Abstract

Coupling of light to and from integrated optical circuits has been recognized as a major practical challenge since the early years of photonics. The coupling is particularly difficult for high index contrast waveguides such as silicon-on-insulator, since the cross-sectional area of silicon wire waveguides is more than two orders of magnitude smaller than that of a standard single-mode fiber. Here, we experimentally demonstrate unprecedented control over the light coupling between the optical fiber and silicon chip by constructing the nanophotonic coupler with ultra-high coupling efficiency simultaneously for both transverse electric and transverse magnetic polarizations. We specifically demonstrate a subwavelength refractive index engineered nanostructure to mitigate loss and wavelength resonances by suppressing diffraction effects, enabling a coupling efficiency over 92% (0.32 dB) and polarization independent operation for a broad spectral range exceeding 100 nm.

© 2015 Optical Society of America

1. Introduction

Integrated optical chips capable of generating, modulating, processing and detecting light offer a viable solution to meet the increasing demands on data speed and bandwidth [1]. Availability of efficient input and output coupling interfaces between chip and optical fibre is a fundamental prerequisite for successful implementations of such photonic chips. In recent years there have been many demonstrations utilizing diffraction waveguide gratings and nanostructures to create new types of microphotonic couplers [2–20]. Specifically, surface grating couplers use a diffraction grating to resonantly couple light between a planar waveguide and an optical fiber positioned above the grating. To achieve high coupling efficiency, the grating operates preferentially in a single diffraction order and the diffracted field should match the mode profile of the optical fiber mode. A judicious control of the grating strength by using a single or multiple etch steps with duty ratio optimization [9–12] or structures with increased silicon thickness [13] are typically used to optimize coupling performance. Recently, couplers with subwavelength structures have been demonstrated with high coupling efficiency [14–17], extended wavelength range [18,19] and polarization independent [20] operation. However, the fundamental drawback of these types of couplers stems from their dispersive operational principle, which imposes intrinsic limits to the maximum spectral bandwidth that can be achieved.

When broadband operation is required, inverse taper couplers in which the waveguide core width is reduced near the chip edge [2–8] presently offer the best performance. The fundamental principle exploits the mode delocalization effect, which allows control of the mode size along the coupler until a spot size which matches the optical fiber mode is reached. Sub-decibel coupling losses have been reported, but the structures require high fabrication accuracy to precisely reproduce the taper tip and the performance is optimized for one polarization only [2,3]. Inverse couplers with reduced polarization sensitivity have been demonstrated [4], but instead of a standard SiO2 cladding a silicon-rich oxide secondary waveguide injector is required, with a specific concentration of silicon nanocrystals to achieve the refractive index of about 1.6. The operational principle of the coupler is based on mode coupling and phase-matching condition between the secondary and the silicon waveguides [4], therefore imposing a fundamental limit to the operational wavelength range. The use of high-index polymer secondary waveguide in combination with an ultra-narrow tip [5] has also been reported, but it requires a complex fabrication process to produce such a narrow tip.

In ref [6], we introduced a new concept of refractive index engineering in optical waveguides. The waveguide is longitudinally patterned with a subwavelength grating (SWG) [21], consisting of segments of a high-refractive-index core material interlaced with a lower-refractive-index cladding material. Since the refractive-index contrast can be changed by simply controlling the grating period, waveguides with different optical parameters can be realized on the same chip. This new concept was illustrated in [6] on several proof-of-concept examples, including a subwavelength grating waveguide, an edge coupler, and a waveguide multiplexer, and later in many other integrated optical devices [22]. The coupler structure in [6] showed encouraging performance, including a measured fiber-chip coupling loss of 0.9 dB (TE) and 1.2 dB (TM). Nevertheless, this fibre-chip coupling efficiency and polarization dependent performance are inferior to that of the best reported polarization insensitive inverse couplers with coupling loss <1 dB and a negligible polarization dependent loss (PDL) for coupling to 3 μm spot size [4]. Furthermore, coupler was implemented in a silicon-on-insulator (SOI) platform with 260-nm-thick silicon layer [6], while 220 nm SOI is typically used in silicon photonic foundries offerings.

There are several factors that combine to limit the performance of the previously reported prototype SWG couplers designs [6]. First is coupling of light to the silicon substrate under buried oxide (BOX) layer as the mode expands. In the first devices this was mitigated by the use of a high index SU-8 polymer cladding to reduced mode coupling to the substrate. Unfortunately the SU-8 polymer is not generally accepted for use in photonic component manufacturing. Second, there is a substantial effective index mismatch at the junction between two coupler sections with different grating geometries, specifically the fully segmented section and the continuous sidewall grating section. This mismatch causes an additional loss of approximately 0.3 dB as light propagates from the facet to the final photonic wire waveguide. To potentially reduce this loss in the previously reported coupler design [6], extremely small gaps (10 - 20 nm) between the grating segments would be required, which would be impossible to fabricate. There is also a loss associated purely with mode shape mismatch between the fiber mode and waveguide mode at the facet, which also substantially influences the polarization dependence of the coupler. In this paper we present design solutions that eliminate these sources of loss and demonstrate that SWG couplers can outperform inverse taper couplers in terms of both coupling loss and polarization dependent loss.

Specifically, we report on the design and experimental demonstration of a subwavelength grating (SWG) edge coupler with a coupling loss less than 0.4 dB and negligible polarization dependence, for the telecom wavelength band centered at 1550 nm. The coupler is compatible with commonly used silicon photonic fabrication processes. A conformal stoichiometric SiO2 cladding is used, without any high-index overlayers. The mode size transformation is achieved by varying the duty ratio of the subwavelength grating formed in the composite waveguide core comprising the Si and SiO2 materials (Fig. 1). Since the two materials are combined at the subwavelength scale, loss and wavelength resonances due to diffraction effects are suppressed and the mode confinement is directly controlled by the volume fractions of Si and SiO2, which are defined in a single lithographic patterning step.

 figure: Fig. 1

Fig. 1 Subwavelength grating nanophotonic coupler. (a) Structure schematic. (b) SEM image of the nanocoupler. (c) Detail view of the coupler tip and (d) intermediate section positioned at 15 μm from the junction with silicon wire waveguide. The images were taken prior to the SiO2 cladding deposition.

