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Abstract
We present chirped anti-symmetric multimode nanobeams (CAMNs) based on silicon-on-insulator platforms, and describe their applications as broadband, compact, reflection-less, and fabrication-tolerant TM-pass polarizers and polarization beam splitters (PBSs). The anti-symmetric structural perturbations of a CAMN ensure that only contradirectional coupling between symmetric and anti-symmetric modes is possible, which can be exploited to block the unwanted back reflection of the device. The new possibility of introducing a large chirp on an ultra-short nanobeam-based device to overcome the operation bandwidth limitation due to the coupling coefficient saturation effect is also shown. The simulation results show that an ultra-compact CAMN with a length of ∼4.68 um can be used to develop a TM-pass polarizer or a PBS with an ultra-broad 20 dB extinction ratio (ER) bandwidth of >300 nm and an average insertion loss of <1.3 dB. The CAMN-based polarizer and PBS were fabricated and experimentally characterized in a wavelength range from 1507 to 1575 nm. The measured ERs were >20 dB over the entire tested wavelength range and the average insertion losses were <0.5 dB for both devices. The mean reflection suppression ratio of the polarizer was ∼26.4 dB. Large fabrication tolerances of ±60 nm in the waveguide widths of the devices were also demonstrated.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Waveguide Bragg gratings are key building blocks in various silicon photonic integrated circuits (PICs) [1], and are used for various applications such as filters [2,3], signal processing [4,5], sensors [6,7], and mode and polarization handling [8–11]. There are generally three main forms of Bragg gratings developed on silicon-on-insulator (SOI) platforms: sidewall-modulated waveguide gratings [2,12], cladding-modulated waveguide gratings [13], and nanobeam waveguides [14,15], which are essentially 1D photonic crystal waveguides with periodical nanoholes [as shown in Fig. 1(a)]. Compared with the other two types of gratings, nanobeams due to their much larger coupling coefficients can offer much broader bandwidths in ultra-small lengths (<10 um), and thus are more suitable for applications where a broad operation bandwidth or wavelength insensitivity of the device is required, such as ultra-broadband filters [15,16] , reflectors [17], and mode and polarization handling [11,18].
Fig. 1. (a) 3D schematic illustration of a traditional SOI-based nanobeam structure. (b) Reflection spectrum of the nanobeam with respect to the nanohole diameters ($d$); for the simulated nanobeam, the wavegudie width is 0.5 um, the waveguide thickness is 0.22 um, and the total period number is 10.
In the area of polarization handling, nanobeams can be used to implement integrated-optics polarizers and polarization beam splitters (PBSs), which are key devices in polarization diversity and polarization multiplexing systems [19]. The principle is to design a nanobeam waveguide for which the photonic bandgap (i.e., the reflection band) for one polarization covers the operation band, while that for the other one is far away from the operation band or is eliminated. By this way, the nanobeam waveguide can reflect one polarization mode while allowing the other one to pass through it as a Bloch mode, which can be exploited to achieve polarizers or PBSs. In addition to nanobeams, other common components that have been used for polarization handling include specially designed waveguides [20–22], hybrid plasmonic/graphene structures [23–25], multimode interference (MMI) couplers [26,27], and asymmetric directional couplers (DCs) [28–32]. Compared with those methods, the nanobeam-based ones offer competitive overall performances with remarkable features of broad bandwidth (generally $>200$ nm), ultra-small size (typically shorter than 10 um), low insertion loss, high extinction ratio, and easy of fabrication [11,14,15,18].
The operational bandwidth of a nanobeam-based device, including polarizers and PBSs focused on in this study, is generally determined by its reflection bandwidth. In theory, using larger nanoholes of a nanobeam should always result in a higher coupling coefficient and thus a wider reflection band. Practically, however, this is only true for nanobeams with small- and moderate-sized nanoholes, but for large-sized nanoholes, the reflection spectrum will be distorted, and the effective bandwidth can not be further improved by increasing the nanohole sizes. Specifically, the spectrum is less flat and the insertion loss is higher as the diameters of the nanoholes ($d$) become larger, as shown in Fig. 1(b), calculated by using the three-dimensional (3D) finite-difference time-domain (FDTD) method. This could be attributed to the fact that when the structural perturbations are too large, the waveguide modes will be no longer in the perturbative regime, resulting in spectral distortion of the Bragg grating. A similar phenomenon can also be found in sidewall-modulated waveguide Bragg gratings [12]. This "coupling coefficient saturation effect" can limit the bandwidths of various nanobeam-based devices.
