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Abstract
The design of grating couplers (GCs) that can (de)multiplex and couple arbitrarily defined spatial light into photonic devices is crucial for miniaturized integrated chips. However, traditional GCs have a limited optical bandwidth due to their wavelength’s dependency on the coupling angle. In this paper, we propose a device that addresses this limitation by combining a dual-broadband achromatic metalens (ML) with two focusing GCs. By controlling the frequency dispersion, the waveguide-mode-based ML achieves excellent dual-broadband achromatic convergence and separates broadband spatial light into opposing directions at normal incidence. The focused and separated light field matches the grating diffractive mode field and is then coupled into two waveguides by the GCs. This ML-assisted GCs device exhibits a good broadband property with −3 dB bandwidths of 80 nm at 1.31 µm (CE ∼ −6 dB) and 85 nm at 1.51 µm (CE ∼ −5 dB), which almost covers the entire designed working bands, representing an improvement over traditional spatial light-GC coupling. This device can be integrated into optical transceivers and dual-band photodetectors to enhance the bandwidth of wavelength (de)multiplexing.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Over the past decade, the photonic integrated circuits (PICs) have emerged as a mature and powerful technology with unique advantages in information transmission [1,2]. One of the main challenges in PICs is how to achieve efficient coupling between the integrated waveguide and the standard optical fiber core due to their substantial size mismatch. Currently, the most widely adopted coupling scheme in integrated photonics is the grating coupler (GC). GCs offer several advantages over other methods, such as edge couplers, including loose positioning tolerances, ease of lithographic manufacturing, and testability without the need of polishing [3–7]. In addition to being used for fiber–chip coupling, GCs are used as power, polarization, and wavelength splitters [8–10]. With the increasing demand for achieving ultra-high link capacity in wavelength-division-multiplexing systems in optical communications, dual-band GCs capable of de/multiplexing wavelengths of 1.31/1.55 µm in the system are drawing much attention. Nevertheless, the coupling between the external light and the traditional GC suffers from narrow spectral bandwidth due to the intrinsic dependence of wavelength on the coupling angle [5,10].
To overcome the limitations of traditional GCs, subwavelength GCs, 2D GCs, and double-layer GCs have been proposed to multiplex or demultiplex two wavelength bands into orthogonal or opposite waveguides [9–13]. These schemes rely on the diffraction property of gratings, which require tilted fiber angles. Recent studies have used aperiodic GC with an infinite BOX layer, dual-etched GC, and GC with polysilicon overlay to break the grating symmetry and enhance directionality, achieving wavelength demultiplexing at normal incidence, but with relatively narrow spectral bandwidths [8,14,15]. However, these works are based on fiber-coupled design, which may lead to low coupling efficiency (CE) when larger mode-field spatial light is incident due to mode field mismatch. To address this challenge, a solution that integrates dielectric metalens (ML) with GC has been proposed to perform spatial light coupling [16,17], of which the wavelength multiplexing is not taken into account. The ML is a planar device that can effectively manipulate phase, frequency, amplitude, and propagation mode of the spatial incident light, providing both flexibility and robustness in design [18–22]. By adjusting the phase of the unit structure, the optical dispersion of the ML can be eliminated within discrete wavelengths or wide bandwidths, allowing arbitrary control of frequency dispersion and construction of large-bandwidth devices [23–27]. It is worth noting that the ML can also be applied in vertical fiber-to-chip coupling, as demonstrated by the 1D achromatic ML-assisted L-shaped grating device that operates specifically within the C-band [28].
This work proposes and numerically demonstrates a GC device assisted by a dual-broadband achromatic ML for simultaneous wavelength-division and vertical coupling of spatial light. Specifically, the proposed GC device is capable of coupling spatial light of both O-band (1.26–1.36 µm) and SC-band (1.46–1.56 µm) into opposite waveguides under normal incidence. The 3 dB bandwidths of the corresponding regions reach 80 and 85 nm, respectively. Through optimizing the geometrical parameters of the GCs to match its dispersion and mode field with that of the ML, peak CEs of −6 and −5 dB are achieved at 1.31 and 1.51 µm, respectively. The performance of the proposed device is benchmarked against reported dual-band GCs, as shown in Table 1. It is found that our device provides both vertical coupling and broader bandwidth. Vertical coupling eliminates the need of a specific incidence tilt angle, which increases the system's flexibility, while broadband coupling widens the bandwidth of wavelength (de)multiplexing, making the device more versatile. Additionally, utilizing the structural dispersion characteristics of the GC and ML enables effective spatial light-to-chip coupling, thus offering a potential solution to the key challenges in PICs.
