1. Introduction

In the past decades, whispering gallery mode (WGM) resonators with high quality (Q) factors and relatively small mode volumes have attracted much attention in various research fields, including the cavity quantum electrodynamics, ultra-low-threshold lasers, cavity optomechanics, nonlinear optics, and sensing [1–10]. For all applications, efficient excitation and collection of the mode is crucial. Previously, the deformed boundary shape, a scatterer, a nanoantenna or a near field coupler are usually introduced [11–18] to couple the light into or out of such high-Q microresonators. Among them, because of the high coupling efficiency, the near field coupler parallel to the rim of a WGM resonator, such as integrated waveguide and fiber-taper, is widely used in experiments. Nevertheless, the phase-matching condition, as well as large coupling area for a sufficient field overlap, should be satisfied for these traveling wave evanescent couplers. The total number of couplers, especially for small-scale microresonators, is limited by the relatively large coupling area. Furthermore, the coupling efficiency of the waveguide is sensitive to the coupling distance, which should be precisely controlled by high-precision nanofabrication for the silicon-on-insulator (SOI) wafer [19,20]. These limitations pose a challenge to potential applications in complex hybrid optical systems.

In recent years, one kind of novel coupling scheme named perpendicular coupler (PC) has been proposed [21–25]. Similar structures were initially applied for microdisk lasers to realize efficient unidirectional emission [16,26–29]. By reversing this laser emission process, the incident light propagating along the perpendicular waveguide can also excite the WGM resonance [30]. Besides, because the PC launches the light into the microresonator through both directions, the standing wave field can be excited in the microresonator, which is different from the traveling wave field excited by the traditional evanescent coupler. However, up to now, the exploration based on the characteristic of the standing wave in WGM resonators coupled with the PC is not yet reported. Compared to previous studies on the generation of standing waves in WGM resonators, whose configurations require extra circulator [31], multiple resonators or sidewall grating [32], the configuration of the PC is easy to fabricate and integrate. Moreover, in previous studies on the PC, one single PC performs both the input and output coupler, limiting the analysis of coupling at other positions around the resonator. Therefore, the configuration of multiple PCs for potential fan-out photonics devices, which may take the full advantages of the PC, has never been studied.

In this letter, we have demonstrated that an on-chip PC can effectively excite the standing wave field in the high-Q silicon microring resonators. The mechanism of the PC, which is significantly different from the traveling-wave evanescent-field coupler, allows a compact coupling region that occupies a wavelength-scale area and the integration of multiple couplers. In our experiments, a Q factor of the optical modes as high as $1.1\times 10^{5}$ with a proper coupling distance is verified by the PC. In addition, multiple PCs were fabricated around the microring, and both numerical and experimental results reveal that they can selectively collect the resonance modes with specific azimuthal numbers $m$. This wavelength selection feature is derived from the standing wave excited by the PC, while the transmission spectrum has a period trend. Therefore, this wavelength selection feature, along with the inherent small coupling area, makes WGM device with multiple PCs a potential platform for applications such as optical filter, optical switch, and multi-port beam splitter for hybrid integrated photonic chips.

2. Structure, mechanism, and fabrication

To study the characteristic of the microresonator with PCs, we first numerically simulate the transmission spectra using a two-dimensional finite element method (FEM). Figure 1(a) shows the schematic configuration of the microresonator with multiple PCs. The light with transverse magnetic (TM) polarization is coupled into the microring resonator through the PC at lower left and others with different azimuth angle $\theta$ around the microring are used to collect the energy from the resonator. In our simulation, the device is based on the SOI platform with $220\:nm$ silicon layer and encapsulated in silica, with the refractive indexes of $3.3$ and $1.45$, respectively. And the microresonator has the radius of $15\:um$, the width of $400\:nm$ and the gap of $200\:nm$, respectively. Once the input light is on resonance with the microcavity, the light can be trapped inside the resonator in two opposite circulating directions and the standing wave field will be excited, which is different from the standing wave mode rooting in the strong backscattering [33,34].

 

Fig. 1. (a) Schematic of a high-Q silicon microresonator with the perpendicular couplers (PCs), where light is input from the left PC and output from two PCs on the right. (b) The numerically calculated field pattern of the microring. Inset: the zoom-in optical field near an output PC. (c) The simulated transmission spectra of PC ports aligns at different locations, with $\theta$ of $0^{\circ }$ , $90^{\circ }$, $45^{\circ }$ and $60^{\circ }$, respectively. Inset: zoom-in field patterns of different azimuthal modes around the output PC.