Another important issue for some nanobeam-based devices, such as polarizers and filters, is the unused strong back reflections from the nanobeam, which could introduce unwanted light interferences and may also de-stabilize the light source, particularly in cases where the light source is integrated onto the chip [11]. Those back reflections could not be easily removed in silicon PICs due to the lack of an on-silicon isolator. Wu et al. in [33] theoretically proposed a symmetric multimode nanobeam which utilizes the coupling between the forward $\text {TE}_0$ mode and the backward $\text {TE}_2$ mode. Then, this structure was used to design a reflection-suppressed polarizer, by placing a single-mode waveguide before the nanobeam to attenuate the reflected $\text {TE}_2$ mode. However, for such symmetric nanobeams, coupling between the forward and backward fundamental modes ($\text {TE}_0$) actually still exists at wavelengths where the phase-matching condition between them is satisfied. This makes the device only reflection-less in a certain range of wavelengths.
In this paper, we propose novel chirped anti-symmetric multimode nanobeams (CAMNs) based on SOI platforms, and describe their applications as broadband, compact, reflection-less, and fabrication-tolerant TM-pass polarizers and PBSs. The anti-symmetric structural perturbations of a CAMN ensure that only coupling between symmetric and anti-symmetric modes is possible [10]. This guarantees that the reflection can only contain higher order modes when the input is a fundamental mode (e.g., $\text {TE}_0$), which can be exploited to realize the true reflection-less feature of a CAMN-based device. The new possibility of introducing a large chirp on an ultra-compact nanobeam-based device to overcome the operation bandwidth limitation due to the coupling coefficient saturation is also shown. Specifically, the simulation results show that the 3 dB reflection bandwidth of a 4.68 um-long anti-symmetric multimode nanobeam can be significantly improved from ∼241 nm to ∼421 nm by introducing a linear chirp with a rate of 25.6 nm/um in the nanobeam period. It is then shown that this compact chirped nanobeam can be used to develop a TM-pass polarizer or a PBS with an ultra-broad 20 dB ER bandwidth of >300 nm. The CAMN-based TM-pass reflection-less polarizers and PBSs were fabricated and experimentally characterized in a wavelength range from 1507 to 1575 nm, mainly limited by the bandwidths of the grating couplers used for the fiber-to-chip coupling. The measured ERs were >20 dB over the whole tested wavelength range and the average insertion losses were <0.5 dB for both devices, and the mean reflection suppression ratio of the polarizer was ∼26.4 dB. Large fabrication tolerances of $\pm 60$ nm in the waveguide widths of the devices were also demonstrated.
2. Device design
2.1 Chirped anti-symmetric multimode nanobeams
2.1.1 Basic principle
A 3D schematic illustration of the proposed chirped anti-symmetric multimode nanobeam (CAMN) based on a SOI platform is given in Fig. 2(a). A CAMN is built on a multimode SOI waveguide with two rows of periodical SiO2 nanoholes that are out-of-phase by $\pi$. The critical parameters of a CAMN, as denoted in Fig. 2(a), include the multimode waveguide width ($W$), the diameters of the nanoholes ($d$), the center-to-center distance between the two rows of the nanoholes ($g$), the initial and final periods ($\Lambda _{0}$ and $\Lambda _{max}$, respectively), and the total number of the periods ($N$). The period of the nanoholes is linear increased from $\Lambda _{0}$ to $\Lambda _{max}$.
Fig. 2. (a) 3D schematic of a chirped anti-symmetric multimode nanobeam. (b) Comparison between cross-sectional mode profiles of $\text {TE}_0$ and $\text {TM}_0$ modes. (c) Top-view of an anti-symmetric multimode nanobeam. (d) TE (left) and TM (right) band structure diagrams of the nanobeam shown in (c).
The anti-symmetric structural perturbations of the proposed nanobeam guarantee that only coupling between symmetric and anti-symmetric modes is possible. This means that an input $\text {TE}_0$ mode for such a nanobeam will be reflected and converted to $\text {TE}_1$ mode. As a TE mode has a strong overlap with the center of the waveguide [top of Fig. 2(b)], the coupling coefficient between the forward $\text {TE}_0$ mode and the backward $\text {TE}_1$ modes for our CAMNs will be ultra-large, resulting in a wide $\text {TE}_0$-to-$\text {TE}_1$ reflection bandwidth. In contrast, a TM mode is not well confined in the waveguide [bottom of Fig. 2(b)]. Therefore, the coupling coefficient between the forward and backward TM modes is much smaller, and, as a result, the input $\text {TM}_0$ mode will travel through the nanobeam with little reflection.
