Abstract

We design and demonstrate broadband directional couplers that use asymmetric-waveguide based phase control sections, on the silicon-on-insulator platform. Broadband directional couplers with various power splitting ratios, including 10%/90%, 20%/80%, 30%/70%, 40%/60% and 50%/50%, were realized for both transverse electric (TE) and transverse magnetic (TM) modes. Some of the devices exhitbit bandwidths in excess of 100 nm, and all in excess of 75 nm. The footprints of the TE mode couplers are 32 μm ×1.3 μm, or less, and those of the TM mode couplers are 13 μm ×1.3 μm, or less.

© 2015 Optical Society of America

1. Introduction

Optical power couplers are essential devices for splitting and combining light in photonic systems. In photonic integrated circuits, a compact, wavelength-independent, power coupler is highly desired, especially for data communication applications, such as wavelength-division-multiplexing [1, 2] and signal switching [35]. Directional couplers (DCs) have been widely used as power couplers due to their simple configurations and the ease with which they can be fabricated in the silicon-on-insulator (SOI) platform. However, the coupling ratios of conventional DCs are known to be highly sensitive to their operating wavelengths.

In the past two decades much effort has gone into developing broadband power couplers and many papers have been published in this topic [613]. Among these works, Mach-Zehender interferometer (MZI) based couplers [9, 12, 13], which integrate an MZI structure into either DCs or multimode-interferometers, exhibit broadband performance, but their footprints are usually on the scale of hundreds of μm2. Adiabatic couplers that use tapered waveguides to split power [6, 7] also have promising broadband properties, but again at the cost of large footprints. The recently proposed hybrid plasmonic couplers [10] are both broadband and small in size. However, they require plasmonic metal deposition, which increases the complexity and cost of fabrication.

In this work, we demonstrate 2×2 asymmetric-waveguide-assisted directional couplers that are broadband (operate over a wide wavelength range), compact in size, simple in structure, and easy to fabricate. Couplers with various splitting ratios were designed to operate in the wavelength region from 1500 nm to 1600 nm, for either transverse electric (TE) mode or transverse magnetic (TM) mode, and were fabricated using SOI strip waveguides. Our measurement results show that the bandwidths of our devices are greater than 75 nm with some of them greater than 100 nm. The footprints of our devices are 31.4 μm ×1.3 μm or less for TE mode couplers, and 12.5 μm ×1.3 μm or less for TM mode couplers.

2. Design

2.1. Schematic

Our 2×2 broadband DCs are based on 220-nm-high SOI strip waveguides. Such a device, as shown in Fig. 1, consists of a symmetric coupler followed by an asymmetric-waveguide based phase control section followed by a second symmetric coupler, where linearly tapered waveguides are used to connect the asymmetric-waveguides to the symmetric couplers. Each of the symmetric couplers consists of two 500 nm wide waveguides separated by a 200 nm gap. The phase control section consists of one 400 nm wide waveguide and one 600 nm wide waveguide separated by a 300 nm gap. The tapered connecting waveguides are each 1 μm long (see the top view in Fig. 1). The lengths of the symmetric couplers and the phase control section are defined as L1 and L2, respectively. We use four 90° waveguide bends with radius R for the inputs and outputs of our couplers. The radius R for the TE and TM mode couplers are chosen to be 5 μm and 10 μm, respectively.

 figure: Fig. 1:

Fig. 1: Schematic of broadband directional coupler.

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As shown in the top view of Fig. 1, which is labeled with white arrows, the light is launched into one of the input ports at the left side of a broadband DC. When propagating along the symmetric coupler on the left side, the light will couple from one waveguide to another and the coupling ratio is wavelength-dependent. In the asymmetric-waveguide-based phase control section, the light confined in each waveguide propagates through without coupling, and will be phase shifted relative to the light in the other waveguide. After that, the light will couple in the symmetric coupler on the right side, and finally exit from the two outputs. The idea behind this design is to introduce a small phase shift between the two symmetric couplers by using the asymmetric-waveguides, to compensate for the wavelength-dependent coupling ratios of the symmetric couplers.

2.2. Theoretical analysis

We use the transfer matrix method (TMM) to analyze our device. The relationship between the input and output electric fields of the coupler can be expressed as:

[E3E4]=CPtPPt1C[E1E2]
where E1 and E2 are the electric fields at the inputs and E3 and E4 represent the electric fields at the two outputs, as shown in Fig. 1. Matrix C is the coupling matrix of the symmetric couplers and matrix P describes the propagation matrix of the phase control section. Matrices Pt and Pt1 are the propagation matrixes of the tapered waveguides at the right and the left sides of the phase control section, respectively. The coupling matrix, C, is given by:
C=[tjkjkt]ejπλ(n++n)L1α2L1,
where α is the propagation loss in 500 nm wide silicon waveguides, and we assume that the propagation losses of all of the waveguides in our devices are the same and have been taken to be 2.7 dB/cm (see for example [14]). The straight-through coefficient, t, and the cross-coupling coefficient, k, are given by [15, 16]:
t=cos(πΔneffλL1);k=sin(πΔneffλL1)
where n+ and n are the effective indices of the lowest order symmetric (+) and anti-symmetric (−) modes (see Fig. 2(a)), respectively. Δneff is the difference of effective indices of the modes, i.e., Δneff = n+n, as shown in Figs. 2(c) and 2(e). λ is the wavelength. The distributions of modes and their effective indices are calculated using the Mode Solutions by Lumerical Solutions, Inc [17].

