Experimental demonstration of a flexible and high-performance mode-order converter using subwavelength grating metamaterials

Zhenzhao Guo; Zhenzhao Guo; Jinbiao Xiao; Jinbiao Xiao; Shengbao Wu

doi:10.1364/OE.484384

1. Introduction

The promising technology termed as mode division multiplexing (MDM), simultaneously exploiting each eigenmode supported by multimode waveguides as an independent channel to encode/carry optical signals, offers a new dimension to significantly enhance transmission capacity requiring only a single operating wavelength for the on-chip photonic integrated circuits (PIC) [1,2]. In MDM systems, mode-order converters are one of the most fundamental components for generating and manipulating guided modes, which are capable of converting a given mode to a specific higher-order mode and vice versa [3]. In addition, mode converters can be also utilized in optical switches [4,5], biosensors [6], and cipher encryptions [7], showing broad applicability in silicon photonics. During the past few years, a considerable amount of structures for converting one mode to another on the silicon-on-insulator (SOI) platform have emerged, including the ones based on asymmetric directional couplers (ADCs) [8,9], multimode interference (MMI) couplers [10], adiabatic tapers [11,12], Mach-Zehnder interferometers (MZIs) [13], hybrid plasmonic waveguides (HPWs) [14], Bragg gratings [15], shallowly etched waveguides (SEWs) or say refractive index perturbations [16–20], Y-junctions [21], inverse design (QR-code-like configuration) [22,23], and subwavelength slots [24]. ADCs consisting of two parallel and asymmetric nanowires are most commonly leveraged, owing to the designing simplicity and feasibility of exciting higher-order modes via the phase-matching condition, but their performance is limited by the narrow bandwidth and tight fabrication tolerance [25]. For mode-order converters using structures of Bragg gratings, Y-junctions, and MZI, an obvious drawback of large converting length can be observed. For example, lengths of the TE₀-to-TE₁ conversion, respectively, are 60-66.8 µm, > 100 µm, and ∼ 50 µm in Refs. [15,21,26], disfavoring the highly integrated density of on-chip PICs. As an alternative approach, inverse design can effectively reduce the converting length and be scalable for arbitrary mode conversions. For instance, the converting length for the TE₀-to-TE₁ conversion is only 2 µm in Ref. [22]. However, such a pixelated structure normally suffers from a large insertion loss, which is 2.2 dB (experiment) for the TE₀-to-TE₁ conversion in this report. Moreover, numerical calculations of the inverse design are rather time-consuming. Another alternative approach for realizing compact mode converters is to introduce refractive index perturbations in the mode converting region, but corresponding shallowly-etched trenches with acute angles require an additional etching step as well as a precise fabrication process [16–20].

Besides the inherent drawbacks of the above-mentioned mode converters, two main challenges are further presented and highlighted: (1) low scalability for achieving more desired modes by using the same scheme, most converting schemes can be only extended to the TE₀-to-TE₂ mode conversion [16–18]; (2) the lack of a direct mode conversion between higher-order modes, thus, a cascading strategy is required. For the first challenge, ADCs are potential solutions since any target higher-order modes can be excited by the phase-matching condition, but they are sensitive to variations of both fabrication dimension and wavelength, as mentioned above. Converters employing the method of inverse designs [22] can be expanded to realize TE₀-to-TE₃ but at the cost of a high insertion loss of 1.8 dB (simulated). In Ref. [27], researchers proposed highly scalable mode-order converters by applying tapered metal caps, which can generate any higher-order modes as desired. However, the insertion loss is as large as ∼2.8 dB for the TE₀-to-TE₄ mode conversion due to the direct absorption of metals, and the loss of the TE₀-to-TE₅ mode conversion is expected to increase to ∼3.5 dB. Moreover, the corresponding fabrication processes are rather complicated regarding metal depositions and might be incompatible with other components on the same wafer. As to the second challenge, much work so far has focused on the mode conversions from the fundamental mode to higher-order modes. Therefore, the mode conversions between higher-order modes are usually implemented by cascaded schemes [11,16], which means that the mode conversion can be efficiently accomplished in a single component. In this way, corresponding footprints are increased and the performance will deteriorate. For example, a cascade scheme is performed in Ref. [11] to realize the TE₂-to-TE₃ mode conversion, leading to a large conversion length of ∼55 µm. To tackle these two challenges, a scalable, flexible, and ultracompact mode-order converting scheme, realizing mode conversions from the fundamental mode to higher-order modes as well as mode conversions between higher-order modes, is greatly desired.

