High-efficiency broadband light coupling between optical fibers and photonic integrated circuits

2.1 Principle of operation

Figure 2A schematically (not drawn to scale) shows a typical end-fire coupling scenario between two waveguides with an arbitrary intermediate coupling region. In this review article, we are mostly interested in passive optical coupling between an optical fiber and an integrated waveguide and assume that the input optical power from the input waveguide (waveguide 1 in Figure 2A, e.g. a silica-based single-mode optical fiber) is carried by a guided optical mode, whose field profile is given by E₁. In this analysis, we pay our attention only to a specific input mode E₁, but the same analysis can be applied to other input modes that are orthogonal to E₁. We further assume that the output waveguide (waveguide 2 in Figure 2A, e.g. a silicon waveguide) can support multiple guided modes, and the field profile for the kth mode is given by E_2,k. Optical coupling efficiencies between two guided modes, E₁ and E_2,k, can be defined using the optical power ratio as (n_eff,2,k/n_eff,1)·|E_2,k |²/|E₁|². Because of the reciprocity theorem, the coupling properties are bidirectional, and the coupling efficiency remains the same when the role of input and output is reversed.

Figure 2:

Schematic diagram of the end-fire coupling process between two waveguides.

The input guided mode in the waveguide 1 (E₁, for example, the HE₁₁ mode in the SMF); incoming electromagnetic field after passing through the intermediate coupling region (E₁′); output guided modes in the waveguide 2 (∑E_2,k). Non-coupled radiation modes (E_β) are not shown.

The guided mode of the input waveguide (E₁) is first radiated through the intermediate coupling region after partial reflection and transmission (with a transmission coefficient of t₁) at the end facets of the waveguide. The radiated optical field (E) propagates through the intermediate coupling region and arrives at the front facet of the waveguide 2. The optical field measured in front of the waveguide facet is given by E₁′, which can be finally coupled to the output guided modes ∑E_2,k. The coupling efficiency between E₁′ and E_2,k can be quantitatively obtained from the overlap integral (η) and the transmittance (|t₂|²). Partial reflections may occur at the interfaces due to the differences in the effective refractive indices, and the corresponding transmission coefficient is given by t₂=2(n_eff,1′×n_eff,2,k)^0.5/(n_eff,1′+n_eff,2,k), where n_eff,1′ is the effective refractive index for the intermediate coupling region and n_eff,2,k is the effective modal index for the kth guided mode in the output waveguide.

A typical single-mode optical fiber has only one guided mode (fundamental HE₁₁ mode) when considering only one polarization state. The incoming electric field (E₁′) can be decomposed into the linear combination of the orthogonal guided modes (E_2,k) of the output waveguide and the non-guided modes (E_β) and is given by [45] the following:

where the expansion coefficient c_k can be obtained using the Poynting theorem and is given by the following:

The overlap integral between the incoming field (E₁′) and the kth guided mode is given by the following:

The overlap integral in Equation 2.3 represents the similarity of the optical field profiles between E₁′ and E_2,k. In addition to the field overlap, we need to take into account the partial optical reflections at the interface, resulting from the abrupt changes in the effective refractive index. Therefore, the total optical power coupling efficiency from the incoming field E₁′ into the kth guided mode for the output waveguide (E_2,k) is finally given by |t₂|²·η_k. The optical power transfer efficiency from the input waveguide mode (E₁) to the field profile in front of the output waveguide (E₁′) can be similarly obtained as described above. When the intermediate coupling region consists of, for example, free-space, the radiated beam from the input waveguide 1 (e.g. silica-based optical fiber) diverges with a numerical aperture (NA) determined by the core (n_core) and cladding (n_cladding) indices [NA=(n_core² ‒ n_cladding²)^1/2], and the full divergence angle is 2θ₀=4λ/(2×π×W₀), where W₀ is the beam waist radius. The detailed electric field profile with respect to the propagation distance from the waveguide end facet can be obtained from the diffraction theory. Because of rapid beam divergence, when the distance between the waveguides is too far, the incident beam profile (E₁′) shows a low overlap integral value with E_2,k and results in a low coupling efficiency to a specific output mode. We also need to consider partial reflections at the interfaces between waveguide 1 and the intermediate coupling region (E₁ and E) and between the intermediate coupling region and waveguide 2 (E₁′ and ∑E_2,k) due to the different effective indices in each region.