Photonic band structures of a typical anti-symmetric multimode nanobeam based on a SOI platform [Fig. 2(c)] is calculated to verify its transmission properties. The calculations are based on simulating one unit cell of the nanobeam using Bloch boundary conditions through the 3D-FDTD method. The obtained band structures for the TE and TM polarization modes are shown in Fig. 2(d). As can be seen, for the band structure of the TE modes, a wide bandgap can be observed between the $\text {TE}_0$ and $\text {TE}_1$ bands, while no bandgap can be found between the two $\text {TE}_0$ bands. This confirms that the input $\text {TE}_0$ mode will be coupled to the backward $\text {TE}_1$ mode with an ultra-large coupling coefficient, while the coupling between the forward and backward $\text {TE}_0$ modes will be forbidden. By comparison, for the band structure of the TM modes, all the bands cross each other and no photonic band gap is observed, implying that the input $\text {TM}_0$ mode will pass through the nanobeam with little reflection. Such a polarization dependence behavior of an anti-symmetric multimode nanobeam can be used to achieve TM-pass polarizers or PBSs, as we shall see later.
2.1.2 Typical spectral responses
The reflection bandwidth of a CAMN will be mainly affected by the coupling coefficient between the forward $\text {TE}_0$ and the backward $\text {TE}_1$ modes, which is determined by the ratio of the area occupied by the nanoholes in a unit cell to that of the unit cell, and the chirp rate, $c$, which can be calculated via
where $L$ is the total length of the nanobeam. The center reflection wavelength of a CAMN is determined by the mean of $\Lambda _{0}$ and $\Lambda _{max}$.A SOI-based CAMN with the parameters shown in Fig. 3(a) is characterized using the 3D-FDTD method. The waveguide thickness is 0.22 um. The period of the CAMN is linear increased from 0.289 um to 0.408 um [bottom of Fig. 3(a)]. This CAMN is designed to have an operate band covering the main part of the whole fiber-optic communication band (1260-1625 nm). The total length of the CAMN is as short as ∼4.68 um. The electrical field distributions of the device at a wavelength of 1550 nm when launching the $\text {TE}_0$ and $\text {TM}_0$ modes are shown at the top and bottom of Fig. 3(b), respectively. It can be seen that the input $\text {TE}_0$ mode is totally reflected and converted to the $\text {TE}_1$ mode, while the input $\text {TM}_0$ mode passes through the device with little reflection. The calculated spectral responses of the CAMN are plotted in Fig. 3(c), and the ER spectrum, which is defined as the ratio of the $\text {TE}_0$-to-$\text {TE}_1$ reflection to the $\text {TE}_0$-to-$\text {TE}_0$ transmission, is plotted in Fig. 3(d). As can be seen, the bandwidth for ER >20 dB is as wide as ∼312 nm (in a wavelength range from 1292 to 1604 nm). The average insertion losses for the TE and TM modes over the 20 dB ER bandwidth are ∼0.6 dB and ∼0.9 dB, respectively. Note that we also simulate the CAMN responses where waveguide sidewall roughness has been taken into account, using the 3D-FDTD method. The RMS amplitude and autocorrelation length of the waveguide sidewall roughness are set to be of 3 nm and 250 nm, respectively, which are typical values for SOI waveguides [34]. The results suggest that waveguide sidewall roughness would have no significant impact on the spectral responses of a CAMN.
Fig. 3. (a) Top-view of a CAMN (upper) and the period versus period number of the CAMN (lower). (b) Electrical field distributions of the CAMN when launching $\text {TE}_0$ (upper) and $\text {TM}_0$ (lower) modes from the input. (c) Spectral responses of the CAMN. (d) Extinction ratio spectrum of the CAMN, which is defined as the ratio of the $\text {TE}_0$-to-$\text {TE}_1$ reflection to the $\text {TE}_0$-to-$\text {TE}_0$ transmission; 20 dB ER BW: bandwidth for extinction ratio >20 dB.