In recent years, subwavelength gratings (SWGs) metamaterials, composed of a periodic arrangement of dielectric nanowires with a period much smaller than the working wavelength, can surmount diffraction, function as a homogenous medium, and locally manipulate refractive index [28]. Quite high degrees of freedoms for researchers are provided by SWGs metamaterials, which enables the on-chip devices to be highly functional while occupying an ultracompact footprint and is used in a large range of applications [29], including mode-order converters [30]. Cheng et al. [31] designed a scalable TE₀-to-TE_q mode converting scheme based on SWGs structures, with q ranging from 1 to 3. The total device length of the TE₀-to-TE₃ mode converter is as large as 14.54 µm, which can be further reduced. Moreover, mode conversions between higher-order modes cannot be achieved by using the same scheme, showing low flexibility and scalability. Recently, we theoretically proposed a novel concept for an expandable and flexible TE_p-to-TE_q mode converting scheme (p < q, p = 0, 1, 2, 3&q = 1, 2, 3, 4), realized using a SWGs multimode waveguide and two tapers embedded at its anterior/posterior end [32]. With this mode converting scheme, the TE_p mode launched from the input taper can be converted to the desired TE_q mode of the output taper. However, the inter-modal crosstalks (CTs) are higher than -20 dB for all converters and insertion losses (ILs) are relatively high with up to 1.17 dB (@ 1.55 µm) for mode conversions between higher-order modes, thus, there is still room for improving performance and reducing device lengths.

In this work, we propose and experimentally demonstrate a significantly improved mode-order converting scheme with sandwiched SWGs and fully etched SWG-arrays at the end of output taper to boost the mode purity and thus improve the insertion loss as well as intermodal crosstalk. Furthermore, the SWGs-wires region is sandwiched by input and output tapers, which introduces a considerable reduction in device lengths. The measurement results, for proofs of concept, show that the fabricated TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, and TE₁-to-TE₃ has low ILs/CTs of 1.8/-15 dB over a broadband of ∼ 100 nm, 38 nm, 25 nm, 45 nm, and 24 nm, with ultracompact device lengths ranged from 3.436 to 7.71 µm. The present mode converting scheme exhibits a low insertion loss, a low crosstalk, and an ultracompact footprint, together with high scalability and flexibility. Notably, the fabrication of this scheme is rather simple since only a one-step etching process is required.

2. Design and operating principle

Figures 1(a) and (b) show the three-dimensional (3D) schematic configuration of the proposed mode-order converting scheme, which consists of an input taper named IT, an output taper named OT, and a sandwiched SWG-wires region. The TE_p-to-TE_q mode-order converters are designed based on the SOI platform with a 220-nm silicon core (n_Si = 3.476), a 2-µm buffer oxide layer (n_SiO2 = 1.444), and a 2.2-µm silicon oxide up-claddings. Here, the IT is tapered down from w_I to w_t along a length of L_IT, in which the positions of IT and its tip are denoted by L_d and w_d, respectively, along lengthwise (z) and crosswise (x) directions. As to the OT started at z = 0, it is tapered up from w_t to w_O along a length of L_OT, whose lateral position is denoted by w_s. The SWG-wires region is sandwiched by the IT and OT, with a period number of N_pq, a pitch length of Λ₁, and a duty cycle of a₁/Λ₁. Specifically, q fully etched SWG-arrays are introduced at the end of output taper OT, whose lengthwise and crosswise positions are denoted by L₁, …, L_q and w₁, …, w_q, respectively. For all fully-etched SWG-arrays, they have the same width of w_t, a pitch length of Λ₂, and a duty cycle of a₂/Λ₂, and for the q-th SWG-array, it has a period number of n_q.

Fig. 1. 3D schematic configuration of the proposed TE_p-to-TE_q mode-order converting scheme, together with enlarged views of (a) input taper, namely IT, and (b) fully etched SWGs-arrays and the light propagation profile of TE₂-to-TE₃ mode conversion as an example. The whole device is covered by upper SiO₂ claddings, which are not shown for clarity.

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Based on the configuration shown in Fig. 1, a mode-order conversion of TE_p-to-TE_q can be realized by adiabatic mode evolutions of TE_p-to-TE₀-like-mode-field (TLMF) and then TLMF-to-TE_q, where TLMF is the acronym for TE₀-like-mode-field, and the operating principle is demonstrated in detail as follows. Figures 2(a) and (b) show the SWGs homogenous behavior and a transverse cross-section of the corresponding taper/SWG-wires waveguide system, where the effective medium index (n_swg) of the SWG-wires region for TE modes can be approximately given by well-known Rytov’s formula [28]:

(1)$$n_{\textrm{swg}}^2 \approx \frac{a}{\Lambda } \cdot n_\textrm{1}^2 + \left( {1 - \frac{a}{\Lambda }} \right) \cdot n_\textrm{2}^2$$

where n₁ and n₂, respectively, are refractive indexes of silicon and silica in our case. For such a waveguide system, the taper width is changing with a constant w_s. Here we perform the finite-difference frequency-domain (FDFD) method [33] to calculate the mode field profiles (E_x) for of TE₀, TE₁, TE₂, and TE₃ modes which are utilized as examples, as shown in Fig. 2(c). Obviously, one could find that a TLMF is gradually formed in the SWG-wires region as the taper is tapered down, for all modes. Hence, the optical mode TE_p launched from the wider side of the taper is converted to a TLMF when the taper is tapered down gradually. As a reverse process, the TLMF can be naturally converted to initial TE_p mode as the same taper is inversely tapered up, or converted to a new mode TE_q by choosing a different taper in which the TE_q mode is supported [32], according to the Lorentz reciprocity theorem [34]. In this way, we use the SWG-wires as a mode exchanging region by sandwiching it between two different tapers IT and OT, which support TE_p and TE_q modes respectively and effective indexes of these two modes are approximately matched. For the input TE_p mode, it is converted to the TLMF from IT to the SWG-wires region via a mode evolution, as IT is tapered down. Next, this TLMF is converted to the desired TE_q mode from the SWG-wires region to OT via a reverse mode evolution as OT is tapered up. Overall, a TE_p-to-TE_q mode conversion can be readily achieved by a two-step process of TE_p-to-TLMF in IT/SWG-wires and TLMF-to-TE_q in OT/SWG-wires region, as shown in Fig. 2(d), showing excellent flexibility and scalability of the proposed mode converting scheme. In particular, phase differences of modal components of the target TE_q mode are further revised by introducing fully etched SWG-arrays at the end of the OT, thereby improving the mode purity with a lower crosstalk as well as insertion loss.

Fig. 2. Working principle of the present mode-order converting scheme: (a) 3D schematic view of the homogenous medium behavior of SWGs-wires waveguide; (b) Cross-section of the taper/SWG-wires waveguide system; (c) Mode field profiles (E_x) of TE₀, TE₁, TE₂, and TE₃ modes of the taper/SWG-wires waveguide system; (d) The two-step process of TE_p-to-TLMF and then TLMF-to-TE_q in the proposed mode-order converting scheme.

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3. Optimization, results and discussions

Based on the device design investigated in Section 2, the three-dimensional finite-difference time-domain (3D-FDTD) method [35] is performed to simulate/optimize performance and verify the feasibility of the proposed mode-order converting scheme. Here, two key figures of merit (FOM) are calculated, i.e., the insertion loss (IL, say conversion efficiency in some reports) and the inter-modal crosstalk (CT), and they are defined as

(2)$$IL\textrm{ }(dB) ={-} 10 \cdot \log \frac{{P_q^\textrm{O}}}{{P_p^\textrm{I}}}$$

(3)$$CT(\textrm{dB}) = \textrm{max} \{10 \cdot \log \frac{P_{\textrm{ohter}}^{\textrm{O}}}{P_q^{\textrm{O}}}\}$$

where $P_p^\textrm{I}$, $P_q^\textrm{O}$, and $P_{\textrm{other}}^\textrm{O}$ are powers of the given TE_p mode at the input port, the desired TE_p mode at the output port, and other unexpected modes at the output port, respectively. Following the TE_p-to-TLMF-to-TE_q mechanism, the particle swarm optimization (PSO) method [36] is particularly adopted here to optimize the designed mode-order converters. During optimization processes, some structural parameters are fixed as h = 220 nm, w_t = 100 nm, a₁ = 125 nm, Λ₁ = 250 nm, a₂ = 100 nm, and Λ₂ = 200 nm. Meanwhile, searching ranges of 8 parameters of {w_I, w_O, L_d, L_IT, L_OT, w_d, N_pq, w_s} for IT, OT, and sandwiched SWG-wires region, and 3 × q parameters of {L₁, …, L_q, n₁, …, n_q, w₁, …, w_q) for fully etched SWG-arrays, are defined by the given lower and upper limits. Basically speaking, 8 + 3 × q geometry parameters in total need to be optimized for realizing the TE_p-to-TE_q mode conversion, which means that the optimization of attaining a target mode with a higher mode-order requires more computing time to complete. Fortunately, appropriate searching ranges for these parameters can be determined by the modal analysis of taper/SWG-wires waveguide system shown in Fig. 2(c), which can effectively reduce the computational complexity as well as computing time. Here, we take the TE₁-to-TE₂ mode converter as an example to show the determination of initial guessing ranges for geometry parameters. Input (IT) and output (OT) parts of the device are first considered, where searching ranges of w_I and w_O are set to be [0.9, 1.1] and [1.35, 1.5] µm, respectively. Under these width ranges, TE₁ and TE₂ modes, respectively, can be well supported by input and output waveguides with approximately phase-matching. To yield a compact design, the lower (upper) limit of L_d is chosen to be 0 (1) µm. Next, w_s/L_IT/L_OT is controlled within a searching range of [2, 2.7]/[1.8, 2.8]/[4,5] µm for forming a clear TLMF, where N_pq × Λ₁ is approximately equal to L_OT and thus the range of N_pqis set to be [15,22]. Finally, w₁, w₂, L₁, L₂, n₁, and n₂, indicating the positions and period numbers of two SWG-arrays fully etched at the end of OT are studied. As is observed, there are three modal components for the target TE₂ mode (can be seen as 3 beams), the phase differences of between two adjacent components can be tuned by introducing a SWG-array to change refractive index distributions for one beam [13], and thus two SWG-arrays are required for three modal components (beams). Generally speaking, q fully etched SWG-arrays are required for target q-th order mode. In this way, the searching ranges of w₁ and w₂ which denote the crosswise positions of two fully etched SWG-arrays are defined to be [0.35, 0.55] and [0.7, 1.1] µm, around w_O/3 and 2w_O/3 where two antiphase components are adjacent. Thus, we can find a pattern here indicating that w₁, …, w_q vary around w_O/(q + 1), …, q × w_O/(q + 1) for target TE_q mode, respectively. Therefore, the initial guessing range for w_q can be obtained by q × w_O/(q + 1) ± Δw. In parallel, searching ranges of L₁, L₂, n₁, and n₂ are chosen based on OT as well as keeping the device compact, i.e., [2,5] µm, [3,5] µm, [1,5], and [1,5], respectively. After the determination of initial searching ranges for the parameters mentioned above, the optimization is conducted, where each generation size is chosen to be 25. Based on the appropriate guessing ranges, the FOM normally becomes saturated with 15 generations. If the FOM is less than satisfactory, a new run of optimization with updated searching ranges will be performed.