There exist various strategies to improve the overall optical coupling efficiencies. For example, three-dimensional tapered waveguide structures can be used to mitigate the MFD mismatches between the input and output waveguides (E₁ and E_2,k) and thereby increase the overlap integral values (η_k). Another way to improve the coupling efficiency is by lowering the partial reflections at the interfaces (increasing t₁ and t₂) with intermediate index regions, such as oxide and polymer layers instead of air, due to the reduced effective index contrast. In addition to using the lower index material in the intermediate coupling region, the waveguide itself can be inversely tapered (sharper waveguide tip) to provide gradual transformation of the effective index as well as to obtain lower effective modal index toward the transition region.

2.2 Tapered waveguides

Lateral [46], [47], vertical [48], and three-dimensional [49], [50] waveguide taper designs have been introduced to enlarge the effective MFD of the integrated waveguides with high-index core materials (e.g. III–V compound semiconductor and silicon). These types of intermediate coupling structures are also referred to as spot-size converters (SSCs or mode-size converters) [51] and gradually increase the width and/or height of the integrated waveguide to provide a large terminating facet area up to 100 μm², which is close to that of the fiber core, as schematically shown in Figure 3A. The tapering angle of the SSC transition region needs to be carefully designed to prevent unwanted light coupling to the higher order modes for the tapered waveguide region. An extended waveguide facet dimension through the SSC can achieve an enlarged electromagnetic field profile, resulting in a higher mode overlap value (η), as described in Section 2.1.

Figure 3:

(A) Schematic diagram of a three-dimensionally tapered intermediate waveguide structure. (B) An example of a vertically tapered waveguide fabricated by gray-tone shadow masking.

Adapted from Ref. [35], Copyright 2007 American Institute of Physics.

Three-dimensionally tapered SSCs have been employed in the silicon-based PIC platform for efficient optical coupling between optical fibers and integrated silicon waveguides [33], [34], [35], [36], [37], [52], [53]. Such SSC structures can be fabricated with conventional silicon waveguides on silicon-on-insulator (SOI) wafers using additional fabrication processing steps, such as polishing [52], etching [34], [36], [37], [53], and gray-tone shadow masking [33], [35], [54]. As shown in a scanning electron microscope (SEM) in Figure 3B, Shiraishi et al. used a metal shadow mask fabrication process [54] to make a vertical waveguide taper [35]. Starting from the silicon waveguide cross-section of 500 nm in height and 300 nm in width, a total taper length of 2 mm and a final waveguide width of 10 μm were achieved with a linear taper. The final waveguide width is close to the standard single-mode fiber MFD. Amorphous hydrated silicon (a-Si:H) was deposited to extend the vertical mode dimensions in the laterally extended silicon waveguide. A measured net transmission loss of 0.5 dB was obtained at the input wavelength of 1.55 μm using a lensed fiber.

Although this type of guided mode expansion approaches offers good coupling efficiency of better than −1 dB and seems straightforward in concept, it requires additional dedicated fabrication steps, such as thick materials deposition and etching. It might also occupy more space when compared to other coupling schemes.

2.3 Enhanced optical coupling with intermediate waveguide regions

Optical mode profiles and their cross-sectional areas can be extended not only by expanding the waveguide dimensions with waveguide tapers as discussed in the previous section but also by shrinking the waveguide dimensions, as schematically shown in Figure 4A. When the waveguide cladding material has an intermediate refractive index (larger than air but smaller than the waveguide core refractive index) and thus provide a smaller index contrast, the optical modes are less confined to the waveguide core as the core dimensions decrease, resulting in larger effective mode areas and smaller effective modal index. The low-index intermediate cladding layers, such as polymer [38], [39], [56], [57], [58], SiO₂ [55], [59], [60], [61], [62], and Si₃N₄ or SiON [40], [62], [63] with effective refractive indices comparable to optical fibers, can efficiently expand the optical mode dimensions and reduce the partial reflections at the interfaces [38], [39], [40], [55], [56], [57], [58], [59], [60], [61], [62], [63]. The input light gets adiabatically expanded through the inversely tapered high-index waveguide and can be finally coupled to the optical fiber with a high coupling efficiency.

