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Abstract
Photonic crystal (PhC) cavities with high Q factor and low volume have been applied in nonlinear, electro-optic and acoustic-optic devices due to the enhancement of the light-matter interactions. However, there are few devices and research on LiNbO3 (LN) PhC cavities due to the difficulty in making hyperfine structures on LN platform. In this work, we propose a PhC nanobeam cavity on the etchless x-cut LiNbO3-On-Insulator (LNOI). The fabrication-friendly device has been designed based on photonic bound states in the continuum (BICs) exhibiting a high Q factor of over 10,000 with the device length of only about 100 µm. Utilizing the electro-optical effect γ13 of LN, we demonstrate an ultra-compact electro-optic modulator based on the PhC nanobeam cavities, which has the modulation efficiency of 1.5 pm/V and the 3 dB bandwidth of 28 GHz.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Recently, LiNbO3-On-Insulator (LNOI) has emerged as a promising platform to realize electro-optic (EO) modulator with high speed, high linearity and low loss for high-capacity, broadband, and intelligent optical systems [1–6]. LNOI based modulators are mainly realized by Mach-Zehnder Interferometers (MZIs) or resonators. For the MZI based modulators, the length of interference arm is usually as large as several centimeter [1], which results in very large device size, not conducive to compact integration. The device size can be reduced by using the resonator structures such as the ring resonators [7], Fabry-Perot (FP) cavities [8], sidewall-modulated photonic nanowires [9] and the photonic crystal (PhC) cavities [10]. However, due to the large anisotropy of LN, the ring resonators have to be manufactured with large footprint because the waveguide bending radius should reach hundreds of microns to suppress mode hybridization [11,12]. While the FP cavities or PhC cavities can reduce the size to dozens of microns, but low etching selectivity with respect to the available lithography resists of LN and the redeposition of the materials during etching result in the limited depth and cone-shape holes, which limit the performance of these cavities [13].
In order to avoid the etching of LN directly, PhC on LNOI can be realized by using the hybrid integration method [14–16]. But on such devices, only few optical mode is in the LN which lead to weaker EO interactions. Recently, Yu. et al. theoretically and experimentally demonstrated low loss bound states in the continuum (BIC) mode in the etchless LNOI thin-film by utilizing the low-refractive-index polymer waveguide on top of the LNOI [17]. Various devices, including the photodetectors [18], the electro-optic modulators [17,18], and the acousto-optic modulators [19] have been demonstrated then. BICs mean a type of waves that can be confined in the continuous spectrum with low radiation. The lifetime of these bound states in the BIC is infinite due to the mutual destructive interference of different radiation channels in the far field [20,21]. Photonic integrated devices operating under the BIC principle are capable of realizing very complex structures and can avoid the limitations of etching nanostructures. However, the footprint of these devices is usually quite large due to their large bending radii. In addition, low loss has been shown only at a specific bending radius which results in the difficulty of device design and the low degree of design freedom of resonators such as the micro-ring cavity.
In this paper, we demonstrate an ultra-compact electro-optic modulator based on the etchless LNOI PhC nanobeam cavity utilizing the BIC principle. To the best of our knowledge, this is the first LNOI PhC nanobeam cavity based on BIC. The measured quality factor of the PhC nanobeam cavity is ∼12,010. The length of the present nanobeam cavity is only ∼100 µm, which is much smaller than the ring resonator of BIC on LNOI proposed before [17,22]. Moreover, we verified the EO modulation performance of the proposed cavity, and the device demonstrated a modulation efficiency of 1.5 pm/V with a 3 dB bandwidth of 28 GHz.
2. Design and fabrication
The cavity is designed based on the LNOI platform with a 240 nm thick LN layer and a 4.7 µm buried silica layer. The cross section of the waveguide structure is shown as Fig. 1(a). Here the width of the polymer waveguide is tuned to obtain a supported BIC mode on the LNOI platform. The waveguide structure is optimized to make interference between the coupling channels and avoid the coupling of TM0 bound states into TE mode at the same time, resulting in the dissipation of photons into the continuum. The calculated propagation loss of the TM0 mode for different polymer waveguide width (w) is shown in Fig. 1(b). When the waveguide width is chosen to be 2.1 µm or 4.5 µm, the waveguide loss is the lowest, and the TM0 mode almost does not radiate which are the expected BIC. The optical field of the BIC are shown in the insets of Fig. 1(b). Compared with the conventional TM0 mode as shown in the central inset of Fig. 1(b), BIC modes have no light field distribution in the LN slab, so they will have negligible propagation loss. In addition, although the transmission loss is smaller for a wider BIC waveguide, the device size will also increase. Thus, the waveguide width is finally chosen to be 2.1 µm.