2.1.3 Impact of a large chirp on the spectral response
This section investigates the impact of the use of a large chirp on the reflection spectrum of an anti-symmetric multimode nanobeam. As described in Introduction, for traditional symmetric nanobeams, due to the coupling coefficient saturation effect, the effective bandwidth will not be increased and the spectral performance will be degraded with increasing the nanohole diameter ($d$) if the nanoholes are already large, which can limit the bandwidths of various nanobeam-based devices. Now, we first investigate if this effect also exists in an unchirped anti-symmetric multimode nanobeam, by calculating the $\text {TE}_0$-$\text {TE}_1$ reflection spectrum with respect to $d$ of the nanobeam using the 3D-FDTD method. For the characterized unchirped nanobeam, the period is 0.335 um, $N$ is 13, $W$ is 0.8 um, and $g$ is 0.3 um. The calculated reflection spectra of the nanobeams with various $d$ are presented in Fig. 4(a). A similar coupling coefficient saturation effect can be seen: the spectrum is less flat and the average insertion loss is higher with increasing $d$. Then, to explore the impact of a large chirp on the reflection spectrum of an anti-symmetric multimode nanobeam, we fix $d$ at 0.2 um, while gradually increasing the chirp rate ($c$) of the nanobeam, from 0 nm/um to 25.6 nm/um. The calculated reflection spectrum versus $c$ is presented in Fig. 4(b). An opposite trend can be found: the response becomes flatter and the average insertion loss is lower as $c$ is higher. The 3 dB bandwidth of the reflection spectrum versus $d$ for the unchirped nanobeam and that with respect to $c$ for the chirped nanobeam are plotted in Fig. 4(c) for comparison. The 3 dB reflection bandwidth for the unchirped nanobeam is saturated for $d>0.18$ um and reaches a maximum of ∼255 nm when $d = 0.185$ um. In contrast, the 3 dB bandwidth for the chirped nanobeam shows a continuous increase with $c$ and is as wide as ∼421 nm for $c = 25.6$ nm/um. For a more specific comparison, the reflection spectrum of the unchirped nanobeam with the largest nanoholes ($d = 0.2$ um) and that of the chirped nanobeam with the highest chirp rate ($c = 25.6$ nm/um) are presented together in Fig. 4(d). These results clearly show the feasibility of overcoming the bandwidth limitation of a nanobeam caused by the coupling coefficient saturation effect by introducing a large chirp onto the device. This provides a promising route to further improve the bandwidths of various nanobeam-based integrated-optics devices.
Fig. 4. (a) Spectral evolution versus nanohole diameter ($d$) of an unchirped anti-symmetric nanobeam. (b) Spectral evolution versus chirp rate ($c$) of a chirped anti-symmetric nanobeam with $d= 0.2$ um. (c) 3 dB bandwidth of the $\text {TE}_0$-to-$\text {TE}_1$ reflection spectrum versus $d$ of the unchirped nanobeam (blue, bottom axis) and that versus $c$ of the chirped nanobeam (red, top axis). (d) Comparison of the reflection spectrum of the unchirped nanobeam with the largest $d$ of 0.2 um and that of the chirped nanobeam with the highest $c$ of 25.6 nm/um.
2.1.4 Fabrication tolerance
The ultra-broad bandwidths and relatively large feature sizes of CAMNs would give them large fabrication tolerances. To verify this, the CAMN designed in Fig. 3(a) with large waveguide width deviations of $\pm$ 60 nm (corresponding to $W$ of 0.74 um and 0.86 um, respectively) are calculated using the 3D-FDTD method. The spectral responses, together with that of the CAMN with the correct width ($W = 0.8$ um), are presented in Fig. 5. No significant degradation of the spectral performances due to the large width deviations is observed, and the bandwidths for ER > 20 dB are comparable with each other for the three CAMNs. These results suggest large fabrication tolerances of CAMN-based devices. One may also notice that the 20 dB ER band is slightly shifted towards longer wavelengths as $W$ is larger. This is because the average effective refractive index of the multimode waveguide is higher with increasing $W$, causing the overall Bragg wavelength of the nanobeam to shift to a longer wavelength.
