Fig 1 Topological photonic crystal and its bulk band diagram on silicon-nitride-loaded LN platform.
Published:30 September 2023,
Published Online:29 August 2023,
Received:06 February 2023,
Revised:14 July 2023,
Accepted:03 August 2023
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Electro-optic modulators are key components in data communication, microwave photonics, and quantum photonics. Modulation bandwidth, energy efficiency, and device dimension are crucial metrics of modulators. Here, we provide an important direction for the miniaturization of electro-optic modulators by reporting on ultracompact topological modulators. A topological interface state in a one-dimensional lattice is implemented on a thin-film lithium-niobate integrated platform. Due to the strong optical confinement of the interface state and the peaking enhancement of the electro-optic response, a topological cavity with a size of 1.6 × 140 μm2 enables a large modulation bandwidth of 104 GHz. The first topological modulator exhibits the most compact device size compared to reported LN modulators with bandwidths above 28 GHz, to the best of our knowledge. 100 Gb/s non-return-to-zero and 100 Gb/s four-level pulse amplitude modulation signals are generated. The switching energy is 5.4 fJ/bit, owing to the small electro-optic mode volume and low capacitance. The topological modulator accelerates the response time of topological photonic devices from the microsecond order to the picosecond order and provides an essential foundation for the implementation of large-scale lithium-niobate photonic integrated circuits.
Lithium-niobate-on-insulator (LNOI) has emerged as an important platform for integrated photonics due to its excellent properties, such as the strong electro-optic effect, large nonlinear coefficient, and wide transparency window
Topological phase transition is an essential component in various physical systems for diverse applications, including condensed matter
In this work, we report high-speed and energy-efficient electro-optic modulation in topological interface states of a 1D microstructure lattice on a silicon-nitride-loaded LNOI platform. A topological interface state is formed between two topological photonic crystals with distinct topological invariants and surface impedance in the 1D lattice based on the classic Su-Schrieffer-Heeger (SSH) model. The interface state enables the first topological modulator with a compact size of only 1.6 × 140 μm2, which is the most compact thin-film LN modulator with a bandwidth exceeding 28 GHz. Low radio frequency (RF) loss and small capacitance are achieved due to the small electro-optic modal volume and short electrode length, yielding ultralow energy consumption of 5.4 fJ/bit. Peaking enhancement in the electro-optic response of the topological cavity is utilized to break the photon lifetime-limited bandwidth, resulting in a large bandwidth of 104 GHz. As an application example, the topological modulator is operated with a non-return-to-zero (NRZ) signal of up to 100 Gbaud. Our topological modulator shows excellent performance in terms of ultrasmall size, high speed, and energy efficiency; our study accelerates the response time of topological photonic devices from the microsecond order to the picosecond order and promotes applications of topological devices in optical communications, microwave photonics, and quantum information processing.
We begin with a dielectric AB layered structure as shown in
1
Fig 1 Topological photonic crystal and its bulk band diagram on silicon-nitride-loaded LN platform.
a 1D TPC cavity based on a dielectric AB layered structure. Band structures of the b left and d right TPCs. The Zak phase of each isolated band is marked with blue letters. The gap topological invariants of each gap are labeled purple when sgn[ζ] > 0 and light green when sgn[ζ] < 0. c Simulated transmission spectrum of the 1D TPC cavity consisting of the two inverted TPC structures. Resonance peaks are located in the center of the 1st, 3rd, and 5th stopbands, which correspond to the topological interface states (TIS). The smaller panels are zoom-in views of the simulated transmission spectra of stopbands 1~5, to provide a clearer illustration of the presence or absence of topological boundary states. e Schematic of the rectangular air holes on an integrated waveguide. Periodic rectangular holes are utilized to tailor the effective index of integrated waveguides and replace the dielectric AB layered structures. f 3D view of the modulator based on the topological interface state. Insets show the simulated optical field distribution of the hybrid Si3N4-LNOI waveguide and the topological boundary state. The simulated optical field distributions of the Si3N4-LN waveguide and the topological boundary state are monitored at the Thru port of the topological structure and the center of the LN thin film, respectively. Band structures of the g left and i right integrated TPC based on periodic rectangular holes. h Simulated transmission spectrum of the integrated TPC cavity. Calculated (j) loaded Q factors and k insertion losses of the topological edge mode for different D1 and D2 values. CW continuous wave, Mod. modulated, TPC_L left TPC, TPC_R right TPC
where uj, k(y) is the periodic-in-cell part of the Bloch electric field eigenfunction of a state on the jth band with wave vector k. uj, k(y) can be calculated using the transfer-matrix method for a binary TPC