Fig. 1. (a) Schematic of the cross section for the waveguide supporting the photonic BIC mode. (b) Calculated (black line) and measured (red dots) propagation loss of the straight waveguides as a function of the width. The Ordinate is logarithmic. The inset is the profiles electric field distribution of the TM0.
After the waveguide structure is determined, the PhC nanobeam cavity is proposed in this work using periodic stack structures formed in the polymer layer on top of the LNOI, as shown in Fig. 2. The polymer we used is ZEP-520A. The thermo-optical coefficient of ZEP-520A is around −10−4 K−1 [23,24] and LN is 4 × 10−5 K−1, which can effectively compensate for the change of effective refractive indices as temperature varies, this structure has been verified to be temperature insensitivity [25]. The device works normally as long as the temperature does not exceed the melting temperature of the polymer. Moreover, ZEP-520A has been demonstrated it can work in higher laser powers [25] and humidity environment [23].
The cavity width of the nanobeam and the photonic crystal period are fixed, and the light resonance is realized by modulating the proportion of the polymer dielectric and air in the stack structure within the period. The inset in Fig. 2 shows an enlarged diagram of the PhC nanobeam cavity, where a is the period and w is the width of the stack along z direction.
The period is selected as a = 510 nm to ensure that the resonant wavelength is close to 1550 nm. Here, we define the filling factor (ff) as the proportion of the air width to the period. ff is modulated from the center of the PhC nanobeam cavity (ffcenter) to both sides (ffend) by the function ff(i) = ffcenter + (i−1)2/(Nmirror−1)2(ffend − ffcenter), where Nmirror is the total number of the stack. Figure 3(a) shows the band diagram of the PhC nanobeam cavity (the band structure is calculated through 3D Finite Difference Time Domain (FDTD)). The PhC structure on both sides forms a band gap for the resonant light, while the dielectric band of the PhC structure in the middle is pulled into the band gap as shown in the inset of Fig. 3(a). Modulated stacks with gradually changed size are added on both sides to achieve high transmission. The number of mirrors influences both the Q factors and the transmittance of the nanobeam cavity. Thus, we chose the ffcenter = 0.627, ffend = 0.490 and investigated the Q factor and the transmittance of the nanobeam cavity with different number of mirrors. To investigate the resonance characteristics of the designed cavity, the Finite Element Method (FEM) based three-dimensional simulations are performed using commercially-available software (COMSOL Multiphysics). The result is shown in Fig. 3(b). The Q factor of the cavity almost linear increases with the Nmirror. However, if Nmirror increase further, the transmittance of the PhC nanobeam cavity will decrease. Balanced the Q factor and transmittance, we chose the number of mirrors is 240. The total device footprint is only 257 µm2.
Fig. 3. (a) The calculated band diagram of the PhC nanobeam cavity. The red line indicates the band structure with ff = 0.627, and the black line indicates the band structure with ff = 0.490. (b) Calculated Q factor and transmittance at the resonance as a function of mirror number.
Fig. 4. (a) Microscope image of the fabricated PhC nanobeam cavities with input/output grating couplers and a pair of electrodes. (b) and (c) Scanning electron microscope (SEM) image of the BIC PhC nanobeam cavity and the grating coupler, respectively.
The BIC PhC nanobeam cavities were then fabricated on the LNOI platform with a 240 nm LN layer and a 4.7 µm oxide buried layer. Firstly, the electrode consisted of 10 nm thick titanium and 150 nm thick gold has been formed by utilizing the electron beam evaporation followed by a lift-off process. Then a 500 nm thick positive tone electron beam resist (ZEP-520A) was spin-coated onto the top of the wafer at 2000 rpm. Then the LNOI wafer was baked on a hot plate at 180 °C for 3 minutes. Electron beam lithography (EBL) was adopted to define the patterns of the waveguide at 50 KeV acceleration voltages and the exposure dose is 110 µC/cm2. After lithography process, ZEP-520A on LNOI was developed for 90 s in the developer (n-Pentyl acetate) at room temperature and then fixed in IPA for 1 min. The microscope image of the fabricated device and the scanning electron microscope (SEM) image of the PhC nanobeam cavity part and the grating coupler are shown in Fig. 4, which shows the smoothness and well-defined fineness of the device structure.