Table 1. The comparison of the simulated coupling performance between the proposed device and previously reported dual-band GCsa
2. Principles and designs
The ML has the ability to manipulate the transmission or reflection to achieve a hyperbolic phase, producing a focused light beam with high diffraction efficiency. In general, the phase profile required for off-axis ML can be described by the following formula:
Fig. 1. Design principles of the proposed device. (a) Schematic diagram of coupling principle of the GC and ML. (b) Schematic of the device composed of the GCs and ML.
The GC facilitates the coupling of light waves in the optical fiber and chip by introducing periodic (or aperiodic) grooves in the optical waveguide. Utilizing the Bragg diffraction effect of the periodic etching structure of the GC, the external light couples into the waveguide and vice versa. This effect is generally described by the following simplified form:
To satisfy the angular dispersion and realize efficient coupling of the ML and GCs, the coupling angle of the GCs is designed as the focusing angle of the off-axis ML. The off-axis angle α in Eq. (1) is substituted by Eq. (2) to derive
Efficient coupling of the ML and GCs can be achieved by adjusting the off-axis position and focal length of the ML, as well as the structural parameters of the GC. Figure 1(b) describes a schematic of the ML-assisted GC (ML-GC). The O- and SC-bands free-space light is collected and modulated by the achromatic ML and then focused and split into two opposite positions. The GC couples the converging light into the waveguide port-1 and port-2. The light blue structure is used to support the ML above, thereby ensuring proper alignment with the grating during testing. In practical applications, this light blue structure can be a silicon dioxide ring.
3. Results and discussions
First, a polarization-independent dual-broadband achromatic ML is designed, and its optical characteristics are simulated using a commercial finite difference time domain (FDTD) solver. Figure 2(a) shows that the waveguide-mode-based dielectric nanopillar unit is composed of silicon (Si) nanopillar and silicon dioxide (SiO2) substrate. The designed regular hexagonal unit structures have a side length P of 0.8 µm, and the upper nanopillars have a height H of 1.5 µm. Five diverse archetypes are chosen, including square, square hole, concentric square hole, cross, and cross hole. The light field is regulated by varying their correlation geometrical sizes, with the maximum size being 0.69 µm and the minimum size being 0.02 µm. The incident light is a Gaussian beam with x-polarization. Here, the insets in Fig. 2(a) depict the normalized field profiles in the y-z plane at wavelengths of 1.31 and 1.51 µm for the square (upper row), square hole (middle row), and cross (lower row) nanopillars, representing various phase and phase dispersion responses. The high concentration of the magnetic field inside the nanopillars suggests the support of waveguide-like resonance modes in each nanopillar. The varying field distributions among different nanopillars indicate their potential to provide different phase responses. Compared to the square nanopillar, the larger difference in resonance modes at different wavelengths of the square hole and cross nanopillar leads to higher phase compensation. To evaluate the achromatic focusing performance of the ML with a designed radius of 30 µm and focal length of 225 µm, the normalized electric field intensity distributions in the axial planes (y–z cross-section) at wavelengths of the O- (the inset in above) and SC-bands (the inset in below) are calculated and explored, as shown in Fig. 2(b). The axial intensity distribution shows that the ML concentrates the incident energy of different wavelengths near the marked focal plane (as indicated by the red dashed line), indicating that the chromatic aberration is relatively slight over the entire operating bandwidth. Moreover, Fig. 2(b) displays the simulated focal lengths of the ML at sampled wavelengths, with the maximum shift from the theoretically predicted focal length (red dotted line) limited to 5% for the entire operational wavelength range. Subsequently, the full-width at half-maximum (FWHM) of the focal spots of the ML at all wavelengths are calculated and compared with the theoretical limit (i.e., ∼0.514λ/NA, red dotted line), as shown in Fig. 2(c). Results show that the focal spots are at or near the diffraction limit for the entire bandwidth of the ML. The inset in Fig. 2(c) shows the normalized intensity distribution in the focal planes (x–z cross-section) for wavelengths of 1.31 and 1.51 µm. The corresponding horizontal cuts of the simulated focal plane follow Gaussian distribution, as shown in the red curve. Furthermore, the relative focusing efficiency is defined as the sum of the light intensities within two times the FWHM of the spot divided by the sum of the intensities across the entire focal plane. As plotted in Fig. 2(d), the average focusing of the ML is about 60% over the whole work bandwidth, exhibiting a good focusing ability. Overall, the ML design effectively focuses and disperses the spatial light in O- and SC-bands to opposite sides of the space, demonstrating excellent achromatic and efficient focusing capabilities. The off-axis angle of the O-band is calculated to be 8.5°, while that of the SC-band is −8.5°.
