Open Access
Add to BibSonomy
Abstract
An efficient, dual-polarization silicon waveguide array with low insertion losses and negligible crosstalks for both TE and TM polarizations has been reported using S-shaped adiabatically bent waveguides. Simulation results for a single S-shaped bend show an insertion loss (IL) of ≤ 0.03 dB and ≤ 0.1 dB for the TE and TM polarizations, respectively, and TE and TM crosstalk values in the first neighboring waveguides at either side of the input waveguide are lower than −39 dB and −24 dB, respectively, over the wavelength range of 1.24 µm to 1.38 µm. The bent waveguide arrays exhibit a measured average TE IL of ≈ 0.1 dB, measured TE crosstalks in the first neighboring waveguides are ≤ −35 dB, at the 1310 nm communication wavelength. The proposed bent array can be made by using multiple cascaded S-shaped bends to transmit signals to all optical components in integrated chips.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Silicon photonics has made substantial progress in developing efficient and large-scale circuit integration for data processing, sensing, and communication. Photonic integrated circuits demand dense merging of photonic devices with high performance, large bandwidth (BW), and negligible crosstalk interconnects [1]. To overcome the inter-connect bottleneck and increase the bandwidth, different techniques have evolved such as the optical phase array [2], arrayed waveguide grating [3], adiabatic elimination procedure [4], space division multiplexing [5], metamaterials [6], and clocking technique [7]. Furthermore, waveguide arrays have been demonstrated on various wafers, such as InP waveguides [8], silicon nitride waveguides (WGs) [9], polymer WGs [10], and Silicon-on-insulator (SOI) waveguides [11]. The SOI platform leads to extremely area-efficient integrated chips due to a high refractive index contrast and, consequently, sharply bent waveguides. Waveguide superlattices on the SOI platform have already been proposed in previous studies [12–16]. In [13], a familiar theory of asymmetric directional coupling has been employed to suppress crosstalk, where light in straight waveguide arrays is not transported to the neighboring waveguides due to a phase-mismatch between the light modes propagating in the closely placed WGs. The needed phase mismatch was achieved by selecting waveguides of slightly dissimilar widths, indicating a −20 dB crosstalk over a 80 nm bandwidth. Moreover, bent waveguide superlattices have already been described in [14]. A similar approach using different widths of the neighboring waveguides was applied to achieve an enhanced phase mismatch. In such designs, strict fabrication control is highly desirable to confirm reasonable crosstalk suppression. However, these expected fabrication deficiencies do not degrade the efficiency of our waveguide superlattices because we obtained a phase mismatch by varying the radii of the neighboring waveguides. In [17,18], authors report waveguide arrays with fixed waveguide widths, where the key to reducing crosstalk between waveguides lies in the sinusoidal bends used. Moreover, in [16], a large number of neighboring channels was realized, where the phase mismatch was obtained by using varying bending radii and making the waveguide widths similar. Nevertheless, the selected curves in these waveguide superlattices are constant-radius bends, leading to the disadvantage of high insertion loss (IL). This elevated IL comes from mode discontinuity at the junctions of the curvatures with opposite signs. To avoid the scattering of light at these junctions, the authors picked a minimum bending radius of $\geq$ 5 µm. However, a radius of $\approx$ 1 µm with insignificant junction loss is highly essential for current dense integrated circuits. Note that all these bent and straight WG superlattices are optimized for a single polarization (transverse electric). However, integrated silicon devices are developed for both transverse electric (TE) [19] and transverse magnetic (TM) [20–22] modes for many applications. Dual-polarization straight waveguide superlattices have been presented in [15,23]. In [15], authors report an $\approx$ −18 dB over a 30 nm wavelength range for both TE and TM modes. However, dual polarization bent waveguide arrays have not been reported yet. We propose TE- and TM-mode adiabatically bent waveguide arrays on the SOI platform. Such adiabatic bends introduce a curvature that linearly changes with waveguide length, exhibiting no scattering of light at the junctions [19,24–28]. Furthermore, the propagating modes in such bent sections do not see mode distortion because they can be slowly transformed, and therefore result in no intermodal crosstalk. We use similar bends in the present design and extend our previous work [29] to demonstrate dense waveguide arrays with a minimum radius of 1.5 µm for the TE polarized light and 3 µm for the TM polarized light. Although the present design is optimized for an SOI platform in the O band, with a judicious choice of materials, this technique can be extended further to larger wavelengths in the infrared, for which there are many applications in medicine, environmental control, security, and industrial quality control in need for new device functionalities [30–36].