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The fundamental problem related to the index mismatch and loss at the junction between two coupler sections with different grating geometries [6] is here solved by a judicious design of the junction, as it is discussed in Section 4. Furthermore, because a single waveguide core is used without a secondary waveguide, the fundamental limits set by the phase-matching condition in coupled-waveguide structures are circumvented. Fundamental to the excellent performance of our coupler is also an original design of the coupler tip near the chip edge, facing the optical fiber (Section 2). This design procedure, reported here for the first time, is critical to obtain high coupling efficiency, as are the effective medium synthesis procedure (Section 3) and the quantitative understanding of the effect of coupling to substrate (Section 5), both presented here for the first time.

2. Taper tip design

We first designed the microscopic geometry of the taper tip (Fig. 1(c)) such that the effective mode index is achieved that yields a mode size with a maximum overlap with the optical fiber mode. The fiber mode field with a diameter of 3.2 μm (MFD, defined at 1/e2 intensity points) was assumed as the target field. Similar spot sizes are typically encountered in many packaged semiconductor integrated optical devices, including semiconductor lasers. The coupler vertical layer structure comprises a silicon waveguide core of thickness 220 nm, a 3-μm-thick buried oxide (BOX) and a 3-μm-thick SiO2 upper cladding. The mode electric field distribution at the coupler tip was calculated using a fully vectorial mode solver. At this design step, the SWG tip is treated as a homogeneous medium of refractive index nSWG and a refractive index of 1.445 for is assumed for all oxide material. Figure 2 shows the calculated mode field diameter as a function of the refractive index of the composite SWG material, nSWG, for the tip widths of 250 nm (A) and 220 nm (B). For a 250 nm tip width, the target MFD value is achieved for the composite refractive index of 2.64 and 2.55 for the TM- and TE-like polarizations, respectively, with a polarization dependent loss (PDL) of 0.1 dB for nSWG = 2.6. For a 220 nm tip width, the target MFD value is achieved for nSWG = 2.77, with negligible polarization dependent loss. The calculated mode intensity profiles for the two orthogonal polarization states are shown in the inset of Fig. 2.

 figure: Fig. 2

Fig. 2 Mode size at the coupler tip. Calculated mode field diameter with respect to the subwavelength grating index at the coupler tip, including both horizontal (solid) and vertical (dash) field diameters at 1/e2 intensity points, for the tip widths of 250 nm (A) and 220 nm (B). Blue (red) lines correspond to quasi-TE (TM) polarizations. Inset shows the calculated intensity profiles at the fiber tip for the two orthogonal polarization states.

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It is observed that the quasi-TE and quasi-TM mode distributions are nearly identical upon a 90° rotation, with closely matched effective mode indexes nTE = 1.4533 and nTM = 1.4529. The modal birefringence is very low (Δn ~1 × 10−4), limited by residual vertical asymmetry due to the influence of the bottom Si wafer and the air on top of the SiO2 overlayer. Therefore, effectively polarization independent coupling is achieved between the mode at the coupler tip and the lensed fiber field at the focal plane, where the chip edge is positioned. Specifically, the calculated mode overlap integrals between the two fields are 0.917 for TE and 0.915 for TM polarizations. The ability to control the mode size directly by engineering the refractive index at the coupler tip is an important advantage of our SWG coupler. The SWG gives an extra degree of design freedom, unavailable in conventional inverse couplers where the mode size is controlled by the tip width alone, making it difficult to achieve the maximum efficiency for both TE and TM polarizations simultaneously. For example, the optimized inverse coupler design for our target MFD and TE polarization yields a tip width of 170 nm and the mode overlap integral of 0.908, but the latter is reduced to 0.754 for TM polarization. The corresponding PDL is 0.8 dB, compared to 0.01 dB for our SWG coupler. It is impossible to simultaneously optimize both coupling efficiency and polarization in a conventional inversely tapered coupler.

In this context, a general remark can be made on the fundamental principle of our SWG tip design. Any square tip in a symmetric cladding will be polarization independent. However, it is often impossible to make an inverse coupler with square tip with optimal coupling efficiency (e.g., an optimal tip width ~150 nm) when the waveguide thickness is fixed to 220 nm, which is the standard offering of Si photonics foundries. The subwavelength engineering allows as to set the coupler tip width equal to SOI thickness (here 220 nm), this way making the coupler polarization independent.

3. Effective medium synthesis

Having identified the optimal cross section and effective material index of the waveguide coupler tip, the next task in our design procedure is to determine the SWG duty ratio, here defined as the ratio between the silicon segment length L and the grating period Λ (Fig. 3, inset), which will yield an optically equivalent SWG waveguide. Since, according to the effective medium theory [21,23], the spatial averaging effect occurs along the axis of periodicity, i.e. along the waveguide in our case, the cross sections of the effective strip waveguide and the equivalent SWG waveguide are identical. In order to determine the appropriate duty ratio, we calculate the waveguide mode effective index neff of the SWG waveguide as a function of its duty ratio for the desired cross section and a fixed period. We use the freely available MIT Photonic Bandgap (MPB) simulator to calculate the dispersion relation between the angular frequency (ω) and the propagation constant (k) of the SWG waveguide around λ = 1.55 μm wavelength and obtain the mode effective index according to neff = c⋅k/ω, where c is the speed of light in vacuum.

 figure: Fig. 3

Fig. 3 Bloch mode effective index. Calculations of the Bloch mode effective index for the SWG waveguide as a function of the segment length using MIT Photonic Bands software package. Blue (red) symbols correspond to quasi TE (TM) polarizations for a waveguide width of 250 nm and period of 400 nm. Green symbols correspond to waveguide width of 220 nm, yielding polarization independent effective index. Inset shows a calculated Bloch mode field.