 figure: Fig. 2:

Fig. 2: Supermode distributions of (a) the symmetric couplers and (b) the phase control section. Effective indices in the symmetric couplers for (c) the TE modes and (e) the TM modes. Effective indices in the phase control section for (d) the TE modes and (f) the TM modes.

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The propagation matrix, P, is given by:

P=[ej2πn1λL2α2L200ej2πn2λL2α2L2]
where n1 and n2 are the effective indices of mode 1 and mode 2 in the phase control section, respectively. Here, as shown in Fig. 2(b), mode 1 refers to the fundamental mode that is, in fact, primarily confined in waveguide 1, and mode 2 refers to the next higher order mode that is, in fact, primarily confined in waveguide 2. The values of n1 and n2 are calculated and shown in Figs. 2(d) and 2(f).

Here, we have assumed that Pt can be approximated by:

Pt=[ejθt1α2Lt00ejθt2α2Lt]
where θt1 and θt2 are the phase shifts in the 500-nm-to-600-nm and the 500-nm-to-400-nm tapered waveguides, respectively. Lt is the tapered waveguide length, which is 1 μm in our design. We determined θt1 and θt2 as function of wavelength using the FDTD Solutions by Lumerical Solutions, Inc [17]

When E1 is the input electric field, the power splitting ratios at the cross port, ηcross, and at the through port, ηthrough, are given by:

ηcross=|E4|2|E3|2+|E4|2;ηthrough=|E3|2|E3|2+|E4|2
Using Eq. (6), we are able to find the values of L1 and L2 for a desired broadband splitting ratio response. We plot the cross splitting ratio, ηcross, as functions of L1 and L2 at the central wavelength of 1550 nm, as shown in Figs. 3(a) and 3(b). We also plot the maximum deviation of ηcross over a 100 nm spectral range (from 1500 nm to 1600 nm) as functions of L1 and L2, as illustrated in Figs. 3(c) and 3(d). The maximum deviation of ηcross is defined as Δηcross = |ηcross(λ) − ηcross(1550)|max. To obtain the optimal L1 and L2 for a desired broadband splitting ratio, we can look for the overlap between a desired ηcross and a small Δηcross region. As shown in Fig. 3, dash lines and stars provide the examples of how to choose optimal parameters for 10%/90% and 50%/50% couplers.

 figure: Fig. 3:

Fig. 3: Contour maps of ηcross as functions of L1 and L2 at λ = 1550 nm for (a) the TE mode and (b) the TM mode. Contours maps of Δηcross as functions of L1 and L2 in the wavelength range from 1500 nm to 1600 nm for (c) the TE mode and (d) the TM mode.

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2.3. FDTD simulation

The TMM simulation provides a basic range of optimal L1s and L2s. The entire structures are further simulated and optimized using the three-dimensional finite-difference time-domain (3D FDTD) method [17]. Here, as an example, we present the simulation results for 50%/50% broadband DCs. Figures 4(a) and 4(b) respectively show the power distributions of the TE and TM modes in broadband DCs at three different wavelengths. The optimal device dimensions for the TE mode coupler are L1 = 12.4 μm and L2 = 4.6 μm; while those for TM mode coupler are L1 = 2.2 μm and L2 = 6.1 μm. Other parameters, such as waveguide widths and gaps, are given in Fig. 1. As shown in Figs. 5(a) and 5(b), the FDTD simulation results for broadband DCs are in good agreements with those calculated by using the TMM.

 figure: Fig. 4:

Fig. 4: Power distributions of the 50%/50% broadband DCs for (a) TE and (b) TM modes, at different wavelengths.

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 figure: Fig. 5:

Fig. 5: Simulated ηcross of (a) TE mode and (b) TM mode couplers. The FDTD and the TMM simulation results for broadband DCs are shown by the red lines and the blue lines, respectively. For comparison, the FDTD simulation results of 50%/50% conventional DCs are also shown by the green lines. The conventional DCs are formed with 500 nm wide, 220 nm high SOI strip waveguides separated by a 200 nm gap.

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In Figs. 5(a) and 5(b) we plot and compare the FDTD simulation results for 50%/50% conventional DCs with our designs. In the comparison, the conventional DCs consist of two 500 nm wide SOI strip waveguides separated by a 200 nm gap. Within the 100 nm wavelength range from 1500 nm to 1600 nm, the deviations of ηcross for our TE mode and TM mode couplers are only ±3.5% and ±1.5%, respectively, as shown in Fig. 5. However, large deviations are seen in both the TE and the TM modes conventional DCs. In conclusion, for both the TE and TM modes, the power splitting ratios of our broadband DCs are much less sensitive to the operation wavelength than those of the conventional DCs.