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Figure 1(b) shows that a standing wave field is established in the resonator, which supports only the fundamental mode at $1600\:nm$ band because of the narrow width of the microring. It can be found that the waveguide is in the evanescent field of the resonance, which implies that the light can be coupled into and out of the microring resonator through the PCs, as shown in Fig. 1(c). It is obvious that the structures of transmission spectra with different $\theta$ are different. When the PC is aligned with the antinode of the standing wave pattern, it can couple the light out efficiently because of the conservation of the parity [21]. By contrast, the PC aligned with the node cannot couple the light out. And the input PC at $\theta$ of $180^{\circ }$ always excites mode with even axial symmetry respect to the axis of $0^{\circ }$. Therefore, the PC at $\theta$ of $0^{\circ }$ has the overlap with the antinode of all optical modes excited by the input PC, corresponding to the transmission spectrum with the single free spectral range (FSR) about $8.4\:nm$. For the PC at $\theta$ of $90^{\circ }$, however, when the $m$ of the resonance mode is even, this PC can overlap with the antinode of the optical field and collect energy efficiently. Otherwise, this PC is at the node of the optical field, corresponding to inefficient coupling from the resonator. Therefore, PC at $\theta$ of $90^{\circ }$ shows a wavelength selection separation with 2FSR called period of 2. It can be inferred that for a PC at azimuth angle $\theta$, the PC can have a maximum overlap with the optical field, if $m$ is an integral multiple of $\frac {180^{\circ }}{\theta }$. For example, as shown in Fig. 1(c), a PC at $45^{\circ }$ couples with the maximum optical field every four resonance modes and a PC at $60^{\circ }$ will couple with the maximum optical field every three resonance modes, respectively. Furthermore, it is worth pointing out that, only when the period of the spectrum is even, such as PCs at $90^{\circ }$ and $45^{\circ }$, the PC can be at the node once in each period and thus nearly no light at corresponding resonance mode can be coupled out through the PC. The spectrum with an odd period (e.g. PC at $60^{\circ }$ ) does not have this phenomenon.

In our experiments, the PCs and microresonators are fabricated from a commercial SOI with $220\:nm$ top silicon layer and $2\:\mu m$ isolating silica ($SiO_{2}$) layer. The device pattern is defined by using e-beam lithography with a negative e-beam resist (XR-1541-006). Following the development of the pattern, the silicon film is etched with a $SF_{6}$ based gas in an inductively coupled plasma (ICP) etcher to transfer the pattern. After removing the residual resist with a buffered oxide etch (BOE), an upper cladding of $2\:\mu m$ $SiO_{2}$ is deposited by using plasma-enhanced chemical vapor deposition (PECVD) to protect the sample and match the refractive index of the upper and lower claddings of the device. The width of the waveguide is $400\:nm$ and the radius of the microresonators is $15\:\mu m$, respectively.

3. Experiment and discussion

To characterize the devices, the light is launched from a semiconductor tunable laser (Toptica CTL 1550) and focused on one facet of the chip by a lensed fiber, which is placed on a translational stage (MDT630A, Thorlabs, with $20\:nm$ resolution). The emitted light from the PCs is also collected by the lensed fiber at the other facet. The output light is then detected by a 125-MHz photoreceiver and finally monitored by an oscilloscope. The coupling loss of the lensed fiber is around 7 dB at each facet.

First, a microdisk with a radius of $15\:\mu m$ is coupled with PCs, as shown in Fig. 2(a). The transmission spectrum from the PC at $\theta$ of $0^{\circ }$ is complicated. It can be found that the higher-order resonance modes can also be excited by the PC, indicating that the PC scheme is quite general for all resonance modes, not only for some specific wavelengths or mode numbers. Moreover, the transmission spectrum has a relatively strong background, which can be attributed to the microdisk structure providing a propagating tunnel from the input PC. The right inset of Fig. 2(a) shows the reflection spectrum with the obvious oscillating background, which is quite different from the reflection spectrum collected in Ref. [30], where the PC directly connected to the microdisk. Because of the existence of two smooth waveguide facets here, PC acts as a Fabry-Perot resonator.