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A calculation example for waveguide widths of 250 nm and 220 nm and periodicity of 400 nm is shown in Fig. 3, where we plot the waveguide Bloch mode effective index as a function of the silicon segment length L of the SWG waveguide (where L = 400 nm would correspond to a duty ratio of 1, or a silicon strip waveguide). The mode effective index neff increases with the duty ratio, corresponding to a lower core index of the equivalent strip waveguide. The segment length (or duty ratio), which results in the desired waveguide effective mode index of the coupler tip, can now simply be obtained from the neff(L) graph (Fig. 3). In the case of the 220 nm wide waveguide (Fig. 3, green curve) the target effective mode index of 1.4533 (TE) and 1.4529 (TM) is numerically obtained for L = 198 nm (TE) or L = 194 nm (TM). The 4-nm difference between the optimal values of segment length for TE and TM is practically irrelevant given typical fabrication tolerances.

4. Mode size transformation

The subwavelength coupler tip is connected to the silicon wire waveguide with a 50-μm long mode size transformation section to assure a smooth low-loss transition from the mode of a photonic wire to the Bloch mode of a periodic SWG waveguide [24]. In this section, the effective index of the waveguide mode is modified by gradually changing the grating duty ratio from about 0.5 at the coupler tip to 1 at the junction with the silicon wire. To account for the corresponding change in effective wavelength λ/neff along the coupler and to avoid formation of the Bragg reflection zones along the device, the grating design is linearly chirped with a pitch of 400 nm near the chip edge and 300 nm near the silicon wire. A judicious choice of the grating period in the high confinement region is important. We choose a 300 nm period to avoid the onset of the Bragg resonance while still yielding structural dimensions larger than the minimum feature size, which is 100 nm to make the design compatible with deep-ultraviolet (DUV) lithography. Since the Bragg resonant wavelength lB is determined by the grating pitch (lB = 2neff, maxΛ), the optical bandwidth is a design parameter which can be directly controlled by the grating pitch. For example, for our nominal design with 300 nm pitch, lB,TE ~1410 nm and lB,TM ~1040 nm. By simply reducing the grating pitch to 250 nm, the Bragg resonance is proportionally shifted to 1180 nm (TE) and 867 nm (TM) wavelengths, largely exceeding the transparency window of silicon.

An important novelty in this design is compensation of the index mismatch and loss at the junction between two coupler sections with different grating geometries, i.e. the segmented section and the section with the gaps partially filled with narrow silicon segments. In Ref. 6, there was an effective index mismatch at the junction between two coupler sections with different grating geometries, i.e. separated segments and segments with partially filled gaps, with the size of the two being identical. The volume fraction of the high-index material (silicon) in the two adjacent grating periods at the junction was different, because of partially filling the gap. This resulted in the effective index mismatch with about 0.3 dB loss penalty. Unlike in ref [6], where the effective index is controlled by grating duty cycle solely and perfect index matching cannot be achieved for minimum feature size of 100 nm, here we judiciously modify the size of the isolated segments following the grating section in which the gaps are partially filled with narrow silicon segments. Specifically, the size of the isolated segment (Fig. 1(a), A) is slightly increased compared to the adjacent segment in the section with partially filled gaps (Fig. 1(a), B), approximately by the size of the first narrow segment (Fig. 1(a), C). This way, the volume fraction of high-index material in the composite core is designed identical at the junction of two different grating geometries. Therefore, the effective mode index is matched in the two sections with different grating geometries and a smooth mode transition is achieved in the intermediate grating region. By implementing this new concept, the loss at the junction is decreased from about 0.3 dB (~7%) (for design as in ref [6].) to near zero, while maintaining the comparatively large 100 nm lithography feature size. To achieve a similar level of index matching with the structure used in [6] extremely small gaps (10 - 20 nm) would be required, which would be impossible to fabricate. The mode transformation efficiency was calculated by using Finite Difference Time Domain (FDTD) simulations, following the procedure outlined in [25]. The calculated loss is below 0.15 dB for both TE and TM polarizations. This calculated residual loss is numerical in origin, being mainly due an artificial roughness created by the small numerical error in SWG waveguide dimensions when digitizing the simulation layout. The high mode transformation efficiency indeed is a remarkable intrinsic property of SWG couplers. This was previously confirmed by a rigorous 3D full-vectorial bi-directional mode expansion method [26], with the theoretical limit of modal transmittance close to 100%.

5. Coupling to substrate

For our experimental demonstration of the coupler efficiency, we use SOI substrates with a silicon layer thickness of 220 nm and a 3-µm-thick BOX layer. This combination is offered in several silicon photonics foundries and is therefore widely accessible for prototype fabrication. The enlarged mode size near the facet required to match the optical fiber field may lead to coupling of the waveguide mode to the silicon substrate through the insulating BOX layer. From our fully vectorial modal field calculations discussed above, we estimated that the BOX thickness of 3 µm is sufficient to optically isolate the mode from the silicon substrate. To further investigate and quantify the expected loss from substrate coupling, we carried out FDTD simulations of two 30 µm long strip waveguides, one with a width of 220 nm and core index of 2.77, the second with a width of 250 nm and core index 2.6. Both waveguides are separated from the silicon substrate by a 3 µm oxide layer. The simulation window extends 2 µm into the silicon substrate and Perfectly Matched Layer (PML) boundary conditions are used. We then run the simulation by launching the quasi-TE or -TM eigenmode at one end of the waveguide and record the power transmitted through a number of cross sectional numerical monitors set up along the length of the waveguide at 5 µm intervals. In both waveguides the loss of the quasi-TM mode is larger than that of the quasi-TE mode. Total loss of the mode by substrate coupling over a distance of 30 µm is found to be 0.025 dB and 0.04 dB for TE and 0.17 dB and 0.15 dB for TM for the 250 nm and 220 nm wide waveguide, respectively. To estimate the influence of BOX layer thickness, we also carried out FDTD calculations for 2 µm BOX, which was used in [6]. For 220 nm wide waveguide with core index of 2.77, the calculated TE loss is 0.19 dB after 30 micrometer propagation, while TM loss is 0.72 dB. Therefore, increasing BOX thickness to 3 µm substantially helps reduce substrate leakage compared to 2 µm BOX. We conclude that to obtain low coupling loss, it is imperative that the length of the tip section of the coupler, where the mode size is at its maximum, be kept as short as possible. In practice, this requires a coupler design in which the transformation to a smaller mode size occurs over a relatively short distance while keeping the mode transformation loss low, as well as a fabrication process which allows for precise placement of the optical facet with respect to the coupler structure. We achieve the latter by defining the optical facets of the chip by optical lithography and dry etching.

