# Evanescently Coupled Rectangular Microresonators in Silicon-on-Insulator with High Q-Values: Experimental Characterization

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## Abstract

**:**

^{2}in silicon-on-insulator in an add-drop filter configuration. The influence of the geometrical parameters of the device was experimentally characterized and a high Q value of 13,000 was demonstrated as well as the multimode optical resonance characteristics in the drop port. We also show a 95% energy transfer between ports when the device is operated in TM-polarization and determine the full symmetry of the device by using an eight-port configuration, allowing the drop waveguide to be placed on any of its sides, providing a way to filter and route optical signals. We used the FDTD method to analyze the device and e-beam lithography and dry etching techniques for fabrication.

## 1. Introduction

^{7}with radius of 2.45 mm [7] and their feasibility to fabricate them with different materials [8,9,10]. Nevertheless, a shape that has a great potential is the rectangular resonator because the advantage of using them as filters is their smaller footprint requirement compared to the demonstrated ring resonators [7]. Also, rectangular resonators are ideal candidates for sensing applications as they maximize the footprint efficiency while providing a significant sensing area in comparison with photonic crystals [11]. Another advantage is the relaxation of the fabrication process because precise periods or gaps are not required as in [12]. However, their intrinsic resonant characteristics lead to a moderate Q-value of 4000 [13], and several attempts have been made to enhance it by cutting the corners [14] or by using different types of polygons such as triangles [15], hexagons [16,17], octagons [18], and deformed versions of these shapes [19,20]. Some of these approaches have not been fabricated and experimentally characterized [21], while others have been fabricated in silica [22], silicon nitride [20], and the coupling has been performed by bulk optics such as prism coupling [23]. In [13], the authors were partially successful in demonstrating a square add-drop filter in silicon, but no power was detected in the drop waveguide mainly because of their high losses due to using very narrow waveguides. In this paper, we experimentally demonstrate the multimode optical resonance characteristics of large rectangular cavities in SOI in the transmitted and drop port and optimize the design parameters to enhance the Q value to provide a way to filter and route optical signals. We present the design, fabrication, and characterization of three different sizes of rectangular microresonators in an add-drop filter configuration, as well as in a novel configuration of eight ports to validate the symmetry of the device and show, for the first time to our knowledge, selective mode coupling and a high Q value of 13,000.

## 2. Design and Analysis

_{wg}and evanescently couples to the microresonator with a coupling coefficient κ, and when in resonance, there is a simultaneous increase in optical power in the drop ports and a decrease in power in the transmitted port. The nature and characteristics of the electromagnetic field profile inside the cavity at resonant wavelengths have been previously studied by mode expansion modeling [24], coupled guided mode [25], exact analytical solutions [26,27], and FDTD simulations [28,29].

_{z}, m

_{x}). Degenerate modes have the same resonant wavelength, but different angle θ of the k-vector in the resonator. These modes are (m

_{z}, m

_{x}) and (m

_{x}, m

_{z}). As the field inside the cavity is a standing wave, it can be analytically described by a superposition of sine waves in the z and x directions, as given by [29].

_{x}, m

_{z}) mode, and δ is the relative phase between degenerate modes.

_{wg}vector with angle φ will couple to the resonator and bounce four times around the cavity with an angle θ. When the bouncing wave inside the cavity matches the waveguide front after the bounces, the system resonates and these modes are called whispering-gallery like-modes (WGM). Only the modes that bounce with angles that meet the total internal reflection (TIR) confinement will be trapped inside, and from these modes, the ones that have an angle similar to φ will preferably couple to the waveguide [29]. A WGM that has a four-bounce travel around the cavity with 45° reflection angles has a Free Spectral Range (FSR) given by $FSR={\lambda}^{2}/(2\sqrt{2}L{n}_{g})$.

^{−17}s, with 2

^{18}time steps; an orthogonal mesh size of 20 nm, and a modulated continuous Gaussian pulse was used as the source. The normalized optical spectra to the input field of the transmitted port and drop R port are displayed in Figure 2.