3. Fabrication and measurement

3.1. Fabrication

Our broadband DCs were fabricated using electron-beam lithography on a SOI wafer with 220 nm thick silicon on a 3 μm thick buried oxide layer. After etching, the chip had a 2 μm thick silicon dioxide layer deposited on the waveguides by using plasma-enhanced chemical vapor deposition.

Broadband DCs with various power splitting ratios have been fabricated. All of the couplers were designed to be characterized using an indirect measurement method. Figure 6(a) shows an optical image of a fabricated test structure. We characterized each of the broadband DCs by using it as the output re-combiner of a 1×2 MZI, where the input splitter was a balanced Y junction power splitter [18]. The asymmetric MZI had a delay length of ΔL = 360 μm. Grating couplers (GCs) [19] were used to couple light into and out of the MZI. Strip waveguides connecting the GCs to the MZI, were 500-nm-wide by 220-nm-high silicon nanowires. To calibrate the insertion loss of the input/output GCs, calibration structures having the same input/output configurations as the test structures, were also fabricated, which is shown in Fig. 6(b).

 figure: Fig. 6:

Fig. 6: Optical images of (a) test structure; (b) calibration structure and (c) broadband DC.

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3.2. Measurements of 50% / 50% broadband DCs

To characterize our devices, we used an Agilent 81600B tunable laser as the input source and both channels of an Agilent 81635A optical power sensor as the output detectors. TE and TM mode fiber arrays were used to inject signals into the input GC and to collect the output signals from the two output GCs. The pitch of fibers within the fiber arrays matched the 127-μm-spacing between the GCs on chip, making it convenient to align fibers to the input and output GCs and to measure the two output spectra simultaneously.

Here, we show and analyze the measurement results of 50% / 50% broadband DCs. Figures 7(a) and 7(b) present the MZI output spectra for the TE and TM modes, respectively, in which the insertion loss introduced by the GCs have been calibrated out. The extinction ratios (ERs) of a MZI refer to the power ratio difference on a logarithmic scale of the two outputs when one is at a minimum and the other is at a maximum. For the TE mode spectra as shown in Fig. 7(a), the ERs are greater than 20 dB over the 100 nm wavelength span from 1500 nm to 1600 nm. The excess loss of the TE mode MZI circuit is less than 1 dB, which indicates the excess loss of the TE mode coupler is less than 1 dB. For the TM mode spectra as shown in Fig. 7(b), the ERs exceed 30 dB over the wavelength range from 1500 nm to 1590 nm, and the excess loss of the TM mode coupler is less than 0.7 dB. We attribute the excess loss to the sidewall roughness of SOI waveguides. As the TE mode has larger overlap with the sidewalls of an SOI waveguide, than the TM mode, the TE mode coupler suffers higher excess loss. It needs to be mentioned that, here, the measured excess loss also includes the loss in the MZI.

 figure: Fig. 7:

Fig. 7: Measurement results for the 50%/50% broadband DCs. Spectra of the MZIs for (a) the TE mode and (b) the TM mode. Extracted data of the broadband DCs for (c) the TE mode and (d) the TM mode. Extinction ratios in (b) at wavelengths above 1590 nm are limited by the measurement due to the grating coupler insertion loss

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Using the ERs of the interference spectra at the MZI outputs, we extracted the power splitting ratios of our couplers, which are given by [20]:

ηcross=12±121(10ERs10110ERs10+1)2;ηthrough=1ηcross
The extracted cross splitting ratios, i.e., ηcross, are shown in Figs. 7(c) and 7(d). We use a ±1 dB bandwidth and an average measured splitting ratio to evaluate the performance of a device. The ±1 dB bandwidth is defined as the wavelength span over which deviations of the extracted ηcross are within ±1 dB of their design value. For example, the ±1 dB bandwidth of a 50%/50% (i.e., −3 dB) coupler is the wavelength span over which its ηcross is within 63.1% (i.e., −2 dB) to 39.8% (i.e., −4 dB); while that of a 10%/90% (i.e., −10 dB) coupler is within 12.6% (i.e., −9 dB) to 7.9% (i.e., −11 dB). As shown in Figs. 7(c) and 7(d), the ±1 dB limits are marked out by black dash lines. We define the average measured splitting ratio for a particular coupler as the mean of the extracted power splitting ratios.