In this context, some general considerations can be made about possible utilization of our concept for coupling to fibers with larger mode size (e.g., SMF-28). From the above discussion it is obvious that the radiation loss to substrate though a limited BOX thickness is the main obstacle that must be circumvented in applications when coupling to fibers with larger mode size is required. By controlling the effective mode index at the coupler tip by SWG engineering, as described in this paper, it is straightforward to design tip geometries which yield larger mode sizes. However, this would require a correspondingly increased BOX thickness, to optically insulate the expanded mode from the silicon substrate. When the BOX thickness is constrained to the 3 μm standard or less, a local substrate removal near the chip facet [27] can be considered as an alternative solution.

6. Fabrication and optical measurements

Samples were fabricated on SOI substrates with silicon and BOX layer thicknesses of 0.22 µm and 3 µm, respectively. The waveguide pattern was defined by electron beam lithography using hydrogen silsesquioxane (HSQ) resist and inductively coupled (ICP) high density plasma etching with SF6-C4F8 chemistry. The waveguides were then coated with a 3-µm-thick SiO2 film by plasma enhanced chemical vapor (PECVD) deposition, to assure a good filling of the gaps in the SWG grating region. Our results clearly demonstrate that using the CMOS compatible PECVD oxide deposition process provides good conformal coverage of our nanostructured coupler, resulting in the excellent coupling performance reported here. PECVD oxide refractive index was measured to be 1.465, which is slightly higher than the value of 1.445 assumed in the design; however, due to the high index contrast between silicon and oxide, the effect of this small deviation is insignificant. We used optical contact lithography to define precisely the position of the optical facets with respect to the waveguide coupler, at a distance of 1.5 µm from the coupler tip, with an estimated alignment tolerance of ± 1 µm. The optical facet was then formed by a two-step ICP etch process, first etching vertically through the oxide cladding and BOX layers, and then into the silicon substrate to a depth of approximately 50 µm. Finally, the chips were diced in proximity to the etched facets with an estimated distance of 25 ± 10 µm. For direct fiber attach on the etched facets a larger etch depth, depending on the geometry of the fiber used, would be necessary. The fabricated coupler structure is shown in Figs. 1(b)-1(d). Some corner rounding and deviations from the rectangular structures can be observed, which is inevitable due to limited patterning resolution and etching. However, because of the effective medium index averaging, rectangular shapes are not strictly required since rounded structures can achieve the same index averaging effect. Therefore, corner rounding is not expected to noticeably affect the performance of the coupler. This is an important practical advantage of subwavelength grating structures. This was also confirmed on some previously reported subwavelength structures where sharp square features were used in the layout design, but the corner rounding yielded oval features, with minimal influence on device performance [28].

To measure the coupler efficiency, light from a C-band tunable semiconductor laser was coupled in and out of the chip with two identical couplers, one at the input and one at the output. Input and output lensed polarization maintaining optical fibers with a Gaussian beam waist of ~3 μm were utilized. The input polarization was set to either TE or TM by a pigtailed half-wave plate polarization rotator. The system loss from the optical fiber and polarization optics system was determined as 1.8 dB by a direct fiber-to-fiber calibration measurement with the chip removed. The measurement was then repeated with the chip inserted. The insertion loss, which comprises the input and output coupling loss and the propagation loss in the interconnecting waveguides, was obtained by subtracting the fiber-to-fiber calibration loss from the measured transmittance data. The fibre-chip coupling loss was obtained directly by subtracting from the insertion loss the propagation loss of the interconnected waveguides. The waveguide propagation loss was determined from a set of spiral waveguide test structures of four different waveguide lengths ranging from 5.9 to 16.7 mm, located on the same chip. The measured propagation loss was 1.6 dB/cm (TE) and 0.5dB/cm (TM) at the wavelength of 1550 nm. The polarization dependent loss (PDL) measurements were performed directly by comparing the coupler loss for two orthogonal input polarizations. The variations in PDL of the measurement setup were below 0.05 dB. The PDL variations in waveguide propagation loss measurement was <0.1 dB.

The measured fiber-chip coupling loss at a 1550 nm wavelength is shown in Fig. 4, for the nominal SWG coupler design (N1) and two additional structures (N2 and N3) for which a small bias was applied to the coupler tip width, specifically −20 nm (N2) and + 30 nm (N3). The coupling loss of the reference conventional inverse taper couplers with design tip widths 155 nm (I1), 160 nm (I2) and 170 nm (I3) is also included for comparison. Our nominal SWG coupler design (tip width 220 nm, tip duty ratio 0.5) yields coupling loss of 0.5 dB and a negligible polarization dependent loss (PDL < 0.05 dB). Even slightly superior performance is achieved for the biased structure N2, with the coupling loss of 0.4 dB and PDL < 0.05 dB. A coupling loss as low as 0.32 dB is measured for TE polarization for the coupler N3, with a PDL of 0.5 dB.

 figure: Fig. 4

Fig. 4 Experimental fibre-chip coupling loss. Loss measured for the nominal (N1) and biased (N2 and N3) subwavelength grating nanophotonic couplers, and three conventional inverse coupler designs (I1, I2 and I3). Square (circle) symbols correspond to TE (TM) polarizations. Inset: Measured fibre-chip coupling loss as a function of wavelength for SWG coupler designs N1, N2 and N3.

