Highly efficient tunable optical filter based on liquid crystal micro-ring resonator with large free spectral range

Abstract

A highly efficient tunable optical filter of liquid crystal (LC) optical micro-ring resonator (MRR) was proposed. The 4-μm-radius ring consists of a silicon-on-insulator (SOI) asymmetric bent slot waveguide with a LC cladding. The geometry of the slot waveguide resulted in the strong electro-optic effect of the LC, and therefore induced an increase in effective refractive index by 0.0720 for the quasi-TE mode light in the slot-waveguide. The ultra-wide tuning range (56.0 nm) and large free spectral range (FSR) (~28.0 nm) of the optical filters enabled wavelength reconfigurable multiplexing devices with a drive voltage of only 5 V. The influences of parameters, such as the slot width, total width of Si rails and slot shift on the device’s performance, were analyzed and the optimal design was given. Moreover, the influence of fabrication tolerances and the loss of device were both investigated. Compared with state-of-the-art tunable MRRs, the proposed electrically tunable micro-ring resonator owns the excellent features of wider tuning ranges, larger FSRs and ultralow voltages.

Keywords

integrated optics devices / liquid crystals / micro-ring resonator / slot waveguide / wavelength tuning

Introduction

Optical networks are widely used in modern communication systems. The use of various optical devices with good performance such as compact size, high fabrication tolerance, low loss, wide tuning range, etc, is becoming more and more significant. Micro-ring resonators (MRR) are one of the key optical devices designed to filter out a very narrow wavelength band from a broad spectrum. To make use of their high wavelength selectivity, they can be used as high-speed tunable filters, add-drop multiplexers, and modulators. As MRRs integrated with silicon-on-insulator (SOI) technology [ 1, 2], they can be very small, high Q factor, and have low losses. Recently, tunable silicon MRRs with wide tuning range and large free spectral range (FSR) are attractive for applications such as reconfigurable dense-wavelength-division-multiplexing (DWDM) [ 3], reconfigurable multichannel matrix switch [ 4] and on-chip waveguide sensor multiplexing [ 5].

Reported tunable optical filters based on MRR can be produced by using various physical effects, including thermo-optic effect [ 6], electro-optic effect [ 7], and free carrier plasma dispersion effect [ 8]. A 10-μm-diameter SOI-based ring resonator with the FSR of 18 nm and the tunable range of 6.4 nm is demonstrated using thermo-optic effect [ 9], however they suffer from large power dissipation, thermal crosstalk and low integration. Alternatively, both approaches using electro-optic effect of LiNbO₃ [ 10] and free carrier plasma dispersion effect of Si [ 11] enable fast modulation, but their tuning ranges are small due to the small effective index change. Another method is to combine strip waveguides with nematic LC cladding [ 12- 14], LC molecules are highly birefringent, and orientation can be electrically controlled by external electric fields. The tuning ranges of 31 and 4.5 nm are demonstrated for strip-waveguide MRRs guiding the TM mode and TE mode, but at the expense of smaller FSRs of 4.27 and 4.0 nm respectively [ 15], and these conventional LC MRRs usually have big sizes (large radii). Moreover, a rather high drive voltage of 100 V is required, which seriously limits the application of such LC MRRs.

In this work, we proposed a novel concept for electrically tunable liquid crystal micro-ring resonator based on an SOI slot-waveguide. The guided-wave slot structure was first proposed in Ref. [ 16], and this kind of waveguide is able to concentrate a large fraction of the guide mode into the slot region sandwiched between two strips, and the guide mode is more sensitive to the materials’ index distribution change of the slot region. In our proposed configuration, the slot waveguide geometry consists of two doped Si strips and liquid crystal cladding also sandwiched within slot region, the Si rails are conductive and are connected to metal electrodes through the thin conductive Si slab. Through optimal design [ 17, 18], a set of optimal parameters of the bent slot-waveguide ring of 4-μm-radius is chosen as below: the overall Si waveguide width of 400 nm, the slot width of 100 nm, the slot shift of 60 nm. And a LC slot MRR with an ultra-wide tuning range (~56.0 nm) and a large free spectral range (~28.0 nm) can be achieved, where the drive voltage was only 5 V. In addition, the influences of parameters such as the slot width, the total width of Si rails and the slot shift on the device’s performance were analyzed. The influence of fabrication tolerances and the loss of device were both also investigated.

Device structure and operational principle

Figure 1 shows the schematic diagram of the proposed novel tunable optical filters based on the LC MRR. It relies on the combination of a SOI MRR formed by slot-waveguide with liquid crystal cladding materials. The cross-sectional view of the bend slot-waveguide forming the ring is illustrated in Fig. 2. Some efficient electro-optical devices were realized by employing this kind of SOI strip-loaded slot waveguide [ 19- 21]. In our configuration, the asymmetric ring waveguide is adopted by using two parallel high-index SOI rails with different width, which are spaced by a slot region part. Since the Si slab and rails are assumed as conductors (doped P-type Si), the electrical contact will be generated by putting metal electrodes on top of the strip-loading at a clearance from the waveguide. The external voltage U applied to the metal electrodes induces a strong field within the slot region, as shown in Figs. 1 and 2.

