Abstract

We demonstrate the design, fabrication and measurement of integrated Bragg gratings in a compact single-mode silicon-on-insulator ridge waveguide. The gratings are realized by corrugating the sidewalls of the waveguide, either on the ridge or on the slab. The coupling coefficient is varied by changing the corrugation width which allows precise control of the bandwidth and has a high fabrication tolerance. The grating devices are fabricated using a CMOS-compatible process with 193 nm deep ultraviolet lithography. Spectral measurements show bandwidths as narrow as 0.4 nm, which are promising for on-chip applications that require narrow bandwidths such as WDM channel filters. We also present the die-to-die nonuniformity for the grating devices on the wafer, and our analysis shows that the Bragg wavelength deviation is mainly caused by the wafer thickness variation.

© 2012 Optical Society of America

1. Introduction

Bragg gratings have been used in various optical devices for applications in communication and sensing systems. The integration of waveguide Bragg gratings in the silicon-on-insulator (SOI) platform has been attracting increasing research interest over the past decade [1]. Typically, the grating is achieved by physically corrugating the silicon waveguide. Although several other methods have been reported to construct grating-based devices [27], in this paper we will discuss the two waveguide structures that are most commonly used for integrated gratings: strip and ridge waveguides with corrugations on them. Strip waveguides, or photonic wires, usually have submicron cross sections (e.g., 220 nm thick and 500 nm wide [8]) and light is strongly confined in the core, due to the high refractive index contrast between the core (silicon) and the cladding (oxide or air). The grating corrugations are normally on the waveguide sidewalls, so the grating and waveguide can be defined in a single lithography step [8]. Due to the small waveguide dimensions and optical mode size, a small perturbation on the sidewalls can cause a considerable grating coupling coefficient [9]. Therefore, it is difficult to obtain a narrow reflection/filtering bandwidth. However, numerous applications require narrow bandwidths, such as wavelength-division-multiplexed (WDM) channel filters. Although we reported a bandwidth of ∼0.8 nm [8], which seems to be the lowest bandwidth for strip waveguide Bragg gratings to date, a very small corrugation width of 10 nm was used in the design and, as will be discussed later, the reproducibility of these devices is an important issue.

Ridge waveguides, on the other hand, typically have much larger cross sections (e.g., a few microns), thus allowing higher fabrication tolerance. The gratings can be achieved by corrugating the top surface [1, 1013] or the sidewalls, where the sidewalls can be corrugated either on the ridge [14] or on the slab [15]. In contrast to the top surface gratings with a fixed etch depth, the sidewall-corrugated configuration has the advantage that the corrugation width can be easily controlled, which is essential for many complex grating profiles, such as apodized gratings that can suppress reflection side-lobes [14, 15]. The waveguide geometry is usually designed to be single-mode [16], although a nominally single-mode ridge waveguide can have higher order leaky modes, which lead to unwanted dips in the transmission spectrum on the shorter wavelength side of the fundamental mode [1, 1013]. To increase the spectral separation of these leaky modes from the fundamental mode, it is necessary to shrink the waveguide dimensions [1]. More importantly, the current trend in silicon photonics also requires small waveguide dimensions for high integration level and improved cost efficiency [17, 18]. However, until now, most integrated Bragg gratings were demonstrated in ridge waveguides with relatively large cross sections. The smallest ridge waveguide dimension for Bragg gratings reported so far is still larger than 1 μm, where the ridge width is 1 μm, the total waveguide width is ∼1.5 μm, and the single-mode condition is not satisfied [15].

In this paper, we demonstrate integrated Bragg gratings in a compact SOI ridge waveguide without sacrificing single-mode operation. The shallow-etched waveguide has a ridge width of 500 nm, a total width of only 1 μm, and a total thickness of 220 nm. The optical fields around the sidewalls are low, thus allowing small coupling coefficients with reasonable corrugation widths. Here, the gratings are realized by corrugating the sidewalls of the ridge or the sidewalls of the slab. We experimentally show that both configurations can achieve narrower bandwidths, as well as higher fabrication tolerances, than the strip waveguide gratings [8]. Besides, no higher order leaky modes were observed in a very wide spectral range. We obtained 3-dB bandwidths as narrow as 0.4 nm, which is, to the best of our knowledge, the lowest bandwidth reported to date for silicon Bragg gratings based on single waveguides with submicron height.

In terms of fabrication, most reported waveguide Bragg gratings were fabricated using electron beam (e-beam) lithography [15,911,14]. Even though e-beam lithography can make very small features, which is especially important for grating structures, it is unsuitable for commercial applications. Alternatively, we used 193 nm deep ultraviolet (UV) lithography in our work, which is CMOS compatible and offers high resolution and mass production capabilities.

One of the major issues with silicon photonics is that most wavelength-selective devices are sensitive to dimensional variations, e.g., deviations in width or thickness can cause a shift in the spectral response. Although completely addressing this issue is difficult, and active components (e.g., thermal tuning) may be required for accurate compensation [19], it is still necessary to improve the uniformity of passive devices to a practical level. Selvaraja et al. [20] demonstrated the nonuniformity of ring resonators, Mach–Zehnder interferometers, and arrayed waveguide gratings, and showed a nonuniformity in the spectral response of <0.6 nm within a chip and <2 nm between chips. Zortman et al. [21] used microdisk resonators to extract thickness and width variations from the resonant wavelength deviations, which were within ∼0.85 nm on a single die and ∼8 nm across the wafer. However, the nonuniformity of silicon integrated Bragg gratings has not been reported yet. In this paper, we present the die-to-die nonuniformity of our grating devices. From the experimental data, we extract the dimensional variations and discuss their contributions to the nonuniformity. Similar to the findings in [21], we show that the wafer thickness variation is the dominant source of the device nonuniformity.