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This is a substantial loss reduction compared to the previous SWG coupler design [6] with the fibre-chip coupling loss of 0.9 dB (TE) and 1.2 dB (TM), that is, the fibre-chip coupling transmittance is increased 240% for TE and 270% for TM polarizations. The measured fibre-chip coupling loss, which includes the mode mismatch at the facet and the mode transformation loss, is very close to the calculated mode mismatch loss at the facet (see Section 2). Therefore, the mode transformation loss is practically eliminated compared to the previous design, in which 0.23 dB (TE) and 0.47 dB (TM) was obtained [6]. This reduction of the mode transformation loss is mainly attributed to excellent index matching between two different coupler sections in this SWG coupler (see Section 4). To the best of our knowledge, this is the highest efficiency yet reported for light coupling to silicon chip with a single waveguide taper.

The coupling is substantially wavelength independent, with less than 0.2 dB loss variations over the measured wavelength range of 1480 - 1580 nm. Performance of all these SWG couplers is notably superior to the reference inverse couplers, both in terms of the absolute loss and PDL. The loss for the best performing inverse coupler (I1) is 0.5 dB (TE) and 1.3 dB (TM). We have characterized the mode profile of the coupler with a commercial far-field beam profiler (Ophir Photonics Corp.), while coupling light from an optical fiber into the other end of the waveguide. A 3D view of the measured far field profile of the quasi-TM mode of the nominal coupler is shown in the top panel of Fig. 5 with the cross sectional scans for both the quasi-TE and -TM modes in the lower panels. The measurements show good circularity of the mode and nearly polarization independent beam profiles.

 figure: Fig. 5

Fig. 5 Experimental mode profile. Top: 3D rendering of a measured far field mode profile for the quasi-TE mode of the nominal coupler design. Bottom: Vertical and horizontal cross-sections of the far field mode profile of the coupler for quasi-TE and quasi-TM modes.

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7. Conclusion

We demonstrated a broadband fiber-chip edge coupler with a coupling loss as low as 0.32 dB and a minimal polarization dependence. The coupler comprises a simple 3-layer waveguide structure implemented in the SOI substrate with SiO2 upper cladding. The coupler exploits the principle of subwavelength refractive index engineering which mitigates loss and wavelength resonances by suppressing diffraction effects. The proposed technique allows precise control of the modal field at the coupler tip to optimize coupling efficiency between the optical fiber and the silicon chip, for both TE and TM polarizations simultaneously, which helps minimizing the polarization dependence. These achievements pave the way for widespread implementation of silicon photonic circuits even in the most demanding applications which require very high coupling efficiencies and broadband polarization independent performance.

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17. C. Alonso-Ramos, P. Cheben, A. Ortega-Moñux, J. H. Schmid, D.-X. Xu, and I. Molina-Fernández, “Fiber-chip grating coupler based on interleaved trenches with directionality exceeding 95%,” Opt. Lett. 39(18), 5351–5354 (2014). [CrossRef]  

18. X. Chen, K. Xu, Z. Cheng, C. K. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett. 37(17), 3483–3485 (2012). [CrossRef]   [PubMed]  

19. Q. Zhong, V. Veerasubramanian, Y. Wang, W. Shi, D. Patel, S. Ghosh, A. Samani, L. Chrostowski, R. Bojko, and D. V. Plant, “Focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces,” Opt. Express 22(15), 18224–18231 (2014). [CrossRef]   [PubMed]  

20. X. Chen and H. K. Tsang, “Polarization-independent grating couplers for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 36(6), 796–798 (2011). [CrossRef]   [PubMed]  

21. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

22. R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015). [CrossRef]  

23. P. Lalanne and J.-P. Hugonin, “High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms,” J. Opt. Soc. Am. A 15(7), 1843–1851 (1998). [CrossRef]  

24. W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011). [CrossRef]  

25. P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006). [CrossRef]   [PubMed]  

26. J. Ctyroký, P. Kwiecien, I. Richter, and P. Cheben, “Analysis of couplers between photonic nanowires and subwavelength grating waveguides,” Proc. SPIE 8781, 87810B (2013). [CrossRef]  

27. T. Barwicz, A. Janta-Polczynski, M. Khater, Y. Thibodeau, R. Leidy, J. Maling, S. Martel, S. Engelmann, J. S. Orcutt, P. Fortier, and W. M. J. Green, “An O-band metamaterial converter interfacing standard optical fibers to silicon nanophotonic waveguides,” in Optical Fiber Communication Conference (OFC, 2015), paper Th3F.3. [CrossRef]  