LC slot waveguide

We use nematic liquid crystal (NLC) as a cladding. It behaves as uniaxial optical properties, where light polarized parallel (perpendicular) to the director experiences the so-called extraordinary (ordinary) refractive index n_e (n_o). The LC’s refractive index n_LC(θ) for the quasi-TE optical mode in the slot waveguide can be expressed by [ 13]

(1) n_{\mathrm{LC}}(\theta )={\displaystyle \frac{n_o{n}_e}{\sqrt{n_o^{\mathrm{2}}{\sin }^{\mathrm{2}}\theta +n_e^2{\cos }^{\mathrm{2}}\theta }}},

where θ is defined as the angle between the LC’s molecular director and the direction of oscillation of an electric field E (x-direction).

To investigate the electrical and optical characteristics of the LC slot waveguide, we assume two extreme extreme states of the LC slot waveguide as shown in Fig. 3(a), where the slot is centered (non-shift) for the sake of simplicity. First one suggests that without applying a voltage, LC’s director field is at a fixed initial state, and LC has a tendency to align to the surface it is attached. Thus, LC molecules align parallel to the waveguide axis [ 22] (z-direction) as shown in inset (1) of Fig. 3(a). The dominant x-polarized proportion of the quasi-TE optical mode within slot region experiences the ordinary refractive index n_o. Second one suggests that a large voltage is applied, LC molecules will shift in the electric field from the initial state. In particular, the LC molecules within the slot region are oriented along horizontal direction (x-direction) as shown in inset (2) of Fig. 3(a). The dominant x-polarized proportion of the quasi-TE optical mode experiences the extraordinary refractive index n_e.

For a given control electric field required to align the LC molecules, the associated operation voltage depends on the gap between the electrodes. Because the gap of strip-loaded slot waveguides can be made very small (100 nm), the operation voltages can hence be kept very low (only up to 5 V) [ 19].

Figure 3(b) shows the calculated refractive index n_LC(θ) on the voltage for the LC slot waveguide, where slot width g = 100 nm. The orientation distributions of the NLC molecules at different voltages are calculated by using the finite element method to minimize the Oseen-Frank energy [ 23]. And the adopted nematic phase liquid crystal is CB5. For the room temperature, the extraordinary (ordinary) refractive indices of the CB5 NLC are shown below: n_o,CB5 = 1.53, n_e,CB5 = 1.71 and Δn_CB5 = n_e,CB5-n_o,CB5 = 0.18.

Wavelength tuning characteristic of the slot micro-ring resonator with LC cladding

The resonance wavelength of a typical MRR is given by [ 12],

(2) {\lambda }_m={\displaystyle \frac{\mathrm{2}\pi R\cdot n_{\mathrm{eff}}}{m}},

where n_eff is the guide mode’s effective refractive index of waveguide, m is an integer, λ_m is the wavelength of the mth resonator mode, R is the radius of resonator (measured from the center of slot waveguide to midpoint of ring).

When a control voltage U is applied to the metal electrodes, a strong electric field will be induced within the slot region. By changing the orientation of the LC molecules with respect to the dominant electric field (E-x) component in the waveguide, we can vary the guide mode’s effective refractive index n_eff at the slot waveguide, and hence tune the resonance wavelength λ_m of the device.

In this paper, the optical mode characteristics of the SOI slot-waveguide with LC cladding and the refractive index of the guided mode were calculated by the full-vectorial mode solver considering the full anisotropy of nematic LC material [ 24]. Some numerical simulations were performed with a commercial mode solution software package from Lumerical. To make it clear, some basic parameters were defined. The heights of the Si rails and Si slab are H = 220 nm and h = 60 nm, respectively. The refractive indices of doped Si and lower cladding SiO₂ are 3.48 and 1.46, respectively.

For tunable liquid crystal microring resonator, there are two key performance characteristics that we are concerning: the wavelength tuning range and free spectral range.

To characterize the tuning efficiency by switching the LC director orientation, the tuning range of resonance wavelength can be defined as [ 14]

(3) \mathrm{\Delta }{\lambda }_{\mathrm{Res}}={\displaystyle \frac{\lambda \cdot _m\mathrm{\Delta }{n}_{\mathrm{eff}}}{n_{\mathrm{ef}\mathrm{f}}}},

which describes the dynamic tuning range and Δn_eff is the corresponding maximum change value of the effective refractive index.