Figure 4:

(A) Schematic diagram of an inversely tapered intermediate waveguide coupler with a low-index cladding. The integrated waveguide core region is represented with blue colors. (B) A typical inversely tapered waveguide coupler with SiO₂ cladding layers. Reprinted from Ref. [55]. Copyright 2003 The Optical Society. (C) A coupler with a very narrow tip fabricated by silicon oxidation process and its SEM image. Silicon nano-taper tip end (I) before and (II) after oxidation process. (III) Top view of the junction point of a polymer core and a silicon waveguide. (IV) Cross-section view of the nano-taper coupler.

Adapted from Ref. [39]. Copyright 2010 Elsevier.

Figure 4B shows an example of an inversely tapered waveguide coupler, which transforms both the effective mode size and effective mode index between an optical fiber and an integrated silicon waveguide [55]. The inversely tapered silicon waveguide (smaller waveguide dimensions toward the terminating end) has a tapering length of ~40 μm, and the waveguide width reduces from ~470 nm (single-mode waveguiding condition) to ~100 nm with a waveguide height of 270 nm. Due to the expanded mode size at the subwavelength-scale waveguide tip, the maximum mode overlap with an input lensed fiber (MFD=~5 μm) was calculated to be as high as 94%, and this corresponds to a mode mismatch loss of 0.26 dB. The total insertion losses with partial reflections and misalignment were measured to be ~3.3 dB and 6.0 dB for the TM (an effective refractive index of 1.51) and TE (an effective refractive index of 1.31) modes, respectively [55]. Although there is a large index contrast between the silicon core material and the SiO₂ cladding layer, the propagating electromagnetic field for the very narrow inversely tapered waveguide structure resides mostly outside the core region and its effective modal index becomes close to the refractive index of the SiO₂ cladding layer.

Using a similar approach with a combination of an intermediate polymer region and a SiO₂ cladding layer, Pu et al. reported very low optical coupling losses of ~0.36 dB and ~0.66 dB for the TM and TE modes, respectively [39] (Figure 4C). The ultra-low losses were obtained using a very narrow silicon taper tip whose width was reduced from ~40 nm to ~12 nm by silicon oxidation.

To further improve the fiber-to-chip optical coupling efficiency with intermediate waveguide structures, suspended waveguide structures with low-index cladding materials, such as SiO₂ [41], [42], [64], [65], [66] and SiON, were investigated [67], as schematically shown in Figure 5A. Figure 5A shows a tapered silicon waveguide, surrounded by a SiO₂ cladding cantilever structure, is suspended [65]. After formation of the tapered silicon waveguide and SiO₂ cladding cantilever structure (13 μm×10 μm), the underlying Si substrate was etched to form a trench, as shown in Figure 5A. The optical power leakage to the substrate was minimized by providing a sufficiently large trench depth. The coupling efficiencies were measured to be −1.5 dB and −1.0 dB for the TM and TE modes, respectively. As the suspended waveguide structures have an alignment tolerance of approximately ±2.0 μm for a 1-dB excess loss, which is better than other end-fire coupling schemes, it may have benefits in the fiber assembly and packaging processes [42], [65]. Multi-layered suspended tapering structures can further improve the coupling efficiencies by gradually transforming the effective refractive index between high-index silicon waveguides and low-index optical fibers [62], [64], [65], [66].

Figure 5:

(A) Schematic diagram of a suspended intermediate waveguide structure. (B) An example of an inversely tapered silicon waveguide surrounded by a SiO₂ cladding with a cantilever structure. The SEM images of the fabricated couplers are shown.

Adapted from Ref. [65]. Copyright (2011) The Optical Society.

This type of end-fire coupling with inversely tapered high-index waveguides can achieve efficient optical coupling with small footprints and low wavelength/polarization dependencies. Similar approaches in this category include waveguide ribbon layers [68], [69], [70], photonic wire bonding [71], [72], [73], and free-form lenses and mirrors [74], [75]. Figure 6A and B show examples of single-channel SSC interconnects [69], [70]. Multi-port coupling examples using photonic wire bonds and free-form components are illustrated in Figure 6C [71] and D [74], respectively. Recently, several researchers have exploited subwavelength grating (SWG) converters based on high-index materials, such as silicon [76], [77], [78]. By engineering the effective refractive index of the waveguides, SWG-based end-fire couplings can achieve coupling efficiencies as high as −0.32 dB (93%) [78].

Figure 6:

Optical interfaces for multiple ports using intermediate mode transformation stages.