2. Design and fabrication

2.1. Ridge waveguide

Figure 1(a) illustrates the basic waveguide structure in which the gratings are designed. The silicon ridge waveguide is on top of a 2 μm buried oxide layer. The total height (H) and width (W2) of the waveguide are 220 nm and 1 μm, respectively. The shallow-etched ridge width (W1) is 500 nm and the etch depth (D) is 70 nm. The devices were fabricated at IMEC using a CMOS-compatible process with 193 nm deep ultraviolet (UV) lithography [22, 23]. Figure 1(b) shows the tilted scanning electron microscope (SEM) image of a fabricated ridge waveguide (with corrugations on the slab). It can be seen that the cross section profile is not perfectly rectangular and has slightly sloped sidewalls. As will be discussed later, such geometric imperfections will affect the effective index of the waveguide, and, consequently, shift the Bragg wavelength from its design value.

 

Fig. 1 (a) Schematic diagram of the cross section of the ridge waveguide. (b) Tilted SEM image of a fabricated device with corrugations on the slab. The imaging was done after using a focused ion beam (FIB) to mill the waveguide.

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We use a 2D simulation method [24] to obtain the optical mode distributions in our proposed waveguides. Figure 2 shows the calculated mode profiles of the fundamental transverse-electric (TE) mode in the ridge waveguide, as well as in a strip waveguide [8] for comparison. The strip waveguide is also 500 nm wide, but does not have the slab region as the ridge waveguide. As shown in Fig. 2(b), the optical field in the strip waveguide has a considerable overlap with the sidewalls. In the ridge waveguide, however, most of the light is confined under the ridge and the optical field’s overlap with the sidewalls is very low around both the ridge and slab sidewalls, as shown in Fig. 2(a). This overlap reduction makes it possible to introduce weaker effective index perturbations by corrugating the sidewalls, thus allowing for smaller grating coupling coefficients and narrower bandwidths. Additionally, the propagation loss is reduced since the propagation loss in silicon waveguides mainly arises from light scattering due to sidewall roughness [18, 25].

 

Fig. 2 Simulated fundamental TE mode profile. (a) Ridge waveguide. (b) Strip waveguide.

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2.2. Bragg gratings on ridge waveguide

The gratings are realized by introducing periodic sidewall corrugations either on the ridge or on the slab. Figure 3 shows top view SEM images of the two configurations. The grating period Λ was designed to be 290 nm, with a duty cycle of 50%, resulting in an expected Bragg wavelength around 1526 nm. The total length of the gratings L is 580 μm, i.e., 2000 grating periods. To keep the Bragg wavelength roughly constant for different corrugation widths, symmetric corrugations (relative to the non-grating waveguide edges) were used so that the average effective index is approximately constant. It should also be noted that we used square corrugations in our mask design, however, the gratings actually fabricated are severely rounded due to the smoothing effect of the fabrication, as can be clearly seen in Fig. 3. With these limitations in mind [8], larger corrugation widths should be used in the mask design than in the simulation to obtain the desired grating coupling coefficient.

 

Fig. 3 Top view SEM images of Bragg gratings fabricated on ridge waveguides. (a) Grating on the ridge: corrugation width on each side is 60 nm (design value). (b) Grating on the slab: corrugation width on each side is 80 nm (design value).

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2.3. Device layout

The device layout schematic is shown in Fig. 4. For input and output ports, we use integrated waveguide-to-fiber grating couplers [22], which were designed for TE polarization. To collect the reflected light, a Y-branch splitter was placed between the input grating coupler and our gratings. We use the 500 nm strip waveguide, as illustrated in Fig. 2(b), for the routing waveguides as well as for the Y-branch splitter in order to minimize their footprints and bending losses. Since the gratings are on the ridge waveguide, a double-layer linear taper was designed for the transition between the strip and ridge waveguides. As shown in the top SEM image of Fig. 4, the taper section connects the strip waveguide and the ridge waveguide gratings and is 30 μm long to ensure that the transition loss is negligible [18].

 

Fig. 4 Schematic diagram of the device layout and SEM images of each of the components.

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2.4. Bragg gratings on strip waveguide

For comparison, we also fabricated Bragg gratings on the 500 nm strip waveguide, which is similar to [8] but with symmetric corrugations. Figure 5 shows SEM images of a fabricated device. In order to obtain a similar Bragg wavelength around 1526 nm, the grating period was increased to 320 nm, since the effective index of the strip waveguide is smaller than that of the ridge waveguide. The device layout is similar to Fig. 4 but without the strip-to-ridge tapers.

 

Fig. 5 SEM images of (a) tilted cross section of a straight strip waveguide and (b) top view of the sidewall grating: corrugation width on each side is 40 nm (design value).

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3. Measurement

The spectral responses of the fabricated devices were measured using an Agilent 81600B tunable laser source with a wide tuning range (1455 nm to 1640 nm). The reflection spectra were normalized using the method in [8]. Figure 6 shows the measured reflection spectra for the two grating configurations on ridge waveguides. It can be observed that the two configurations show similar performance, although the 3-dB bandwidths are slightly smaller for gratings on the slab than for gratings on the ridge, which can be attributed to the fact that the optical field distribution at the slab sidewalls is slightly less than at the ridge sidewalls, as shown in Fig. 2(a). The measured Bragg wavelength is roughly constant at about 1515 nm, which is shorter than the design value (∼1526 nm). This blue shift in the Bragg wavelength is due to the fact that the fabricated waveguide is more like a slightly smaller trapezoid instead of the perfect rectangular shape, which results in a lower effective index. To ensure the gratings work at the intended Bragg wavelengths, such fabrication imperfections should be considered and the grating periods should be adjusted, although this is still fabrication-sensitive and will usually require multiple fabrication runs to obtain the necessary calibration.