This is the first report of a high-density integration of bent silicon waveguides that works effectively for both TE and TM polarizations. The proposed waveguide array (waveguide superlattice) exhibits the following traits: 1) negligible IL, 2) ultra-low crosstalk, 3) area-efficient, 4) works for dual polarization 5) broadband, and 6) can also be implemented as a configuration of multiple cascaded S-shaped bends to carry signals to all optical components in the integrated chips. Most importantly, this design can be fabricated with the conventional CMOS process in present silicon foundries. A comparison of this work with previously reported designs is presented in Table 1.
Table 1. Performance Comparison with the Literature
- • In a nutshell, the main goal of this paper is to enhance the performance of a bent waveguide array, which can effectively guide both TE and TM modes. In contrast, a prior publication [29] demonstrated a bent waveguide array that only guides TE mode, and there is currently no existing literature reporting on bent waveguide arrays that support both TE and TM modes.
- • This paper suggests that the bent array can be constructed by arranging multiple S-shaped bends in a cascade configuration to transmit signals to all optical components in the integrated chips. Notably, Ref. [29] lacks information about the cascaded bends.
- • Here, a comprehensive numerical analysis is presented to examine the coupling coefficients as a function of the waveguide gap. The results indicate that waveguide gaps of less than 300 nm and 500 nm are optimal for the TE and TM modes, respectively.
- • The bent waveguide design incorporates adiabatic transition for gradual curvature change, achieving minimum radii of 1.5 µm for TE mode and 3 µm for TM mode, reducing footprint for integrated circuits, and further differs from Ref. [29] by including information on the TM mode.
2. Design, results, and discussion
The schematic diagram of the dual-polarization waveguide superlattices is shown in Fig. 1(a). The fundamental goal of the proposed array is to acquire enhanced crosstalk suppression in the neighboring channels. Its working principle depends on the condition of phase-mismatch, i. e. the effective index of the mode in one WG is unlike the effective index of the mode in the neighboring waveguides. An enhanced phase mismatch leads to a significant crosstalk suppression for optimal performance. We acquire a phase mismatch by making the radii of the neighboring bent waveguides different. Additionally, we introduce a change in curvature with the waveguide length of each individual waveguide in an array, further leading to an enhanced phase mismatch. Furthermore, sharp bends with negligible leakage of light are of immense need to avoid additional crosstalk. This crosstalk can be more significant in densely-packed waveguide superlattices. To avoid this undesired leakage, a minimum bend radius of 5 µm is utilized in [14,16]. However, smaller radii bend are highly desirable, and bends with a radius of $\geq$ 5 µm are not practicable for modern dense integrated circuits. We utilize adiabatic bends with $R_{min}$ = 1.5 µm for the TE mode, and $R_{min}$ = 3 µm for the TM mode to overcome this obstacle. A schematic of the 7-channel waveguide array with $R_{min}$ = 1.5 µm, a constant WG width of 500 nm, and a channel gap of 300 nm, is shown in Fig. 1(a). Waveguide gaps of 300 nm and 500 nm are designed for the TE and TM modes, respectively. The cross-section of Fig. 1(b) depicts that the waveguide thickness in the present design is 220 nm, on the SOI platform with a 2 µm-thick buried oxide. In a two-waveguide coupler, the coupling of light from the input straight WG to the neighboring straight WG is given by the following equation: $\frac {P_{1\rightarrow 2}}{P_1}$ =$\frac {1}{(\frac {\Delta \beta }{2 \kappa })^2+1} \sin ^2 \left (L \sqrt {(\frac {\Delta \beta }{2})^2 + \kappa ^2 } \right )$, Where $\kappa$ and L are the coupling coefficient and the propagation distance, respectively. It is clear from the above equation that the maximum crosstalk occurs