28. R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012). [CrossRef]  

References

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  2. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
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  3. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
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  4. B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
    [Crossref]
  5. R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
    [Crossref]
  6. P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D. X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
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  7. S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III-V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200611 (2014).
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  8. L. Vivien, X. Le Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, realization, and characterization of 3-D taper for fiber micro-waveguide coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
    [Crossref]
  9. A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
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  10. F. Van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. Van Thourhout, T. F. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007).
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  11. C. Li, H. Zhang, M. Yu, and G. Q. Lo, “CMOS-compatible high efficiency double-etched apodized waveguide grating coupler,” Opt. Express 21(7), 7868–7874 (2013).
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  12. W. S. Zaoui, A. Kunze, W. Vogel, M. Berroth, J. Butschke, F. Letzkus, and J. Burghartz, “Bridging the gap between optical fibers and silicon photonic integrated circuits,” Opt. Express 22(2), 1277–1286 (2014).
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  13. D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express 18(17), 18278–18283 (2010).
    [Crossref] [PubMed]
  14. R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
    [Crossref] [PubMed]
  15. X. Chen, C. Li, K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photonics Technol. Lett. 22(15), 1156–1158 (2010).
    [Crossref]
  16. Y. Ding, H. Ou, and C. Peucheret, “Ultrahigh-efficiency apodized grating coupler using fully etched photonic crystals,” Opt. Lett. 38(15), 2732–2734 (2013).
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    [Crossref]
  18. X. Chen, K. Xu, Z. Cheng, C. K. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett. 37(17), 3483–3485 (2012).
    [Crossref] [PubMed]
  19. Q. Zhong, V. Veerasubramanian, Y. Wang, W. Shi, D. Patel, S. Ghosh, A. Samani, L. Chrostowski, R. Bojko, and D. V. Plant, “Focusing-curved subwavelength grating couplers for ultra-broadband silicon photonics optical interfaces,” Opt. Express 22(15), 18224–18231 (2014).
    [Crossref] [PubMed]
  20. X. Chen and H. K. Tsang, “Polarization-independent grating couplers for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 36(6), 796–798 (2011).
    [Crossref] [PubMed]
  21. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  22. R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
    [Crossref]
  23. P. Lalanne and J.-P. Hugonin, “High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms,” J. Opt. Soc. Am. A 15(7), 1843–1851 (1998).
    [Crossref]
  24. W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011).
    [Crossref]
  25. P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
    [Crossref] [PubMed]
  26. J. Ctyroký, P. Kwiecien, I. Richter, and P. Cheben, “Analysis of couplers between photonic nanowires and subwavelength grating waveguides,” Proc. SPIE 8781, 87810B (2013).
    [Crossref]
  27. T. Barwicz, A. Janta-Polczynski, M. Khater, Y. Thibodeau, R. Leidy, J. Maling, S. Martel, S. Engelmann, J. S. Orcutt, P. Fortier, and W. M. J. Green, “An O-band metamaterial converter interfacing standard optical fibers to silicon nanophotonic waveguides,” in Optical Fiber Communication Conference (OFC, 2015), paper Th3F.3.
    [Crossref]
  28. R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
    [Crossref]

2015 (1)

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

2014 (4)

2013 (3)

2012 (3)

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

X. Chen, K. Xu, Z. Cheng, C. K. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett. 37(17), 3483–3485 (2012).
[Crossref] [PubMed]

R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
[Crossref]

2011 (3)

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

X. Chen and H. K. Tsang, “Polarization-independent grating couplers for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 36(6), 796–798 (2011).
[Crossref] [PubMed]

W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011).
[Crossref]

2010 (6)

D. Vermeulen, S. Selvaraja, P. Verheyen, G. Lepage, W. Bogaerts, P. Absil, D. Van Thourhout, and G. Roelkens, “High-efficiency fiber-to-chip grating couplers realized using an advanced CMOS-compatible silicon-on-insulator platform,” Opt. Express 18(17), 18278–18283 (2010).
[Crossref] [PubMed]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

X. Chen, C. Li, K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photonics Technol. Lett. 22(15), 1156–1158 (2010).
[Crossref]

P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D. X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
[Crossref] [PubMed]

Editorial, “Simply silicon,” Nat. Photonics 4(8), 491 (2010).
[Crossref]

B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
[Crossref]

2007 (1)

2006 (2)

L. Vivien, X. Le Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, realization, and characterization of 3-D taper for fiber micro-waveguide coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

2003 (1)

2002 (1)

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

1998 (1)

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Absil, P.

Almeida, V. R.

Alonso-Ramos, C.

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

C. Alonso-Ramos, P. Cheben, A. Ortega-Moñux, J. H. Schmid, D.-X. Xu, and I. Molina-Fernández, “Fiber-chip grating coupler based on interleaved trenches with directionality exceeding 95%,” Opt. Lett. 39(18), 5351–5354 (2014).
[Crossref]

Ayre, M.

Baets, R.

Bedard, D.

Ben Bakir, B.

B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
[Crossref]

Berroth, M.

Bock, P.

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Bock, P. J.

Bogaerts, W.

Bojko, R.

Burghartz, J.

Butschke, J.

Cassan, E.

L. Vivien, X. Le Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, realization, and characterization of 3-D taper for fiber micro-waveguide coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Cheben, P.

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

C. Alonso-Ramos, P. Cheben, A. Ortega-Moñux, J. H. Schmid, D.-X. Xu, and I. Molina-Fernández, “Fiber-chip grating coupler based on interleaved trenches with directionality exceeding 95%,” Opt. Lett. 39(18), 5351–5354 (2014).
[Crossref]

J. Ctyroký, P. Kwiecien, I. Richter, and P. Cheben, “Analysis of couplers between photonic nanowires and subwavelength grating waveguides,” Proc. SPIE 8781, 87810B (2013).
[Crossref]

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D. X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
[Crossref] [PubMed]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

Chen, X.

Cheng, Z.

Chrostowski, L.

Ctyroký, J.

J. Ctyroký, P. Kwiecien, I. Richter, and P. Cheben, “Analysis of couplers between photonic nanowires and subwavelength grating waveguides,” Proc. SPIE 8781, 87810B (2013).
[Crossref]

De Dobbelaere, P.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

de Gyves, A. V.

B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
[Crossref]

Delâge, A.

Densmore, A.

Ding, Y.

Editorial,

Editorial, “Simply silicon,” Nat. Photonics 4(8), 491 (2010).
[Crossref]

Fedeli, J.-M.

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
[Crossref]

Fournier, M.

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

Fung, C. K.

Fung, K. Y.

X. Chen, C. Li, K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photonics Technol. Lett. 22(15), 1156–1158 (2010).
[Crossref]

Ghosh, S.

Gloeckner, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Halir, R.

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

Hall, T. J.

Hugonin, J.-P.

Janz, S.

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D. X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
[Crossref] [PubMed]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

Kamei, T.

R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
[Crossref]

Krauss, T. F.

Kunze, A.

Kwiecien, P.

J. Ctyroký, P. Kwiecien, I. Richter, and P. Cheben, “Analysis of couplers between photonic nanowires and subwavelength grating waveguides,” Proc. SPIE 8781, 87810B (2013).
[Crossref]

Lalanne, P.