3. Characterization and discussion
To characterize the fabricated BIC PhC nanobeam cavity, a broadband amplified spontaneous emission (ASE) source with the wavelength ranging from 1520 to 1610 nm and an optical spectrum analyzer (OSA, Yokogawa AQ6370D) are utilized to measure the output spectra. Light was coupled into and out of the device via the grating couplers. Firstly, the propagation loss of the waveguide working at BIC mode with different width is measured for the fabricated waveguide with different lengths, and the measured data is shown in Fig. 1(b). The measured propagation loss of the waveguide with width of 2.1 µm is about 0.26 dB/cm, and it is basically consistent with the calculated results.
The measured transmission spectra of the BIC PhC nanobeam cavities is shown in Fig. 5(a). From the figure, it can be found that the resonant wavelength for the fundamental mode of the PhC nanobeam cavity is around 1549.3 nm. It deviates from the calculated one due to the fabrication imperfections, i.e., the waveguide width variations and the dielectric stack length variations. The inset of Fig. 5(a) shows the measured transmission spectrum of the fundamental mode, with the optical field converged in the center of the cavity, as shown in Fig. 5(b). The full width at half maximum (FWHM) is 0.129 nm from the Lorentzian fitting of the spectrum, which indicate a Q-factor of 12,010 with the transmittance ∼ 0.15 at the resonant wavelength which much higher than the reported hybrid integrated LN nanobeam cavities [14].
Fig. 5. (a) Measured transmission spectrum of the BIC PhC nanobeam cavity. In the inset, the black circles represent the enlarge view of the measured spectrum and the red line represents the Lorentz fitting of the fundamental mode; (b), (c), and (d) the electric field (EX) profiles of the fundamental, second-order and third-order cavity modes in XY plane, respectively. The electric field profiles are simulated by the Finite Element Method (FEM). The inset on bottom right corner of (b) is the enlarged diagram.
The high quality and low mode volume of the BIC PhC nanobeams enables us to control the light by external physical field, such as the electric [10,26] and acoustic fields [27]. Due to the BIC mode is TM0, it is difficult to apply electric field on the same direction with optical mode. Utilizing γ13 electro-optic coefficient of LN, a pair of electrodes (Fig. 2) were added to both sides of the PhC nanobeam cavity to electrically modulate the optical signal. The transverse component of the electric field changes the refractive index of LN slab and then shifts the resonant wavelength of the cavity. The experimental results are shown in Fig. 6. The transmission spectrum of the fundamental mode of the device blue shifts as the voltage increases. By measuring the resonant wavelength in Fig. 6(a), the linear relationship between the resonant wavelength and the voltage is shown Fig. 6(b). The 3 dB switch voltage is determined by λres/(2·Q·T), where T is the EO tuning efficiency. The slope of the fit line indicates an EO tuning efficiency (T) Δλ/ΔV of 1.5 pm/V. From the result, the 3 dB switch voltage can be computed as about 43 V. The switch voltage can be further reduced by increasing Q-factor [10].
Fig. 6. (a) Measured transmission response of the PhC nanobeam cavity with different on-load voltage (from −20 V to 80 V). (b) The resonant wavelengths of the cavity with different voltage, and the measured modulation efficiency is 1.5 pm/V by linear fit.
The device also demonstrates excellent dynamic response. The wavelength of the input light was set around the resonance by a tunable laser with a polarization controller. RF signals generated by a vector network analyzer (VNA) was loaded onto the chip using a high-speed probe. The output light through the device modulated by the RF signal was amplified by an erbium-doped fiber amplifier (EDFA), filtered by a bandpass filter and finally detected by a 50 GHz photodetector. Figure 7(a) shows the measured small-signal EO response (S21) of the fabricated PhC nanobeam cavity based EO modulator utilizing VNA. The 3 dB EO bandwidth of the fabricated modulator is about 28 GHz. The EO bandwidth is closed to the lifetime limits of photons in the cavity, which can be calculated from the Q factor and the resonant optical frequency (fres) of the cavity with the formula of fres/Q [28]. The capacitance and resistance of the circuit is very small, and the RC bandwidth is over 200 GHz, so it is not a factor limiting the modulation efficiency. Finally, high-speed digital data transmission of the fabricated EO modulator has been characterized and the temporal response is shown in Fig. 7(b). A square wave electrical signal with 20 V peak-to-peak voltage is utilized as the driving signal. From Fig. 7(b), it can be clearly found that the modulator can operate at signal rates greater than 10 MHz, limited by our signal generator speed with an extinction ratio of ∼0.7 dB.
Fig. 7. (a) Measured small-signal electro-optic response (S21) of the fabricated BIC PhC nanobeam modulator. The red dashed line indicates the 3-dB limit of S21. (b) Temporal response of the device.
