupling length of 2 and 4 μm (corresponding to a power coupling ratio of about 7.6% and 15% at 1550 nm), the notch depth of the filter was measured to be >5 and 10 dB, respectively, and the maximum Q was estimated to be about 14312 and 4683. In practice, the notch depth and Q can be tailored to desired values based on specific applications. When T was reduced to a much smaller value of 8 μm (corresponding to a micro-ring radius of ∼2.5 μm), a larger FSR of 30 nm was achieved, as shown in the figure. However, as the coupling ratio of this filter was not optimized at the time of fabrication (which is only about 1.4% with Lc set at 0 μm), the notch depth was very limited to <3 dB. In practice, the notch depth can be significantly increased by increasing the coupling strength, e.g., based on simulation results, a deep notch of >20 dB can be achieved for the short-cavity notch filter under critical coupling condition. The proposed notch filter has low IL regardless of the cavity length, mainly attributed to the low loss of the proposed circular grating mirror, and this becomes specially advantageous in applications where large FSR and low loss are required. On the other hand, the IL of a micro-ring filter based on this thin-Si-layer SOI could increase substantially for <3 μm radius, due to the bending loss.

4. Conclusion

In this paper, a compact circular Bragg grating mirror with relaxed fabrication requirements and a broad high-reflectivity (>95%) bandwidth has been proposed based on the 220 nm SOI platform. Compared to the previously presented circular grating mirror which has an overall device footprint of 4.03 µm × 4.32 µm [7], the overall footprint of the grating proposed in this paper is slightly larger (4.49 µm × 4.54 µm). However, the minimum radius of the circular grating is enlarged from 170 nm to over 2 µm, which significantly reduces the fabrication challenge. In addition, the minimum device feature size is increased from 30 to 100 nm, and it allows a much larger fabrication tolerance. Furthermore, simulation results have shown that the improved grating here can achieve a high reflectivity of >95% over an ultrabroad bandwidth of 397 nm which doubles the high-efficiency band achieved in [7], and experimental measurement results have shown that the fabricated circular grating can achieve a high reflectivity of 93% to 98% within the measured band of 1530 to 1610 nm, which matches with the simulation results. Based on the simulation results, the proposed circular grating also shows a comparable performance in polarization selectivity when compared to the previous design, and it exhibits a high PER of >16.5 dB over a broadband of 330 nm. Based on the proposed grating mirror, a compact notch filter with large notch depth, high Q, and low transmission loss has also been designed and demonstrated, and the proposed filter could find various applications in optical communications and sensing applications. With the advantages of broad bandwidth, high reflectivity and compact size, the proposed circular Bragg grating is expected to be a promising element for wide use in large-scale photonic integrated circuits and applications that require ultra-broadband and high-efficiency on-chip optical reflections.

Funding

Australian Research Council’s DECRA funding scheme (project number DE150100924).

Acknowledgment

This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF).

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13. M. Born and E. Wolf, “Elements of the theory of diffraction,” in Principles of Optics, 7th ed. (Cambridge University. 1999), pp. 412–514.

14. T. E. Murphy, “Design, Fabrication and Measurement of Integrated Bragg Grating Optical Filters,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, MIT, 2001), pp. 72–78.

15. K. Ghoumid, I. Elhechmi, S. Mekaoui, C. Pieralli, and T. Gharbi, “Analysis of optical filtering in waveguides with a high index modulation using the extended coupled mode theory by hybridization of a matrix method,” Opt. Commun. 289, 85–91 (2013). [CrossRef]  

16. Lumerical Solutions, Inc., http://www.lumerical.com/tcad-products/fdtd/.

17. P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D. X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010). [CrossRef]   [PubMed]  

18. R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015). [CrossRef]  

19. G. T. Reed, “Passive silicon photonic devices,” in Silicon Photonics: The State of The Art (J. W. & Sons Ltd, 2008), pp. 255–257.