We optimize and experimentally demonstrate five design examples of the proposed mode-order converting scheme, i.e., TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, TE₁-to-TE₃, and TE₂-to-TE₅ mode-order converters, and the optimized parameters are listed in Table 1.

Table 1. Optimized parameters of TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, TE₁-to-TE₃ converters, where the length of L and width of w are in units of µm, and n is period number with no units.

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Figures 3(a)-(d) show the calculated ILs and CTs of TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, TE₁-to-TE₃ mode-order converters, respectively, over a wavelength range from 1450 to 1650 nm. For mode-order conversions from fundamental mode to higher-order modes, it is noteworthy that considerably low CTs of -34.5 dB and -33.7 dB can be achieved around the central wavelength (≈ 1550 nm), respectively, for TE₀-to-TE₁ and TE₀-to-TE₂ mode converters, with low ILs of 0.35 dB and 0.27 dB. Meanwhile, IL/CT of 0.45 dB/-21.39 dB is obtained for the TE₀-to-TE₃ mode converter at the central wavelength of 1550 nm. As to mode-order conversion between the first-order mode and higher-order modes, one could find that performance of TE₁-to-TE₂ and TE₁-to-TE₃ mode converters is degraded compared with the TE₀-to-TE_q (q = 1, 2, 3) mode converters. Fortunately, CTs (ILs) are still lower than -20 dB (0.6 dB) around the central wavelength of 1550 nm for TE₁-to-TE₂ and TE₁-to-TE₃ mode converters, which are -25.7 dB (0.53 dB) and -22.1 dB (0.54 dB) @ 1550 nm, respectively. Overall, the bandwidths for achieving CTs of < -15 dB and ILs of < 0.8 dB are as large as 200 nm, 180 nm, 120 nm, 200 nm, and 160 nm, respectively, in theory, for TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, and TE₁-to-TE₃ mode-order converters, which shows an ultra-broadband operation for the proposed mode-order converting scheme. Notably, the working bandwidths of the designed TE₀-to-TE_q (q = 1, 2, 3) mode converters are quite wider than converters using subwavelength metamaterials reported in Ref. [31], with much shorter device lengths in our proposed converters. More importantly, even for a CT of < -20 dB and an IL < 0.55 dB, the present TE₀-to-TE₁ and TE₀-to-TE₂ converters can exhibit bandwidths as large as 150 nm (1470-1620 nm) and 100 nm (1510-1610 nm), which are larger than those of previous reported mode-order converters [17], [22], [24], [27]. To clarify the necessity and effectiveness of SWG-arrays, The device performance without fully-etched SWG-arrays is calculated and summarized as follows: IL = 0.22 dB/CT = -22.58 dB, IL = 0.41 dB/CT = -15.6 dB, IL = 0.38 dB/CT = -13.95 dB, IL = 0.87 dB/CT = -10.38 dB, and IL = 1.3 dB/CT = -8.52 dB at 1.55 µm, for the TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, and TE₁-to-TE₃ mode-order converters, respectively. One can see that CTs degrade significantly without fully-etched SWG-arrays.