Accrodingly, as shown in Fig. 7(c), the 50%/50% TE mode coupler has a 88 nm bandwidth over the wavelength range from 1512 nm to 1600 nm, as well as an average measured splitting ratio of 46.1%/53.9%. As shown in Fig. 7(d), the 50%/50% TM mode coupler has a bandwidth of 97 nm, from 1500 nm to 1597 nm, and an average measured splitting ratio of 48.76%/51.24%. It also shows its best performance in the wavelength span from 1500 nm to 1590 nm, where the deviations of the extracted ηcross are within ±0.15 dB. For the wavelengths above 1590 nm, the extracted ηcross of the 50%/50% TM mode coupler deviates from the simulation results. The reason is that our TM mode GCs [19] show high insertion loss at wavelengths above 1590 nm, and they suppress the measurable ERs. According to Eq. (7), smaller ERs indicates more deviation from 50%/50% power splitting. At wavelengths above 1590 nm, the ERs shown in Fig. 7(b) are limited by our measurement due to the insertion loss of the TM mode GCs, and, thus, the extracted ηcross shown in Fig. 7 (d) deviates from 50%/50% power splitting. Our 50%/50% TM mode coupler would appear to work better if the insertion loss of our TM mode GCs are lower at wavelengths above 1590 nm. In addition, please note that although the definition of the ±1 dB bandwidth appear to be loose for evaluating the 50%/50% couplers, the extracted ηcross of our 50%/50% couplers are well confined within a 1 dB band (i.e., from 0 dB to −1 dB of their design value), which are shown in Figs. 7(c) and 7(d).

The FDTD simulation results are also shown by the blue dash lines in Figs. 7(c) and 7(d). Good agreement is seen between the simulated and the measured results. When comparing the performance of the 50%/50% TE mode and the 50%/50% TM mode couplers, the extracted ηcross of the TE mode coupler is found to be less uniform than that of the TM mode coupler. This phenomenon will be discussed below.

3.3. Measurements of broadband DCs with other power splitting ratios

Broadband DCs with other power splitting ratios, including 10%/90%, 20%/80%, 30%/70%, 40%/60%, were also designed and fabricated with the same configuration as shown in Fig. 6(a). We obtained ERs from their respective MZI spectra, and then used Eq. (7) to extract the power splitting ratios of these devices. The extracted results for them are shown in Figs. 8, 9, 10, and 11, respectively. Table 1 summarizes the device dimensions and performance of all of the couplers. The ±1 dB bandwidth and average measured splitting ratio are also used to evaluate the performance of these couplers. As shown by circles in Figs. 8(a), 9(a), and 11(a), there are three isolated data points that are just silghtly outside the ±1 dB limits while the trends of their respective data curves are well confined within the limits. Considering a ±0.3 dB measurement uncertainty on the ERs of the TE mode MZI spectra, which will be discussed in section 3.4, these three isolated data points were ignored when evaluating the bandwidths of couplers. Accordingly, all of the couplers show bandwidths of more than 75 nm, with some of them having bandwidths in excess of 100 nm. The excess losses for all of the TE and TM mode couplers are below 1 dB and 0.7 dB, respectively. As discussed in the previous section, the higher excess loss of TE mode couplers can be attributed to the sidewall roughness of the SOI waveguides.

 figure: Fig. 8:

Fig. 8: Measurement results for the 10%/90% broadband DCs for the (a) TE and (b) TM modes.

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 figure: Fig. 9:

Fig. 9: Measurement results for the 20%/80% broadband DCs for the (a) TE and (b) TM modes.

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 figure: Fig. 10:

Fig. 10: Measurement results for the 30%/70% broadband DCs for the (a) TE and (b) TM modes.

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 figure: Fig. 11:

Fig. 11: Measurement results for the 40%/60% broadband DCs for the (a) TE and (b) TM modes.

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Tables Icon

Table 1:. Device dimensions and performance of broadband DCs

The extracted ηcross of all of the TE mode couplers are found to be less uniform than those of the TM mode couplers. The sidewall roughness, due to lithography and etching, of silicon-on-insulator waveguide leads to scattering at the sidewalls. The scattering not only contributes to waveguide loss but also results in back-reflections. The back-reflections lead to random Fabry-Perot effects inside our MZI, changing the transmission intensity through each waveguide and introducing phase shifts. When the light goes into the combiner with random amplitude and phase, versus wavelength, the ERs of the MZI spectra will be non-uniform. As the TE mode has higher overlap with the sidewalls of waveguides, the TE mode couplers suffer higher waveguide loss and back-reflection, and, thus, their spectra and power splitting ratios are more random. In contrast, the TM mode has lower overlap with the sidewalls of waveguides, suffering lower waveguide loss and back-reflection, and thus everything looks more uniform (A study of the waveguide loss and back-reflection for the TE and the TM modes can be found in [21]). We hypothesize that the ERs and the power splitting ratios of the TE mode couplers would have been more uniform if the devices had been fabricated using 193 nm optical projection lithography, which introduces much less sidewall roughness, instead of using electro-beam lithography.