20. W. S. Cleveland, “Robust Locally Weighted Regression and Smoothing Scatter Plots,” J. Am. Stat. Assoc. 74(368), 829–836 (1979). [CrossRef]  

21. C. J. Chae, D. Y. Choi, E. Skafidas, and Y. T. Lee, “Compact Waveguide Resonator Filter for Wavelength-Selective Reflection and Rejection in Silicon Waveguides,” in Opto-Electronics and Communications Conference (OECC),2015, pp. 1–3. [CrossRef]  

References

  • View by:

  1. K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
    [Crossref]
  2. T. Mukaihara, N. Yamanaka, N. Iwai, M. S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP Laser Diodes with Monitoring Photodiodes Through Semiconductor/Air Bragg Reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5(3), 469–475 (1999).
  3. C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband Mirror Using Low-Index Cladded Subwavelength Grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
    [Crossref]
  4. T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
    [Crossref]
  5. C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact Silicon Tunable Fabry-Perot Resonator With Low Power Consumption,” IEEE Photonics Technol. Lett. 16(2), 506–508 (2004).
    [Crossref]
  6. M. W. Pruessner, T. H. Stievater, and W. S. Rabinovich, “Integrated waveguide Fabry-Perot microcavities with silicon/air Bragg mirrors,” Opt. Lett. 32(5), 533–535 (2007).
    [Crossref] [PubMed]
  7. S. Gao, Y. Wang, K. Wang, and E. Skafidas, “High contrast circular grating reflector on silicon-on-insulator platform,” Opt. Lett. 41(3), 520–523 (2016).
    [Crossref] [PubMed]
  8. W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
    [Crossref]
  9. H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express 17(13), 10731–10737 (2009).
    [Crossref] [PubMed]
  10. M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
    [Crossref]
  11. E. Hecht, “Diffraction,” in Optics, 5th ed. (Pearson, 2017), pp. 449–528.
  12. Lumerical Solutions, Inc., http://www.lumerical.com/tcad-products/mode/ .
  13. M. Born and E. Wolf, “Elements of the theory of diffraction,” in Principles of Optics, 7th ed. (Cambridge University. 1999), pp. 412–514.
  14. T. E. Murphy, “Design, Fabrication and Measurement of Integrated Bragg Grating Optical Filters,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, MIT, 2001), pp. 72–78.
  15. K. Ghoumid, I. Elhechmi, S. Mekaoui, C. Pieralli, and T. Gharbi, “Analysis of optical filtering in waveguides with a high index modulation using the extended coupled mode theory by hybridization of a matrix method,” Opt. Commun. 289, 85–91 (2013).
    [Crossref]
  16. Lumerical Solutions, Inc., http://www.lumerical.com/tcad-products/fdtd/ .
  17. P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D. X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010).
    [Crossref] [PubMed]
  18. R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
    [Crossref]
  19. G. T. Reed, “Passive silicon photonic devices,” in Silicon Photonics: The State of The Art (J. W. & Sons Ltd, 2008), pp. 255–257.
  20. W. S. Cleveland, “Robust Locally Weighted Regression and Smoothing Scatter Plots,” J. Am. Stat. Assoc. 74(368), 829–836 (1979).
    [Crossref]
  21. C. J. Chae, D. Y. Choi, E. Skafidas, and Y. T. Lee, “Compact Waveguide Resonator Filter for Wavelength-Selective Reflection and Rejection in Silicon Waveguides,” in Opto-Electronics and Communications Conference (OECC),2015, pp. 1–3.
    [Crossref]

2016 (1)

2015 (1)

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

2013 (1)

K. Ghoumid, I. Elhechmi, S. Mekaoui, C. Pieralli, and T. Gharbi, “Analysis of optical filtering in waveguides with a high index modulation using the extended coupled mode theory by hybridization of a matrix method,” Opt. Commun. 289, 85–91 (2013).
[Crossref]