The gap topological invariants of the nth gap, i.e., the sum of Zak phases of all the isolated bands below the nth gap, can be used to predict the existence of an interface state in a bandgap. The gap topological invariants of the nth gap can be obtained from the following relationship
2
where the integer n is the number of the gaps, and l is the number of crossing points under the nth gap. Using Eq. (2), the gap topological invariants of each gap for the left and right TPCs are obtained and labeled by purple when sgn[ζ] > 0 and light green when sgn[ζ] < 0. The 1st, 3rd, and 5th gaps of the TPCs exhibit different gap topological invariants, indicating that a topological phase transition occurs when the lower and upper edges of the gap cross each other. The topological interface state exists in these photonic gaps when combining the left and right TPCs together. We use the finite-difference time-domain (FDTD) method to simulate the transmission spectrum of the 1D topological cavity consisting of the two inverted TPC structures, as shown in
Next, we consider the transformation of topological photonic crystals with the abovementioned layered structures into an integrated topological cavity on a thin-film LN platform. Si3N4-loaded LNOI integrated waveguide is used in the design to avoid directly etching the LN thin film and offers a promising direction to achieve large-scale integration of passive and active LNOI devices. The calculated optical confinement factor in the thin-film LN is 61.5%, which can take advantage of the strong electro-optic effect of the thin-film LN. The cross-section and simulated optical field distribution of the hybrid Si3N4-LNOI waveguide are shown in the insets of
The Q factor, mode volume, insertion loss, and extinction ratio are important metrics for electro-optic modulators to evaluate the LN-based TPC integrated cavity. We calculate the loaded Q factors and insertion losses of the topological edge modes for different D1 and D2 values (
The 3D schematic of the proposed modulator based on the topological cavity is depicted in
Fig 2 Fabrication and static characterization of a topological Pockels modulator.
a Optical microscope graph of the fabricated topological modulator with grating couplers. b Magnified photo of the device with gold electrodes. c Scanning electron microscope (SEM) image of the topological structure. d Measured transmission spectrum of the TPC cavity without gold electrodes. e Measured transmission spectra of the fabricated TPC cavity upon applying different voltages. f Electro-optic tuning of the boundary states versus applied voltages
To demonstrate electro-optic tuning, a topological cavity with gold microelectrodes is fabricated and characterized.
We test the sidebands generated by the modulation of RF signals at different frequencies, to investigate the high-frequency response of the topological modulator.
Fig 3 Modulator bandwidth and electro-optic characterization.
a Measurement setup for sideband testing. b Optical spectra at the output of the topological modulator for various input RF frequencies. The peak located in the center of the spectra is the input optical carrier, while the two peaks on both sides correspond to the generated modulation sidebands. c Experimental setup for measuring the electro-optic bandwidth of the topological modulator. d Measured electro-optic S21 responses with different wavelength detuning Δλ. EDFA erbium-doped fiber amplifier, PC polarization controller, EA electrical amplifier, OBPF optical bandpass filter, VOA variable optical attenuator, PD photodetector, EO electro-optic
The modulation bandwidth for a cavity modulator is mainly limited by the photon lifetime τ in the cavity, resulting in a first-order filter with a bandwidth of 1/2πτ, and the RC time constant of the phase shifter, leading to another first-order filter
A small-signal model based on perturbation theory can be used to analyze the peaking enhancement in the electro-optic response
3
where δωr is the resonant angular frequency change when applying a small voltage, a is the optical field traveling inside the topological cavity, τr is the radiation coupling between the topological cavity and the cladding, and ωm, ω0, and ωr represents the modulation frequency, the input light frequency, and the resonance frequency, respectively. The detailed perturbative derivation of Eq. (3) and the simulated small-signal response of the topological cavity modulation can be found in Supplementary Note S7. The simulated bandwidth closely matches the experimentally tested bandwidth.
We use the large bandwidth and ultracompact topological modulator to generate advanced modulation formats of up to 100 Gb/s. The experimental setup is shown in
Fig 4 Data modulation testing.
a Measurement setup for data transmission testing. Eye diagrams for the NRZ signals at data rates of b 80 Gb/s and c 70 Gb/s, the PAM-4 signals at data rates of d 100 Gb/s and e 80 Gb/s, the PAM-6 signal at a data rate of f 77 Gb/s, and the PAM-8 signal at a data rate of g 90 Gb/s. h The BER versus ROP curves for different NRZ signals. Insets illustrate the calculated eye diagrams after DSP for the recovered 80, 90, and 100 Gb/s NRZ signals. i Measured footprint-bandwidth performance comparison of various reported thin film LN modulators. The circle symbols correspond to the results of MZI modulators, and the rectangle symbols correspond to those of cavity-based modulators. OSC oscilloscope
Four-level pulse amplitude modulation (PAM-4), PAM-6, and PAM-8 modulation formats at high baud rates are utilized to further increase the data rates supported by the topological modulators.