W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011).
[Crossref]

P. Lalanne and J.-P. Hugonin, “High-order effective-medium theory of subwavelength gratings in classical mounting: application to volume holograms,” J. Opt. Soc. Am. A 15(7), 1843–1851 (1998).
[Crossref]

Lamontagne, B.

Lapointe, J.

Laval, S.

L. Vivien, X. Le Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, realization, and characterization of 3-D taper for fiber micro-waveguide coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Le Roux, X.

L. Vivien, X. Le Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, realization, and characterization of 3-D taper for fiber micro-waveguide coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Lederer, F.

W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011).
[Crossref]

Lepage, G.

Letzkus, F.

Li, C.

C. Li, H. Zhang, M. Yu, and G. Q. Lo, “CMOS-compatible high efficiency double-etched apodized waveguide grating coupler,” Opt. Express 21(7), 7868–7874 (2013).
[Crossref] [PubMed]

X. Chen, C. Li, K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photonics Technol. Lett. 22(15), 1156–1158 (2010).
[Crossref]

Lipson, M.

Lo, G. Q.

Lo, S. M. G.

X. Chen, C. Li, K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photonics Technol. Lett. 22(15), 1156–1158 (2010).
[Crossref]

Lyan, P.

B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
[Crossref]

Ma, R.

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

Manako, S.

R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
[Crossref]

Marris-Morini, D.

L. Vivien, X. Le Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, realization, and characterization of 3-D taper for fiber micro-waveguide coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Marzban, B.

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III-V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200611 (2014).
[Crossref]

Masini, G.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Mekis, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Merget, F.

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III-V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200611 (2014).
[Crossref]

Molina-Fernandez, I.

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

Molina-Fernández, I.

Mori, M.

R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
[Crossref]

Morita, H.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Narasimha, A.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Omoda, E.

R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
[Crossref]

Orobtchouk, R.

B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
[Crossref]

Ortega-Moñux, A.

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

C. Alonso-Ramos, P. Cheben, A. Ortega-Moñux, J. H. Schmid, D.-X. Xu, and I. Molina-Fernández, “Fiber-chip grating coupler based on interleaved trenches with directionality exceeding 95%,” Opt. Lett. 39(18), 5351–5354 (2014).
[Crossref]

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

Ou, H.

Panepucci, R. R.

Patel, D.

Paul, T.

W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011).
[Crossref]

Peucheret, C.

Pinguet, T.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Plant, D. V.

Porzier, C.

B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
[Crossref]

Richter, I.

J. Ctyroký, P. Kwiecien, I. Richter, and P. Cheben, “Analysis of couplers between photonic nanowires and subwavelength grating waveguides,” Proc. SPIE 8781, 87810B (2013).
[Crossref]

Rockstuhl, C.

W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011).
[Crossref]

Roelkens, G.

Roman, A.

B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
[Crossref]

Romero-García, S.

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III-V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200611 (2014).
[Crossref]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Sahni, S.

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

Sakakibara, Y.

R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
[Crossref]

Samani, A.

Schmid, J.

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Schmid, J. H.

Schrauwen, J.

Selvaraja, S.

Shen, B.

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III-V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200611 (2014).
[Crossref]

Shi, W.

Shoji, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Smigaj, W.

W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011).
[Crossref]

Suzuki, M.

R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
[Crossref]

Taillaert, D.

Takei, R.

R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
[Crossref]

Tsang, H. K.

Tsuchizawa, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Van Laere, F.

Van Thourhout, D.

Veerasubramanian, V.

Verheyen, P.

Vermeulen, D.

Vivien, L.

L. Vivien, X. Le Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, realization, and characterization of 3-D taper for fiber micro-waveguide coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

Vogel, W.

Wang, Y.

Wangüemert-Pérez, J. G.

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Watanabe, T.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Witzens, J.

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III-V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200611 (2014).
[Crossref]

Xu, D. X.

Xu, D.-X.

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

C. Alonso-Ramos, P. Cheben, A. Ortega-Moñux, J. H. Schmid, D.-X. Xu, and I. Molina-Fernández, “Fiber-chip grating coupler based on interleaved trenches with directionality exceeding 95%,” Opt. Lett. 39(18), 5351–5354 (2014).
[Crossref]

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

P. Cheben, D.-X. Xu, S. Janz, and A. Densmore, “Subwavelength waveguide grating for mode conversion and light coupling in integrated optics,” Opt. Express 14(11), 4695–4702 (2006).
[Crossref] [PubMed]

Xu, K.

Yamada, K.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

Yang, J.

W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011).
[Crossref]

Yu, M.

Zaoui, W. S.

Zavargo-Peche, L.

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

Zhang, H.

Zhong, Q.

Appl. Phys. Express (1)

R. Takei, E. Omoda, M. Suzuki, S. Manako, T. Kamei, M. Mori, and Y. Sakakibara, “Ultranarrow silicon inverse taper waveguide fabricated with double-patterning photolithography for low-loss spot-size converter,” Appl. Phys. Express 5(5), 052202 (2012).
[Crossref]

Appl. Phys. Lett. (1)

W. Śmigaj, P. Lalanne, J. Yang, T. Paul, C. Rockstuhl, and F. Lederer, “Closed-form expression for the scattering coefficients at an interface between two periodic media,” Appl. Phys. Lett. 98(11), 111107 (2011).
[Crossref]

Electron. Lett. (1)

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 μm square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

S. Romero-García, B. Marzban, F. Merget, B. Shen, and J. Witzens, “Edge couplers with relaxed alignment tolerance for pick-and-place hybrid integration of III-V lasers with SOI waveguides,” IEEE J. Sel. Top. Quantum Electron. 20(4), 8200611 (2014).
[Crossref]

L. Vivien, X. Le Roux, S. Laval, E. Cassan, and D. Marris-Morini, “Design, realization, and characterization of 3-D taper for fiber micro-waveguide coupling,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1354–1358 (2006).
[Crossref]

A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quantum Electron. 17(3), 597–608 (2011).
[Crossref]