2012 (1)

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

2010 (1)

2009 (2)

H. Sun, A. Chen, and L. R. Dalton, “A reflective microring notch filter and sensor,” Opt. Express 17(13), 10731–10737 (2009).
[Crossref] [PubMed]

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

2007 (1)

2005 (1)

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

2004 (2)

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact Silicon Tunable Fabry-Perot Resonator With Low Power Consumption,” IEEE Photonics Technol. Lett. 16(2), 506–508 (2004).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband Mirror Using Low-Index Cladded Subwavelength Grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

1999 (1)

T. Mukaihara, N. Yamanaka, N. Iwai, M. S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP Laser Diodes with Monitoring Photodiodes Through Semiconductor/Air Bragg Reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5(3), 469–475 (1999).

1995 (1)

K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
[Crossref]

1979 (1)

W. S. Cleveland, “Robust Locally Weighted Regression and Smoothing Scatter Plots,” J. Am. Stat. Assoc. 74(368), 829–836 (1979).
[Crossref]

Aers, G. C.

Aitchison, J. S.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Almeida, V. R.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact Silicon Tunable Fabry-Perot Resonator With Low Power Consumption,” IEEE Photonics Technol. Lett. 16(2), 506–508 (2004).
[Crossref]

Angelis, C. D.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Arai, S.

K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
[Crossref]

Arakawa, M. S.

T. Mukaihara, N. Yamanaka, N. Iwai, M. S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP Laser Diodes with Monitoring Photodiodes Through Semiconductor/Air Bragg Reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5(3), 469–475 (1999).

Barrios, C. A.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact Silicon Tunable Fabry-Perot Resonator With Low Power Consumption,” IEEE Photonics Technol. Lett. 16(2), 506–508 (2004).
[Crossref]

Bates, R.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Beattie, J.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Bock, P. J.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D. X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010).
[Crossref] [PubMed]

Bogaerts, W.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Carothers, D.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Chae, C. J.

C. J. Chae, D. Y. Choi, E. Skafidas, and Y. T. Lee, “Compact Waveguide Resonator Filter for Wavelength-Selective Reflection and Rejection in Silicon Waveguides,” in Opto-Electronics and Communications Conference (OECC),2015, pp. 1–3.
[Crossref]

Chang-Hasnain, C. J.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband Mirror Using Low-Index Cladded Subwavelength Grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Cheben, P.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D. X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010).
[Crossref] [PubMed]

Chen, A.

Chen, Y.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Choi, D. Y.

C. J. Chae, D. Y. Choi, E. Skafidas, and Y. T. Lee, “Compact Waveguide Resonator Filter for Wavelength-Selective Reflection and Rejection in Silicon Waveguides,” in Opto-Electronics and Communications Conference (OECC),2015, pp. 1–3.
[Crossref]

Claes, T.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Cleveland, W. S.

W. S. Cleveland, “Robust Locally Weighted Regression and Smoothing Scatter Plots,” J. Am. Stat. Assoc. 74(368), 829–836 (1979).
[Crossref]

Dalton, L. R.

Delâge, A.

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband Mirror Using Low-Index Cladded Subwavelength Grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Densmore, A.

Driel, H. M.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Dumon, P.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Elhechmi, I.

K. Ghoumid, I. Elhechmi, S. Mekaoui, C. Pieralli, and T. Gharbi, “Analysis of optical filtering in waveguides with a high index modulation using the extended coupled mode theory by hybridization of a matrix method,” Opt. Commun. 289, 85–91 (2013).
[Crossref]

Fernandez, I. M.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Gao, S.

Gharbi, T.

K. Ghoumid, I. Elhechmi, S. Mekaoui, C. Pieralli, and T. Gharbi, “Analysis of optical filtering in waveguides with a high index modulation using the extended coupled mode theory by hybridization of a matrix method,” Opt. Commun. 289, 85–91 (2013).
[Crossref]

Ghoumid, K.