2.2 CAMN-based reflection-less TM-pass polarizer
A CAMN can be used to realize a broadband, compact, reflection-less, and fabrication-tolerant TM-pass polarizer, by simply placing a sufficiently long single-mode routing waveguide before the CAMN that acts as a higher-order mode filter. The principle is illustrated in Fig. 6(a). The input $\text {TE}_0$ mode is reflected and converted to $\text {TE}_1$ mode via the CAMN, which is then radiated out of the single-mode waveguide that does not support the $\text {TE}_1$ mode. Note that due to the anti-symmetric structural perturbations of a CAMN, only coupling between symmetric and anti-symmetric modes is possible. This means that the reflection will only contain higher-order modes (which is mainly the $\text {TE}_1$ mode in our case) for the input mode of $\text {TE}_0$, which can always be attenuated by a higher-mode filter. This is different from [33], where coupling between the forward and backward fundamental modes ($\text {TE}_0$) still exists for wavelengths where the phase-matching condition between them is satisfied. In those wavelengths, the reflection will contain $\text {TE}_0$ mode for the input mode of $\text {TE}_0$, which can pass through the higher-order mode filter placed before the nanobeam and still act as undesired back reflection.
Fig. 6. (a) Schematic illustration of the operation principle of a reflection-less TM-pass polarizer using a CAMN. (b) Electric field distributions of the poalrizers with single-mode (upper) and multimode (lower) waveguides placed before the CAMN. (c) $\text {TE}_1$ mode transmission as a function of the length of a 0.35 um-wide SOI waveguide at various wavelengths. (d) Spectral responses of a CAMN-based polarizer.
A TM-pass polarizer based on the CAMN shown in Fig. 3(a) is designed and simulated using the 3D-FDTD method. A 0.35 um-wide, 60 um-long single-mode waveguide is placed before the CAMN to act as a $\text {TE}_1$ mode filter. The electrical field distribution of the polarizer when launching the $\text {TE}_0$ mode is presented at the top of Fig. 6(b). No reflected light can be observed before the source, demonstrating the reflection-less feature of the polarizer. The electrical field distribution of a polarizer where the single-mode waveguide is replaced by a multimode waveguide having the same width as the CAMN is also calculated. The result is shown at the bottom of Fig. 6(b), where a strong reflection can be found before the source. The comparison demonstrates that the reflection suppression is due to the use of the single-mode waveguide. To explore the reflection suppression ratio with respect to the length of the single-mode waveguide, the transmission of the $\text {TE}_1$ mode versus the length of a 0.35 um-wide single-mode waveguide at various wavelengths is calculated using the 3D-FDTD method, and the result is plotted in Fig. 6(c). As can be seen, the $\text {TE}_1$ mode transmission for each wavelength is decreased with increasing the single-mode waveguide length. Also, the transmission is lower at a longer wavelength for a given waveguide length. This is because the waveguide mode at a longer wavelength is less confined in the waveguide compared with that at a shorter wavelength, and thus is easier to be radiated out of the waveguide. Specifically, to attenuate the $\text {TE}_1$ mode by 20 dB, the required lengths of the 0.35 um-wide waveguide for wavelengths of 1500 nm, 1550 nm, and 1600 nm are ∼29 um, ∼22 um, and ∼17 um, respectively.
Figure 6(d) plots the calculated spectral responses of the CAMN-based TM-pass polarizer designed above. The bandwidth for ER $>20$ dB of the polarizer is as wide as ∼309 nm (1294-1603 nm). The average insertion loss over the 20 dB ER bandwidth for the TM mode is ∼0.73 dB. It can also be seen that the $\text {TE}_0$ back-reflection suppression ratio, which here is defined as the ratio of the $\text {TM}_0$ transmission to the $\text {TE}_0$ reflection, is higher at longer wavelengths, which agrees with the results obtained in Fig. 6(c). Specifically, the reflection suppression ratio is larger than 10 dB, 20 dB, and 30 dB for wavelengths longer than ∼1282 nm, ∼1317 nm and ∼1346 nm, respectively. The overall reflection suppression ratio can be further increased by using a longer length or a smaller width of the single-mode waveguide.
