# Double-Slot Hybrid Plasmonic Ring Resonator Used for Optical Sensors and Modulators

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## Abstract

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^{−6}RIU) can be achieved after loaded Q factor modifications. In addition, the plasmonic metal structures offer also the way to process optical and electronic signals along the same hybrid plasmonic circuits with small capacitance (~0.275 fF) and large electric field, which leads to possible applications in compact high-efficiency electro-optic modulators, where no extra electrodes for electronic signals are required.

## 1. Introduction

## 2. Double-Slot Hybrid Plasmonic Ring

#### 2.1. Schematic and Simulation Method

**Figure 1.**(

**a**) Schematic of a double-slot hybrid plasmonic ring resonator; (

**b**) x-z plane cross-section view; (

**c**) power distribution of the x-z plane cross-section simulated by the axisymmetric finite element method. IPA, 2-isopropanol.

_{2}is used as the buffer layer, and liquids to be tested (or electro-optic polymer) are filling the slots and covering the device (infiltrating the device). The radius of the DSHP ring r is equal to the middle radius of the Si ring, as shown in Figure 1b. The width of the Si ring is denoted by w

_{Si}; the heights of the Si and metal layers are identical and denoted by h

_{WG}; the widths of the slots are w

_{slot}, and w is the total width (w = w

_{Si}+ 2w

_{slot}).

_{WG}= 250 nm, w

_{Si}= 300 nm and w

_{slot}= 150 nm. The refractive indices of Si and SiO

_{2}are 3.45 and 1.45, respectively, for the operation wavelength of 1550 nm. The infiltrating material is pure 2-isopropanol (IPA), whose refractive index is 1.3739 [24] at 1550 nm.

#### 2.2. Model Investigation

_{Si}= 350 nm and h

_{WG}= 250 nm. In the simulation process, the resonant wavelength is fixed around 1550 nm, and the azimuthal numbers (m) are changed from 15 to 55 with a step of five. The radii of the DSHP ring are adjusted according to the resonant condition of whispering-gallery mode:

_{eig}(real) and f

_{eig}(imag) are the real and imaginary parts of the eigenvalue of the m-th order whispering-gallery mode, which can be directly readout from the simulation software.

_{abs}and Q

_{rad}are the absorption and radiation quality factors of the ring, respectively.

_{abs}factor) is the major property of a DSHP ring with a large enough radius. In order to study the Q

_{abs}factor of the DSHP ring, one can fix the radius of the DSHP ring at 6 μm (radiation loss can be ignored) and change the geometry of the DSHP waveguide. In this way, the normal FEM simulation method can be used to study the properties of a DSHP waveguide per se. Since the hybrid propagation mode is a mixture between photonic and Surface Plasmon Polariton (SPP) modes, a q-parameter (q = w

_{Si}/w), representing the occupancy of a photonic mode, is used to study and optimize the performance of the DSHP ring resonator.

_{abs}factor versus the q-parameter, when the total width of the DSHP ring is changed from 500 nm to 1000 nm. The Q

_{abs}factor is estimated by:

_{g}is the group index of the confined whispering-gallery mode, which is expressed by:

_{eff}(real) is the real part of effective refractive index. The dispersion of n

_{eff}, $d{n}_{eff}(real)/d\lambda $, is computed by re-simulating the DSHP waveguide with a wavelength of $\lambda +\Delta \lambda $, and the n

_{eff}at $\lambda +\Delta \lambda $ can be obtained, which is denoted as ${n}_{eff}(\lambda +\Delta \lambda )$.

**Figure 2.**(

**a**) Q factor versus the radius of the double-slot hybrid plasmonic (DSHP) ring resonator with various widths of the slots (150 nm, 250 nm and 350 nm); the other geometrical parameters are: w

_{Si}= 350 nm and h

_{WG}= 250 nm; (

**b**,

**c**,

**d**) the Q

_{abs}factor, effective refractive index and sensitivity changes with the q-parameter for waveguides with a total width w of 500 nm, 600 nm, 700 nm, 800 nm, 900 nm and 1000 nm.

_{eff}(imag) is the imaginary part of effective refractive index.

_{abs}factors versus the q-parameter are calculated according to Equation (5), as shown in Figure 2b, where the total widths of the DSHP waveguide are changed from 500 nm to 1000 nm with a step of 100 nm. One can observe that the Q

_{abs}factor of the DSHP ring decreases with a smaller width due to the larger influence of the plasmonic layers in the narrower DSHP waveguide. For the DSHP rings with the same total width, there are optimal values of the q-parameter giving the maximum Q

_{abs}factor, which expresses the hybrid propagation modes of the DSHP ring, where the propagation loss is much lower than that of a pure plasmonic slot waveguide (when q is equal to either zero or one).