_{wg}which in turns selects the matching angle in the k-vector of the resonator. In other words, the phase of the mode in the cavity needs to match the one in the waveguide, and only the modes that match, will strongly couple. In our case, we fixed the waveguide dimensions to a single mode to avoid losses from coupling to higher-order modes. The spectral response is irregular due to the multimode nature of the cavity as can be seen in-between these two main resonances, where there are low-quality factor modes and their power is much less than the two dominant modes as also found in [29]. For large square resonators, the shape of the electro-magnetic pattern inside the cavity at resonances seems very similar and some have m

_{x}= 64 and m

_{z}= 16, as displayed on Figure 2b for the resonance of λ = 1599.6 μm. This pattern pulsates with time, creating a standing-wave resonator, and thus, it couples the same amount of power to the Drop R and Drop L ports. In Figure 2b, we can intuitively see this effect with the dashed and solid lines that couple to the opposite direction in the drop waveguide. Furthermore, as the bounces have similar angles in all walls to meet the resonance condition, it is foreseeable that the same results will be obtained regardless of which wall the drop waveguide couples to in a rectangular resonator. Departing from this design, and referencing Equation (2), we first optimized the Q value by tuning the coupling length and gap size (coupling coefficient κ), and then accounted for the effect of different rectangular sizes (the FSR in Equation (2)). We also investigated the performance of the same devices under TM-mode propagation, and demonstrate the symmetry of the device via an eight-port configuration. The results are presented in that order in Section 4.

## 3. Fabrication and Experimental Setup

_{2}box of 3 μm. A spin coater was used to apply the positive resist ZEP520A from ZEON chemicals to a chip. The devices were then patterned directly in the resist using EBL at 75 kV accelerating voltage. Immediately after, the resist was developed with ZED-N50 for 60 s. Then, the device was etched in a single step by ICP-RIE using SF

_{6}gas at low pressures and an etching time of 2 min to achieve smooth sidewalls. Finally, the resist was removed with the organic dissolver ZDMAC. The fabricated waveguides were 450-nm wide and no upper cladding was added. To access the device, we used fully-etched grating couplers fabricated in the same single etch step as the device. Two sets of devices are fabricated—one with grating couplers designed for TE polarization at the end of the waveguides, and another set with grating couplers for TM polarization. Both grating couplers consist of a matrix of rectangular holes with periods of Λ

_{x}= 700 nm and Λ

_{Y}= 600 nm for TE-polarization [31], and Λ

_{x}= 940 nm and Λ

_{Y}= 650 nm for the TM mode followed by a linear taper. Both diffraction gratings were designed to have their Bragg wavelength at 1580 nm. Figure 3a shows the flow diagram of the fabrication process, Figure 3b displays a scanning electron microscopy (SEM) image of the fabricated device of 20 × 10 μm

^{2}with a gap of 160 nm and Figure 3c displays the TM grating coupler.

## 4. Results and Discussion

^{2}rectangle, with a gap of 160 nm, are presented in Figure 4 for the TE mode. The powers shown in the following graphs have been normalized using a reference straight waveguide fabricated next to the device. From the experimental results, we can observe the two main resonances (A and B) in the transmission and drop R port spaced 4.4 nm apart with an FSR of 13 nm consistent with our simulations and a theoretical bounce of θ ≈ 42° with a Q value of 4100. A behavior not observed in the simulation is that resonance A approaches resonance B and eventually they resonate at the same wavelength, becoming indistinguishable, because of the group dispersion inside the cavity, which is not considered in the simulations; nevertheless, the simulation is in good agreement with the experimental results. The low-quality resonances cannot be spectrally resolved with our system and those that are close to a main resonance, couple to it, broadening the linewidth of the main one, making most of the resonant peaks asymmetric with fine features as can be seen in the inset of Figure 4 for resonance C. Also, the reason that, at longer wavelengths, there are more fluctuations is that those wavelengths are in the cutoff frequency of the grating coupler.

#### 4.1. Coupling Length

#### 4.2. Gap Size

^{2}is still a bit lower than a ring resonator of a similar footprint and Q value of 20,000 [35], with the advantage being that the optical mode is completely distributed inside the cavity, rather than mostly propagating in a nanowire, which is beneficial in sensing applications, where the propagating area of the mode is important for detecting particles.