2.3 CAMN-based polarization beam splitter (PBS)
A CAMN can also be used to implement a broadband, compact and fabrication-tolerant PBS, by placing a $\text {TE}_0$ $\&$ $\text {TE}_1$ mode (de)multiplexer before it. The principle, as illustrated in Fig. 7(a), is that the reflected $\text {TE}_1$ mode from the CAMN is coupled to the $\text {TE}_0$ mode due to the mode de(multiplexer) and eventually exits through the drop port, while the $\text {TM}_0$ mode passes through the CAMN and is finally output from the through port, thereby splitting the two polarization modes. Here, an adiabatic mode coupler consisting of two counter-tapered waveguides is used to serve as the $\text {TE}_0$ $\&$ $\text {TE}_1$ mode (de)multiplexer, as it has a broad operation bandwidth, high fabrication tolerance, and simple structure. The length of the mode coupler is 46 um, the widths of the upper and lower waveguides of the coupler are tapered from to 0.7 um to 0.8 um and from 0.42 um to 0.31 um, respectively, and the gap between the two tapered waveguides is ∼0.08 um. The designed PBS is simulated using the 3D-FDTD method. The electrical field distributions of the device at a wavelength of 1550 nm when launching the $\text {TE}_0$ and $\text {TM}_0$ modes are shown at the top and bottom of Fig. 7(b), respectively, and the results confirm the polarization splitting functionality of the device. The spectral responses of the PBS under the input modes of $\text {TE}_0$ and $\text {TM}_0$ are plotted in Figs. 7(c) and 7(d), respectively. The bandwidths for ER $> 20$ dB for the $\text {TE}_0$ and $\text {TM}_0$ modes are as large as ∼314 nm (1292-1606 nm) and $> 373$ nm (for wavelengths longer than 1377 nm), respectively, and the average insertion losses over the 20 dB ER bandwidth for the $\text {TE}_0$ and $\text {TM}_0$ modes are ∼0.7 dB and ∼1.3 dB, respectively.
Fig. 7. (a) Schematic illustration of the operation principle of a CAMN-based PBS. (b) Electric field distributions of the PBS when launching $\text {TM}_0$ (upper) and $\text {TE}_0$ (lower) modes from the input. (c) Spectral responses for the $\text {TE}_0$ input mode. (d) Spectral responses for the $\text {TM}_0$ input mode.
3. Fabrication and measurement results
3.1 Fabrication and measurement setup
The designed devices were fabricated based on 100 keV electron-beam lithography in Applied Nanotools, Inc [35]. The fabrication used a single etch process on an SOI wafer with 220 nm thick silicon on a 3 $\mathrm{\mu}$m thick buried oxide layer. Once the material had been chemically developed, an anisotropic ICP-RIE etching process was performed on the substrate to transfer the pattern into the underlying silicon layer. A 2 $\mathrm{\mu}$m thick silicon dioxide cladding layer was deposited on the etched sample. Vertical grating couplers from the foundry Process Design Kit (PDK), spaced on 127 $\mathrm{\mu}$m centers, were used to couple light into and out of the chip from a 8-degree polished single-mode optical fiber array with a 127-$\mathrm{\mu}$m fiber-to-fiber pitch. A tunable continuous wave (CW) laser (Keysight 81960A) was used as the light source. The laser power was set at 6 dBm. A fiber-optic polarization controller was used after the laser source to adjust the polarization state of the incident light in the optical fiber. The light output from the chip was finally collected by a multiport optical power meter (Keysight N7745A) to measure the spectral responses of the integrated circuits. The layouts of the integrated-optics circuits used to test the CAMN-based polarizer and PBS are shown in Fig. 8(a). To measure the spectral responses of different polarization modes of a single device, two circuits with the same tested device but having different grating couplers designed for TE and TM polarization modes were fabricated and measured individually.
Figure 8(b) shows typical experimental transmission responses of the TE and TM calibration circuits (i.e., a circuit which contains only input and output grating couplers and an uniform waveguide connecting the two grating couplers), respectively. It can be seen that the current grating couplers have acceptable coupling efficiencies for wavelengths shorter than 1575 nm. Limited by the bandwidth of the grating coupler and the wavelength range of the tunable laser source (from 1507 to 1630 nm), the devices were characterized over the wavelength from 1507 to 1575 nm. The scanning electron microscopy (SEM) images of a fabricated CAMN, a grating coupler, and a portion of the adiabatic mode coupler are presented in Fig. 8(c).
Fig. 8. (a) Layouts of the testing circuits of the polarizer (left) and PBS (right). (b) Typical experimental transmission responses of the TE and TM calibration circuits. (c) Scanning electron microscopy (SEM) images of a fabricated CAMN, a grating coupler, and a portion of the adiabatic mode coupler.