_{eff}versus the q-parameter for different total widths are shown in Figure 2c. The n

_{eff}increases with the occupancy of the slot by the Si ring (increase of q), which needs to be explained from two aspects: (1) the high refractive index of Si has greater influence and causes higher n

_{eff}of the DSHP waveguide; and (2) with the higher q-parameter, w

_{slot}of the DSHP ring is small, and so, the optical confinement is larger. The former explanation concerns the photonic mode, and the latter one concerns the plasmonic optical enhancement. The interaction between photonic and plasmonic modes leads to the nonlinear behavior of n

_{eff}.

_{res}is the resonant wavelength shift and ∂n

_{cover}is the refractive index change of infiltrating materials (∂n

_{cover}is set to be 0.003 in the simulation); Δn

_{eff}is the change of effective indices of the DSHP waveguide infiltrated with different materials.

_{abs}factor. The trade-off between the Q

_{abs}factor and sensitivity is similar to the one between propagation loss and optical confinement, which is a general behavior in hybrid plasmonic and plasmonic waveguides [21,27]. Based on the different behaviors of the Q

_{abs}factor and the sensitivity of the DSHP ring, one needs to carefully design the geometry of the DSHP ring to satisfy the requirements for particular applications.

## 3. Experimental Realization

#### 3.1. Si Side-Coupled DSHP Ring Resonator Design

_{slot1}= 250 nm, w

_{slot2}= 350 nm, w

_{Si}= 350 nm and h

_{WG}= 250 nm. Special attention needs to be paid here to the different widths of slots, which is in accordance with the conformal mapping theory of a ring resonator [28]: the power of the outer slot of the whispering-gallery mode is larger than the inner slot, which results in the unbalance between the two slots of the DSHP ring. The unbalance will cause larger propagation loss (or lower Q factor) due to a large part of the light confined at the slot material-Ag interface compared to the DSHP waveguide without bending. In order to compensate such unbalance, the outer slot can be designed to be slightly wider than the inner one. Besides, the wider outer slot will also decrease the n

_{eff}mismatch between the modes propagating in the open and closed areas of the DSHP ring, hence reducing the propagation loss of the designed, partly open DSHP ring resonator. Grating couplers are applied at each end of the device for the coupling between an optical fiber to on-chip devices.

**Figure 3.**Schematic of the Si bus waveguide side-coupled double-slot hybrid plasmonic ring sensor. The sub-figures are the detailed structures of the coupling area and the DSHP ring. The measurement setup is also illustrated. OSA, optical spectrum analyzer.

#### 3.2. Fabrication and Measurement Setup

_{2}buffer layer. E-beam lithography (EBL) is used to pattern the Si structure. Then, inductively-coupled plasma (ICP) dry etching with 10% over etch is performed, followed by a second EBL and ICP dry etching processes to fabricate the highly-efficient non-uniform grating couplers [29]. Finally, the pattern of the silver pads is introduced by the third E-beam exposure. After patterning, 20-nm Ge and 230-nm Ag layers are evaporated by a metal evaporation tool, where the Ge layer is used to increase the adhesive strength between silver and substrate material (SiO

_{2}). Then, a metal lift-off process is used to open the silver structures.

#### 3.3. Characterization Results

**Figure 4.**Scanning electron microscope picture of the fabricated double-slot hybrid plasmonic ring sensor.

**Figure 5.**Characterization results of the double-slot hybrid plasmonic ring sensor (black curves) and a silicon ring resonator with the same radius (red curves) infiltrated with 100% and 80% 2-isopropanol. The reference level is the transmission response of the straight waveguide with input/output grating couplers.

_{abs}factor (larger than 10,000), the measured loaded Q factor is much lower (~300). Neglecting the radiation losses from waveguide bends, the coupling loss from the Si bus waveguide to the DSHP ring and fabrication-induced roughness, the phase mismatch between the open and closed areas of the DSHP ring resonator is the major reason that leads to the small loaded Q factor. It can be modified by decreasing the difference of n

_{eff}between the two propagating modes, which will be shown in the following section.

## 4. Loaded Q Factor Modification

_{abs}factor shown in Figure 2b, which is mainly due to the phase mismatch between the different propagation modes (open and closed areas of the DSHP ring), in other words, the mismatch of n

_{eff}. In order to compensate for such a mismatch, the difference between the n

_{eff}of these two areas needs to be reduced. Since the n

_{eff}of the closed DSHP ring is higher than that of the partly open area with the same w

_{Si}due to better optical confinement, one can broaden the Si waveguide in the coupling area to get a higher Q factor, as shown in Figure 6a.

**Figure 6.**(

**a**) Schematic of the modified double-slot hybrid plasmonic ring sensor. (

**b**) Finite difference time domain (FDTD) simulation results of the modified DSHP ring sensor with different w

_{Si}(modified). The sub-figure shows the loaded Q factor as a function of w

_{Si}(modified).