Fig. 3. Simulated IL and CT versus wavelength of (a) TE₀-to-TE₁, (b) TE₀-to-TE₂, (c) TE₀-to-TE₃, (d) TE₁-to-TE₂, and (e) TE₁-to-TE₃ mode-order converters.

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According to the optimized parameters in Table 1, light propagation profiles of TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, TE₁-to-TE₃, and TE₂-to-TE₅ mode-order converters (@ 1.55 µm) are calculated by the 3D-FDTD method and shown in Figs. 4(a)-(e), which verifies the mode converting functionality of the proposed scheme. The total device length for each converter is labeled for easy reading. It can be clearly seen that the input TE_p mode (p = 0, 1) is first converted to a TLMF from IT to the sandwiched SWG-wires region via a mode evolution. Afterwards, this TLMF is converted to the target TE_q mode (q = 1, 2, 3) from SWG-wires region to OT via a reverse mode evolution, where phase differences of modal components are revised by fully etched SWG-arrays at the end of OT. Essentially, the TLMF here serves as an exchanging mode between given TE_p mode and target TE_p mode, thereby flexible mode-order conversion can be realized as long as both input TE_p mode in IT and output TE_q mode in IT can form an effective TLMF in the sandwiched SWG-wires region, with appropriate geometry parameters. In particular, we study and simulate a mode-order converter for TE₂-to-TE₅ mode conversion to validate the scalability as well as flexibility of the present mode conversion scheme, as shown in Fig. 4(f). It can be seen that the input TE₂ mode can be converted to the output TE₅ mode by a two-step process of TE₂-to-TLMF and then TLMF-to-TE₅, with an IL/CT of 0.98 dB/-16.1 dB at 1550 nm. Remarkably, the total length of this converter is only 12.271 µm, indicating an ultracompact mode-order converting scheme.

Fig. 4. Simulated electric filed E_x propagation profiles of (a) TE₀-to-TE₁, (b) TE₀-to-TE₂, (c) TE₀-to-TE₃, (d) TE₁-to-TE₂, (e) TE₁-to-TE₃, and (f) TE₂-to-TE₅ mode-order converters, at the wavelength of 1.55 µm.

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4. Fabrication and characterization

To verify the proposed theoretical scheme and corresponding numerical simulation results, the TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, TE₁-to-TE₃ mode-order converters are fabricated on an SOI platform with a 220-nm-thick Si device layer and a 2-µm buried oxide (BOX) layer by using electron beam lithography (EBL) and reactive ion etching (RIE) processes. The patterns of mode-order converters are defined into a material that is sensitive to electron beam exposure (EBL) and an anisotropic inductively coupled plasma (ICP) RIE etching process is subsequently carried out on the substrate to transfer the patterns into the underlying silicon device layer. As a final step, a SiO₂ upper-cladding layer of 2.2-µm is deposited using plasma-enhanced chemical vapor deposition (PECVD).

Figures 5(a)-(e) show the microscope images of the measure schemes for TE₀-to-TE₁, TE₁-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₃, and TE₀-to-TE₂ mode conversions, respectively. Meanwhile, Figs. 5(f)-(j) give the corresponding scanning electron microscopy (SEM) images of TE₀-to-TE₁, TE₁-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₃, and TE₀-to-TE₂ mode-order converters in five device sets, respectively. For the measurement of each mode-order converter, a device set and an identical reference set without the mode-order converter fabricated on the same chip for comparison and normalization, are cooperatively carried out to characterize all output modes of each mode-order converter. Here, the TE_i multiplexer (MUX) can couple, the TE₀ mode launched from input port named as I-TE_i, to TE_i mode in the bus waveguide, and the TE_i DeMux can convert the TE_i mode to the TE₀ mode at output port named as O-TE_i. From the reference set, the transmissions of the TE_i (De)Mux with a connecting grating coupler can be obtained by feeding the light into I-TE_i port, measuring the O-TE_i port and then dividing the measurement result by two (i = 0 for attaining the transmission of just the grating coupler), which can be used for normalizations. Thereupon, in the device set, the transmissions for all output modes of each mode-order converter are obtained by feeding light at I-TE_i port, measuring the O-TE_i port, and then normalizing the transmissions of corresponding TE_i (De)Muxs and connecting grating couplers.

Fig. 5. Microscope images of the measure schemes for: (a) TE₀-to-TE₁, (b) TE₁-to-TE₂, (c) TE₀-to-TE₃, (d) TE₁-to-TE₃, and (e) TE₀-to-TE₂ mode conversions, respectively. Corresponding pseudocolor SEM images of the (f) TE₀-to-TE₁, (g) TE₁-to-TE₂, (h) TE₀-to-TE₃, (i) TE₁-to-TE₃, (j) TE₀-to-TE₂ mode-order converters, respectively.