(A) Schematic diagram of a multi-channel SSC interconnecting multiple fibers and waveguide arrays. Reprinted from Ref. [70]. Copyright (2011) The Optical Society/IEEE. (B) Schematic diagram of the polymer interface linking an array of standard SMFs to an array of nanophotonic waveguides. Reprinted from Ref. [69]. Copyright (2014) IEEE. (C) SEM image of a multi-core fiber-to-chip interface using photonic wire bonds to connect the individual cores of the multi-core fiber to an array of silicon waveguides. Reprinted from Ref. [71]. Copyright (2015) The Optical Society/IEEE. (D) Schematic diagram of free-form lenses and expanders. Reprinted from Ref. [74]. Copyright (2018) Nature Publishing Group.

2.4 Vertically curved and suspended waveguide structures

One of the main disadvantages of the conventional end-fire coupling methods is that the optical interfaces to the input/output fibers need to be located at the PIC chip edges and the dicing process is required to expose the end-fire coupler structures to the optical fibers. However, the out-of-plane light coupling can be achieved by physically bending the waveguides toward the upward direction from which the optical fibers are approached [43], [44], [79], [80], as schematically shown in Figure 7A. While providing the advantages of conventional end-fire coupling, such as low wavelength and polarization dependencies, this out-of-plane coupling scheme does not require the optical couplers to be located at the chip edges.

Figure 7:

(A) Schematic diagram of a vertically curved intermediate waveguide structure. (B) SEM image of a curved coupler using thermal annealing. Reprinted from Ref. [79]. Copyright (2009) The Optical Society. (C) SEM image of a bent waveguide coupler with a radius of curvature of 3 μm using ion implantation.

Reprinted from [44]. Copyright (2016) The Optical Society/IEEE.

The bent waveguide couplers can be fabricated by introducing stress gradients to the waveguide structure so that the waveguide termination region can be bent upward when released from the substrate [81], [82]. The overall footprint for the bent waveguide coupler is closely related with its bending radius. As highly confined optical modes in the high-index waveguides allow small bending radii of less than 10 μm without too much radiation losses occurring, the vertically curved waveguide coupler design can be compact and scalable while providing the benefits of end-fire coupling.

For example, out-of-plane optical coupling to the optical fibers or free-space optical beams was obtained by stress-engineered Si/SiO₂ cantilevers deflected upward by thermal annealing stress, as shown in Figure 7B [79]. Tapered silicon waveguides were embedded in the center of the SiO₂ cantilevers. After the deposition of PECVD SiO₂ layer, the SiO₂ cantilevers are released from the substrate by reactive ion etching and subsequently annealed for stress control. Maximum deflection and tilt angles at the end of a 40-μm-long SiO₂ cantilever with silicon core in the center are 2.6 μm and 4.7°, respectively. Because of limitations in maximum stress level from the thermal annealing process, the bending radii obtained from this method were limited to approximately 100 μm [79], [83]. To introduce higher stress gradients and thereby reduce the bending radius of the curved waveguide structure for smaller coupler dimensions, an ion beam implantation method was applied to intentionally introduce lattice defects. As a result, a bending radius of approximately 3 μm was obtained, as shown in Figure 7C [44]. The vertically curved waveguide coupler structures showed ~−1 dB (80%) optical coupling efficiencies with tapered fibers [43], [79] and lensed fibers [44], [80].

3.1 Principle of operation

Although the analytic framework discussed here is based on a simple diffraction theory, it can predict various aspects of diffraction grating-based optical coupling behaviors with reasonable accuracy [116]. A grating coupler is usually composed of periodically located multiple diffractive elements, and the light diffraction angles from such optical structures can be described by the conventional diffraction theory and the so-called Bragg condition [84]. The Bragg condition for wavevectors parallel to the optical waveguide axis (z-axis in Figures 8 and 9, and in this section, we assume that the light propagation direction is toward –z from the integrated waveguide to the optical fiber) shows that the difference between the waveguide propagation constant (β=2π·n_eff/λ₀, where n_eff is the effective refractive index of the waveguide and λ₀ is the free-space optical wavelength) and the surface-parallel component of the wavevector of the diffracted wave (k_z) should be matched to an integer multiple (m) of the grating’s wavevector (K=2π/Λ, where Λ is the grating period) and is given by β – k_z=m·K. Depending on the input wavelength and grating period, multiple diffraction orders can be generated toward both the superstrate (diffracted toward the upward direction with a corresponding in-plane wavevector component of k_super=2π ·n_super/λ₀) and the substrate (downward direction with an in-plane wavevector component of k_sub=2π·n_sub/λ₀), as illustrated in Figure 9.