 

Fig. 6 Measured reflection spectra of the Bragg gratings fabricated on ridge waveguides. (a) Grating on ridge with 40 nm corrugations. (b) Grating on ridge with 60 nm corrugations. (c) Grating on slab with 40 nm corrugations. (d) Grating on slab with 60 nm corrugations.

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By using 60 nm corrugations, a peak reflectivity of greater than 90% was achieved in both configurations. As the corrugation width is reduced to 40 nm, the bandwidth becomes smaller and the reflectivity decreases. To increase the reflectivity, longer gratings should be used. Note that, increasing the length of the gratings does not change the coupling coefficient and the bandwidth will not increase due to the following relationships [26]:

R=tanh2(κL)
Δλ=λ02πngκ2+(π/L)2
where R is the peak reflectivity, κ is the coupling coefficient, Δλ is the bandwidth at the first nulls, λ0 is the Bragg wavelength, and ng is the group index.

Figure 7 shows an example of the measured spectral responses for the ridge waveguide gratings without normalization. We can clearly see that only one dip exists in the transmission spectrum in a wide wavelength range (150 nm), indicating that the higher order leaky modes are so far away from the fundamental mode that they can be ignored (our simulation predicts that the first leaky-mode-induced transmission dip is about 100 nm away).

 

Fig. 7 Measured spectral responses of the Bragg grating on ridge waveguides designed with 80 nm corrugations on the slab. The spectra are plotted without normalization. The inset shows the enlarged plot around the Bragg wavelength.

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Figure 8 shows the measured reflection spectra for the strip waveguide gratings. It can be seen that the Bragg wavelength also deviates from the design value (∼1526 nm). More importantly, the bandwidth is much larger than that of the ridge waveguide gratings for the same corrugation width. As shown in Fig. 8(b), the bandwidth using 40 nm corrugations is 5.21 nm, which is more than 10 times larger than using the same corrugation width on the ridge waveguide (0.43 nm or 0.47 nm). It should also be noted that, the bandwidth using 10 nm corrugations is 1.56 nm, which is almost twice the reported value in [8] (which is from a previous run at IMEC). This indicates that the strip waveguide gratings are highly sensitive to fabrication runs even using a relatively mature fabrication process at the same foundry [27]. The nonuniformity between different dies within the wafer will be discussed later.

 

Fig. 8 Measured reflection spectra of the Bragg gratings fabricated on strip waveguides. (a) 10 nm corrugations. (b) 40 nm corrugations.

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The measured bandwidth is plotted as a function of the designed corrugation width in Fig. 9 for each of the three grating structures on the same die. We can see that the green curve (strip waveguide gratings) has a much higher slope than the other two curves (ridge waveguide gratings). To obtain a bandwidth below 1 nm, if using the strip waveguide, then a corrugation width less than 10 nm will be required, whereas, if using the slab region of the ridge waveguide, then an 80 nm corrugation width should be enough. This means that the ridge waveguide gratings have a much relaxed fabrication tolerance. For the ridge waveguide gratings, the slope is almost the same for the two configurations, and the 3-dB bandwidth ranges from 0.4 nm to 0.75 nm, which makes the devices suitable for many narrow-band applications such as WDM channel filters, although apodization may be required to suppress the side-lobes.

 

Fig. 9 Measured 3-dB bandwidth versus the designed corrugation width for different grating structures on the same die.

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4. Sensitivity to fabrication variation

The results shown above were measured from devices on one die, with the temperature controlled at 25°C. Actually, the desired mask pattern is replicated on a 6 inch multi-project wafer that results in many dies or chips. Each die has a size of ∼12×13 mm2, in which the grating devices are located within in a small area of only ∼0.65×0.4 mm2. The wafer has 13 dies in the centre row, which are labeled −6 to 6 from left to right (die −2 was used for the demonstrations in the previous section). For the deep etch process, the exposure dose across the wafer is increased from left to right for research purposes [23]. This results in a reduction in width for the deep-etched structures (strip waveguides or slab region of ridge waveguides) from die −6 to die 6, and therefore, is an intentional fabrication variation. The shallow etch is a separate processing step with a fixed exposure dose which takes place before the deep etch, so the shallow-etched structures are supposed to be on target everywhere across the wafer.

To evaluate the device nonuniformity between these dies, we chose three representative grating devices and measured their spectral responses: strip waveguide gratings with 40 nm corrugations (SG), ridge waveguide gratings with 60 nm corrugations on ridge (RGR), and ridge waveguide gratings with 80 nm corrugations on slab (RGS). Table 1 lists the statistics of the collected data of the three devices, and Fig. 10 shows the deviations from the mean values.

 

Fig. 10 Measured nonuniformity of the three grating devices on different dies. (a) Bragg wavelength deviation from mean. (b) Bandwidth deviation from mean.

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Tables Icon

Table 1. Mean, standard deviation and range for the measured Bragg wavelength and bandwidth of the three devices on dies across the centre row.

As shown in Fig. 10(a), SG has a very large wavelength range of about 50 nm, while RGR and RGS have much smaller ranges and their wavelengths overlap very well, which is expected because they have the same waveguide geometry. For SG we measured a standard deviation of 17.28 nm for the Bragg wavelength, which is three time larger than those of RGR and RGS. The bandwidth variation of SG is also much larger than those of RGR and RGS, as shown in Fig. 10(b). The standard deviation of the bandwidth is 0.04 nm and 0.08 nm for RGR and RGS, respectively, while SG has a much larger value of about 0.6 nm.

Both the Bragg wavelength and the bandwidth are influenced by dimensional variations, but, for simplicity, we will focus on the Bragg wavelength for the discussion. Figure 11 shows the simulated Bragg wavelength shifts due to major dimensional variations. Since all of the curves in Fig. 11 are nearly linear, we can define their slopes as their sensitivities S. We can see that both waveguide structures are more sensitive to thickness variations than to width variations. This is particularly true in the case of the ridge waveguide, which has a very weak sensitivity to width variations. This is consistent with the earlier conclusion that the optical field intensity in the ridge waveguide is very low around the sidewalls.