Fig. 2. Performances of achromatic ML. (a) Schematic of the meta-unit, basic shapes (i.e., square, square hole, concentric square hole, cross, and cross hole), and their corresponding normalized magnetic field distribution. The white line indicates the boundary of the meta-unit. (b) Focal lengths, (c) FWHM, and (d) focusing efficiencies as a function of wavelength. The normalized far-field intensity distributions in the y–z cross-section for O- (above) and SC-bands (below) are shown in the insets of (b).
Since GC is the key component of the proposed device and determines the upper limit of the multiplexer’s coupling performance, we investigate the transmission characteristics of the proposed GCs using the focusing field of the ML as the input light field. Figure 3(a) shows that the focusing GC consists of a 2D array of periodically arranged curved strips with a length of L. The thickness and length of the waveguide are 220 nm and 8 µm, respectively; the length and width of the taper are 20 and 10 µm, respectively; and the etching depth is 70 nm. To achieve dual-band operation in the O- and SC-bands, appropriate structure parameters are obtained through optimization using an FDTD solver. The coupling angle θ is fixed as the off-axis angle α, i.e., ± 8.5° (as Fig. 1(a) shown). The optimization process involves sweeping the parameters and evaluating the performance for each setting to obtain the optimal Λ and D. Figure 3(b) shows the calculated peak CE as a function of Λ and D for wavelengths of 1.31 and 1.51 µm. As marked by the pentagram, a parameter set (Λ, D) = (0.49 µm, 0.5) and (0.59 µm, 0.5) is chosen as it exhibits high CEs. In addition to Λ and D, the peak CEs of the GC also depend on the number of periodic strips due to the overlap between the focusing field of the ML and the diffracted field of the GC. As illustrated in Fig. 3(c), the peak CEs for wavelengths of 1.31 and 1.51 µm initially increase and then decrease with an increasing period number. Thus, to attain the maximum CE for both wavebands, the number of periodic strips is set to 19 and 17, respectively. The GC length L for the O-band is 9.3 µm, and that for the SC-band is 10 µm, which is twice the FWHM of the ML.
Fig. 3. Performances of ML- GCs. (a) Schematic view of the GC. (b) Peak CE contour for sweeping pitch Λ and the duty cycle D for wavelengths of 1.31 and 1.51 µm. (c) Peak CE with varied period number for wavelengths of 1.31 and 1.51 µm. (d) Simulated CE spectra for two wavelength bands with x-polarization for proposed ML-GC and spatial light-to-GC (SL-GC) coupling. The simulated crosstalk of the ML-GC coupling as a function of wavelength is shown on the right in the figure. The inset in (d) shows the simulated light field propagations at 1.31 and 1.51 µm.
To highlight the performance of the proposed device, a comparison is made between its coupling performance and that of GCs under spatial light illumination, where the incident Gaussian beam has a size of 60 µm. Figure 3(d) demonstrates the CE spectra of different coupling styles as a function of wavelength for the O- and SC-bands, respectively. The peak CEs for traditional FS-GC coupling are −9 and −10 dB at wavelengths of 1.31 and 1.51 µm, respectively. On the other hand, ML-GC shows higher CE values of −5 and −6 dB. This efficient coupling benefits from the mode field matching and angle dispersion matching of the ML and GCs. The −3 dB bandwidth of the ML-GCs is 80 nm for the O-band and 85 nm for the SC-band, showing a broadband property that covers almost the entire working band, which is primarily due to the continuous achromatic and splitting performance of the ML. Moreover, the proposed device only requires one vertical broadband incidence rather than two strict oblique incidences for FS-GC coupling, which simplifies the subsequent alignment process. The beam receiving area of the ML-GC (ML area) is 9.5 times larger than that of the FS-GCs (GC area), significantly improving the device’s light receiving capacity. Additionally, the simulated crosstalk (i.e., the total amount of power coupled out to the opposite port) of ML-GC coupling for each spectral band is shown in Fig. 3(d). For wavelengths of 1.31 µm and 1.51 µm, the simulation predicts a crosstalk less than −32 dB. The electric field profiles of the focused GCs at different peak wavelengths under x-polarization are displayed in the inset of Fig. 3(d). The equal distribution of coupling powers into port-1 for the O-band and port-2 for the SC-band indicates that the device has accomplished wavelength demultiplexing and uniform splitting of the two bands.