Another important characteristic for this proposed LC MRR based on a slot-waveguide is the free spectral range (FSR), which can be denoted as below:

(4) \mathrm{\Delta }{\lambda }_{\mathrm{FSR}}={\displaystyle \frac{{\lambda }^{\mathrm{2}}}{\mathrm{2}\pi R\cdot n_g}},

where n_g is the group index of the slot waveguide.

Results and discussion

LC microring resonator based on the slot and strip waveguide

Compared with the conventional tunable liquid crystal MRR based on strip waveguide, the performance characteristic of LC slot MRR is analyzed. Figure 4 shows that E-field amplitude of the optical mode field for slot- and strip- waveguide with LC cladding. TE and TM mode are both taken into consideration for strip-waveguide.

Figure 5 shows that the relationship between the resonant wavelength and the voltage for the quasi-TE mode in our proposed LC MRR, and for the TE and TM mode in the conventional LC MRR as comparisons. A set of optimal parameters of the strip-loaded bend slot-waveguide is specified as below: the radius R = 4 μm, the overall Si waveguide width W = 400 nm, the slot width g = 100 nm, the slot shift x = 60 nm. The optimal design is discussed in Section 3.2. The results illustrate a large resonant wavelength shift of 56.2 nm for our LC MRR, at the same time, the tuning ranges are 31 and 4.5 nm for strip-waveguide MRRs guiding the TM mode and TE mode, respectively. Thus, the dynamic tuning range of resonance wavelength can be enhanced using the slot-waveguide. The significant difference lies to the maximum change value of the effective refractive index. It is easily calculated that, for the LC slot waveguide, Δn_eff can reach to about 0.0720. However, for typical strip waveguide with LC cladding, W = 450 nm, h = 220 nm, Δn_eff is calculated to be 0.0113 for TE mode and 0.0663 for TM mode by the same numerical method.

From Eq. (4), the corresponding FSR of the proposed LC slot-MRR is calculated to Δλ_FSR = 28.0 nm. It is larger than that of conventional LC MRRs. And it has seven and eight times the FSRs of 4.27 nm for TM and 4.0 nm for TE mode [ 15], respectively.

In addition, Fig. 5 shows that another key merit for the slot waveguide-based ring resonator is that the maximum operation voltage only requires 5 V, while it is 100 V for the conventional strip-waveguide. It is because this slot gap can be fabricated with a very small size (in 100 nm) for slot waveguide, whereas all other configurations [ 12- 15] must have electrode separations of at least a few microns, by applying the voltage between an indium-tin-oxide (ITO) top electrode and the substrate as bottom electrodes.

Optical design and analysis of liquid crystal micro-ring resonator

In this section, the influences of parameters including slot width, total width of Si rails and slot shifts on the performance of the micro-ring resonator with small radius (R = 4 μm) will be investigated in detail.

Referring to Eq. (4), it is obviously shown that small radii lead to large FSRs of MRR, the FSR is calculated 28.0 nm when R = 4 μm. In addition, the tuning range drops down when the radii of MRRs decrease. This is because the light in the slot is greatly diminished when traveling around a sharp bend, then the overlap of the optical mode and the LC cladding is diminished. Therefore, the bending effect of waveguide has an important role on the performance characteristics of this device such as the dynamic tuning range of wavelength and FSR. In the following section, we concentrate on the design and analysis of slot-waveguide micro-ring resonator with small radius (R = 4 μm).

Figure 6 shows the tuning range of resonance wavelength calculated as a function of g. Slot width g varies from 40 to 200 nm at a step of 20 nm, at W = 400, 480 and 600 nm (w_l = w_r is fixed at either 200, 240, 300 nm), no slot shift x = 0 nm. It can be seen that, with the increase of g, the tuning range increases at the beginning and reaches to the maximum value. Then after that it drops down. In principle, when the slot waveguide is designed with an optimal wide slot gap, the majority of the modal light lies within the slot sandwiched between two high-index rails. However, the light intensity inside the slot decreases with the increase of the slot width. Therefore, the proportion of the light inside the slot to the overall light in the slot-waveguide reduces. To make a tradeoff between the output wavelength tuning range and the LC molecules infiltrating fabrication, we could not choose too small slot width (the slot is usually at around 100 nm), because the LC molecules should be easily infiltrated into the slot area.

In addition, the tuning range is relatively large at smaller W while the tuning range is relatively small at larger W. The slot waveguide of LC MRR using a very narrow silicon rail is able to obtain large tuning range due to a large evanescent field in the LC cladding of slot. However, the surface roughness significantly increases the waveguide loss. Thus the waveguide width in a slot-waveguide needs to be sufficiently wide to avoid large surface roughness scattering loss.