Due to the light is insufficiently confined in the lithium niobate and we exploit γ13 because the electric field of light and modulated signal is orthogonal, the tuning efficiency is lower than the cavity based etched LNOI directly [8,10]. However, our devices have set a new scheme for exploring EO modulation on an etchless integrated photonic platform which is friendly to be fabricated.
Moreover, from the transmission of the cavity shown in Fig. 5(a), one can find that the device exhibits more than one resonances, which correspond to the second-order and third-order cavity modes and their optical mode field profiles are shown in Figs. 5(c) and (d), respectively. These high order modes can be considered in the applications require higher transmittance.
4. Conclusion
In summary, we demonstrated a PhC nanobeam cavity working at BIC mode on x-cut LNOI platform which can be fabricated without etching into the LN film. The measured propagation loss for the waveguide TM0 mode loss is 0.26 dB/cm. Using the periodic stack structure and the modulated filling factor to optimize the device performance, the measured Q factor is 12,010. And the total device size is only 257 um2. We also verify the electro-optic modulation performance of the device. The tuning efficiency of the device is about 1.5 pm/V, and the operating bandwidth can up to 28 GHz. Furthermore, such fabrication-friendly BIC PhC nanobeam cavity structure avoiding the etching of the high-refractive-index single crystal materials has the potential to apply to other platforms to realize hyperfine structure.
Funding
National Major Research and Development Program (2019YFB2203603); "Pioneer" and "Leading Goose" R&D Program of Zhejiang (2022C01103); National Natural Science Foundation of China (61922070, 6213000026); Fundamental Research Funds for the Central Universities.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. C. Wang, M. Zhang, X. Chen, M. Bertrand, A. Shams-Ansari, S. Chandrasekhar, P. Winzer, and M. Loncar, “Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages,” Nature 562(7725), 101–104 (2018). [CrossRef]
2. M. He, M. Xu, Y. Ren, J. Jian, Z. Ruan, Y. Xu, S. Gao, S. Sun, X. Wen, L. Zhou, L. Liu, C. Guo, H. Chen, S. Yu, L. Liu, and X. Cai, “High-performance hybrid silicon and lithium niobate Mach–Zehnder modulators for 100 Gbit s−1 and beyond,” Nat. Photonics 13(5), 359–364 (2019). [CrossRef]
3. A. Boes, B. Corcoran, L. Chang, J. Bowers, and A. Mitchell, “Status and Potential of Lithium Niobate on Insulator (LNOI) for Photonic Integrated Circuits,” Laser Photonics Rev. 12(4), 1700256 (2018). [CrossRef]
4. M. Xu, M. He, H. Zhang, J. Jian, Y. Pan, X. Liu, L. Chen, X. Meng, H. Chen, Z. Li, X. Xiao, S. Yu, S. Yu, and X. Cai, “High-performance coherent optical modulators based on thin-film lithium niobate platform,” Nat. Commun. 11(1), 3911 (2020). [CrossRef]
5. M. Zhang, B. Buscaino, C. Wang, A. Shams-Ansari, C. Reimer, R. Zhu, J. M. Kahn, and M. Loncar, “Broadband electro-optic frequency comb generation in a lithium niobate microring resonator,” Nature 568(7752), 373–377 (2019). [CrossRef]
6. M. Xu, Y. Zhu, F. Pittalà, J. Tang, M. He, W. C. Ng, J. Wang, Z. Ruan, X. Tang, M. Kuschnerov, L. Liu, S. Yu, B. Zheng, and X. Cai, “Dual-polarization thin-film lithium niobate in-phase quadrature modulators for terabit-per-second transmission,” Optica 9(1), 61 (2022). [CrossRef]
7. C. Wang, M. Zhang, B. Stern, M. Lipson, and M. Loncar, “Nanophotonic lithium niobate electro-optic modulators,” Opt. Express 26(2), 1547–1555 (2018). [CrossRef]
8. B. Pan, H. Cao, Y. Huang, Z. Wang, K. Chen, H. Li, Z. Yu, and D. Dai, “Compact electro-optic modulator on lithium niobate,” Photonics Res. 10(3), 697 (2022). [CrossRef]