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Here, a tunable laser (Santec TSL-710) and an optical power meter (Santec MPM-210) are employed for measuring the transmittance spectra of the fabricated TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, and TE₁-to-TE₃ mode-order converters, where the measured and normalized transmittances for all output modes of each mode converter are shown in Figs. 6(a)-(e). For the TE₀-to-TE₁ converter from Fig. 6(a), one has IL < 1.8 dB and CT < -15.8 dB for the 100 nm bandwidth ranged from 1480 nm to 1580 nm, showing an efficient and broadband mode conversion. At the central wavelength of 1550 nm, the TE₀-to-TE₁ converter exhibits a low loss and small crosstalk of IL = 1.27 dB and CT = -21.31 dB. From Fig. 6(b), one can obverse that TE₀-to-TE₂ converter can keep the IL/CT lower than 1.8 dB/-15 dB in the wavelength range of 1523-1561 nm, which shows a 38 nm operating bandwidth. If IL < 1.8 dB/CT < -10 dB is required for a relaxed requirement, the bandwidth can be extended to 81 nm (1480-1561 nm). As to the TE₀-to-TE₃ converter, one can see that the IL is lower than 1.8 dB for the TE₀-to-TE₃ mode conversion and the CT is below -15 dB within the wavelength range of 1538-1563 nm, i.e., a 25 nm working bandwidth, as shown in Fig. 6(c). Besides the mode conversions from fundamental mode to higher-order modes, flexible mode conversions between higher-order modes are also realized by using the proposed mode converting scheme. From Figs. 6(d) and (e), the TE₁-to-TE₂ and TE₁-to-TE₃ converters, respectively, have 45 nm (1515-1560 nm) and 25 nm (1528-1552 nm) operating bandwidths for simultaneously keeping IL < 1.8 dB and CT < -15 dB. Notably, the TE₁-to-TE₂ converter can even exhibit a lower crosstalk of CT < -17 dB within that wavelength range, showing a broadband mode conversion between higher-order modes. For the central wavelength 1550 nm, one has IL = 0.73 dB/CT = 21.46 dB for TE₁-to-TE₂ converter and IL = 1.7 dB/CT = 15.86 dB for TE₁-to-TE₃ converter, respectively.

Fig. 6. Measured transmittance T_TEi spectra for all output modes of the fabricated (a) TE₀-to-TE₁, (b) TE₀-to-TE₂, (c) TE₀-to-TE₃, (d) TE₁-to-TE₂, and (e) TE₁-to-TE₃ mode-order converters, respectively.

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Table 2 gives a brief summary and comparison with previously reported mode-order converters. For those mode-order converters with wide working bandwidths, their footprints are large [16,31], and some of them require an extra etching step for shallowly-etched trenches. As to the mode-order converters with ultracompact device lengths, the device performance is limited, including large insertion losses and high crosstalks. By contrast, the present mode-order converters show large operating bandwidths for achieving low ILs (< 1.8 dB) as well as CTs (< -15 dB), in ultracompact device lengths ranging from 3.436 to 7.71 µm. Furthermore, different from previous reports in which a cascade strategy is needed for performing the mode conversion between higher-order modes, the proposed scheme can realize not only the mode conversion from fundamental mode to a higher-order mode, but also the mode conversion between higher-order modes in a single device, showing great scalability and flexibility.

Table 2. Comparison of several scalable mode-order converters at the wavelength of 1.55 µm

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5. Conclusion

In conclusion, we have proposed a universal and scalable mode-order converting scheme by using SWGs metamaterials which are sandwiched by tapered-down input and tapered-up output tapers. With this design, TE_q mode can be transformed into a TLMF and vice versa according to optical reciprocity. By using TLMF as an exchange between input TE_p and output TE_q modes, the mode-order conversion can be realized through a two-step process of TE_p-to-TLMF in IT/SWG-wires and TLMF-to-TE_q in OT/SWG-wires region. Based on this mechanism, five proof-of-concept mode-order converters are designed and experimentally demonstrated, including TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, and TE₁-to-TE₃ converters with ultracompact lengths ranged from 3.436 to 7.71 µm. Compared with previous reports, the proposed scheme not only can perform mode conversion from fundamental mode to higher-order modes but also can implement mode conversions between higher-order modes, showing great universality and scalability. In theory, TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, and TE₁-to-TE₃ converters show low ILs (CTs) of 0.35 dB (-34.5 dB), 0.28 dB (-28.6 dB), 0.45 dB (-21.39 dB), 0.53 dB (-25.7 dB), and 0.54 dB (-22.1 dB) respectively, at 1550 nm. From measurement results, working bandwidths for keeping IL <1.8 dB (CT < -15 dB) are 100 nm, 38 nm, 25 nm, 45 nm, and 24 nm, respectively, for TE₀-to-TE₁, TE₀-to-TE₂, TE₀-to-TE₃, TE₁-to-TE₂, and TE₁-to-TE₃ mode-order converters. With advantages of the universality, scalability, an ultracompact size, and high performance, we believe that the present mode-order converting scheme will find its applications in ultrahigh-density MDM systems and other multimode based technologies.