Next, the tuning range of resonance wavelength Δλ_Res and FSR Δλ_FSR of Si slot-waveguide LC MRR with the change of slot shift are investigated. The light in the slot is greatly diminished when traveling around a sharp bend. Thus, for a bending (especially sharp bend) slot waveguide, we could shift the slot position toward the outside of the bend to maintain the tuning efficiency. This is because shifting the slot ensures that the slot is placed at the region, where the maximum overlap between the two evanescent tails of the high index waveguide modes [ 17].

Figure 7(a) shows the tuning range of the resonance wavelength as a function of the slot shifts x at different overall Si rail widths with the following fixed parameters: g = 100 nm, W = 400, 480, 600 nm, and R = 4 μm. It can be seen that the tuning range is maximized at different x for different overall Si rail widths. For example, the maximum of Δλ_Res occurs at x≈60 nm, x≈40 nm and x≈40 nm for W = 400, 480 and 600 nm, respectively. Appropriate slot shift x is then chosen according to this figure to achieve the maximum tuning range of wavelength. Figure 7(b) shows the tuning range of resonance wavelength as a function of slot shifts x at different slot gap widths with the following fixed parameters: W = 400 nm, g = 60, 100, 140 nm, and R = 4 μm. It can be seen that the tuning range is maximized at different x for different slot gap widths. The maximum of Δλ_Res occurs at x≈40 nm, x≈60 nm and x≈80 nm for g = 60, 100 and 140 nm, respectively. Similarly, appropriate slot shift x is then chosen according to this figure to achieve the maximum tuning range. The values of tuning range drop tragically when x deviates from the optimal slot shift. Therefore, the tuning range of the proposed LC micro-ring is very sensitive to the slot shift.

Figures 8(a) and 8(b) show the corresponding FSRs as a function of the slot shift x at different overall Si rail widths W or different slot widths g. From the results, the above FSRs are in range from 24 to 30 nm, and the maximum value is at the corresponding slot shift. The slot shift has little influence on the FSRs of the proposed LC micro-ring.

In a word, considering the influences of parameters including slot width, total width of Si rails and slot shifts, we could choose a set of optimal parameters: the overall Si waveguide width W = 400 nm, slot width g = 100 nm, and slot shift x = 60 nm.

Fabrication tolerances and loss analysis

We further study the fabrication deviation tolerances of the device. For the 4-μm-radius LC slot MRR, assuming the slot with is fixed at 100 nm for g and the slot position x = 60 nm. The dynamic tuning range of the LC slot MRRs is calculated as a function of total Si strips width. From Fig. 9(a), in general, it has a wavelength tuning range above 45 nm throughout a wider range of W (from 300 to 500 nm), and the optimal value of W is equal to 400 nm.

Moreover, slot waveguide fabrication also induces silicon deep etching [ 25] that could produce non vertical side-walls in the structure. The wavelength tuning ranges are also significantly influenced by this kind of fabrication tolerance. Thus, non vertical sidewall effect on the dynamic tuning range of the slot-waveguide LC MRRs has been investigated in Fig. 9(b). A small decrease of wavelength tuning range on tilting angle θ has been observed.

Concerning the total optical loss of the devices, there are two major sources that contribute to the propagation losses of the slot ring: bending radiation losses due to the bent slot waveguide and additional material losses due to the deposition of the LC cladding. Displacing the slot region from the center of the waveguide toward the outside not only maximizes the power inside the slot, but also reduces the bending losses in the slot waveguide. This is due to the increased confinement in the slot. Figure 10 has shown the electric intensity |E|² of the quasi-TE optical mode field for the bent asymmetric LC slot-waveguide, the major part of light is confined in the shifting slot. Bending radiation losses could be calculated by monitoring the optical power of the quasi-TE mode in the bent slot waveguide as a function of the propagation distance, resulting radiation losses of 4.54 dB/mm. The deposition of the LC cladding led to an additional loss of below 2 dB/mm by using special materials with low infrared absorption such as CB5 or E7 [ 26].

Conclusions

This paper presented a novel tunable optical filter of microring resonator with wide tuning range large free spectral range and low operation voltage by realigning NLC molecules. By applying a control voltage on the electrodes connected to the thin conductive Si slab, a strong electric field will be induced within the slot region, and it will change the orientation of the LC molecules with respect to the dominant electric field (E-x) component in the waveguide, therefore we can tune the guide mode’s effective refractive index n_eff at the slot waveguide. After the optimal design, a set of optimal parameters of the slot micro-ring resonator is specified as below: the radius of 4 μm, the overall Si waveguide width of 400 nm, the slot width of 100 nm, the slot shift of 60 nm. The proposed LC MRR provides the excellent performances of an ultra-broadband tuning range (~56.0 nm) and a large free spectral range (~28.0 nm) and an ultralow operation voltage (~5 V). The fabrication of the proposed LC MRR based on an SOI slot waveguide and the design of the electrode structure can be easily demonstrated. For further research of LC micro-ring resonator based on slot waveguide, we will focus on the device fabrication.

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