IEEE Photonics Technol. Lett. (2)

B. Ben Bakir, A. V. de Gyves, R. Orobtchouk, P. Lyan, C. Porzier, A. Roman, and J.-M. Fedeli, “Low-Loss (<1 dB) and polarization-insensitive edge fiber couplers fabricated on 200-mm silicon-on-insulator wafers,” IEEE Photonics Technol. Lett. 22(11), 739–741 (2010).
[Crossref]

X. Chen, C. Li, K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photonics Technol. Lett. 22(15), 1156–1158 (2010).
[Crossref]

J. Lightwave Technol. (1)

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

Laser Photonics Rev. (1)

R. Halir, P. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso-Ramos, J. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, I. Molina-Fernández, and S. Janz, “Waveguide sub-wavelength structures: a review of principles and applications,” Laser Photonics Rev. 9(1), 25–49 (2015).
[Crossref]

Nat. Photonics (1)

Editorial, “Simply silicon,” Nat. Photonics 4(8), 491 (2010).
[Crossref]

Opt. Express (5)

Opt. Lett. (7)

X. Chen and H. K. Tsang, “Polarization-independent grating couplers for silicon-on-insulator nanophotonic waveguides,” Opt. Lett. 36(6), 796–798 (2011).
[Crossref] [PubMed]

P. Cheben, P. J. Bock, J. H. Schmid, J. Lapointe, S. Janz, D. X. Xu, A. Densmore, A. Delâge, B. Lamontagne, and T. J. Hall, “Refractive index engineering with subwavelength gratings for efficient microphotonic couplers and planar waveguide multiplexers,” Opt. Lett. 35(15), 2526–2528 (2010).
[Crossref] [PubMed]

R. Halir, P. Cheben, J. H. Schmid, R. Ma, D. Bedard, S. Janz, D.-X. Xu, A. Densmore, J. Lapointe, and I. Molina-Fernández, “Continuously apodized fiber-to-chip surface grating coupler with refractive index engineered subwavelength structure,” Opt. Lett. 35(19), 3243–3245 (2010).
[Crossref] [PubMed]

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003).
[Crossref] [PubMed]

Y. Ding, H. Ou, and C. Peucheret, “Ultrahigh-efficiency apodized grating coupler using fully etched photonic crystals,” Opt. Lett. 38(15), 2732–2734 (2013).
[Crossref] [PubMed]

C. Alonso-Ramos, P. Cheben, A. Ortega-Moñux, J. H. Schmid, D.-X. Xu, and I. Molina-Fernández, “Fiber-chip grating coupler based on interleaved trenches with directionality exceeding 95%,” Opt. Lett. 39(18), 5351–5354 (2014).
[Crossref]

X. Chen, K. Xu, Z. Cheng, C. K. Fung, and H. K. Tsang, “Wideband subwavelength gratings for coupling between silicon-on-insulator waveguides and optical fibers,” Opt. Lett. 37(17), 3483–3485 (2012).
[Crossref] [PubMed]

Opt. Quantum Electron. (1)

R. Halir, L. Zavargo-Peche, D.-X. Xu, P. Cheben, R. Ma, J. H. Schmid, S. Janz, A. Densmore, A. Ortega-Moñux, I. Molina-Fernandez, M. Fournier, and J.-M. Fedeli, “Single etch grating couplers for mass fabrication with DUV lithography,” Opt. Quantum Electron. 44(12-13), 521–526 (2012).
[Crossref]

Proc. SPIE (1)

J. Ctyroký, P. Kwiecien, I. Richter, and P. Cheben, “Analysis of couplers between photonic nanowires and subwavelength grating waveguides,” Proc. SPIE 8781, 87810B (2013).
[Crossref]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Other (1)

T. Barwicz, A. Janta-Polczynski, M. Khater, Y. Thibodeau, R. Leidy, J. Maling, S. Martel, S. Engelmann, J. S. Orcutt, P. Fortier, and W. M. J. Green, “An O-band metamaterial converter interfacing standard optical fibers to silicon nanophotonic waveguides,” in Optical Fiber Communication Conference (OFC, 2015), paper Th3F.3.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Subwavelength grating nanophotonic coupler. (a) Structure schematic. (b) SEM image of the nanocoupler. (c) Detail view of the coupler tip and (d) intermediate section positioned at 15 μm from the junction with silicon wire waveguide. The images were taken prior to the SiO2 cladding deposition.
Fig. 2
Fig. 2 Mode size at the coupler tip. Calculated mode field diameter with respect to the subwavelength grating index at the coupler tip, including both horizontal (solid) and vertical (dash) field diameters at 1/e2 intensity points, for the tip widths of 250 nm (A) and 220 nm (B). Blue (red) lines correspond to quasi-TE (TM) polarizations. Inset shows the calculated intensity profiles at the fiber tip for the two orthogonal polarization states.
Fig. 3
Fig. 3 Bloch mode effective index. Calculations of the Bloch mode effective index for the SWG waveguide as a function of the segment length using MIT Photonic Bands software package. Blue (red) symbols correspond to quasi TE (TM) polarizations for a waveguide width of 250 nm and period of 400 nm. Green symbols correspond to waveguide width of 220 nm, yielding polarization independent effective index. Inset shows a calculated Bloch mode field.
Fig. 4
Fig. 4 Experimental fibre-chip coupling loss. Loss measured for the nominal (N1) and biased (N2 and N3) subwavelength grating nanophotonic couplers, and three conventional inverse coupler designs (I1, I2 and I3). Square (circle) symbols correspond to TE (TM) polarizations. Inset: Measured fibre-chip coupling loss as a function of wavelength for SWG coupler designs N1, N2 and N3.
Fig. 5
Fig. 5 Experimental mode profile. Top: 3D rendering of a measured far field mode profile for the quasi-TE mode of the nominal coupler design. Bottom: Vertical and horizontal cross-sections of the far field mode profile of the coupler for quasi-TE and quasi-TM modes.

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