A Demultiplexing Filter With Box-Like Response and Large FSR Based on LNOI Second-Order Micro-Ring Resonators

We propose and experimentally demonstrate a high-performance micro-ring resonator (MRR) with a large free-spectral range (FSR) on the lithium niobate-on-insulator (LNOI) platform. Mode crosstalk happens in LNOI waveguide bends because more than one mode is generated from the anisotropy of lithium niobate, which limits the minimum bending radius of MRRs. Mode properties of ridge waveguides on X-cut LNOI with different bend radii and wavelengths have been analyzed to remove the effect of mode hybridization and reduce the mode crosstalk. On this basis, a small radius MRR with large FSR and 3dB bandwidth is achieved. Further, to deal with the wavelength shift caused by fabrication error, a second-order micro-ring resonators (2nd-order MRRs) filter with a box-like response and a high out-of-band rejection ratio is realized. Besides, a multichannel demultiplexing filter is realized based on 2nd-order MRRs with low crosstalk (<−13 dB) at a channel spacing of 1.16 nm. The demonstration of the demultiplexing filter with a box-like response paves an important step for high-density photonic integration on the LNOI platform.


I. INTRODUCTION
M ICRO-RING resonator (MRR) is one of the most versatile and attractive integrated photonic devices due to its small footprint [1], which is widely used in wavelength division multiplexer (WDM) [2], filters [3], optical switches [4], modulators [5] and other optical integrated devices [1], [6]. Since the combination of a high index contrast and the availability of CMOS fabrication technology based on silicon on insulator (SOI) platform, SOI-based micro-rings have achieved numerous excellent performances [1], [7], [8]. It is reported that the SOI micro-rings have achieved a large free spectral range (FSR) of 93 nm, 3 dB bandwidth of 0.8 nm, and insertion loss of 1.8dB in the C-band [9]. Generally, the spectral response of a single MRR is Lorentzian-like. To realize a high-performance photonic filter, a box-like spectrum with a maximally flat response is often desired because it can tolerate wavelength shifts caused by fabrication Manuscript  error [10], [11], [12], [13]. The principles of a demultiplexing filter with a box-like spectral response can be achieved conveniently by using multiple MRRs. For example, high-order MRRs are proposed to achieve filter with a box-like response [13]. By introducing high-order adiabatic elliptical micro-rings, a filter is achieved with box-like spectral responses and ultra large FSR (∼37 nm), which can be used to form an eight-channel silicon photonic filter with a channel-spacing of ∼3.2 nm and high extinction ratios >30 dB [14]. Additionally, numerous MRRs with different structures have been demonstrated on the SOI platform, including using the Vernier effect to expand FSR [15], using the Bezier curve to reduce loss [16], and using an MZI structure to realize reconfigurable [17], and so on. Remarkable achievements have been made in the research of the SOI-based MRRs over the past years.
Over the past few years, research on Lithium niobate on insulator (LNOI) has blossomed. One of the key benefits of developing thin film LN is that a variety of different components (including tunable filters) can be integrated into the same chip to achieve a more functional chip. [18]. Various structures based on LNOI can fully leverage the extraordinary linear, nonlinear, and electro-optic properties of LN to achieve many integrated devices with record-high performance [19]. Compared with thermo-optic tuning in silicon-based filters, elector-optic tuning enables a much higher speed and thus has broader application perspectives. Effective refractive index changes with the variety of electric fields, which will affect the 3dB bandwidth and resonance wavelength to realize a reconfigurable spectrum. LNOI-based filters allow low power consumption to realize high tuning efficiency. There is a promising future for LNOI-based filters to realize multiple functionalities and be applied to various applications. Although many achievements about micro-rings have been made on the SOI platform, up to date, few theoretical designs have been reported on the LNOI platform [16], [17], and experimental demonstrations are still lacking. Mainly owing to its large structural birefringence, sub-micrometer photonic integrated devices suffer from severe polarization-dependent effects [20]. When light is transmitted around a bent waveguide on an X-cut LNOI platform, the propagation characteristics of TE modes change along with bending transmission because of the anisotropic refractive index tensor of LN, leading to mode hybridization and mode crosstalk, which present challenges to minimize the radius of MRRs. There are two methods to reduce the effect of mode hybridization. One approach is choosing geometrical parameters to achieve constructive interference between the excited modes [21]. Another one is designing special waveguide structures to ensure the effective refractive indices n eff,TE of the quasi-TE mode are always greater than the effective refractive indices n eff,TM of the quasi-TM mode in C-band to avoid mode hybridization. In order to achieve a large FSR, a small bending radius of MRR without mode crosstalk is necessary on the LNOI platform. Besides, to realize high-performance photonic filters with box-like responses as well as high out-of-band rejection ratios, high-order MRRs are needed. However, most research based on LNOI micro-rings focuses on realizing high quality factors rather than box-like spectral response. Therefore, it is still an open challenge to realize demultiplexing filters on the LNOI platform with large FSR, low mode crosstalk, box-like response, and high out-of-band rejection ratio.
In this paper, we propose an add-drop racetrack resonator with a small footprint on the LNOI platform to remove the fundamental-mode crosstalk by designing a rational ridge waveguide. In particular, a large FSR is achieved by selecting small radii of MRRs. Furthermore, a 2 nd -order MRRs filter is designed to realize a box-like spectral response, which greatly improves the roll-off rate and increases fabrication tolerance. Besides, in order to verify that the 2 nd -order MRRs can be feasibility applied to WDM systems, a demultiplexing filter is designed and fabricated with low adjacent crosstalk∼−13 dB, which is helpful for realizing high-performance multichannel WDM systems with MRRs in the future.