when max($\frac {P_{1\rightarrow 2}}{P_1}$) = 1/[$({\Delta \beta /2 \kappa )}^2+1$], $\Delta \beta$ is phase mismatch i.e. the difference in propagation constant. An enhanced crosstalk suppression is obtained if the condition $\Delta \beta > > \kappa$ is satisfied. For a large number of closely placed waveguides, the above Eq. 1 of the two-waveguide coupler cannot be applied. The cross-coupling in such dense integrated waveguides is studied in detail in Ref. [12]. We calculate the phase-mismatch for the TE and TM modes by simulating a two-waveguide bent coupler, using the Lumerical Finite Difference Eigenmode Solver [37]. The selected parameters of this coupler have a waveguides width and gap of 500 nm and 300 nm, respectively, at the communication wavelength of 1310 nm. We explain the coupling between the two bent waveguides by supermode theory. The two supermodes (for both TE and TM) in the bent coupler are shown in Fig. 1(d, e, g, h). The effective indices of these supermodes, $n_{eff-outer}$ and $n_{eff-inner}$, are calculated as a function of radius and are plotted for TE and TM supermodes in Fig. 1(c) and Fig. 1(f), respectively. The effective index is described as the ratio of the speed of light in free space (c) and the phase velocity of the waveguide ($\omega$/$\beta$). i.e. $n_{eff}$ = c$\beta$/$\omega$, and phase mismatch $\Delta \beta$ = ($\omega$/c)($n_{eff-outer}$-$n_{eff-inner}$). To validate negligible crosstalk, the difference in calculated effective indices, $\Delta _{neff}$ (phase mismatch) must be larger than 0.1. It is evident from Fig. 1(c) that the difference is $\geq$ 0.1 for R$\leq$ 23 µm for the TE supermode, and is fairly larger at the smaller radii. Likewise, a $\Delta _{neff}$ $\geq$ 0.1 is calculated for R$\leq$ 18 µm for the TM polarization. Hence, the chosen curves with $R_{min}$ = 1.5 µm for the TE mode and $R_{min}$ = 3 µm for the TM mode permit a large number of channels. Additionally, the supermode profiles confirm no mode overlap and absolute confinement of both modes in one individual waveguide is clearly observed from the profiles of Fig. 1(d), (e) and Fig. 1(g), (h).
Fig. 1. Schematic drawing of the 7-channel S-shaped adiabatic bend waveguide array: (a) 3D view, (b) cross-sectional view, (c) Calculated effective indices ($n_{eff-outer}$ and $n_{eff-inner}$) of TE supermodes, as a function of radius, at the communication wavelength of 1310 nm. (d, e) Profiles of both TE supermodes at a 4 µm radius, with a constant waveguide width and gap of 500 nm and 300 nm, respectively. (f) Calculated effective indices of TM supermodes, (g, h) Profiles of both TM supermodes at a radius of 5 µm, with a constant waveguide width and gap of 500 nm and 300 nm, respectively.
In addition, calculations were performed to determine the coupling coefficients for both fundamental modes as a function of bend radius and coupling gap, as shown in Fig. 2. The analysis was done for a two-waveguide bent coupler with a fixed $90^o$ bend angle. The coefficients of coupling were computed for a wavelength of 1310 nm. The calculated values of $\kappa$ for the fundamental TE mode are shown in Fig. 2(a), revealing extremely weak coupling for waveguide gaps of $\geq$ 200 nm. Additionally, a minor variation in $\kappa$ is demonstrated as the radius transitions from 1 µm to 5 µm. It is also evident from the plot shown in Fig. 1(c) that the radii falling within this range result in a significant phase mismatch, which effectively eliminates any interference between signals (i.e., crosstalk). Moreover, the TM mode is found to have an optimal minimum coupling strength for all bending radii when the waveguide gap is greater than or equal to 400 nm, as shown in Fig. 2(b). Consequently, to achieve negligible crosstalks, the waveguide gaps for the TE and TM modes were selected as 300 nm and 500 nm, respectively.
Fig. 2. Maps of coupling coefficients ($\kappa$) as a function of waveguide gap and bend radius, calculated for a two-waveguide bent coupler with a fixed bend angle of $90^o$ at the central wavelength of 1310 nm: (a) TE mode, (b) TM mode.