 

Fig. 11 Simulated Bragg wavelength variations versus major dimensional variations. Note: for the ridge waveguide in (a), the shallow etch depth is kept constant at the target 70 nm.

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To further investigate the sources of the Bragg wavelength variation, we can write the pair of equations describing the variations in a compact matrix form similar to [21]:

[dλSGdTdλSGdWdλRGdTdλRGdW][ΔTΔW]=[ΔλSGΔλRG]
where λSG is the Bragg wavelength of SG, λRG is the Bragg wavelength of RGS, ΔT and ΔW are the thickness and width variations from the wafer mean, and the terms in the 2×2 matrix are the simulated sensitivities. Here, we have made several approximations about the ridge waveguide in order to simplify the analysis: (1) ΔW is the variation of the slab width and is equal to that of the strip waveguide width since both experience the same exposure dose in each die [23], (2) the variations of ridge width and height are negligible because of the fixed shallow etch process, and (3) since SG, RGR, and RGS are very close to each other on each die, the within-die thickness is uniform [21].

By inserting the simulated sensitivities in Fig. 11 into the left side of Eq. (3) and the experimental data in Fig. 10(a) into the right side of Eq. (3), the dimensional variations across the wafer can be extracted, as shown in Fig. 12(a). We can clearly see that the width decreases with the die number, which is consistent with the exposure dose sweep [23]. In contrast, the thickness variation has a much smaller range of about 7.2 nm (+2.4/−4.8 nm) and a standard deviation of only about 2 nm, showing good agreement with previous measurements on similar wafers [20]. However, this does not mean that the thickness variation is less important than the width variation. Figure 12(b) shows their separate contributions to the Bragg wavelength variation. For SG, the width variation contributes more because the strip waveguide is still sensitive to width, but using a fixed exposure dose for the deep etch can significantly reduce its contribution. For RGS (as also be the case for RGR), the thickness variation contributes much more than the width does, so it is actually the dominant source of variation.

 

Fig. 12 (a) Dimensional variations extracted from the data in Fig. 10(a) using Eq. (3). (b) Thickness and width contributions to the Bragg wavelength variation.

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Though the above analysis is based on a few simplifications and a limited number of data points, it clearly indicates that the Bragg wavelength variation of the ridge waveguide gratings is mainly caused by the wafer thickness variations, as observed in Fig. 12 (b), rather than the large and intentional width variations induced by the exposure dose sweep. To improve the SOI thickness uniformity, adaptive process control (e.g., corrective etching) could be used [28].

5. Conclusions

We have designed and characterized integrated Bragg gratings in a compact shallow-etched SOI ridge waveguide. In contrast to the simple strip waveguide, the ridge waveguide is optimized to reduce the optical fields around the sidewalls, while keeping the cross section small and maintaining single-mode operation. The sidewall corrugations are either on the ridge or on the slab; both allow for a small coupling coefficient with a reasonable corrugation width. Experimental results show only one dip in a wide transmission spectrum, which is a unique advantage compared to ring resonators with relatively small free spectral ranges or gratings on bulky ridge waveguides with higher-order leaky modes. Compared with the strip waveguide gratings, the ridge waveguide gratings can achieve much narrower bandwidths, as well as much relaxed fabrication tolerances. We have demonstrated bandwidths as narrow as 0.4 nm that are suitable for practical WDM applications. It is also worth noting that the devices were fabricated using 193 nm deep UV lithography, which is CMOS-compatible. We have also investigated the die-to-die nonuniformity of the grating devices and extracted the dimensional variations and their contributions. We conclude that the Bragg wavelength variation is mainly caused by the wafer thickness nonuniformity.

Acknowledgments

The authors would like to thank CMC Microsystems for making this project possible, Lumerical Solutions Inc. for the MODE Solutions, and Design Workshop Technologies Inc. for the mask layout software. The authors are also grateful to Dr. Li Yang and the SFU Nanoimaging facility for assistance with the FIB cross-section images. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada.

References and links

1. T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19, 1938–1942 (2001). [CrossRef]  

2. D. T. H. Tan, K. Ikeda, and Y. Fainman, “Cladding-modulated Bragg gratings in silicon waveguides,” Opt. Lett. 34, 1357–1359 (2009). [CrossRef]   [PubMed]  

3. D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on-chip group velocity dispersion engineering,” Appl. Phys. Lett. 95, 141109 (2009). [CrossRef]  

4. S. Zamek, D. T. H. Tan, M. Khajavikhan, M. Ayache, M. P. Nezhad, and Y. Fainman, “Compact chip-scale filter based on curve waveguide Bragg gratings,” Opt. Lett. 35, 3477–3479 (2010). [CrossRef]   [PubMed]  

5. D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, and Y. Fainman, “Wide bandwidth, low loss 1 by 4 wavelength division multiplexer on silicon for optical interconnects,” Opt. Express 19, 2401–2409 (2011). [CrossRef]   [PubMed]  

6. W. Shi, X. Wang, W. Zhang, L. Chrostowski, and N. A. F. Jaeger, “Contradirectional couplers in silicon-on-insulator rib waveguides,” Opt. Lett. 36, 3999–4001 (2011). [CrossRef]   [PubMed]  

7. R. Loiacono, G. T. Reed, G. Z. Mashanovich, R. Gwilliam, S. J. Henley, Y. Hu, R. Feldesh, and R. Jones, “Laser erasable implanted gratings for integrated silicon photonics,” Opt. Express 19, 10728–10734 (2011). [CrossRef]   [PubMed]  