II. DESIGN AND SIMULATION
Devices based on LNOI have distinctive characteristics compared with SOI and other isotropic platforms because of the strong material birefringence [20]. The orientations of TE polarizations and the optical axis of LN are constantly changing in different locations of MRRs, making it complicated to analyze the propagation characteristics of TE modes on the X-cut LNOI platform. We choose the waveguide structure with a total thickness of the LN film t total = 0.6 μm, the etching thickness t co = 0.3 μm, the width of the ridge (defined at the top of the ridge) w top = 1 μm, the sidewall angle θ etch = 60°, and the air is considered as the cladding, as shown in Fig. 1(a). The upper-case X/Y/Z represents the coordinate system of the LN crystal while the lower-case x/y/z represents the coordinate system of the waveguide. The angle between the coordinate axis y and the optical axis Y of the LN material is defined as ϕ. With light propagation in the arc-bend, the ϕ changes from 0°to 180°, as shown in Fig. 1(b). The quasi-TM mode always sees the same refractive index n o , while the quasi-TE mode experiences a large refractive index change from n o to n e , which may cause mode hybridization. The process of partial TE mode translated into TM mode is present in Fig. 1(c). Here, n o and n e represent the refractive indices of ordinary and extraordinary light of LN respectively. Mode hybridization is the phenomenon in the waveguide whereby two orthogonally polarized modes propagate with similar phase velocity and couple to each other. Fig. 2(a) and (c) show the effective refractive indices n eff,TE under the wavelength of 1.31 μm and 1.55 μm with radii at 10 μm and 20 μm when the ϕ varies from 0°to 180°respectively. Obviously, the values of n eff,TE and n eff,TM are closer at 1.31 μm than 1.55 μm in X-Z plane, which means the TE mode is converted into TM mode conveniently. The same conclusion can be obtained by analyzing the TE-fraction. Here, the TE-fraction is used to represent the ratio of the energy of TE polarization to the total energy. In the process of mode hybridizing, TE-fraction is decreasing, which means that the TE mode is transformed into TM mode. As shown in Fig. 2(b), the TE-fraction fell to 0.60 and 0.72 for radii of 10 μm and 20 μm respectively at the wavelength of 1.31 μm. In contrast, for the injected light with the wavelength of 1.55 μm, the TE-fraction is close to 1 both in radii of 10 μm and 20 μm. Therefore, mode hybridization takes place in the waveguide when the wavelength of injected light is around 1.31 μm, and the effect of it is removed at the C-band.
Based on the above analysis, we design a single MRR with a width of 1 μm and a radius of 10 μm, where the bus waveguide has the same width as the MRR. A small radius brings a large bend loss which leads to the round-trip transmission of electric field α being 0.83. Here, α is the transmission loss factor, which represents the loss of light transmitted in the micro-ring for one cycle. In order to increase coupling coefficients, we introduce  a racetrack with a length of 3 μm. And the gap, between the bus waveguide and the racetrack waveguide is set to 220 nm, as shown in Fig. 3(a). For cascaded 2 nd -order MRRs, the waveguide width, bending radius, and racetrack length are1.2 μm, 20 μm and, 10 μm, as shown in Fig. 3(b). MRRs and the bus waveguide have the same width. The round-trip transmission of electric field α is 0.946 for a single MRR. According to the maximally-flat criterion [10], the coupling ratios of 2 nd -order MRRs structure is designed as (κ1, κ2) = (0.5, 0.15). Where κ1 and κ2 are the amplitude coupling coefficient from the bus waveguide to the racetrack waveguide and ring to ring respectively. Corresponding the gap from the bus waveguide to the racetrack waveguide and ring to ring are set to 250 nm and 500 nm.
We attempt to design 2 nd -order MRRs to improve the tolerance of fabrication errors by the flat top response, which can solve the problem of wavelength shift. The group indices for the two structures are calculated. Considering the birefringence property of LNOI, the group index n g above the X-Z plane and X-Y plane will be different but put the equivalent effects on the characteristics of light [20]. Therefore, the average group index of MRR as calculated: where n xz is the group index of the X-Z plane in the MRRs, n xy is the group index of the X-Y plane in the MRRs, n ave is the equivalent group index of MRRs. n str is the group index of the track. The values of different parts are shown in Table I. The scanning electron microscopy (SEM) images for MRRs are shown in Fig. 3(c)-(d).