The dual-polarization waveguide superlattices are investigated using the Lumerical package [37], with the 3D finite-difference time-domain method (FDTD) simulations. The transmissions at the output of all channels are calculated after sending TE and TM modes at the input of each channel, over a wavelength range of 1.24 µm to 1.38 µm. The power loss at the output of the channel with input light is referred to as the insertion loss (IL). However, the power reaching the output of the neighboring channels is defined as crosstalk. Mathematically, it is illustrated by the following equations.
where $P_{nn}$ is the power delivered to the nth output port when light is launched to the corresponding nth input port, and $P_{nm}$ are the transferred powers from the input n channel to the m output ports (m indicate neighboring waveguides with m = n${\pm }$1, n${\pm }2\cdots$.). To rephrase, $P_{nm}$ is an overlap integral with the propagating modes of the individual waveguide. Having analyzed the effective index calculations, we now turn our attention to calculating the insertion loss and crosstalk in a 7-channel WG array. We select the sharply bent waveguides that are defined with two different angles of $\theta = 45^{\circ }$ and $\theta = 60^{\circ }$. The mode propagation (electric field) through central waveguide number 4 is depicted in Fig. 3. Figure 3(a) depicts TE light propagation through a middle waveguide of an array with $R_{min}$ = 1.5 µm, $\theta = 60^{\circ }$, and a channel gap of 300 nm. TM mode transmission through a middle waveguide of an array with $\theta = 60^{\circ }$, $R_{min}$ = 3 µm and channel gap of 500 nm is shown in Fig. 3(b). It is clearly observed that the light is effectively and tightly confined in the input waveguide, with no power transfer into the adjacent waveguides. Furthermore, the footprints of 9 µm $\times$ 10 µm and 14 µm $\times$ 15 µm are well compatible with the advanced and densely-packed photonic devices. The transmitted powers at each output port are calculated over the entire wavelength range of 1.24 µm to 1.38 µm, as shown in Fig. 4. The 7-channel adiabatic bends designed with $\theta = 45^{\circ }$ and $\theta = 60^{\circ }$ are investigated, with minimum radii of $R_{min}$ = 1.5 µm and $R_{min}$ = 3 µm for the TE and TM modes, respectively. Additionally, waveguide gaps of 300 nm and 500 nm are considered for the TE and TM modes, respectively. The TE mode transmission depicted in Fig. 4(a) and Fig. 4(b) with $\theta = 45^{\circ }$ and $\theta = 60^{\circ }$, respectively, indicates an IL of $\leq$ 0.03 dB over an entire wavelength range. Moreover, exceptionally low crosstalk values, which are $\leq$ −37 dB for bend angle $\theta = 45^{\circ }$, are observed in the first neighboring waveguides (m=n${\pm }$1), at the communication wavelength of 1310 nm. This cross-talk in the first neighboring waveguides can be further reduced to below −50 dB when the bends are implemented with $\theta = 60^{\circ }$ (Fig. 4(b)). Moreover, the crosstalk values in the second and third nearest neighbors are $\leq$ −55 dB, over the entire wavelength range of 1240 nm to 1380 nm. Similarly, Fig. 4(c) and Fig. 4(d) plot the transmissions of the TM mode with $\theta = 45^{\circ }$ and $\theta = 60^{\circ }$, respectively. These Figures indicate an IL of $\leq$ 0.1 dB over the whole wavelength range for both angles. The crosstalks are $\leq$ −21 dB and $\leq$ −24 dB in the first neighboring waveguides over the entire wavelength range, with $\theta = 45^{\circ }$ and $\theta = 60^{\circ }$, respectively. Extremely low crosstalks of $\leq$ −35 dB are observed for a $\theta = 60^{\circ }$ bend angle, at the central wavelength of 1310 nm. Both bend angles show negligible crosstalks in the second and third neighboring waveguides. It is evident from Fig. 4 that a high-performance and broadband WG array has been implemented successfully. Although the optimized parameters for TE and TM modes are $R_{min}$ = 1.5 µm (300 nm WG gap) and $R_{min}$ = 3 µm (500 nm WG gap) respectively, it is worth noting that the TE mode propagates equally and effectively in both cases of Rmin (1.5 µm and 3 µm). A larger radius is required for the TM mode due to its reduced confinement within the waveguide. In contrast, the TE mode, being well confined, propagates with negligible loss through all waveguides with radii greater than or equal to 1.5 µm. Therefore, the design utilizing $R_{min}$ = 3 µm effectively accommodates both TE and TM modes.Fig. 3. Electric field profiles for the fundamental modes: (a) top view of TE mode propagation through a middle WG number 4 in a bent array of $R_{min}$ = 1.5 µm, a waveguide separation of 300 nm $\theta = 60^{\circ }$ for the TE mode, (b) top view of TM mode propagation through a middle WG number 4 in a bent array of $R_{min}$ = 3 µm, waveguide gap = 500 nm, and $\theta = 60^{\circ }$ for the TM mode. The footprints (FP) are written on each panel.