 

Fig. 2. (a) Transmission spectrum of the microdisk with PCs. The optical modes are excited through the left PC and the transmission spectrum is collected through another PC with $\theta$ of $0^{\circ }$. Inset: the optical microscope picture of the sample and the reflection spectrum collected from the excited PC. (b) Transmission spectra of microring collected with PCs at different positions. Inset: the optical microscope picture of the sample and the close-up scanning electron microscope (SEM) picture of the coupling region. (c-d) Transmission spectra of optical modes around $1612\:nm$ with different gap between microring and waveguide and the corresponding Q factor of the resonance modes. Scale bar $=5\:\mu m$.

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Compared with the microdisk, the typical transmission spectra of microring devices with PCs at different azimuth angles are depicted in Fig. 2(b). Here, the width of the microring is $1\:\mu m$, which can support higher-order resonance modes in theory. However, because the external loss introduced by the PC is quite low, only fundamental mode, which in our experiment is transverse electric (TE) mode, can be excited through the PC. Compared to the complex spectrum of the microdisk, these single-mode spectra can avoid the mode crossing and distinguish optical modes much more easily. Estimated from the transmission, the coupling efficiency of the PC is about $35\%$ except the coupling loss of the waveguide. The measured FSR describing the distance between two adjacent azimuthal modes is about $7.5\:nm$. Furthermore, benefitting from the silica cladding layer at the center of the microring, nothing but little light can directly scatter into the collection PC. Although, the transmission spectrum of port $2$ ($\theta \sim 0^{\circ }$) still has a slight background, which hides a small peak of resonance mode around $1607\:nm$. We believe that this PC can collect the whole mode family. On the contrary, transmission spectra of port 3 ($\theta \sim 90^{\circ }$) and port 4 ($\theta \sim -90^{\circ }$) just show modes with 2FSR separation. Obviously, those PCs at symmetric directions can collect the same series of modes, which are only with the even $m$. It can be found that the experimental results are in great agreement with the numerical prediction. Moreover, in both simulated and experimental transmission spectra, lineshapes of some resonance modes exhibit asymmetric Fano-like lineshapes. This phenomenon can be derived from the reflection at the end face of multiple PCs. The collected light of the PC consists of the light coupled from the resonance mode and the reflected light on each interface. The interference between these components leads to the formation of Fano-like lineshapes [21,35].

Figure 2(c) shows the coupling efficiency gradually decreases with the gap increased from $100\:nm$ to $400\:nm$. It is noted that the coupling strength is mainly dependent on the overlap between standing wave mode in microresonator and the waveguide mode in PC. The resonance peak can barely be detected when the gap is beyond $400\:nm$. Figure 2(d) shows the relevant loaded Q factors. The highest loaded Q in our experiments is $1.1\times 10^{5}$ with the gap of $400\:nm$, which reaches the limitation in our fabrication and is comparable to that of traditional microring with evanescent coupler. Since the PC introduces external coupling and scattering loss, the loaded Q increases with the gap simultaneously. Therefore, to make a trade off between the coupling efficiency and the Q factor, the gap of $200\:nm$ is used in our experiments.

To compare the PC with the traditional evanescent coupler, we combine these two kinds of couplers on one microresonator, as shown in Fig. 3(b). A bus waveguide is placed nearby the microring to excite or collect the optical modes inside the microring by evanescent field. The width of the bus waveguide is $400\:nm$ and the gap between the waveguide and the microring resonator is $600\:nm$. First, the light is injected into the bus waveguide from port 1 to excite the optical modes in the microring, as shown in Fig. 3(a). It can be found that the optical modes in the typical transmission are separated by single FSR. These two transmission spectra collected from ports 2 and 3 are almost the same and the phenomenon of the wavelength selection no longer exists. Therefore, we believe that the traveling wave field is excited through the bus waveguide. Although three PCs around the microresonator at $\theta$ of $0^{\circ }$, $90^{\circ }$ and $-90^{\circ }$ can induce the backscattering, there is no obvious mode splitting in our experiment. For further study, we launch the light from port $4$ and the standing wave field is excited inside the microring at this time. As shown in Fig. 3(b), the transmission spectrum of port $2$ indicates that the wavelength selection based on the azimuthal number still can be realized with the existence of evanescent coupler. Meanwhile, the transmission spectrum of evanescent coupler shows every resonance modes are coupled to the bus waveguide regardless of the $m$. This phenomenon can be attributed to the relatively large coupling area of the evanescent coupler, which always exists an overlap between the optical field and the evanescent coupler in each mode. Therefore, the evanescent coupler is unable to be used for wavelength selection directly. Besides, different from coupling with the traveling wave field, where the light propagates in one direction, both ports $1$ and $5$ have similar transmission spectrum (not shown here). Therefore, we can conclude that PCs are necessary for the wavelength selection feature based on the standing wave field and the PCs can also be used to couple the traveling wave field.