8. X. Wang, W. Shi, R. Vafaei, N. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

9. D. T. H. Tan, K. Ikeda, R. E. Saperstein, B. Slutsky, and Y. Fainman, “Chip-scale dispersion engineering using chirped vertical gratings,” Opt. Lett. 33, 3013–3015 (2008). [CrossRef]   [PubMed]  

10. S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007). [CrossRef]  

11. I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express , 17, 18518–18524 (2009). [CrossRef]  

12. S. Homampour, M. P. Bulk, P. E. Jessop, and A. P. Knights, “Thermal tuning of planar Bragg gratings in silicon-on-insulator rib waveguides,” Phys. Status Solidi C 6, S240–S243 (2009). [CrossRef]  

13. I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009). [CrossRef]  

14. J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B , 20, 2753–2757 (2002). [CrossRef]  

15. G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).

16. R. A. Soref, J. Schmidtchen, and K. Peterman, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27, 1971–1974 (1991). [CrossRef]  

17. S. P. Chan, C. E. Png, S. T. Lim, G. T. Reed, and V. M. N. Passaro, “Single-mode and polarization-independent silicon-on-insulator waveguides with small cross section,” J. Lightwave Technol. 23, 2103–2111 (2005). [CrossRef]  

18. P. Dong, W. Qian, S. Liao, H. Liang, C.-C. Kung, N.-N. Feng, R. Shafiiha, J. Fong, D. Feng, A. V. Krishnamoorthy, and M. Asghari, “Low loss shallow-ridge silicon waveguides,” Opt. Express 18, 14474–14479 (2010). [CrossRef]   [PubMed]  

19. A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

20. S. K. Selvaraja, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16, 316–324 (2010). [CrossRef]  

21. W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18, 23598–23607 (2010). [CrossRef]   [PubMed]  

22. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23, 401–412 (2005). [CrossRef]  

23. S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. V. Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27, 4076–4083 (2009). [CrossRef]  

24. Software: MODE Solutions, Lumerical Solutions, Inc.

25. W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photonics Journal 3, 422–432 (2011). [CrossRef]  

26. V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993). [CrossRef]  

27. http://www.epixfab.eu

28. S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011). [CrossRef]  

References

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  1. T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19, 1938–1942 (2001).
    [Crossref]
  2. D. T. H. Tan, K. Ikeda, and Y. Fainman, “Cladding-modulated Bragg gratings in silicon waveguides,” Opt. Lett. 34, 1357–1359 (2009).
    [Crossref] [PubMed]
  3. D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on-chip group velocity dispersion engineering,” Appl. Phys. Lett. 95, 141109 (2009).
    [Crossref]
  4. S. Zamek, D. T. H. Tan, M. Khajavikhan, M. Ayache, M. P. Nezhad, and Y. Fainman, “Compact chip-scale filter based on curve waveguide Bragg gratings,” Opt. Lett. 35, 3477–3479 (2010).
    [Crossref] [PubMed]
  5. D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, and Y. Fainman, “Wide bandwidth, low loss 1 by 4 wavelength division multiplexer on silicon for optical interconnects,” Opt. Express 19, 2401–2409 (2011).
    [Crossref] [PubMed]
  6. W. Shi, X. Wang, W. Zhang, L. Chrostowski, and N. A. F. Jaeger, “Contradirectional couplers in silicon-on-insulator rib waveguides,” Opt. Lett. 36, 3999–4001 (2011).
    [Crossref] [PubMed]
  7. R. Loiacono, G. T. Reed, G. Z. Mashanovich, R. Gwilliam, S. J. Henley, Y. Hu, R. Feldesh, and R. Jones, “Laser erasable implanted gratings for integrated silicon photonics,” Opt. Express 19, 10728–10734 (2011).
    [Crossref] [PubMed]
  8. X. Wang, W. Shi, R. Vafaei, N. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).
  9. D. T. H. Tan, K. Ikeda, R. E. Saperstein, B. Slutsky, and Y. Fainman, “Chip-scale dispersion engineering using chirped vertical gratings,” Opt. Lett. 33, 3013–3015 (2008).
    [Crossref] [PubMed]
  10. S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
    [Crossref]
  11. I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express,  17, 18518–18524 (2009).
    [Crossref]
  12. S. Homampour, M. P. Bulk, P. E. Jessop, and A. P. Knights, “Thermal tuning of planar Bragg gratings in silicon-on-insulator rib waveguides,” Phys. Status Solidi C 6, S240–S243 (2009).
    [Crossref]
  13. I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
    [Crossref]
  14. J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B,  20, 2753–2757 (2002).
    [Crossref]
  15. G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).
  16. R. A. Soref, J. Schmidtchen, and K. Peterman, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27, 1971–1974 (1991).
    [Crossref]
  17. S. P. Chan, C. E. Png, S. T. Lim, G. T. Reed, and V. M. N. Passaro, “Single-mode and polarization-independent silicon-on-insulator waveguides with small cross section,” J. Lightwave Technol. 23, 2103–2111 (2005).
    [Crossref]
  18. P. Dong, W. Qian, S. Liao, H. Liang, C.-C. Kung, N.-N. Feng, R. Shafiiha, J. Fong, D. Feng, A. V. Krishnamoorthy, and M. Asghari, “Low loss shallow-ridge silicon waveguides,” Opt. Express 18, 14474–14479 (2010).
    [Crossref] [PubMed]
  19. A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).
  20. S. K. Selvaraja, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16, 316–324 (2010).
    [Crossref]
  21. W. A. Zortman, D. C. Trotter, and M. R. Watts, “Silicon photonics manufacturing,” Opt. Express 18, 23598–23607 (2010).
    [Crossref] [PubMed]
  22. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23, 401–412 (2005).
    [Crossref]
  23. S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. V. Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27, 4076–4083 (2009).
    [Crossref]
  24. Software: MODE Solutions, Lumerical Solutions, Inc.
  25. W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photonics Journal 3, 422–432 (2011).
    [Crossref]
  26. V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
    [Crossref]
  27. http://www.epixfab.eu
  28. S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011).
    [Crossref]