Funding

National Natural Science Foundation of China (11574046, 12004092); Natural Science Foundation of Jiangsu Province (BK20211163); Scientific Research Foundation of the Graduate School of Southeast University (YBPY2135).

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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Structure	Function	Footprint (µm²)	IL (dB)		CT (dB)		Bandwidth (nm)^c
Structure	Function	Footprint (µm²)	Sim^a	Exp^b	Sim	Exp	Sim	Exp
SEW^d [16]	TE₀-to-TE₁	∼24 × 2	0.013	-	-27.3	-	100 (CT < -20)	-
SEW^d [16]	TE₀-to-TE₂	∼8 × 2	0.026	-	-26.4	-	100 (CT < -23)	-
SEW [17]	TE₀-to-TE₁	5.75 × 1.1	-	< 1	∼ -12	∼ -13	25 (CT < -12)	21 (IL < 1, CT < -10)
	TE₀-to-TE₂	6.736 × 1.4	-	< 0.5	∼ -12.5	∼ -10	20 (CT < -12)	20 (IL < 1, CT < -10)
	TE₀-to-TE₃	8.975 × 1.9	1.316	-	-10.1	-	-	-
Inverse design [22]	TE₀-to-TE₁	2 × 2	<0.6	<2.2	∼ -24	∼ -22	40 (IL<0.6, CT< -20.3)	40 (IL<2.2, CT< -16.2)
	TE₀-to-TE₂	2.5 × 2.5	<1.1	-	∼ -30	-	40 (IL<1.1, CT< -16.8)	-
	TE₀-to-TE₃	3 × 3	<1.8	-	∼ -27	-	40 (IL<1.8, CT< -12.4)	-
Slots [24]	TE₀-to-TE₁	0.88 × 2.3	<0.15	-	<20	-	60 (IL< 0.15, CT< -20)	60 (IL< 0.5, CT< -7)
Slots [24]	TE₀-to-TE₂	1.4 × 2.4	<0.22	-	<20	-	50 (IL< 0.22, CT< -18)	50 (IL< 0.3, CT< -9)
SWG-Meta [31]	TE₀-to-TE₁	8.72 × 1.2	0.092	-	∼ -40 (TE₀)	-	100 (IL < 0.25, CT < -15.33)	-
	TE₀-to-TE₂	4.98 × 1.4	0.061	-	∼ -33 (TE₀)	-	100 (IL < 0.19, CT < -17.36)	-
	TE₀-to-TE₃	14.54 × 2	0.467	-	∼ -18	-	100 (IL < 0.77, CT < -11.48)	-
This work	TE₀-to-TE₁	3.436 × 1.5	0.35	1.27	-34.5	-21.31	200 (IL < 0.8, CT < -15)	100 (IL < 1.8, CT < -15.8)
	TE₀-to-TE₂	4.9 × 2.3	0.28	1.05	-28.6	-19.04	100 (IL < 0.8, CT < -15)	38 (IL < 1.8, CT < -15)
	TE₀-to-TE₃	7.71 × 3	0.45	1.23	-21.39	-17.61	120 (IL < 0.8, CT < -15)	25 (IL < 1.8, CT < -15)
	TE₁-to-TE₂	5.295 × 2.4	0.53	0.73	-25.7	-21.46	200 (IL < 0.8, CT < -15)	45 (IL < 1.8, CT < -17)
	TE₁-to-TE₃	6.883 × 3.6	0.54	1.7	-22.1	-15.86	160 (IL < 0.8, CT < -15)	24 (IL < 1.8, CT < -15)