Fig. 4. Spectral transmissions for a single S-shaped 7-channel WG superlattice. (a, b) TE transmission with an array of $R_{min}$ = 1.5 µm and WG gap=300 nm: (a) $\theta = 45^{\circ }$, (b) $\theta = 60^{\circ }$. (c, d) TM transmission with an array of $R_{min}$ = 3 µm and WG gap=500 nm: (c) $\theta = 45^{\circ }$, (d) $\theta = 60^{\circ }$.
Thus far, we have discussed a waveguide array that is made of one S-shaped bend and neatly serves in the region where the waveguides are bent. However, in order to carry signals to optical components that are located far away from the bends, a configuration of multiple cascaded S-shaped bends can be used instead of straight waveguides. Straight waveguides require different widths of the neighboring channels to obtain different propagation constants, ultimately demanding strict fabrication control. However, we obtain a propagation constant difference in the neighboring bent channels with different bending radii. In this case, the most important task is to shrink the footprint while spanning the cascaded S bends from the edge couplers to the on-chip devices. The present waveguide array can be optimized for all bend angles. The bend with $\theta = 30^{\circ }$ is a good alternative and will result in a compact footprint that is compatible with current close-packed integrated circuits. Figure 5(a) depicts a 3D view of the 7-channel waveguide superlattices with n number of cascaded S-shaped bends. We calculated the electric field distributions and spectral transmissions of the TE and TM modes through 7-channel waveguide superlattices with 10 cascaded S-shaped bends. The analysis was done with input light at channel number four. The top views of both mode propagations (electric fields), for two angles $\theta = 30^{\circ }$ and $\theta = 60^{\circ }$, are depicted in Fig. 5(b-e). Figure 5(b), and Fig. 5(d) depict TE light propagation through a middle waveguide of 10 cascaded S bends, with $R_{min}$ = 1.5 µm, and a channel gap of 300 nm, for $\theta = 60^{\circ }$ and $\theta = 30^{\circ }$, respectively. TM mode transmissions through a middle waveguide with $R_{min}$ = 3 µm, and a channel gap of 500 nm are shown in Fig. 5(c) and Fig. 5(e), for $\theta = 60^{\circ }$ and $\theta = 30^{\circ }$, respectively. It is clearly noted that the light is effectively and firmly confined in the input waveguide with no power transfer into the adjacent waveguides. The footprints of all four variations in Fig. 5(b)-(e) are written on each panel, confirming that the bends implemented with $\theta = 30^{\circ }$ are well compatible with the advanced and densely-packed photonic devices. The spectral transmissions through these four variations are calculated with input light at channel number 4. The curves shown in Figs. 5(f-i) indicate the transmissions at all output channels. Figure 5(f) and Fig. 5(g) show the TE spectral transmissions for $\theta = 60^{\circ }$ and $\theta = 30^{\circ }$, respectively. Similarly, the TM spectral transmissions are shown in Fig. 5(h) and Fig. 5(i) for $\theta = 60^{\circ }$ and $\theta = 30^{\circ }$, respectively. All four panels (Figs. 5(f)-(i)) indicate that the insertion losses are negligible over the wavelength range of 1260 nm to 1360 nm. As far as crosstalks are concerned, the second and third nearest neighbors exhibit extremely low values as expected. Moreover, the coupling losses in the first nearest neighbors are less than 20 dB and 30 dB, for the TM and TE modes, respectively, over the entire wavelength range. As a result, the proposed multiple cascaded S-shaped bent array is ultra-low loss and efficient and can carry signals to all optical components in the integrated chips.
Fig. 5. (a) 3D view of a 7-channel waveguide array with n cascaded S bends. (b-e) Top view of light propagation (electric fields) through a middle WG number 4. The footprints (FP) are written on each panel: (b) $\theta = 60^{\circ }$, TE mode, (c) $\theta = 60^{\circ }$, TM mode, (d) $\theta = 30^{\circ }$, TE mode, (e)$\theta = 30^{\circ }$, TM mode, (f-i) Spectral transmissions through 7-channel WG superlattices with 10 cascaded S bends, and the light is launched into WG number four: (f) $\theta = 60^{\circ }$, TE mode, (g) $\theta = 30^{\circ }$, TE mode, (h) $\theta = 60^{\circ }$, TM mode, (i) $\theta = 30^{\circ }$, TM mode.