Furthermore, the effect of the structural misalignment tolerance on the CE performance of the designed device is investigated. As illustrated in Fig. 4(a), a spatial light beam is incident at an angle β into the center (z0) of the ML with a focal position zf along the z axis. The relative displacement between the ML and GC centers is set to zf. The peak CEs for incident light with different angles and positional misalignments at wavelengths of 1.31 and 1.51 µm are first simulated. As shown in Fig. 4(b), the maximum CE degradation for both wavelengths is approximately 3 dB and 5 dB within a deviation of ±4° in β, respectively. This relaxes the stringent requirement of traditional GC for a specific oblique incidence angle, greatly reducing the alignment difficulty. Within an offset of ±15 µm in z0, the CE only degrades less than 1 dB, showing a good misalignment tolerance, as displayed in Fig. 4(c). The slight offset in the position of the incident light only results in a decrease in the optical power, without affecting the focusing position and angle of the ML. Therefore, the focused and diffracted fields of the GC still match, resulting in minimal impact on the coupling of the ML and GCs. However, the coupling performance is more sensitive to the misalignment between the ML and GCs. Figure 4(d) shows that a dislocation of approximately ±3 µm from the optimal position zf leads to a loss of around 3 dB due to the mismatched mode field. Subsequently, the impact of fabrication deviations in etch depth (h) of the grating on the optical properties of the device is investigated, as shown in Fig. 4(e). Deviations in h of up to ±20 nm lead to a maximum CE degradation of 2 dB with respect to the central operating wavelengths. Decreasing h reduces the effective refractive index difference of the grating, enhancing the transmission of optical wave energy primarily in the horizontal direction. Conversely, increasing h enhances reflection, causing the optical wave to reflect mainly back to the input. The ML-assisted GC scheme offers advantages such as vertical incidence, relatively large incident angular tolerance, and insensitive incident position deviation, making it applicable in optical transceivers and dual-band photodetectors. However, efforts are still anticipated to improve the fabrication alignment accuracy of the ML and GC to further enhance the coupling performance. Finally, to verify the influence of achromatic ML characteristics on the wavelength demultiplexing performance of the proposed device, the CE spectra of five MLs with different numerical aperture (NA) values are calculated while the GCs are fixed. The diameter of the ML remains constant at 60 µm, while the focal length varies from 176 to 330 µm, corresponding to an increase in NA from 0.09 to 0.17. All five MLs can achieve achromatic focusing and splitting of the input O- and SC-bands light. With an increase in NA, the size of focal spots of the ML decreased, causing a mismatch of the mode field and a reduction in the CEs of the ML-GCs device, as displayed in Fig. 4(f).
Fig. 4. Tolerance analysis of designed ML-GCs. (a) The structural parameters. Peak CEs as a function of errors in (b) the angle (Δβ) and (c) position (Δz0) of incident light, (d) the dislocation (Δzf) between ML and GCs layer, (e) etched depth (Δh), and (f) NA value of the ML.
4. Conclusion
In summary, this paper proposes a dual-band ML-assisted GC design that accomplishes wavelength demultiplexing of dual-band free-space light under normal incidence. The design takes advantage of the dispersion characteristics of the ML and GCs to achieve broadband performance covering almost the entire O- and SC-bands. Simulated results show that the device has −3 dB bandwidths of 80 nm for 1.31 µm (CE ∼ −6 dB) and 85 nm for 1.51 µm (CE ∼ −5 dB), with crosstalk less than −32 dB. The efficient coupling benefits from the mode field matching and angle dispersion matching of the ML and GCs. The device is highly practical due to its insensitivity to incident positional deviation, large incident angular tolerance, and vertical incidence. The proposed scheme can be extended to other bands by selecting different microstructure materials and geometric sizes for the ML.
Funding
National Natural Science Foundation of China (62135004); Key Technologies Research and Development Program of Shenzhen (JSGG20201102173200001).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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