3.2 CAMN-based polarizer
A CAMN-based reflection-less TM-pass polarizer was designed and fabricated. For the parameters of the CAMN, $\Lambda _0$ and $\Lambda _{max}$ were 0.354 um and 0.433 um, respectively, $d$ was 0.215 um, $g$ was 0.3 um, $W$ was 0.8 um, and $N$ was 12. The corresponding total length of the CAMN was ∼5.18 um. A single-mode waveguide with a width of 0.35 um and a length of ∼58.8 um was placed before the CAMN to act as the higher-order mode filter. The measured spectral responses of the polarizer are shown in Fig. 9(a) (red and blue solid lines), in which the insertion losses introduced by the grating couplers have been calibrated out. The simulation results obtained using the 3d-FDTD method are also included in the figure for comparison (dashed lines). The experimental TM transmission response is flat and the average insertion loss is smaller than 0.5 dB over the measured wavelength range. One may notice that the measured TM transmission is slightly higher than 0 dB at some longer wavelengths. This could be attributed to the fact that the grating couplers in the calibration circuit are not exactly the same as those of the device circuits due to the fabrication variations, and thus may have slightly lower transmission efficiencies. This could cause the transmissions of the measured devices to be $> 0$ dB after the calibration if the devices have very low insertion losses. Similar phenomenons can also be observed in Fig. 10(a) and Fig. 11. The experimental ER spectrum of the polarizer, defined as the ratio of the $\text {TM}_0$-to-$\text {TM}_0$ transmission to the $\text {TE}_0$-to-$\text {TE}_0$ transmission, is calculated from Fig. 9(a) and is plotted in Fig. 9(b) (red solid line). It can be seen that the ER is larger than 30 dB over the whole measured wavelength range.
Fig. 9. (a) Measured and simulated spectral responses of the CAMN-based polarizer. (b) Measured and simulated extinction ratio and reflection suppression ratio spectra of the polarizer, calculated from (a).
Fig. 10. (a) Measured and simulated spectral responses of the CAMN-based PBS. (b) Measured and simulated extinction ratio spectra for the two polarization modes of the PBS, calculated from (a). The through and drop ports of the PBS are as defined in Figs. 7(a) and 8(a).
Fig. 11. (a) and (b) are experimental data of $W$-deviated CAMN-based polarizers. (c) and (d) are experimental data of $W$-deviated CAMN-based PBSs. In each of (a)-(d), the upper figure shows the spectral responses of the device, while the lower plot presents the corresponding extinction ratio spectra.
The back reflection response of the polarizer was also measured, through another integrated-optics circuit where an additional broadband 3 dB directional coupler [36] was placed before the polarizer to route the reflected light to an output grating coupler. The result is plotted in Fig. 9(a) (yellow solid line), where the 6 dB round-trip loss of the directional coupler has been calibrated out. The reflection suppression ratio, defined as the ratio of the $\text {TM}_0$-to-$\text {TM}_0$ transmission to the $\text {TE}_0$-to-$\text {TE}_0$ reflection, is calculated and presented in Fig. 9(b) (yellow solid line). The average suppression ratio over the measured wavelength range is ∼26.4 dB. The suppression ratio shows an increase trend versus wavelength, which agrees with the theoretical result shown in Fig. 6(c). One can also notice that the overall suppression ratio level is significantly smaller than the simulation result (yellow dashed line), which could be attributed to reflections occurring in the practical circuits that have not been considered in the simulations, such as those from the grating couplers, fiber interfaces, etc. Those additional reflections could be significantly reduced in all-in-one fully-integrated circuits, or by using low back-reflection grating couplers for the fiber-to-chip coupling [37].
3.3 CAMN-based PBS
A CAMN-based PBS was also designed and fabricated. The included CAMN is the same as that of the polarizer measured in the last section. The experimental spectral responses of the PBS in which the insertion losses of the grating couplers have been calibrated out are plotted in Fig. 10(a), where the simulated results using the 3D-FDTD method are also included. The through and drop ports are as defined in Figs. 7(a) and 8(a). As can be seen, the experimental responses of the PBS show good agreement with the 3D-FDTD simulation results. The measured transmission responses of the TM mode to the through port and the $\text {TE}_0$ mode to the drop port are flat over the measured wavelength region, and the average insertion losses of the two modes are both smaller than 0.5 dB. The experimental ER spectra for the two polarization modes are plotted in Fig. 10(b), which are larger than 20 dB over the measured wavelength range for both polarization modes.