K. Ghoumid, I. Elhechmi, S. Mekaoui, C. Pieralli, and T. Gharbi, “Analysis of optical filtering in waveguides with a high index modulation using the extended coupled mode theory by hybridization of a matrix method,” Opt. Commun. 289, 85–91 (2013).
[Crossref]

Gill, D. M.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Halir, R.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Hall, T. J.

Heyn, P. D.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Huang, M. C. Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband Mirror Using Low-Index Cladded Subwavelength Grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Ishikawa, T.

T. Mukaihara, N. Yamanaka, N. Iwai, M. S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP Laser Diodes with Monitoring Photodiodes Through Semiconductor/Air Bragg Reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5(3), 469–475 (1999).

Iwai, N.

T. Mukaihara, N. Yamanaka, N. Iwai, M. S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP Laser Diodes with Monitoring Photodiodes Through Semiconductor/Air Bragg Reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5(3), 469–475 (1999).

Janz, S.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D. X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010).
[Crossref] [PubMed]

Kasukawa, A.

T. Mukaihara, N. Yamanaka, N. Iwai, M. S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP Laser Diodes with Monitoring Photodiodes Through Semiconductor/Air Bragg Reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5(3), 469–475 (1999).

K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
[Crossref]

Kimerling, L. C.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Kleckner, T. C.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Kurihashi, S.

K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
[Crossref]

Lapointe, J.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D. X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010).
[Crossref] [PubMed]

Lee, Y. T.

C. J. Chae, D. Y. Choi, E. Skafidas, and Y. T. Lee, “Compact Waveguide Resonator Filter for Wavelength-Selective Reflection and Rejection in Silicon Waveguides,” in Opto-Electronics and Communications Conference (OECC),2015, pp. 1–3.
[Crossref]

Linden, S.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Lipson, M.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact Silicon Tunable Fabry-Perot Resonator With Low Power Consumption,” IEEE Photonics Technol. Lett. 16(2), 506–508 (2004).
[Crossref]

Locatelli, A.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband Mirror Using Low-Index Cladded Subwavelength Grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Mekaoui, S.

K. Ghoumid, I. Elhechmi, S. Mekaoui, C. Pieralli, and T. Gharbi, “Analysis of optical filtering in waveguides with a high index modulation using the extended coupled mode theory by hybridization of a matrix method,” Opt. Commun. 289, 85–91 (2013).
[Crossref]

Michel, J.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Modotto, D.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Mondia, J. P.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Monux, A. O.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Morandotti, R.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Mukaihara, T.

T. Mukaihara, N. Yamanaka, N. Iwai, M. S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP Laser Diodes with Monitoring Photodiodes Through Semiconductor/Air Bragg Reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5(3), 469–475 (1999).

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband Mirror Using Low-Index Cladded Subwavelength Grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

P. Bienstman, D.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Panepucci, R. R.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact Silicon Tunable Fabry-Perot Resonator With Low Power Consumption,” IEEE Photonics Technol. Lett. 16(2), 506–508 (2004).
[Crossref]

Patel, S. S.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Perez, J. G. W.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Pieralli, C.

K. Ghoumid, I. Elhechmi, S. Mekaoui, C. Pieralli, and T. Gharbi, “Analysis of optical filtering in waveguides with a high index modulation using the extended coupled mode theory by hybridization of a matrix method,” Opt. Commun. 289, 85–91 (2013).
[Crossref]

Pomerene, A.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Pruessner, M. W.

Rabinovich, W. S.

Ramos, C. A.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Rasras, M. S.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Schmid, J. H.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delâge, S. Janz, G. C. Aers, D. X. Xu, A. Densmore, and T. J. Hall, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251–20262 (2010).
[Crossref] [PubMed]

Schmidt, B. S.