 

Fig. 3. (a) Typical transmission spectra of Port 2 and 3. The light launched from Port 1 is coupled into the microring by evanescent coupling, which excites the traveling wave field in the microring. (b) Typical transmission spectra of Port 2 and 5. The light launched from Port 4 is coupled into the microring by perpendicular coupling, which excites the standing wave field in the microring. Inset: optical microscope picture of the microring with PCs and an evanescent coupler. Scale bar $=5\:\mu m.$

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In addition, the devices with PCs at few other azimuth angles are also fabricated and tested in our experiments. Figures 4(a-b) show the transmission spectra of azimuth angle of $45^{\circ }$ and $60^{\circ }$, respectively. Just as the aforementioned inference, the transmission spectrum of the PC at $45^{\circ }$ has a period of four modes and the transmission spectrum of the PC at $60^{\circ }$ has a period of three modes. Within each period, there exists a maximum coupling efficiency, corresponding to the coupling aligning with the maximum optical field.

 

Fig. 4. The transmission spectra collected from the azimuth angles $\theta$ of $45^{\circ }$(a) and $60^{\circ }$ (b), respectively.

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As discussed before, the PC works as a wavelength selector in some special angles. For other angles, i.e. $\theta$ of $60^{\circ }$, there exists all resonance modes in the whole spectrum. Nevertheless, we can slightly alter the PC position to regain the function. And this method is robust for the current nanofabrication technology. First, we fabricate the PC with a tilt angle of $4^{\circ }$ at $\theta$ of $90^{\circ }$, as shown in Fig. 5(a). The transmission spectrum is similar to before (Fig. 3(b)) and the wavelength selection feature is evident. It means that the performance of the wavelength selection is insensitive to the small tilt angle of the waveguide. However, when the position of the PC has a tiny azimuthal displacement, as depicted in the inset of Fig. 5(b), from $60^{\circ }$ to $60.6^{\circ }$, the numerical simulation indicates that the position of the PC will move from the antinode to the neighboring node of the optical field, resulting in the inefficient coupling from the resonator. In this case, the position of the PC has been moved about $50\:nm$ [36], which is in the state of art of the EBL accuracy. Furthermore, as above numerical and experimental results shown, only when the period of the spectrum is even, the PC can be at the node once per period and no light can be coupled out through the PC at the corresponding resonance mode. By introducing a tiny change to the position of the PC, as shown in Fig. 5(b), even for the odd period, the inefficient coupling for specific resonance mode can also be realized in our simulation range. Consequently, for every resonance mode, by precisely controlling the azimuth angle, the efficient or inefficient coupling can be realized.

 

Fig. 5. (a) The typical transmission spectrum collected from the azimuth angle $\theta$ of $90^{\circ }$, while the waveguide has a tilt angle of $4^{\circ }$. (b) The simulated transmission spectrum of the azimuth angle at $60.6^{\circ }$. Inset: the resonance peak with the tiny change of the coupling angle around $\theta$ of $60^{\circ }$.

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4. Conclusion

In conclusion, we have experimentally demonstrated the microring resonator with PCs at different azimuth angles for wavelength selection. By using the waveguides perpendicular to the sidewall of the microresonator, the standing wave can be excited and collected, which is compared with the evanescent field coupler. Besides, PCs are insensitive to the refractive index of the waveguide [21,30] and have a much smaller coupling area compared with the evanescent coupler. Based on these advantages, WGM devices with multiple PCs could provide a powerful platform for applications like multiport beam splitter and low crosstalk planar intersection, and have great potential for future hybrid integrated photonic chips.