3.4 Fabrication tolerance of the CAMN-based polarizer and PBS
To explore the fabrication tolerances of CAMN-based devices, the above designed CAMN-based TM-pass polarizer and PBS with waveguide width deviations ($\Delta W$) of $\pm 60$ nm were also fabricated and experimentally characterized. The measurement data for the polarizers with $\Delta W = - 60$ nm and $\Delta W = + 60$ nm are presented in Figs. 11(a) and 11(b), respectively. As can be seen, both polarizers still exhibit low insertion losses and high ERs, which are larger than 20 dB over the measured wavelength range. The measurement data for the waveguide width-deviated PBSs are presented in Figs. 11(c)–11(d). Again, no significant spectral performance degradation is found for the two PBSs. The ERs of the two polarization modes for both PBSs are higher than 20 dB over the major part of the measured wavelength range. These experimental results demonstrate the large fabrication tolerances of CAMN-based devices. Such high robustness against geometry variations are owning to the ultra-broad bandwidths and relatively large feature sizes of CAMNs. It is thus expected that the fabrication tolerances of CAMN-based devices could be further increased by using a wider multimode waveguide with larger-sized nanoholes to increase the feature sizes.
4. Discussion and conclusion
A performance comparison between the present polarizer and other recently reported SOI-based polarizers is given in Table 1. It can be seen that in addition to the attractive reflection-less feature, our CAMN-based polarizer can also provide a wide bandwidth and low insertion loss with a moderate footprint. It should be note that the length of the current polarizer can be significantly reduced via simply using a narrower and shorter single-mode waveguide (e.g., 0.15 um instead of 0.35 um used here) to serve as the TE1 mode filter. As a reference, our simulations show that to achieve a 30 dB back-reflection suppression ratio for the proposed polarizer, the required length when using a 0.15 um-wide waveguide as the TE1 mode filter is 8.8 um, which is much shorter than 32.8 um required by the current 0.35 um-wide waveguide. Also note that the experimental bandwidth of our polarizer is limited by the bandwidths of the grating couplers.
Table 1. Performance comparison of reported SOI-based polarizers; BW$_{20 \; \text {dB}}$: 20 dB ER bandwidth; IL: insertion loss.
Table 2 also shows a performance comparison between the present PBS and other SOI-based PBSs reported in recent years. As can be seen, our CAMN-based PBS can simultaneously offer a broad bandwidth, loss insertion loss, and a relatively small size. Note that the size of our PBS can be significantly decreased by using other more advanced mode demultiplexers (such as the one with an ultra-compact size of 2.4 $\times$ 3 $\mathrm{\mu}$m$^2$ demonstrated in [47]). Again, the measured bandwidth of our PBS is limited by the grating couplers.
Table 2. Performance comparison of reported SOI-based PBSs; here the minimum 20 dB ER bandwidth between the two polarizations is used to represent BW$_{20\; \text {dB}}$.
In conclusion, chirped anti-symmetric multimode nanobeams (CAMNs) based on silicon-on-insulator platforms have been proposed, and their applications as broadband, compact, reflection-less, and fabrication-tolerant TM-pass polarizers and PBSs have also been shown. The anti-symmetric structural perturbations of a CAMN permit only coupling between symmetric and anti-symmetric modes, which is utilized to achieve the reflection-less feature of the polarizer. The introduced large chirp can significantly increase the reflection bandwidth of the nanobeam, which was previously limited by the coupling coefficient saturation effect. This provides a viable route to further expand the operation bandwidths of various nanobeam-based devices. The simulation results show that a 4.68 um-long CAMN can be used to develop a TM-pass polarizer or a PBS that has an ultra-wide 20 dB ER bandwidth of >300 nm and an average insertion loss of <1.3 dB. The CAMN-based TM-pass polarizer and PBS were fabricated and experimentally characterized over a wavelength range from 1507 to 1575 nm, mainly limited by the bandwidths of the grating couplers. The experimental results show that, for each device, the ERs and the average insertion losses for both polarization modes were >20 dB and <0.5 dB, respectively, over the measured wavelength range, and the mean reflection suppression ratio of the polarizer was ∼26.4 dB. The measurement results also demonstrate that the polarizer and PBS with large fabrication variations of $\pm$60 nm in the waveguide width can still provide acceptable performances. The proposed CAMNs possess several important advantages compared with traditional nanobeams, including significantly broader bandwidth, back-reflection suppression feature, and mode conversion capability. These features give them greater potential for various integrated-optics applications, including not only polarization handling, but also ultra-broadband filters, reflectors, and mode control.
Funding
National Key Research and Development Program of China (2021YFB2801500); Project of Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education (NJ20210003); Fundamental Research Funds for the Central Universities (JZ2021HGTA0149); National Natural Science Foundation of China (62105089).
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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