_{Si}(modified). One needs to notice that the widths of the Si bus waveguide and the Si ridge of the open area of the DSHP ring have to be identical to achieve the phase match condition. The size and other parameters of the modified DSHP ring are similar to the fabricated one (w

_{Si}= 350 nm, w

_{slot1}= 250 nm and w

_{slot2}= 350 nm). In order to decrease the coupling loss, Si tapers are used to connect the coupling area to the DSHP ring area.

_{Si}(modified) increases from 350 nm to 550 nm. The transmission responses are shown in Figure 6b, where the different colors represent different w

_{Si}(modified). One can see that when w

_{Si}(modified) is around 500 nm, a maximum loaded Q factor is achieved (larger than 1000), which means that the n

_{eff}of the DSHP ring and the coupling are nearly matched, and the coupling loss comes to the minimum value.

## 5. Discussion

^{–5}RIU (5.37 × 10

^{–6}RIU after loaded Q factor modification). Table 1 shows the comparisons between the fabricated DSHP ring sensor and other experimentally-demonstrated label-free ring sensors. Due to the high sensitivity of the DSHP ring, the DL after loaded Q factor modifications is low.

**Table 1.**Comparison between different kinds of ring-type label-free sensors (* results after loaded Q factor modifications).

Waveguide structure | Width × Height | Radius | Q Factor | S (nm/RIU) | DL (RIU) | Reference |
---|---|---|---|---|---|---|

Si waveguide | 500 nm × 220 nm | ≈ 5 μm | 20,000 | 70 | 3.75 × 10^{−6} | [2] |

Si slot waveguide | 640 nm × 220 nm | > 5 μm | 500 | 298 | 4.2 × 10^{−5} | [16] |

SiN slot waveguide | 1150 nm × 250 | 70 μm | 1,800 | 212.13 | 2.3 × 10^{−5} | [15] |

DSHP waveguide | 950 nm × 250 nm | 6 μm | 300 (1034) * | 687.5 | 2.57 × 10^{−5}(5.37 × 10 ^{−6}) * | This paper |

_{33}= 300 pm/V [32], and assuming 80% of the resonant peak shift is provided by the slot material. Based on the given experimental results, the modulation voltage,

_{WG}is the average area of the capacitance formed by inner and outer Ag rings and w is the total width of the DSHP ring (w = w

_{Si}+ w

_{slot1}+ w

_{slot2}). By taking a reasonable resistance of electronic circuits (below 1500 Ω from [12]), the resistor-capacitor (RC) time constant is above 2 THz. For photon lifetime limitation, estimated from the Q factor, the bandwidth can reach a value larger than 600 GHz. The power consumption, expressing the energy dissipation during the charge-discharge cycles, is given by:

## 6. Conclusions

_{abs}factors when the radius is large enough (larger than about 6 μm), where the waveguide absorption loss dominants the performance of the DSHP ring rather than radiation loss. Then, optimizations are made for Q

_{abs}factors by defining the q-parameter (q = w

_{Si}/w) as the occupancy of the photonics mode. Simulation results show that the Q

_{abs}factors for hybrid plasmonic-photonics mode (0 < q < 1) are much larger than that for a pure plasmonic slot waveguide (q = 0 or 1), as shown in Figure 2b, where the optimized Q

_{abs}factors can reach as high a value as 300,000 in theory (w = 1000 nm and q = 0.55). Due to the interactions of the hybrid photonic-plasmonic mode, optimal q-parameters for sensitivity are also observed, which can reach 700 nm/RIU (w = 500 nm and q = 0.35), as shown in Figure 2d.

_{eff}between open and closed areas of the DSHP ring. FDTD simulation results show that the modified Q factor can be over 1000, when phase matching is achieved, as shown in Figure 6b.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Sun, X.; Dai, D.; Thylén, L.; Wosinski, L.
Double-Slot Hybrid Plasmonic Ring Resonator Used for Optical Sensors and Modulators. *Photonics* **2015**, *2*, 1116-1130.
https://doi.org/10.3390/photonics2041116

**AMA Style**

Sun X, Dai D, Thylén L, Wosinski L.
Double-Slot Hybrid Plasmonic Ring Resonator Used for Optical Sensors and Modulators. *Photonics*. 2015; 2(4):1116-1130.
https://doi.org/10.3390/photonics2041116

**Chicago/Turabian Style**

Sun, Xu, Daoxin Dai, Lars Thylén, and Lech Wosinski.
2015. "Double-Slot Hybrid Plasmonic Ring Resonator Used for Optical Sensors and Modulators" *Photonics* 2, no. 4: 1116-1130.
https://doi.org/10.3390/photonics2041116