3.4. Discussion of measurement methods

Throughout this work the indirect measurement method was used in characterizing all of our couplers, because it has several advantages when compared with the direct measurement method. Firstly, the indirect measurement method is much less sensitive to ripples in the responses of the GCs, than the direct measurement method. According to [19], the ripples in the responses of our TE mode and TM mode GCs are 0.3 dB and 0.15 dB, respectively. These ripples vary from one grating coupler to another in a fabrication run, and, thus, they cannot be calibrated out. According to Eq. (7), an ideal 50%/50% coupler provides infinite ERs in the MZI output spectra, as a result the influence of a ±0.3 dB ripple on the ERs of MZI spectra are negligible. For an ideal 10%/90% coupler, which provides 6 dB ERs in the MZI outputs, the influence of a ±0.3 dB ripple on the 6 dB ERs leads to only a splitting ratio deviation of ±0.8% on a linear scale, which is acceptable. In comparison, when directly measuring an ideal 50%/50% coupler, the influence of a ±0.3 dB ripple would lead to a splitting ratio deviation of ±3.7% on a linear scale in both outputs. This is even worse for directly measuring an ideal 10%/90% coupler, where the same ripple would cause a deviation of about ±6.4% on a linear scale in its higher power output. Secondly, the insertion loss our GCs [19] are sensitive to fabrication variations, such as wafer thickness non-uniformity. As the indirect measurement method does not depend on the absolute output power, it can provide more accurate results.

4. Conclusion

We have demonstrated broadband TE mode and TM mode DCs. Our couplers show large bandwidths, of more than 75 nm, and low excess losses, of less than 1 dB. Our couplers have simple structures, compact footprints and are easy to fabricate. Using our approach and the contour maps shown in Fig. 3, arbitrary power splitting ratios can be realized by simply setting the lengths of the symmetric couplers, L1, and the length of the phase control section, L2. While here the demostrated couplers are cladded by silicon dioxide, couplers with other claddings including air cladding can also be realized by using our approach presented in section 2. As fundemental components in photonic integrated circuits, the demostrated broadband DCs would likely find many applications in areas, such as optical switching [22,23] and wavelength-division-multiplexing [24], and in devices, such as polarization splitter-rotators [25] and modulators [26].

Acknowledgments

We acknowlege the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), particular the Silicon Electronic-Photonic Integrated Circuits (SiEPIC) Program. The devices were fabricated by Richard Bojko at the University of Washington WNF, part of the NSF NNIN. Zeqin Lu appreciates the China Scholarship Council (CSC) for the financial support of his PhD program. We would like to thank Miguel Guillen (UBC) for his assistance with the optical images, and thank Michael Caverley (UBC) and Minglei Ma (UBC) for discussions. We acknowledge CMC Microsystems, Lumerical Solutions and Mentor Graphics for the design software.

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References

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  1. C. A. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. Sel. Areas Comm. 8, 948–964 (1990).
    [Crossref]
  2. F. Horst, W. M. Green, S. Assefa, S. M. Shank, Y. A. Vlasov, and B. J. Offrein, “Cascaded mach-zehnder wavelength filters in silicon photonics for low loss and flat pass-band wdm (de-)multiplexing,” Opt. Express 21, 11652–11658 (2013).
    [Crossref] [PubMed]
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2014 (6)

2013 (5)

2012 (3)

R. Halir, A. Maese-Novo, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, P. Cheben, D.-X. Xu, J. H. Schmid, and S. Janz, “Colorless directional coupler with dispersion engineered sub-wavelength structure,” Opt. Express 20, 13470–13477 (2012).
[Crossref] [PubMed]

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

X. Zhang, B. Lee, C. yun Lin, A. Wang, A. Hosseini, and R. Chen, “Highly linear broadband optical modulator based on electro-optic polymer,” Photonics Journal 4, 2214–2228 (2012).
[Crossref]

2011 (1)

Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon.Technol. Lett. 23, 525–527 (2011).
[Crossref]

2010 (2)

S.-H. Hsu, “Signal power tapped with low polarization dependence and insensitive wavelength on silicon-on-insulator platforms,” J. Opt. Soc. Am. B 27, 941–947 (2010).
[Crossref]

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref] [PubMed]

2009 (2)

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

J. V. Campenhout, W. M. Green, S. Assefa, and Y. A. Vlasov, “Low-power, 2 × 2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks,” Opt. Express 17, 24020–24029 (2009).
[Crossref]

2006 (1)

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photon. Technol. Lett. 18, 2287–2289 (2006).
[Crossref]

1990 (2)

A. S. K Jinguji, N Takato, and M. Kawachi, “Mach-zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio,” Electron. Lett. 26, 1326–1327 (1990).
[Crossref]

C. A. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. Sel. Areas Comm. 8, 948–964 (1990).
[Crossref]

1975 (1)

J. Campbell, F. Blum, D. Shaw, and K. Lawley, “Gaas electro-optic directional-coupler switch,” Applied Physics Letters 27, 202–205 (1975).
[Crossref]

Aalto, T.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photon. Technol. Lett. 18, 2287–2289 (2006).
[Crossref]

Aguinaldo, R.