3. Fabrication and measurements
The practicality and efficiency of the proposed WG superlattices are confirmed by fabricating a waveguide array with channel widths of $W$ = 500 nm, $\theta$=$60^{\circ }$ $R_{min}$ = 1.5 µm, and WG gaps of 500 nm. An array with $R_{min}$ = 3 µm was not fabricated in the first fabrication run, which is why TM measurements are not carried out (a $R_{min}$ = 1.5 µm bend is too sharp for the TM mode). The 220 nm-thick waveguides were fabricated using electron-beam lithography on a SOI platform with a 2 µm-thick buried oxide. The cross-sectional view (SEM image) and top view (optical image) are represented in Fig. 6(a) and Fig. 6(d), respectively. The TE mode from a tunable laser (1.24 µm to 1.38 µm) was edge-coupled into the silicon chip. The transmitted power was measured at the output using an InGaAs photodetector. In order to obtain a reliable measurement of the insertion loss, we fabricated test structures consisting of $16$ cascaded devices. This approach aids in reducing measurement errors resulting from fiber misalignment and the potential unreliability of the experimental setup. By comparing the transmission through these $16$ cascaded devices to the transmission through a reference straight waveguide, we subtracted the input/output coupling loss from the measurement. The transmissions through the reference straight waveguide and 16 cascaded S bends are shown in Fig. 6(c) (refer to the inset on the right-hand side). The total length of the 16 cascaded S bends is 144 µm. It is evident that both curves overlap, indicating negligible insertion loss for the 16 cascaded S bends. The normalized insertion loss is represented by the green curve in Fig. 6(c) (the enlarged view is also displayed in the inset on the left-hand side), demonstrating an extremely small IL (approximately 0.1 dB) at the communication wavelength of 1310 nm. Additionally, the enlarged views of the IL in the insets of Fig. 6(b) and Fig. 6(c) confirm the excellent agreement between the calculated and measured insertion loss.
Fig. 6. (a) cross-sectional view (SEM image) of a 7-channel waveguide array. (b, c) TE transmission spectra calculated/measured for $\theta = 60^{\circ }$, with waveguides width and gap of 500 nm, and minimum radius of curvature is 1.5 µm. The crosstalks are measured at two adjacent ports at both sides of the fourth port: (b) calculated, (c) measured, (d) top view (optical image).
The normalized crosstalks in the first neighboring waveguides are below −35 dB, covering the entire wavelength range. The calculated and measured transmissions through the adjacent ports in Fig. 6(b) and Fig. 6(c) confirm negligible coupling of the light, leading to ultra-low crosstalks. We ascribe the variations between calculated and measured results to alteration in the waveguide dimensions during fabrication.
4. Conclusion
This work is the first report of adiabatically bent waveguide superlattices on the SOI platform, leading to a negligible IL for both fundamental TE and TM modes. This approach further verifies extremely low crosstalks in the neighboring waveguides. The footprints of the waveguide arrays are well-compatible with advanced and densely packed integrated circuits. TE mode measurements of the fabricated waveguide superlattices manifest the practicality of the suggested idea. Furthermore, this bent array can also be implemented as a configuration of low-loss multiple cascaded S-shaped bends to carry signals to all optical components.
Funding
Khalifa University of Science, Technology and Research (CIRA-2021-108, FSU-2021-023); Horizon 2020 Framework Programme (101021857, (Odysseus)).
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the findings of this study are available from the corresponding author.