When the effective optical wavelength inside the waveguide (λ₀/n_eff) matches the grating period (Λ=λ₀/n_eff), the waveguide propagation constant (β) becomes equivalent to the grating’s wavevector (β=K), as shown in Figure 9A. In this case, the second-order diffraction (m=2) corresponds to the back-reflection (k_back=β – 2K) toward the silicon waveguide [117] and inevitably reduces the optical power in the first-order diffracted beam (m=1) toward the vertical direction (k_z=0). The vertically diffracted optical beam also has to go through multiple reflections between parallel optical interfaces, such as the silicon substrate, and therefore experiences Fabry-Pérot-type vertical oscillations. Therefore, such a grating coupler design with surface-normal diffraction (β=K, k_x=0) is rarely used, and detuned off-normal grating designs are usually employed to improve the overall coupling efficiency [118], as shown in Figure 9B.

The diffraction angle to the superstrate (θ_super) is a crucial parameter for grating coupler designs, and the diffraction angle for the first order beam (m=1) can be expressed as n_eff – n_super·sin θ_super=λ₀/Λ. According to this relationship, the diffraction angle strongly depends on the grating period (Λ), the optical wavelength (λ₀), and the effective index of the etched waveguide (n_eff). The effective refractive index for the waveguide also depends on the input polarization state. When the fill factor of the grating is f=W/Λ, where W is the width of the un-etched grating teeth, the effective index of the grating (n_eff) is approximately given by n_eff=f·n_{eff, unetched}+(1– f )·n_{eff, etched}, where n_{eff, unetched} and n_{eff, etched} represent the effective index of the unetched and etched grating slot, respectively [84]. The fundamental TM mode typically shows a smaller effective index than that of the fundamental TE mode [96]. As can be seen from this analysis, the main drawbacks of grating-based coupling are its strong wavelength and polarization dependence, which limits the operating wavelength range and input polarization states.

3.2 Apodized grating structures

A variety of apodized grating couplers with spatially varying fill factors and etch depths has been reported to achieve high coupling efficiencies with large overlap integral values between the field profiles of diffracted light from the grating coupler structure and the free-space propagating beam from the optical fiber, as schematically shown in Figure 10A. In this schematic illustration, unlike our previous convention used in the previous section (e.g. Figure 2), we assume that the light propagation direction is from the integrated waveguides (waveguide 2 in Figure 2) to the optical fibers (waveguide 1 in Figure 2) for simplicity. Due to the reciprocity theorem, this does not change the results. The uniform grating structures cannot achieve very high coupling efficiencies because the output beam diffracted through the grating structure has an exponentially decaying asymmetric electric field profile (E₁′, top in Figure 10A), rather than having a Gaussian-like symmetric distribution (E₁′, bottom in Figure 10A) similar to the fiber mode (∑E_2,k) [119]. When the guided light in the waveguide is diffracted from an apodized grating coupler with spatially varying non-uniform grating elements, the output field distribution at the grating surface can resemble a Gaussian-like shape that can result in a higher mode overlap at the fiber facet [120], [121].

Figure 10:

Diffraction grating-based optical coupling with apodized grating.

Schematic diagram of mode overlap difference between (A) the uniform and (B) apodized gratings. Depending on the grating apodization, exponentially decaying or Gaussian-like electric field profiles (red curves, E₁′) are propagated from waveguide 1 (grating-based optical couplers) and Gaussian modes (blue curves, ∑E_2,k) are the guided modes in waveguide 2 (optical fibers). (C, D) Cross-section and SEM image for the apodized grating couplers based on optimized fill factors. Adapted from Ref. [109]. Copyright (2013) The Optical Society.

Figure 10B shows a shallow-etched apodized grating coupler with an optimized fill factor variation [122]. More specifically, the diffraction grating-based coupler was designed to provide an optical link between the single-mode optical fiber with a 10.4-μm MFD and the fundamental TE mode in the SOI-based PIC waveguide. The grating couplers were fabricated from an SOI wafer with a 340-nm-thick silicon device layer and a 2-μm-thick buried oxide layer. In order to achieve efficient mode matching and reduce back-reflection, the etch depth was optimized to 200 nm while the grating element fill factor was gradually changed from 0.08 to 0.4 along the waveguide propagation axis. As a result, the apodized grating structure achieved −1.2 dB (75.9%) efficiency at 1533 nm [122]. Recently, a high-efficiency grating coupler without a bottom reflector was reported by optimizing both the grating elements’ fill factor and their periodicity [111]. The theoretical coupling efficiency for such an optimized grating coupler was estimated to be −0.8 dB (83.2%), and the experimental coupling efficiency of −0.9 dB (81.3%) was obtained. The samples were fabricated on an SOI wafer with a 260-nm device layer by electron beam lithography and a single-etch fabrication process.