Aitchison, J. S.

Alam, M. Z.

Assefa, S.

Baehr-Jones, T.

Baets, R.

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

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

Bienstman, P.

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

Blum, F.

J. Campbell, F. Blum, D. Shaw, and K. Lawley, “Gaas electro-optic directional-coupler switch,” Applied Physics Letters 27, 202–205 (1975).
[Crossref]

Bogaerts, W.

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

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

Bojko, R.

Brackett, C. A.

C. A. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. Sel. Areas Comm. 8, 948–964 (1990).
[Crossref]

Cai, H.

Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon.Technol. Lett. 23, 525–527 (2011).
[Crossref]

Campbell, J.

J. Campbell, F. Blum, D. Shaw, and K. Lawley, “Gaas electro-optic directional-coupler switch,” Applied Physics Letters 27, 202–205 (1975).
[Crossref]

Campenhout, J. V.

Canciamilla, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref] [PubMed]

Caspers, J. N.

Chagnon, M.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Cheben, P.

Chen, R.

X. Zhang, B. Lee, C. yun Lin, A. Wang, A. Hosseini, and R. Chen, “Highly linear broadband optical modulator based on electro-optic polymer,” Photonics Journal 4, 2214–2228 (2012).
[Crossref]

Chrostowski, L.

Y. Wang, X. Wang, J. Flueckiger, H. Yun, W. Shi, R. Bojko, N. A. F. Jaeger, and L. Chrostowski, “Focusing sub-wavelength grating couplers with low back reflections for rapid prototyping of silicon photonic circuits,” Opt. Express 22, 20652–20662 (2014).
[Crossref] [PubMed]

H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-db coupler on silicon-on-insulator rib waveguides,” Proc. SPIE, Photonics North 8915, p. 89150V (2013).
[Crossref]

L. Chrostowski and M. Hochberg, Silicon Photonics Design (Cambridge University, 2014).

Claes, T.

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

Cyr, M.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Davidson, C.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

De Heyn, P.

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

De Vos, K.

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

DeRose, C.

Ding, Y.

Dumon, P.

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

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

Fainman, Y.

Fang, Q.

Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon.Technol. Lett. 23, 525–527 (2011).
[Crossref]

Ferrari, C.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref] [PubMed]

Flueckiger, J.

Forencich, A.

Gagné, J.-F.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Galland, C.

Gan, F.

Green, W. M.

Guy, M.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Halir, R.

Harjanne, M.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photon. Technol. Lett. 18, 2287–2289 (2006).
[Crossref]

Hochberg, M.

Horst, F.

Hosseini, A.

X. Zhang, B. Lee, C. yun Lin, A. Wang, A. Hosseini, and R. Chen, “Highly linear broadband optical modulator based on electro-optic polymer,” Photonics Journal 4, 2214–2228 (2012).
[Crossref]

Hsu, S.-H.

Huang, B.

Jaeger, N. A. F.

Jaenen, P.

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

Janz, S.

Jinguji, A. S. K

A. S. K Jinguji, N Takato, and M. Kawachi, “Mach-zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio,” Electron. Lett. 26, 1326–1327 (1990).
[Crossref]

Kapulainen, M.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photon. Technol. Lett. 18, 2287–2289 (2006).
[Crossref]

Kawachi, M.

A. S. K Jinguji, N Takato, and M. Kawachi, “Mach-zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio,” Electron. Lett. 26, 1326–1327 (1990).
[Crossref]

Kumar Selvaraja, S.

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

Kwong, D.-L.

Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon.Technol. Lett. 23, 525–527 (2011).
[Crossref]

Latrasse, C.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Lawley, K.

J. Campbell, F. Blum, D. Shaw, and K. Lawley, “Gaas electro-optic directional-coupler switch,” Applied Physics Letters 27, 202–205 (1975).
[Crossref]

Lee, B.

X. Zhang, B. Lee, C. yun Lin, A. Wang, A. Hosseini, and R. Chen, “Highly linear broadband optical modulator based on electro-optic polymer,” Photonics Journal 4, 2214–2228 (2012).
[Crossref]

Lentine, A.

Lim, A. E.-J.

Liow, T.-Y.

Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon.Technol. Lett. 23, 525–527 (2011).
[Crossref]

Lo, G.-Q.

Y. Zhang, S. Yang, A. E.-J. Lim, G.-Q. Lo, C. Galland, T. Baehr-Jones, and M. Hochberg, “A compact and low loss y-junction for submicron silicon waveguide,” Opt. Express 21, 1310–1316 (2013).
[Crossref] [PubMed]

Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon.Technol. Lett. 23, 525–527 (2011).
[Crossref]

Maese-Novo, A.

Martinelli, M.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref] [PubMed]

Melloni, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref] [PubMed]

Mojahedi, M.

Molina-Fernández, I.

Mookherjea, S.