References
1. N. Margalit, C. Xiang, S. M. Bowers, A. Bjorlin, R. Blum, and J. E. Bowers, “Perspective on the future of silicon photonics and electronics,” Appl. Phys. Lett. 118(22), 220501 (2021). [CrossRef]
2. D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1× 12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011). [CrossRef]
3. P. Cheben, J. Schmid, A. Delâge, A. Densmore, S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Waldron, and D.-X. Xu, “A high-resolution silicon-on-insulator arrayed waveguide grating microspectrometer with sub-micrometer aperture waveguides,” Opt. Express 15(5), 2299–2306 (2007). [CrossRef]
4. M. Mrejen, H. Suchowski, T. Hatakeyama, C. Wu, L. Feng, K. O’Brien, Y. Wang, and X. Zhang, “Adiabatic elimination-based coupling control in densely packed subwavelength waveguides,” Nat. Commun. 6(1), 7565 (2015). [CrossRef]
5. E. Ip, G. Milione, M.-J. Li, N. Cvijetic, K. Kanonakis, J. Stone, G. Peng, X. Prieto, C. Montero, V. Moreno, and J. Li nares, “SDM transmission of real-time 10GbE traffic using commercial SFP+ transceivers over 0.5 km elliptical-core few-mode fiber,” Opt. Express 23(13), 17120–17126 (2015). [CrossRef]
6. S. Jahani, S. Kim, J. Atkinson, J. C. WJuan Villegasirth, F. Kalhor, A. A. Noman, W. D. Newman, P. Shekhar, K. Han, V. Van, R. G. DeCorby, L. Chrostowski, M. Qi, and Z. Jacob, “Controlling evanescent waves using silicon photonic all-dielectric metamaterials for dense integration,” Nat. Commun. 9(1), 1893 (2018). [CrossRef]
7. B. Shen, R. Polson, and R. Menon, “Increasing the density of passive photonic-integrated circuits via nanophotonic cloaking,” Nat. Commun. 7(1), 13126 (2016). [CrossRef]
8. P. Pan, J. An, J. Zhang, Y. Wang, H. Wang, L. Wang, X. Yin, Y. Wu, J. Li, Q. Han, and X. Hu, “Flat-top AWG based on InP deep ridge waveguide,” Opt. Commun. 355, 376–381 (2015). [CrossRef]
9. Q. Han, M. Ménard, and W. Shi, “Superlattice arrayed waveguide grating in silicon nitride,” IEEE Photonics Technol. Lett. 32(22), 1411–1414 (2020). [CrossRef]
10. B. Yang, Y. Zhu, Y. Jiao, L. Yang, Z. Sheng, S. He, and D. Dai, “Compact arrayed waveguide grating devices based on small SU-8 strip waveguides,” J. Lightwave Technol. 29(13), 2009–2014 (2011). [CrossRef]
11. Y. Onawa, H. Okayama, D. Shimura, H. Takahashi, H. Yaegashi, and H. Sasaki, “Polarisation insensitive wavelength de-multiplexer using arrayed waveguide grating and polarisation rotator/splitter,” Electron. Lett. 55(8), 475–476 (2019). [CrossRef]
12. N. Yang, H. Yang, H. Hu, R. Zhu, S. Chen, H. Zhang, and W. Jiang, “Theory of high-density low-cross-talk waveguide superlattices,” Photonics Res. 4(6), 233–239 (2016). [CrossRef]
13. W. Song, R. Gatdula, S. Abbaslou, M. Lu, A. Stein, W. Y. Lai, J. Provine, R. F. W. Pease, D. N. Christodoulides, and W. Jiang, “High-density waveguide superlattices with low crosstalk,” Nat. Commun. 6(1), 7027 (2015). [CrossRef]
14. R. Gatdula, S. Abbaslou, M. Lu, A. Stein, and W. Jiang, “Guiding light in bent waveguide superlattices with low crosstalk,” Optica 6(5), 585–591 (2019). [CrossRef]
15. Y. Xie, Y. Yin, M. Zhang, L. Liu, Y. Shi, and D. Dai, “Ultra-dense dual-polarization waveguide superlattices on silicon,” Opt. Express 28(18), 26774–26782 (2020). [CrossRef]
16. H. Xu and Y. Shi, “Ultra-broadband 16-channel mode division (de) multiplexer utilizing densely packed bent waveguide arrays,” Opt. Lett. 41(20), 4815–4818 (2016). [CrossRef]
17. X. Yi, H. Zeng, S. Gao, and C. Qiu, “Design of an ultra-compact low-crosstalk sinusoidal silicon waveguide array for optical phased array,” Opt. Express 28(25), 37505–37513 (2020). [CrossRef]
18. X. Yi, Y. Zhang, H. Zeng, S. Zeng, S. Guo, and C. Qiu, “Demonstration of an Ultra-compact 8-channel sinusoidal silicon waveguide array for optical phased array,” Opt. Lett. 47(2), 226–229 (2022). [CrossRef]
19. H. Zafar, Y. Zhai, J. E. Villegas, F. Ravaux, K. L. Kennedy, M. F. Pereira, M. Rasras, A. Shamim, and D. H. Anjum, “Compact broadband (O, E, S, C, L & U bands) silicon TE-pass polarizer based on ridge waveguide adiabatic S-bends,” Opt. Express 30(6), 10087–10095 (2022). [CrossRef]
20. A. P. Jacob, V. Dahlem, S. Marcus, H. Zafar, A. Khilo, and S. Chandran, “Slot assisted grating based transverse magnetic (TM) transmission mode pass polarizer,” (2020). US Patent 10,557,989.