III. EXPERIMENTAL RESULTS
The proposed devices are fabricated on a 600-nm-thick X-cut single-crystalline LN thin film sitting on a 2-µm-thick buried silicon dioxide layer. The pattern is defined by electron beam lithography (EBL) and transferred onto the LN layer at a height of 300 nm by reactive ion-etching (RIE). We performed the measurement of MRRs using a continuously tunable laser in the range of 1.5-1.6 μm. As shown in Fig. 4, light emits from a tunable laser with a wavelength in the range of 1.5-1.6 μm. After passing through the polarization controller (PC), the injected light is kept in TE polarization. Then, the TE light in small mode field diameter fiber arrays (mode field diameter of about 4.0 μm) is coupled to our chip. Next, we put the same devices on the right side, and this fiber array is regarded as output ports and connected to an optical spectrum analyzer (OSA). The transmission spectrum of the MRRs is obtained by continuous scanning of the wavelength from 1.5 μm to 1.6 μm. Fig. 5(a) and (b) are the measured spectra for a single MRR (1 st -order MRR) and the cascaded 2 nd -order MRRs. These results are normalized by the transmission of a straight singlemode LNOI strip waveguide on the same chip. As shown in Fig. 5(a), for a single MRR with a radius of 10 μm, FSR is 13.33 nm, the bandwidth of 1 dB and 3 dB are 1.02 nm and 2.05 nm, and the variation range of 3 dB bandwidth is less than 0.3 nm, out of band rejection ratio is 8.68 dB. As shown in Fig. 5(b), for high-order MRRs with the radii of 20 μm, the FSR is 6.25 nm, and the bandwidth of 1 dB and 3 dB are 0.59 nm and 0.9 nm, corresponding to the variation range of 1 dB and 3 dB bandwidth are 0.12 nm and 0.14 nm respectively, the out-of-band rejection ratio is 16.98 dB. The roll-off rates for the 1 st -and 2 nd -order MRRs are 5.16 dB/nm and 19.9 dB/nm, respectively. Obviously, the roll-off rate of the high-order MRRs is nearly 4 times higher than that of the single MRR, which shows a higher out-of-band rejection ratio and a better box-like spectral response.
The above advantages of MRRs make the present design attractive for realizing WDM on-chip photonic integration in the future [22]. Here, we attempt to design MRRs with different radii to realize a demultiplexing filter. As shown in Fig. 6(a), the radius difference of the MRRs is 0.28 μm, and a 2-channel demultiplexing filter based on 2 nd -order MRRs is demonstrated. The measurement results are shown in Fig. 6(b), a low crosstalk (< −13 dB) is realized with a channel spacing of 1.16 nm. Notably, this design can accommodate more channels due to its large FSR. In addition, it is predictable that the out-of-band rejection ratio and crosstalk can be further improved to meet the requirements for more applications by cascading MRRs. Besides, expanding the channel spacing and reducing bandwidth appropriately are also useful methods to avoid coherent crosstalk.
As a note, the potential applications for 2 nd -order MRRs in WDM have been provided in our paper. In addition, by designing electrodes to meet the condition that the extraordinary optical axis is aligned to the applied lateral electric field, it is possible to efficiently tune the index of MRRs. Taking advantage of the excellent electro-optic effect of LNOI, we can achieve a reconfigurable spectrum with low power.

IV. CONCLUSION
In this paper, we have proposed and demonstrated a highperformance add-drop racetrack MRR with a large FSR. By analyzing the effective refractive indices of ridge waveguides, we propose a waveguide structure with appropriate parameters to remove mode hybridization on the X-cut LNOI platform in the C-band. In this way, a sharp LNOI bend waveguide with a radius of ∼10 μm has been designed and a large FSR∼13.33 nm is achieved. Furthermore, a high out-of-band rejection ratio and a box-like spectrum can be obtained by cascading 2 nd -order MRRs. It can be predicted that cascading more MRRs can further optimize the spectral shape. In particular, a 2-channel WDM filter based on the 2 nd -order MRRs is demonstrated with a channel spacing of 1.16 nm and low crosstalk of < −13 dB. Moreover, more channels can be realized by adding MRRs with different radii. With the fabrication technologies becoming more and more mature, it is expected to realize more LNOI photonic integrated devices with better performance, which makes large-scale photonic integrated circuits on LNOI more and more competitive.