Structure	Function	Footprint (µm²)	IL (dB)		CT (dB)		Bandwidth (nm)^c
Structure	Function	Footprint (µm²)	Sim^a	Exp^b	Sim	Exp	Sim	Exp
SEW^d [16]	TE₀-to-TE₁	∼24 × 2	0.013	-	-27.3	-	100 (CT < -20)	-
SEW^d [16]	TE₀-to-TE₂	∼8 × 2	0.026	-	-26.4	-	100 (CT < -23)	-
SEW [17]	TE₀-to-TE₁	5.75 × 1.1	-	< 1	∼ -12	∼ -13	25 (CT < -12)	21 (IL < 1, CT < -10)
	TE₀-to-TE₂	6.736 × 1.4	-	< 0.5	∼ -12.5	∼ -10	20 (CT < -12)	20 (IL < 1, CT < -10)
	TE₀-to-TE₃	8.975 × 1.9	1.316	-	-10.1	-	-	-
Inverse design [22]	TE₀-to-TE₁	2 × 2	<0.6	<2.2	∼ -24	∼ -22	40 (IL<0.6, CT< -20.3)	40 (IL<2.2, CT< -16.2)
	TE₀-to-TE₂	2.5 × 2.5	<1.1	-	∼ -30	-	40 (IL<1.1, CT< -16.8)	-
	TE₀-to-TE₃	3 × 3	<1.8	-	∼ -27	-	40 (IL<1.8, CT< -12.4)	-
Slots [24]	TE₀-to-TE₁	0.88 × 2.3	<0.15	-	<20	-	60 (IL< 0.15, CT< -20)	60 (IL< 0.5, CT< -7)
Slots [24]	TE₀-to-TE₂	1.4 × 2.4	<0.22	-	<20	-	50 (IL< 0.22, CT< -18)	50 (IL< 0.3, CT< -9)
SWG-Meta [31]	TE₀-to-TE₁	8.72 × 1.2	0.092	-	∼ -40 (TE₀)	-	100 (IL < 0.25, CT < -15.33)	-
	TE₀-to-TE₂	4.98 × 1.4	0.061	-	∼ -33 (TE₀)	-	100 (IL < 0.19, CT < -17.36)	-
	TE₀-to-TE₃	14.54 × 2	0.467	-	∼ -18	-	100 (IL < 0.77, CT < -11.48)	-
This work	TE₀-to-TE₁	3.436 × 1.5	0.35	1.27	-34.5	-21.31	200 (IL < 0.8, CT < -15)	100 (IL < 1.8, CT < -15.8)
	TE₀-to-TE₂	4.9 × 2.3	0.28	1.05	-28.6	-19.04	100 (IL < 0.8, CT < -15)	38 (IL < 1.8, CT < -15)
	TE₀-to-TE₃	7.71 × 3	0.45	1.23	-21.39	-17.61	120 (IL < 0.8, CT < -15)	25 (IL < 1.8, CT < -15)
	TE₁-to-TE₂	5.295 × 2.4	0.53	0.73	-25.7	-21.46	200 (IL < 0.8, CT < -15)	45 (IL < 1.8, CT < -17)
	TE₁-to-TE₃	6.883 × 3.6	0.54	1.7	-22.1	-15.86	160 (IL < 0.8, CT < -15)	24 (IL < 1.8, CT < -15)

Experimental demonstration of a flexible and high-performance mode-order converter using subwavelength grating metamaterials

Abstract

1. Introduction

2. Design and operating principle

3. Optimization, results and discussions

4. Fabrication and characterization

5. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (6)

Tables (2)

Equations (3)

Optics Express

Fun^a	w_I	w_O	w_d	L_d	L_IT	L_OT	N₀₁	w_s	w₁	L₁	n₁
0-to-1	0.5	0.9	0.22	0	2.125	3.436	14	1.5	0.435	2.41	2
0-to-2	w_I	w_O	w_d	L_d	L_IT	L_OT	N₀₂	w_s	w₁	L₁	n₁
	0.5	1.44	0.316	0	1.875	4.582	18	2.3	0.437	4.2	4
	w₂	L₂	n₂
	0.84	3.22	2
0-to-3	w_I	w_O	w_d	L_d	L_IT	L_OT	N₀₃	w_s	w₁	L₁	n₁
	0.5	1.951	0.6	0.5	2.5	7.71	31	3	0.492	6.892	4
	w₂	L₂	n₂	w₃	L₃	n₃
	0.76	5.07	2	1.2	3.324	2
1-to-2	w_I	w_O	w_d	L_d	L_IT	L_OT	N₁₂	w_s	w₁	L₁	n₁
	0.904	1.43	0	0.7	2.175	4.575	18	2.4	0.521	4.395	5
	w₂	L₂	n₂
	0.728	2.95	4
1-to-3	w_I	w_O	w_d	L_d	L_IT	L_OT	N₁₃	w_s	w₁	L₁	n₁
	0.9	2	0	0.365	2.98	6.375	26	3.6	0.272	6.197	4
	w₂	L₂	n₂	w₃	L₃	n₃
	1	5.783	6	1.471	4.3	6
2-to-5	w_I	w_O	w_d	L_d	L_IT	L_OT	N₂₅	w_s	w₁	L₁	n₁
	1.43	3.061	0	1.388	4.5	9.625	39	4.9	0.247	9.175	4
	w₂	L₂	n₂	w₃	L₃	n₃	w₄	L₄	n₄	w₅	L₅
	0.6	10.3	2	0.9	7.8	3	1.524	9.97	7	2.5	2.5
	n₅
	1