2011 (7)

D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, and Y. Fainman, “Wide bandwidth, low loss 1 by 4 wavelength division multiplexer on silicon for optical interconnects,” Opt. Express 19, 2401–2409 (2011).
[Crossref] [PubMed]

W. Shi, X. Wang, W. Zhang, L. Chrostowski, and N. A. F. Jaeger, “Contradirectional couplers in silicon-on-insulator rib waveguides,” Opt. Lett. 36, 3999–4001 (2011).
[Crossref] [PubMed]

R. Loiacono, G. T. Reed, G. Z. Mashanovich, R. Gwilliam, S. J. Henley, Y. Hu, R. Feldesh, and R. Jones, “Laser erasable implanted gratings for integrated silicon photonics,” Opt. Express 19, 10728–10734 (2011).
[Crossref] [PubMed]

X. Wang, W. Shi, R. Vafaei, N. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photonics Journal 3, 422–432 (2011).
[Crossref]

2010 (4)

2009 (6)

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Cladding-modulated Bragg gratings in silicon waveguides,” Opt. Lett. 34, 1357–1359 (2009).
[Crossref] [PubMed]

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on-chip group velocity dispersion engineering,” Appl. Phys. Lett. 95, 141109 (2009).
[Crossref]

I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express,  17, 18518–18524 (2009).
[Crossref]

S. Homampour, M. P. Bulk, P. E. Jessop, and A. P. Knights, “Thermal tuning of planar Bragg gratings in silicon-on-insulator rib waveguides,” Phys. Status Solidi C 6, S240–S243 (2009).
[Crossref]

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. V. Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27, 4076–4083 (2009).
[Crossref]

2008 (1)

2007 (1)

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

2005 (2)

2002 (1)

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B,  20, 2753–2757 (2002).
[Crossref]

2001 (1)

1993 (1)

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

1991 (1)

R. A. Soref, J. Schmidtchen, and K. Peterman, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27, 1971–1974 (1991).
[Crossref]

Absil, P.

S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011).
[Crossref]

Asghari, M.

Ayache, M.

Baets, R.

Bauer, J.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

Beckx, S.

Bienstman, P.

Bogaerts, W.

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photonics Journal 3, 422–432 (2011).
[Crossref]

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16, 316–324 (2010).
[Crossref]

S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. V. Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27, 4076–4083 (2009).
[Crossref]

W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. V. Campenhout, P. Bienstman, and D. V. Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23, 401–412 (2005).
[Crossref]

S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011).
[Crossref]

Bruns, J.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express,  17, 18518–18524 (2009).
[Crossref]

Bulk, M. P.

S. Homampour, M. P. Bulk, P. E. Jessop, and A. P. Knights, “Thermal tuning of planar Bragg gratings in silicon-on-insulator rib waveguides,” Phys. Status Solidi C 6, S240–S243 (2009).
[Crossref]

Campenhout, J. V.

Chan, S. P.

Chen, R.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).

Chrostowski, L.

X. Wang, W. Shi, R. Vafaei, N. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

W. Shi, X. Wang, W. Zhang, L. Chrostowski, and N. A. F. Jaeger, “Contradirectional couplers in silicon-on-insulator rib waveguides,” Opt. Lett. 36, 3999–4001 (2011).
[Crossref] [PubMed]

Chuang, Z.-M.

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

Coldren, L. A.

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

Cunningham, J. E.

D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, and Y. Fainman, “Wide bandwidth, low loss 1 by 4 wavelength division multiplexer on silicon for optical interconnects,” Opt. Express 19, 2401–2409 (2011).
[Crossref] [PubMed]

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

Dong, P.

Dumon, P.

Edura, T.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

Fainman, Y.

Feldesh, R.

Feng, D.

Feng, N.-N.

Fernandez, L.

S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011).
[Crossref]

Fong, J.

Gajda, A.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express,  17, 18518–18524 (2009).
[Crossref]

Giuntoni, I.

I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express,  17, 18518–18524 (2009).
[Crossref]

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

Goodberlet, J. G.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B,  20, 2753–2757 (2002).
[Crossref]

Gwilliam, R.

Hastings, J. T.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B,  20, 2753–2757 (2002).
[Crossref]

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19, 1938–1942 (2001).
[Crossref]

Hautala, J.

S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011).
[Crossref]

Henley, S. J.

Homampour, S.

S. Homampour, M. P. Bulk, P. E. Jessop, and A. P. Knights, “Thermal tuning of planar Bragg gratings in silicon-on-insulator rib waveguides,” Phys. Status Solidi C 6, S240–S243 (2009).
[Crossref]

Honda, S.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

Hu, Y.

Ikeda, K.

Jaeger, N.

X. Wang, W. Shi, R. Vafaei, N. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

Jaeger, N. A. F.

Jaenen, P.

Jayaraman, V.

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

Jessop, P. E.

S. Homampour, M. P. Bulk, P. E. Jessop, and A. P. Knights, “Thermal tuning of planar Bragg gratings in silicon-on-insulator rib waveguides,” Phys. Status Solidi C 6, S240–S243 (2009).
[Crossref]

Jiang, G.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).

Jiang, X.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).

Jones, R.

Khajavikhan, M.

Knights, A. P.

S. Homampour, M. P. Bulk, P. E. Jessop, and A. P. Knights, “Thermal tuning of planar Bragg gratings in silicon-on-insulator rib waveguides,” Phys. Status Solidi C 6, S240–S243 (2009).
[Crossref]

Krause, M.