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact Silicon Tunable Fabry-Perot Resonator With Low Power Consumption,” IEEE Photonics Technol. Lett. 16(2), 506–508 (2004).
[Crossref]

Selvaraja, S. K.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Serizawa, N.

K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
[Crossref]

Shin, K.

K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
[Crossref]

Skafidas, E.

S. Gao, Y. Wang, K. Wang, and E. Skafidas, “High contrast circular grating reflector on silicon-on-insulator platform,” Opt. Lett. 41(3), 520–523 (2016).
[Crossref] [PubMed]

C. J. Chae, D. Y. Choi, E. Skafidas, and Y. T. Lee, “Compact Waveguide Resonator Filter for Wavelength-Selective Reflection and Rejection in Silicon Waveguides,” in Opto-Electronics and Communications Conference (OECC),2015, pp. 1–3.
[Crossref]

Stanley, C. R.

T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

Stievater, T. H.

Sun, H.

Tamura, M.

K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
[Crossref]

Tamura, S.

K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
[Crossref]

Tu, K.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Vaerenbergh, T. V.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Van Thourhout,

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Vos, K. D.

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Wang, K.

Wang, Y.

White, A. E.

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Xu, D.

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Xu, D. X.

Yamanaka, N.

T. Mukaihara, N. Yamanaka, N. Iwai, M. S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP Laser Diodes with Monitoring Photodiodes Through Semiconductor/Air Bragg Reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5(3), 469–475 (1999).

IEEE J. Sel. Top. Quantum Electron. (1)

T. Mukaihara, N. Yamanaka, N. Iwai, M. S. Arakawa, T. Ishikawa, and A. Kasukawa, “Integrated GaInAsP Laser Diodes with Monitoring Photodiodes Through Semiconductor/Air Bragg Reflector (SABAR),” IEEE J. Sel. Top. Quantum Electron. 5(3), 469–475 (1999).

IEEE Photonics Technol. Lett. (3)

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband Mirror Using Low-Index Cladded Subwavelength Grating,” IEEE Photonics Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

C. A. Barrios, V. R. Almeida, R. R. Panepucci, B. S. Schmidt, and M. Lipson, “Compact Silicon Tunable Fabry-Perot Resonator With Low Power Consumption,” IEEE Photonics Technol. Lett. 16(2), 506–508 (2004).
[Crossref]

K. Shin, M. Tamura, A. Kasukawa, N. Serizawa, S. Kurihashi, S. Tamura, and S. Arai, “Low threshold current density operation of GaInAsP-InP laser with multiple reflector microcavities,” IEEE Photonics Technol. Lett. 7(10), 1119–1121 (1995).
[Crossref]

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W. S. Cleveland, “Robust Locally Weighted Regression and Smoothing Scatter Plots,” J. Am. Stat. Assoc. 74(368), 829–836 (1979).
[Crossref]

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T. C. Kleckner, D. Modotto, A. Locatelli, J. P. Mondia, S. Linden, R. Morandotti, C. D. Angelis, C. R. Stanley, H. M. Driel, and J. S. Aitchison, “Design, Fabrication, and Characterization of Deep-Etched Waveguide Gratings,” J. Light. Tech. 23(11), 3832–3842 (2005).
[Crossref]

M. S. Rasras, K. Tu, D. M. Gill, Y. Chen, A. E. White, S. S. Patel, A. Pomerene, D. Carothers, J. Beattie, J. Michel, and L. C. Kimerling, “Demonstration of a Tunable Microwave-Photonic Notch Filter Using Low-Loss Silicon Ring Resonators,” J. Light. Tech. 27(12), 2105–2110 (2009).
[Crossref]

Laser Photonics Rev. (2)

R. Halir, P. J. Bock, P. Cheben, A. O. Monux, C. A. Ramos, J. H. Schmid, J. Lapointe, D. Xu, J. G. W. Perez, I. M. Fernandez, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