More recently, a coupling efficiency of −0.7 dB (85.1%) near the 1310-nm wavelength was obtained by dual-etch apodized grating couplers [123]. High-efficiency grating couplers can be realized with multi-step etching techniques [109], [110], [123] and SWG structures [100], [101], [124], [125]. For example, a grating coupler with multiple etch depths achieved −1.9 dB (64.6%) coupling efficiency (Figure 10C) [109]. Subwavelength-scale diffractive elements, such as a photonic crystal structure, can also be used to implement a more efficient grating coupler [125].

3.3 Directionality-enhanced grating structures

Directionality (P_up/P_wg) shows the fraction of the waveguide input power (P_wg) that is diffracted to the upward direction (P_up). One of the main factors that reduce the grating coupler’s coupling efficiency is its low directionality because a significant fraction (35%~45% [112]) of the input optical power to the waveguide is diffracted downward from the grating structure and becomes lost in the substrate, as shown in Figure 9. The basic rule of thumb for improving the directionality is to control the interference between the diffracted and reflected light components, which can be simply accomplished by tuning the thicknesses of the buried silicon oxide and cladding layers [114], [126] to maximize the outcoupled optical power toward the desired direction.

Figure 11A [127] schematically shows a method to improve the directionality with a substrate reflector, which is typically a Bragg reflector composed of alternating materials with high and low refractive indices, and reflects the downward diffracted light toward the upward direction to improve the directionality. Similar approaches have been introduced [113], [118], [127], [128], [129]. The reflectivity of the multilayer reflector is determined by the thicknesses of each layer, the refractive indices, and the number of such layers. For example, grating coupling structures with a Bragg bottom mirror made of Si/SiO₂ layers were demonstrated, and the measured coupling efficiency was −1.58 dB (69.5%) with a 1-dB bandwidth of 36 nm [127], as shown in Figure 11B.

Figure 11:

Diffraction grating-based optical coupling methods using directionality-enhanced grating structures.

(A) Schematic diagram of a grating coupler with a backside mirror, enhancing the upward power (P_up) using interference effects. (B) SEM image of an example of the substrate reflector structure. Reprinted from Ref. [127]. Copyright (2009) The Optical Society. (C) Schematic diagram of a grating coupler with an overlay grating structure to reduce leakage. (D) SEM image of an example of a silicon overlay structure. Reprinted from Ref. [112]. Copyright (2010) The Optical Society.

The directionality can also be enhanced by employing a single mirror-like layer. A metal layer, such as an aluminum or gold layer, is also usually used to realize such a mirror-like layer [114], [130], [131], [132], [133], and even an amorphous silicon layer can be adopted as a bottom mirror [134]. After the grating structures and the waveguides were defined on the SOI wafer, a SiO₂ top cladding layer was deposited. Then, the substrate of the wafer underneath the grating area was etched, and finally, a bottom reflector layer was deposited. The maximum measured coupling efficiency was −2 dB (63.1%) with a 1-dB bandwidth of 29 nm. The bottom reflector layer can also be assembled to the grating structures using flip-chip bonding [114], [134].

In addition, overlay grating elements can also improve the directionality by achieving constructive interference of P_up and reducing light leakage to the silicon substrate, as schematically described in Figure 11C. An epitaxially grown silicon layer can be used as an additional degree of freedom to the grating coupler design [112], [115], [135], and an example of a SEM image of a typical overlay grating is shown in Figure 11D [112]. The additional silicon layer on the un-etched grating teeth introduces an additional degree of freedom in the grating coupler design, and both the directionality and coupling length of the grating could be simultaneously optimized, overcoming the typical trade-off between the directionality and coupling length [112], [135]. After the grating structures were defined, an additional silicon layer was deposited and subsequently patterned and etched. When the unnecessary silicon overlay was removed by dry etching, the maximum coupling efficiency and 1-dB bandwidth were measured to be −1.6 dB (69.2%) and 44 nm, respectively [112]. In ref. [115], two grating couplers were stacked by adding a second layer. Total film thickness was set to be 220 nm, and a simulated coupling efficiency of −0.137 dB was achieved.