Morichetti, F.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref] [PubMed]

Morsy-Osman, M.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Niu, B.

Offrein, B. J.

Ortega-Moñux, A.

Ou, H.

Painchaud, Y.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Papen, G.

Paquet, C.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Paquet, S.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Pelletier, F.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Pelletier, M.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Peucheret, C.

Picard, M.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Plant, D. V.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Porter, G.

Poulin, M.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Qi, M.

Robidoux, G.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Ros, F. D.

Savard, S.

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Schmid, J. H.

Selvaraja, S.

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

J. Campbell, F. Blum, D. Shaw, and K. Lawley, “Gaas electro-optic directional-coupler switch,” Applied Physics Letters 27, 202–205 (1975).
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Sheng, Z.

Shi, W.

Solehmainen, K.

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photon. Technol. Lett. 18, 2287–2289 (2006).
[Crossref]

Song, J. F.

Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon.Technol. Lett. 23, 525–527 (2011).
[Crossref]

Soref, R.

R. Soref, “Mid-infrared 2 × 2 electro-optical switching by silicon and germanium three-waveguide and four-waveguide directional couplers using free-carrier injection,” Photon. Res. 2014, 102–110 (2014).

Takato, N

A. S. K Jinguji, N Takato, and M. Kawachi, “Mach-zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio,” Electron. Lett. 26, 1326–1327 (1990).
[Crossref]

Torregiani, M.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref] [PubMed]

Trotter, D. C.

Van Thourhout, D.

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

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

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

Vlasov, Y. A.

Wang, A.

X. Zhang, B. Lee, C. yun Lin, A. Wang, A. Hosseini, and R. Chen, “Highly linear broadband optical modulator based on electro-optic polymer,” Photonics Journal 4, 2214–2228 (2012).
[Crossref]

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Wang, X.

Wang, Y.

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Wu, A.

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Xu, J.

Yang, S.

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A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2006).

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A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2006).

Yu, M.-B.

Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon.Technol. Lett. 23, 525–527 (2011).
[Crossref]

Yun, H.

yun Lin, C.

X. Zhang, B. Lee, C. yun Lin, A. Wang, A. Hosseini, and R. Chen, “Highly linear broadband optical modulator based on electro-optic polymer,” Photonics Journal 4, 2214–2228 (2012).
[Crossref]

Zhang, X.

X. Zhang, B. Lee, C. yun Lin, A. Wang, A. Hosseini, and R. Chen, “Highly linear broadband optical modulator based on electro-optic polymer,” Photonics Journal 4, 2214–2228 (2012).
[Crossref]

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Zou, S.

Applied Physics Letters (1)

J. Campbell, F. Blum, D. Shaw, and K. Lawley, “Gaas electro-optic directional-coupler switch,” Applied Physics Letters 27, 202–205 (1975).
[Crossref]

Electron. Lett. (1)

A. S. K Jinguji, N Takato, and M. Kawachi, “Mach-zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio,” Electron. Lett. 26, 1326–1327 (1990).
[Crossref]

IEEE J. Sel. Areas Comm. (1)

C. A. Brackett, “Dense wavelength division multiplexing networks: principles and applications,” IEEE J. Sel. Areas Comm. 8, 948–964 (1990).
[Crossref]

IEEE Photon. Technol. Lett. (1)

K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, “Adiabatic and multimode interference couplers on silicon-on-insulator,” IEEE Photon. Technol. Lett. 18, 2287–2289 (2006).
[Crossref]

IEEE Photon.Technol. Lett. (1)

Q. Fang, J. F. Song, T.-Y. Liow, H. Cai, M.-B. Yu, G.-Q. Lo, and D.-L. Kwong, “Ultralow power silicon photonics thermo-optic switch with suspended phase arms,” IEEE Photon.Technol. Lett. 23, 525–527 (2011).
[Crossref]

J. Lightw. Technol. (1)

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

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

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

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Y. Zhang, S. Yang, A. E.-J. Lim, G.-Q. Lo, C. Galland, T. Baehr-Jones, and M. Hochberg, “A compact and low loss y-junction for submicron silicon waveguide,” Opt. Express 21, 1310–1316 (2013).
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J. Wang, B. Niu, Z. Sheng, A. Wu, X. Wang, S. Zou, M. Qi, and F. Gan, “Integrated optics devices; waveguides; polarization-selective devices,” Opt. Express 22, 4137–4143 (2014).
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J. V. Campenhout, W. M. Green, S. Assefa, and Y. A. Vlasov, “Low-power, 2 × 2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks,” Opt. Express 17, 24020–24029 (2009).
[Crossref]

F. Horst, W. M. Green, S. Assefa, S. M. Shank, Y. A. Vlasov, and B. J. Offrein, “Cascaded mach-zehnder wavelength filters in silicon photonics for low loss and flat pass-band wdm (de-)multiplexing,” Opt. Express 21, 11652–11658 (2013).
[Crossref] [PubMed]

Opt. Lett. (1)

Photon. Res. (1)

R. Soref, “Mid-infrared 2 × 2 electro-optical switching by silicon and germanium three-waveguide and four-waveguide directional couplers using free-carrier injection,” Photon. Res. 2014, 102–110 (2014).