W. Bogaerts, P. D. Heyn, T. V. Vaerenbergh, K. D. Vos, S. K. Selvaraja, T. Claes, P. Dumon, D. P. Bienstman, Van Thourhout, and R. Bates, “Silicon microring resonators,” Laser Photonics Rev. 6(1), 47–73 (2012).
[Crossref]

Opt. Commun. (1)

K. Ghoumid, I. Elhechmi, S. Mekaoui, C. Pieralli, and T. Gharbi, “Analysis of optical filtering in waveguides with a high index modulation using the extended coupled mode theory by hybridization of a matrix method,” Opt. Commun. 289, 85–91 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Other (7)

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Lumerical Solutions, Inc., http://www.lumerical.com/tcad-products/mode/ .

M. Born and E. Wolf, “Elements of the theory of diffraction,” in Principles of Optics, 7th ed. (Cambridge University. 1999), pp. 412–514.

T. E. Murphy, “Design, Fabrication and Measurement of Integrated Bragg Grating Optical Filters,” Ph.D. dissertation (Department of Electrical Engineering and Computer Science, MIT, 2001), pp. 72–78.

G. T. Reed, “Passive silicon photonic devices,” in Silicon Photonics: The State of The Art (J. W. & Sons Ltd, 2008), pp. 255–257.

Lumerical Solutions, Inc., http://www.lumerical.com/tcad-products/fdtd/ .

C. J. Chae, D. Y. Choi, E. Skafidas, and Y. T. Lee, “Compact Waveguide Resonator Filter for Wavelength-Selective Reflection and Rejection in Silicon Waveguides,” in Opto-Electronics and Communications Conference (OECC),2015, pp. 1–3.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 (a): The lateral schematic of the circular Bragg grating proposed in [7]. (b): The lateral schematic of the new circular Bragg grating design proposed in this paper (size scaled).
Fig. 2
Fig. 2 The field distribution (1550 nm) within the 2 µm long taper simulated with angles (θ) of (a) 270°, (b) 180°, (c) 60°, and (d) 20°. Note that the above field distributions were captured to illustrate the wave diffraction from strip waveguide to taper, and no grating blades were set in the simulation. The reflection observed was due to the refractive index contrast between taper and cladding, rather than Bragg reflection. The red circles in (a) and (b) indicate the branches formed in the 270° taper and the index-contrast interface in the 180° taper, respectively. The dashed line in (b) shows the 60° boundary. The tapers were all covered by 2 µm thick SiO2.
Fig. 3
Fig. 3 (a): The grating reflection spectra simulated with different sets of W1, Wt, Wb, and the reflection spectrum of the optimized grating when TM-polarized light is launched. (b - e): The vertical field intensity distributions of the proposed grating captured at y = 0 plane, based on different input wavelengths (1.3 µm and 1.75 µm). The width of the first grating trench (W1) is adjusted while the widths of all other grating trenches and blades are fixed at 181 nm.
Fig. 4
Fig. 4 (a): The grating spectra simulated with different W1 values. (b): The change of the grating reflectivity (1550 nm) and ∆λ with dc. (c): The grating spectra simulated with different angles (θ). (d): The change of the reflectivity (1550 nm) and ∆λ with the taper length (L) for gratings with a 20° and 60° angle. (e): The change of the grating reflectivity (1550 nm) and ∆λ with the number of blade (N). (f): The grating spectra simulated with 6, 8, and 10 periods.
Fig. 5
Fig. 5 (a): The schematic of the measurement setup and the SEM images of the fabricated grating mirror (right), and a notch filter (left) with the following parameters: Lw = 4 μm, Lc = 0 μm, rb = 5 μm. (b): The measured spectra of the circular grating mirror, reference waveguide, and chip-facet reflections. (c): The measured IL of the circular grating mirror. (d): The transmission spectra of the fabricated notch filters with different cavity and coupling lengths.

Equations (2)

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n t W t + n b W b = λ 0 2
filte r transmission (dB)= filte r output power -W G output power

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