Interleaved etching (dual-etch) processes were also adopted to improve directionality [136], [137]. A bi-level grating can be treated as a linear superposition of two gratings and generates constructive interference toward the superstrate and destructive interference toward the substrate [138]. Interleaved etching (70-nm and 220-nm depth) of a standard 220-nm-thick SOI platform resulted in a grating coupler with a coupling efficiency of −1.3 dB and a 3-dB bandwidth of 52 nm [137].

Enhancing the directionality is crucial to ensure that the grating coupler achieves high coupling efficiencies. The design strategies and fabrication schemes for the grating-based optical coupler should be carefully chosen considering the overall fabrication process flows and packaging situations.

4.1 Principle of operation

To further improve the optical coupling efficiency of conventional end-fire coupling methods, the adiabatic waveguide coupling scheme uses a longer coupling distance with the slower transformation of the guided modes with the tapered input and output waveguides, as schematically shown in Figure 12A. The key idea of adiabatic light coupling between tapered fibers and inversely tapered waveguides is to slowly and adiabatically transform the waveguides modal cross-section along the propagation direction such that the propagating electromagnetic field profile remains in a single eigenmode through the composite waveguide region where both the tapered input and output waveguides overlap with each other (e.g. a combination of tapered optical fibers and silicon waveguides). To suppress higher order mode excitation and the corresponding optical losses, both waveguides should be gradually tapered and fulfill the adiabatic condition [151], [152]. For example, specially designed fibers, such as tapered and pulled fibers with wavelength- or subwavelength-scale core/cladding dimensions in contrast to the cleaved or lensed fibers in the previous sections, are used to efficiently generate evanescent optical fields. With adiabatically varying waveguides, the optical coupling length between two waveguides is given by λ₀/(n_eff,1 – n_eff,2), where n_eff,1 and n_eff,2 are the effective refractive indices of the two eigenmodes [153]. As a result, nearly 100% power transfer can be obtained between two waveguides when the waveguide interaction length is longer than the coupling length, λ₀/(n_eff,1 – n_eff,2).

Figure 12:

(A) Schematic diagram of the fiber-waveguide coupling scheme. (B) Adiabatic coupling between high-index SiN waveguide (right) and low-index tapered optical fiber (left). (C) The corresponding cross-sectional of |E|² obtained from the FDTD simulations at various positions along the adiabatic couplers.

Adapted from Ref. [145]. Copyright (2015) The Optical Society.

4.2 Broadband optical coupling in the visible and infrared wavelength range

To obtain evanescent coupling between the optical fibers and the integrated waveguides, biconical tapered optical fibers were used [143], [144], [147], [148]. The waveguide interaction distance was up to ~25-μm long [147]. Single-sided conical tapered fibers can also be used for adiabatic coupling [145], [149], [150]. For single-sided conical tapered fiber fabrication, a chemical etching method was used [149], [150]. In contrast to the biconical fibers, single-sided geometries can offer better mechanical stability and compactness suitable for coupling with the PIC chips [145]. Highly efficient optical coupling, up to −0.13 dB (97%), was achieved with very compact coupling interfaces [145]. Figure 12B shows a schematic diagram of fiber-to-silicon nitride waveguide coupling [145]. By following the adiabatic tapering condition discussed in Section 4.1, the optical modes can be evanescently coupled between two waveguides, as shown in Figure 12C. The reported results have focused on the visible wavelength range operation with silicon nitride [145] and diamond [149] waveguides. High-efficiency optical coupling schemes with silicon waveguides in the near-infrared wavelengths were also proposed with an adiabatically tapered silica fiber whose full tip angle was ~1.2° [150].

The advantages of adiabatic coupling include a large 1-dB alignment tolerance dimensions up to ~50 μm along the waveguide optical axis [149], a wide 1-dB bandwidth larger than a wavelength range of 200 nm [147], [149], [150], and very high coupling efficiencies. However, in this scheme, the integrated waveguides need to be suspended and surrounded by lower index materials, such as air, to prevent the optical power leakage to the other cladding layers, and therefore, additional processing steps are required as in Section 2.3.