9. A. Prencipe, M. A. Baghban, and K. Gallo, “Tunable Ultranarrowband Grating Filters in Thin-Film Lithium Niobate,” ACS Photonics 8(10), 2923–2930 (2021). [CrossRef]
10. M. Li, J. Ling, Y. He, U. A. Javid, S. Xue, and Q. Lin, “Lithium niobate photonic-crystal electro-optic modulator,” Nat. Commun. 11(1), 4123 (2020). [CrossRef]
11. B. Pan, Y. Tan, P. Chen, L. Liu, Y. Shi, and D. Dai, “Compact Racetrack Resonator on LiNbO3,” J. Lightwave Technol. 39(6), 1770–1776 (2021). [CrossRef]
12. J. Wang, P. Chen, D. Dai, and L. Liu, “Polarization Coupling of X-Cut Thin Film Lithium Niobate Based Waveguides,” IEEE Photonics J. 12(3), 1–10 (2020). [CrossRef]
13. D. Zhu, L. Shao, M. Yu, R. Cheng, B. Desiatov, C. J. Xin, Y. Hu, J. Holzgrafe, S. Ghosh, A. Shams-Ansari, E. Puma, N. Sinclair, C. Reimer, M. Zhang, and M. Lončar, “Integrated photonics on thin-film lithium niobate,” Adv. Opt. Photonics 13(2), 242–352 (2021). [CrossRef]
14. J. D. Witmer, J. A. Valery, P. Arrangoiz-Arriola, C. J. Sarabalis, J. T. Hill, and A. H. Safavi-Naeini, “High-Q photonic resonators and electro-optic coupling using silicon-on-lithium-niobate,” Sci. Rep. 7(1), 46313 (2017). [CrossRef]
15. L. Chang, Y. Li, N. Volet, L. Wang, J. Peters, and J. E. Bowers, “Thin film wavelength converters for photonic integrated circuits,” Optica 3(5), 531 (2016). [CrossRef]
16. A. Rao, A. Patil, P. Rabiei, A. Honardoost, R. DeSalvo, A. Paolella, and S. Fathpour, “High-performance and linear thin-film lithium niobate Mach-Zehnder modulators on silicon up to 50 GHz,” Opt. Lett. 41(24), 5700–5703 (2016). [CrossRef]
17. Z. Yu, X. Xi, J. Ma, H. K. Tsang, C.-L. Zou, and X. Sun, “Photonic integrated circuits with bound states in the continuum,” Optica 6(10), 1342 (2019). [CrossRef]
18. Z. Yu, Y. Wang, B. Sun, Y. Tong, J. B. Xu, H. K. Tsang, and X. Sun, “Hybrid 2D-Material Photonics with Bound States in the Continuum,” Adv. Opt. Mater. 7(24), 1901306 (2019). [CrossRef]
19. Z. Yu and X. Sun, “Gigahertz Acousto-Optic Modulation and Frequency Shifting on Etchless Lithium Niobate Integrated Platform,” ACS Photonics 8(3), 798–803 (2021). [CrossRef]
20. Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113(3), 037401 (2014). [CrossRef]
21. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, “Electro–optically tunable microring resonators in lithium niobate,” Nat. Photonics 1(7), 407–410 (2007). [CrossRef]
22. Z. Yu and X. Sun, “Acousto-optic modulation of photonic bound state in the continuum,” Light: Sci. Appl. 9(1), 1 (2020). [CrossRef]
23. Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, “High-Q, low index-contrast polymeric photonic crystal nanobeam cavities,” Opt. Express 19(22), 22191–22197 (2011). [CrossRef]
24. H. Ma, A. K. Y. Jen, and L. R. Dalton, “Polymer-Based Optical Waveguides: Materials, Processing, and Devices,” Adv. Mater. 14(19), 1339–1365 (2002). [CrossRef]
25. F. Ye, Y. Yu, X. Xi, and X. Sun, “Second-Harmonic Generation in Etchless Lithium Niobate Nanophotonic Waveguides with Bound States in the Continuum,” Laser Photonics Rev. 16(3), 2100429 (2022). [CrossRef]
26. X. Li, X. Liu, Y. Qin, D. Yang, and Y. Ji, “Ultra-Low Index-Contrast Polymeric Photonic Crystal Nanobeam Electro-Optic Modulator,” IEEE Photonics J. 12(3), 1–8 (2020). [CrossRef]
27. W. Jiang, R. N. Patel, F. M. Mayor, T. P. McKenna, P. Arrangoiz-Arriola, C. J. Sarabalis, J. D. Witmer, R. Van Laer, and A. H. Safavi-Naeini, “Lithium niobate piezo-optomechanical crystals,” Optica 6(7), 845 (2019). [CrossRef]
28. G. Li, X. Zheng, J. Yao, H. Thacker, I. Shubin, Y. Luo, K. Raj, J. E. Cunningham, and A. V. Krishnamoorthy, “25Gb/s 1V-driving CMOS ring modulator with integrated thermal tuning,” Opt. Express 19(21), 20435–20443 (2011). [CrossRef]