Krishnamoorthy, A. V.

Kung, C.-C.

Li, G.

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

Liang, H.

Liao, S.

Lim, M. H.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B,  20, 2753–2757 (2002).
[Crossref]

Lim, S. T.

Loiacono, R.

Luo, Y.

D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, and Y. Fainman, “Wide bandwidth, low loss 1 by 4 wavelength division multiplexer on silicon for optical interconnects,” Opt. Express 19, 2401–2409 (2011).
[Crossref] [PubMed]

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

Luyssaert, B.

Marschmeyer, S.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

Mashanovich, G. Z.

Matsui, J.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

Mekis, A.

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

Mizrahi, A.

Murphy, T. E.

Nezhad, M. P.

Passaro, V. M. N.

Peterman, K.

R. A. Soref, J. Schmidtchen, and K. Peterman, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27, 1971–1974 (1991).
[Crossref]

Petermann, K.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

I. Giuntoni, A. Gajda, M. Krause, R. Steingrüber, J. Bruns, and K. Petermann, “Tunable Bragg reflectors on silicon-on-insulator rib waveguides,” Opt. Express,  17, 18518–18524 (2009).
[Crossref]

Pinguet, T.

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

Png, C. E.

Qian, W.

Raj, K.

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, and Y. Fainman, “Wide bandwidth, low loss 1 by 4 wavelength division multiplexer on silicon for optical interconnects,” Opt. Express 19, 2401–2409 (2011).
[Crossref] [PubMed]

Reed, G. T.

Richter, H.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

Rosseel, E.

S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011).
[Crossref]

Saperstein, R. E.

Schmidtchen, J.

R. A. Soref, J. Schmidtchen, and K. Peterman, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27, 1971–1974 (1991).
[Crossref]

Selvaraja, S. K.

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photonics Journal 3, 422–432 (2011).
[Crossref]

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16, 316–324 (2010).
[Crossref]

S. K. Selvaraja, P. Jaenen, W. Bogaerts, D. V. Thourhout, P. Dumon, and R. Baets, “Fabrication of photonic wire and crystal circuits in silicon-on-insulator using 193-nm optical lithography,” J. Lightwave Technol. 27, 4076–4083 (2009).
[Crossref]

S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011).
[Crossref]

Shafiiha, R.

Shi, W.

X. Wang, W. Shi, R. Vafaei, N. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

W. Shi, X. Wang, W. Zhang, L. Chrostowski, and N. A. F. Jaeger, “Contradirectional couplers in silicon-on-insulator rib waveguides,” Opt. Lett. 36, 3999–4001 (2011).
[Crossref] [PubMed]

Shubin, I.

D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, and Y. Fainman, “Wide bandwidth, low loss 1 by 4 wavelength division multiplexer on silicon for optical interconnects,” Opt. Express 19, 2401–2409 (2011).
[Crossref] [PubMed]

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

Slutsky, B.

Smith, H. I.

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B,  20, 2753–2757 (2002).
[Crossref]

T. E. Murphy, J. T. Hastings, and H. I. Smith, “Fabrication and characterization of narrow-band Bragg-reflection filters in silicon-on-insulator ridge waveguides,” J. Lightwave Technol. 19, 1938–1942 (2001).
[Crossref]

Soref, R. A.

R. A. Soref, J. Schmidtchen, and K. Peterman, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27, 1971–1974 (1991).
[Crossref]

Steingrüber, R.

Stolarek, D.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

Tabat, M.

S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011).
[Crossref]

Taillaert, D.

Tan, D. T. H.

Thacker, H.

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

Thourhout, D. V.

Tillack, B.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

Tokuda, M.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

Trotter, D. C.

Tsutsui, K.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

Utaka, K.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

Vafaei, R.

X. Wang, W. Shi, R. Vafaei, N. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

Wada, Y.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

Wang, M.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).

Wang, X.

X. Wang, W. Shi, R. Vafaei, N. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

W. Shi, X. Wang, W. Zhang, L. Chrostowski, and N. A. F. Jaeger, “Contradirectional couplers in silicon-on-insulator rib waveguides,” Opt. Lett. 36, 3999–4001 (2011).
[Crossref] [PubMed]

Watts, M. R.

Wiaux, V.

Wu, Z.

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

Yang, J.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).

Yao, J.

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

Zamek, S.

Zhang, W.

Zheng, X.

D. T. H. Tan, K. Ikeda, S. Zamek, A. Mizrahi, M. P. Nezhad, A. V. Krishnamoorthy, K. Raj, J. E. Cunningham, X. Zheng, I. Shubin, Y. Luo, and Y. Fainman, “Wide bandwidth, low loss 1 by 4 wavelength division multiplexer on silicon for optical interconnects,” Opt. Express 19, 2401–2409 (2011).
[Crossref] [PubMed]

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

Zhou, Q.

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).

Zimmermann, L.

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

Zortman, W. A.

Appl. Phys. Lett. (1)

D. T. H. Tan, K. Ikeda, and Y. Fainman, “Coupled chirped vertical gratings for on-chip group velocity dispersion engineering,” Appl. Phys. Lett. 95, 141109 (2009).
[Crossref]

Electron. Lett. (1)

S. Honda, Z. Wu, J. Matsui, K. Utaka, T. Edura, M. Tokuda, K. Tsutsui, and Y. Wada, “Largely-tunable wideband Bragg gratings fabricated on SOI rib waveguides employed by deep-RIE,” Electron. Lett. 43, 630–631 (2007).
[Crossref]

IEEE J. Quantum Electron. (2)

R. A. Soref, J. Schmidtchen, and K. Peterman, “Large single-mode rib waveguides in GeSi-Si and Si-on-SiO2,” IEEE J. Quantum Electron. 27, 1971–1974 (1991).
[Crossref]

V. Jayaraman, Z.-M. Chuang, and L. A. Coldren, “Theory, design, and performance of extended tuning range semiconductor lasers with sampled gratings,” IEEE J. Quantum Electron. 29, 1824–1834 (1993).
[Crossref]

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

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Subnanometer linewidth uniformity in silicon nanophotonic waveguide devices using CMOS fabrication technology,” IEEE J. Sel. Top. Quantum Electron. 16, 316–324 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (3)

G. Jiang, R. Chen, Q. Zhou, J. Yang, M. Wang, and X. Jiang, “Slab-modulated sidewall Bragg gratings in silicon-on-insulator ridge waveguides,” IEEE Photon. Technol. Lett. 23, 6–9 (2011).