#### 4.3. Microresonator Size

^{2}resonator to reduce the footprint to even less than the required footprint of a ring resonator. The most immediate result is the change in the FSR to 22 nm for the 10 × 10 resonator and 44 nm for the 5 × 5 resonator which both belong to a bounce angle of θ = 50°. Next, the coupling length was changed to 0, 5, and 10 μm for the 10 × 10 μm

^{2}resonator and to 0 and 5 μm for the 5 × 5 μm

^{2}resonator. The optimum coupling length in terms of Q factor was found to be the full length of the square, yielding a Q of 4200 and 1000, respectively. From this trend, we can confirm that the Q factor is inversely proportional to the size of the resonator as expected by Equation (2) and also as the Q factor is proportional to the lifetime of the photon inside the cavity, which is longer in bigger cavities. Then we found that the gap size has a similar behavior as in the rectangle case, and the best condition for both cases is when the gap is 160 nm, observing the multimode resonant spectra in the drop port R and enough power to resolve the resonances. The experimental results are presented in Figure 7 with the optimized parameters for both squares with a 160-nm gap.

#### 4.4. TM Polarization

^{2}resonator with a 160-nm gap as we obtain the highest power transfer of 95% from the transmission to the drop port, as shown in Figure 8, from 1570 to 1600 nm.

#### 4.5. Eight-Port Devices

^{2}rectangle and detected the power coupled to all ports of the resonator. Taking into consideration that the best design for the 20 × 10 resonator is the one with a 160-nm gap, we fabricated a device with that characteristics for all waveguides. Considering all waveguides have the same coupling length, we chose 10 μm since it is the longest possible size for all waveguides. The SEM image of the proposed device is displayed in Figure 10a as well as the optical power in Figure 10b from ports 5, 6, and 8 when port 2 is excited by the TE mode. We found that the system is completely symmetrical in all ports, confirming that the standing wave inside the resonator couples outwards to all the drop waveguides. At resonance, the standing wave inside the resonator suggests that the evanescent field from all sides of the rectangle is identical. Analyzing the system with ray optics, we have a symmetrical response on all waveguides because the bounce angles on all the sidewalls are very similar, and since all waveguides are identical, they preferentially couple to the same resonant mode. This kind of configuration has applications in power splitting, signal routing, and 90° bends.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Theoretical (

**a**) Spectra for the transmitted and drop R port and (

**b**) the electromagnetic field inside the cavity for λ = 1599.6 μm obtained by FDTD.

**Figure 3.**(

**a**) Flow diagram of the fabrication process; (

**b**) SEM image of the fabricated rectangular resonator; (

**c**) TM grating coupler.

**Figure 4.**Experimental results for the 20 × 10 μm

^{2}rectangular resonator with a gap of 160 nm. The inset shows a magnification of resonance C and D.

**Figure 5.**(

**a**) Schematic of the device; (

**b**) experimental Drop R spectrum for different coupling lengths.

**Figure 8.**Experimental transmitted and dropped powers for a 20 × 10 μm

^{2}rectangle with a 160-nm gap for the TM mode.

**Figure 10.**(

**a**) SEM image of the fabricated design; (

**b**) Experimental optical spectra from ports 5, 6, and 8 when port 2 is excited.

Size of Resonator (μm) | Polarization | Gap (nm) | Coupling Length (μm) | Maximum Q |
---|---|---|---|---|

20 × 10 | TE | 300 | 20 | 13,888 |

10 × 10 | TE | 160 | 10 | 4287 |

5 × 5 | TE | 160 | 5 | 1107 |

20 × 10 | TM | 300 | 20 | 1921 |

10 × 10 | TM | 200 | 10 | 1285 |

5 × 5 | TM | 300 | 5 | 853 |

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**MDPI and ACS Style**

Mendez-Astudillo, M.; Okayama, H.; Nakajima, H.
Evanescently Coupled Rectangular Microresonators in Silicon-on-Insulator with High *Q*-Values: Experimental Characterization. *Photonics* **2017**, *4*, 34.
https://doi.org/10.3390/photonics4020034

**AMA Style**

Mendez-Astudillo M, Okayama H, Nakajima H.
Evanescently Coupled Rectangular Microresonators in Silicon-on-Insulator with High *Q*-Values: Experimental Characterization. *Photonics*. 2017; 4(2):34.
https://doi.org/10.3390/photonics4020034

**Chicago/Turabian Style**

Mendez-Astudillo, Manuel, Hideaki Okayama, and Hirochika Nakajima.
2017. "Evanescently Coupled Rectangular Microresonators in Silicon-on-Insulator with High *Q*-Values: Experimental Characterization" *Photonics* 4, no. 2: 34.
https://doi.org/10.3390/photonics4020034