21. H. Zafar, M. Odeh, A. Khilo, and M. S. Dahlem, “Low-loss broadband silicon TM-pass polarizer based on periodically structured waveguides,” IEEE Photonics Technol. Lett. 32(17), 1029–1032 (2020). [CrossRef]
22. H. Zafar, M. Odeh, A. Khilo, and M. S. Dahlem, “Broadband silicon TM-pass polarizer using a slot-assisted periodic waveguide,” in 2019 IEEE Photonics Conference (IPC), (IEEE, 2019), pp. 1–2.
23. S. Zhao, J. Chen, and Y. Shi, “Dual polarization and bi-directional silicon-photonic optical phased array with large scanning range,” IEEE Photonics J. 14(2), 1–5 (2022). [CrossRef]
24. H. Zafar, P. Moreira, A. M. Taha, B. Paredes, M. S. Dahlem, and A. Khilo, “Compact silicon TE-pass polarizer using adiabatically-bent fully-etched waveguides,” Opt. Express 26(24), 31850–31860 (2018). [CrossRef]
25. H. Zafar, R. Flores, R. Janeiro, A. Khilo, M. S. Dahlem, and J. Viegas, “High-extinction ratio polarization splitter based on an asymmetric directional coupler and on-chip polarizers on a silicon photonics platform,” Opt. Express 28(15), 22899–22907 (2020). [CrossRef]
26. H. Zafar, M. F. Pereira, K. L. Kennedy, and D. H. Anjum, “Fabrication-tolerant and CMOS-compatible polarization splitter and rotator based on a compact bent-tapered directional coupler,” AIP Adv. 10(12), 125214 (2020). [CrossRef]
27. A. P. Jacob, V. Dahlem, S. Marcus, H. Zafar, A. Khilo, and S. Chandran, “Waveguide structures,” (2021). US Patent 11,061,186.
28. B. Paredes, H. Zafar, M. S. Dahlem, and A. Khilo, “Silicon photonic TE polarizer using adiabatic waveguide bends,” in 2016 21st OptoElectronics and Communications Conference (OECC) held jointly with 2016 international conference on Photonics in Switching (PS), (IEEE, 2016), pp. 1–3.
29. H. Zafar, B. Paredes, I. Taha, J. E. Villegas, M. Rasras, and M. F. Pereira, “Compact and broadband adiabatically bent superlattice-waveguides with negligible insertion loss and ultra-low crosstalk,” IEEE Journal of Selected Topics in Quantum Electronics (2023).
30. M. F. Pereira and O. Shulika, Terahertz and mid infrared radiation: generation, detection and applications (Springer, 2011).
31. M. F. Pereira and O. Shulika, Terahertz and mid infrared radiation: detection of explosives and CBRN (using terahertz) (Springer, 2014).
32. S. Dhillon, M. Vitiello, E. Linfield, et al., “The 2017 terahertz science and technology roadmap,” J. Phys. D: Appl. Phys. 50(4), 043001 (2017). [CrossRef]
33. A. Apostolakis and M. F. Pereira, “Controlling the harmonic conversion efficiency in semiconductor superlattices by interface roughness design,” AIP Adv. 9(1), 015022 (2019). [CrossRef]
34. M. F. Pereira, V. Anfertev, Y. Shevchenko, and V. Vaks, “Giant controllable gigahertz to terahertz nonlinearities in superlattices,” Sci. Rep. 10(1), 15950 (2020). [CrossRef]
35. M. F. Pereira, “Harmonic Generation in Biased Semiconductor Superlattices,” Nanomaterials 12(9), 1504 (2022). [CrossRef]
36. V. Vaks, V. Anfertev, M. Chernyaeva, E. Domracheva, A. Yablokov, A. Maslennikova, A. Zhelesnyak, A. Baranov, Y. Schevchenko, and M. F. Pereira, “Sensing nitriles with THz spectroscopy of urine vapours from cancers patients subject to chemotherapy,” Sci. Rep. 12(1), 18117 (2022). [CrossRef]