I. Giuntoni, D. Stolarek, H. Richter, S. Marschmeyer, J. Bauer, A. Gajda, J. Bruns, B. Tillack, K. Petermann, and L. Zimmermann, “Deep-UV technology for the fabrication of Bragg gratings on SOI rib waveguides,” IEEE Photon. Technol. Lett. 21, 1894–1896 (2009).
[Crossref]

X. Wang, W. Shi, R. Vafaei, N. Jaeger, and L. Chrostowski, “Uniform and sampled Bragg gratings in SOI strip waveguides with sidewall corrugations,” IEEE Photon. Technol. Lett. 23, 290–292 (2011).

IEEE Photonics Journal (2)

A. V. Krishnamoorthy, X. Zheng, G. Li, J. Yao, T. Pinguet, A. Mekis, H. Thacker, I. Shubin, Y. Luo, K. Raj, and J. E. Cunningham, “Exploiting CMOS manufacturing to reduce tuning requirements for resonant optical devices,” IEEE Photonics Journal 3, 567–579 (2011).

W. Bogaerts and S. K. Selvaraja, “Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends,” IEEE Photonics Journal 3, 422–432 (2011).
[Crossref]

J. Lightwave Technol. (4)

J. Vac. Sci. Technol. B (1)

J. T. Hastings, M. H. Lim, J. G. Goodberlet, and H. I. Smith, “Optical waveguides with apodized sidewall gratings via spatial-phase-locked electron-beam lithography,” J. Vac. Sci. Technol. B,  20, 2753–2757 (2002).
[Crossref]

Opt. Express (5)

Opt. Lett. (4)

Phys. Status Solidi C (1)

S. Homampour, M. P. Bulk, P. E. Jessop, and A. P. Knights, “Thermal tuning of planar Bragg gratings in silicon-on-insulator rib waveguides,” Phys. Status Solidi C 6, S240–S243 (2009).
[Crossref]

Other (3)

Software: MODE Solutions, Lumerical Solutions, Inc.

http://www.epixfab.eu

S. K. Selvaraja, E. Rosseel, L. Fernandez, M. Tabat, W. Bogaerts, J. Hautala, and P. Absil, “SOI thickness uniformity improvement using corrective etching for silicon nano-photonic device,” in 2011 8th IEEE Conference on Group IV Photonics (GFP), 71–73 (2011).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 (a) Schematic diagram of the cross section of the ridge waveguide. (b) Tilted SEM image of a fabricated device with corrugations on the slab. The imaging was done after using a focused ion beam (FIB) to mill the waveguide.
Fig. 2
Fig. 2 Simulated fundamental TE mode profile. (a) Ridge waveguide. (b) Strip waveguide.
Fig. 3
Fig. 3 Top view SEM images of Bragg gratings fabricated on ridge waveguides. (a) Grating on the ridge: corrugation width on each side is 60 nm (design value). (b) Grating on the slab: corrugation width on each side is 80 nm (design value).
Fig. 4
Fig. 4 Schematic diagram of the device layout and SEM images of each of the components.
Fig. 5
Fig. 5 SEM images of (a) tilted cross section of a straight strip waveguide and (b) top view of the sidewall grating: corrugation width on each side is 40 nm (design value).
Fig. 6
Fig. 6 Measured reflection spectra of the Bragg gratings fabricated on ridge waveguides. (a) Grating on ridge with 40 nm corrugations. (b) Grating on ridge with 60 nm corrugations. (c) Grating on slab with 40 nm corrugations. (d) Grating on slab with 60 nm corrugations.
Fig. 7
Fig. 7 Measured spectral responses of the Bragg grating on ridge waveguides designed with 80 nm corrugations on the slab. The spectra are plotted without normalization. The inset shows the enlarged plot around the Bragg wavelength.
Fig. 8
Fig. 8 Measured reflection spectra of the Bragg gratings fabricated on strip waveguides. (a) 10 nm corrugations. (b) 40 nm corrugations.
Fig. 9
Fig. 9 Measured 3-dB bandwidth versus the designed corrugation width for different grating structures on the same die.
Fig. 10
Fig. 10 Measured nonuniformity of the three grating devices on different dies. (a) Bragg wavelength deviation from mean. (b) Bandwidth deviation from mean.
Fig. 11
Fig. 11 Simulated Bragg wavelength variations versus major dimensional variations. Note: for the ridge waveguide in (a), the shallow etch depth is kept constant at the target 70 nm.
Fig. 12
Fig. 12 (a) Dimensional variations extracted from the data in Fig. 10(a) using Eq. (3). (b) Thickness and width contributions to the Bragg wavelength variation.

Tables (1)

Tables Icon

Table 1 Mean, standard deviation and range for the measured Bragg wavelength and bandwidth of the three devices on dies across the centre row.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

R = tanh 2 ( κ L )
Δ λ = λ 0 2 π n g κ 2 + ( π / L ) 2
[ d λ S G d T d λ S G d W d λ R G d T d λ R G d W ] [ Δ T Δ W ] = [ Δ λ S G Δ λ R G ]

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