Photonics Journal (1)

X. Zhang, B. Lee, C. yun Lin, A. Wang, A. Hosseini, and R. Chen, “Highly linear broadband optical modulator based on electro-optic polymer,” Photonics Journal 4, 2214–2228 (2012).
[Crossref]

Phys. Rev. Lett. (1)

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, “Roughness induced backscattering in optical silicon waveguides,” Phys. Rev. Lett. 104, 033902 (2010).
[Crossref] [PubMed]

Proc. SPIE (1)

Y. Painchaud, M. Poulin, F. Pelletier, C. Latrasse, J.-F. Gagné, S. Savard, G. Robidoux, M. Picard, S. Paquet, C. Davidson, M. Pelletier, M. Cyr, C. Paquet, M. Guy, M. Morsy-Osman, M. Chagnon, and D. V. Plant, “Silicon-based products and solutions,” Proc. SPIE 8988, 89880L (2014).
[Crossref]

Proc. SPIE, Photonics North (1)

H. Yun, W. Shi, Y. Wang, L. Chrostowski, and N. A. F. Jaeger, “2×2 adiabatic 3-db coupler on silicon-on-insulator rib waveguides,” Proc. SPIE, Photonics North 8915, p. 89150V (2013).
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Other (3)

L. Chrostowski and M. Hochberg, Silicon Photonics Design (Cambridge University, 2014).

A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (Oxford University, 2006).

https://www.lumerical.com/ .

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Figures (11)

Fig. 1:
Fig. 1: Schematic of broadband directional coupler.
Fig. 2:
Fig. 2: Supermode distributions of (a) the symmetric couplers and (b) the phase control section. Effective indices in the symmetric couplers for (c) the TE modes and (e) the TM modes. Effective indices in the phase control section for (d) the TE modes and (f) the TM modes.
Fig. 3:
Fig. 3: Contour maps of ηcross as functions of L1 and L2 at λ = 1550 nm for (a) the TE mode and (b) the TM mode. Contours maps of Δηcross as functions of L1 and L2 in the wavelength range from 1500 nm to 1600 nm for (c) the TE mode and (d) the TM mode.
Fig. 4:
Fig. 4: Power distributions of the 50%/50% broadband DCs for (a) TE and (b) TM modes, at different wavelengths.
Fig. 5:
Fig. 5: Simulated ηcross of (a) TE mode and (b) TM mode couplers. The FDTD and the TMM simulation results for broadband DCs are shown by the red lines and the blue lines, respectively. For comparison, the FDTD simulation results of 50%/50% conventional DCs are also shown by the green lines. The conventional DCs are formed with 500 nm wide, 220 nm high SOI strip waveguides separated by a 200 nm gap.
Fig. 6:
Fig. 6: Optical images of (a) test structure; (b) calibration structure and (c) broadband DC.
Fig. 7:
Fig. 7: Measurement results for the 50%/50% broadband DCs. Spectra of the MZIs for (a) the TE mode and (b) the TM mode. Extracted data of the broadband DCs for (c) the TE mode and (d) the TM mode. Extinction ratios in (b) at wavelengths above 1590 nm are limited by the measurement due to the grating coupler insertion loss
Fig. 8:
Fig. 8: Measurement results for the 10%/90% broadband DCs for the (a) TE and (b) TM modes.
Fig. 9:
Fig. 9: Measurement results for the 20%/80% broadband DCs for the (a) TE and (b) TM modes.
Fig. 10:
Fig. 10: Measurement results for the 30%/70% broadband DCs for the (a) TE and (b) TM modes.
Fig. 11:
Fig. 11: Measurement results for the 40%/60% broadband DCs for the (a) TE and (b) TM modes.

Tables (1)

Tables Icon

Table 1: Device dimensions and performance of broadband DCs

Equations (7)

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

[ E 3 E 4 ] = C P t P P t 1 C [ E 1 E 2 ]
C = [ t j k j k t ] e j π λ ( n + + n ) L 1 α 2 L 1 ,
t = cos ( π Δ n eff λ L 1 ) ; k = sin ( π Δ n eff λ L 1 )
P = [ e j 2 π n 1 λ L 2 α 2 L 2 0 0 e j 2 π n 2 λ L 2 α 2 L 2 ]
P t = [ e j θ t 1 α 2 L t 0 0 e j θ t 2 α 2 L t ]
η cross = | E 4 | 2 | E 3 | 2 + | E 4 | 2 ; η through = | E 3 | 2 | E 3 | 2 + | E 4 | 2
η cross = 1 2 ± 1 2 1 ( 10 ERs 10 1 10 ERs 10 + 1 ) 2 ; η through = 1 η cross

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