The demonstrated topological modulator shows excellent performance in terms of device footprint and modulation bandwidth (
Structures | Footprint | VπL/tuning efficiency | Extinction ratio | Bandwidth | Vpp | Data rate | Energy consumption |
---|---|---|---|---|---|---|---|
LN MZI on silicon | 100 × 20000 μm2 | 2.8 Vcm | 30 dB | 45 GHz | 0.2 V | 70 Gb/s | / |
Hybrid LN-silicon MZI | ~100 × 3000 μm2 | 2.2 Vcm | 40 dB | >70 GHz | 4 V | 100 Gb/s OOK | 170 fJ/bit |
LN MZI on quartz | 175 × 20,000 μm2 | 2.6 Vcm | 20 dB | >100 GHz | / | / | / |
Ring-assisted MZI | 700 × 3400 μm2 | 0.35 Vcm | 20 dB | >67 GHz | 0.75 V | 224 Gb/s PAM-4 | 2.7 fJ/bit |
Racetrack | 100 × 450 μm2 | 7 pm/V | 6.5 dB | 30 GHz | 5.66 V | 40 Gb/s NRZ | 240 fJ/bit |
Racetrack SiN loaded LN | 600 × 210 μm2 | / | 9 dB | / | / | 70 Gb/s NRZ | 212 fJ/bit |
Bragg grating | 10 × 400 μm2 | / | 53.8 dB | 60 GHz | 0.9 V | 100 Gb/s NRZ | / |
BIC photonic crystal | 2.1 × 123 μm2 | 1.5 pm/V | / | 28 GHz | / | / | / |
FP cavity | 4 × 500 μm2 | 7 pm/V | 20 dB | >110 GHz | 2 V | 100 Gb/s OOK | 4.5 fJ/bit |
Photonic crystal | 1.2 × 30 μm2 | 16 pm/V | 11.5 dB | 17.5 GHz | 2 V | 11 Gb/s NRZ | 22 fJ/bit |
Topological modulator (this work) | 1.6 × 140 μm2 | 11 pm/V | 32 dB | 104 GHz | 2 V | 100 Gb/s NRZ 100 Gb/s PAM-4 | 5.4 fJ/bit |
Bold values highlight the size and bandwidth of our topological modulator, which represents a significant improvement over previously reported results
We have demonstrated a topological interface state in a 1D microstructure lattice based on the classic SSH model using an integrated thin film LNOI platform. The LN-based interface state, which arises from band crossing, exhibits the advantages of a high Q factor, small mode volume, single mode operation, avoidance of mode number control, and robustness to defects or disorders. To the best of our knowledge, we have implemented the first high-speed topological electro-optic modulator using this topological boundary state. Owing to the strong optical confinement of the interface state, the size of the topological modulator is only 1.6 × 140 μm2. Due to good electro-optic overlap and peaking enhancement in the topological cavity, the LN-based interface state is capable of a large modulation bandwidth of 104 GHz. High-speed modulation of up to 100 Gbaud NRZ signal is achieved with switching energy as low as 5.4 fJ/bit, which is attributed to the small device footprint and short electrode length. Furthermore, a 100 Gb/s PAM-4 signal is enabled by the topological modulator.
Our topological modulator shows great promise for applications of high-speed modulation in fully integrated LN photonics, but there are some improvements needed for future work. First, the width and thickness of the microelectrodes can be further optimized to obtain a smaller RC time constant. Second, the unit cells of the TPC can be decreased to achieve a lower Q factor, thus reducing the limitation of the photon lifetime on the electro-optic bandwidth. Third, considering the wavelength drift of the topological interface states due to the fabrication or temperature variations in practical applications, a power-efficient thermo-tuning element can be integrated into the LN topological cavity with the capability of resonance tuning. Finally, due to its compact footprint, low switching energy, and the absence of complicated resonant mode control, a large number of LN topological cavities are attainable for integration on the same chip to achieve a communication link with an aggregate data rate beyond Tb/s using wavelength division multiplexing technology
The fabrication process starts from an X-cut LNOI wafer with a 300-nm-thick LN layer and a 2-μm-thick buried silica layer (purchased from NanoLN). A 300-nm-thick silicon-nitride layer is deposited on the LNOI substrate using plasma-enhanced chemical vapor deposition (PECVD). The topological structures and grating couplers are patterned on the resist (AR-P 6200.09) and transferred to the silicon-nitride layer by electron-beam lithography (EBL, Vistec EBPG 5200+) and inductively coupled plasma (ICP) dry etching (NMC), respectively. After residue removal, the microelectrodes and contact pads (10 nm Ti/300 nm Au) are deposited by electron-beam evaporation and patterned by the lift-off process.
The band diagrams of the topological photonic crystal are calculated by the finite element method. The equivalent refractive index of the waveguides with subwavelength-scale rectangular air holes is calculated using effective-medium theory (see Supplementary Note S2). The transmission spectrum, Q factor, and mode volume of the topological cavity are simulated by the finite-difference time-domain (FDTD, Lumerical FDTD solutions) method with perfectly matched layer boundary conditions.
The topological devices are characterized by using a tunable laser scanning system (EXFO T100S-HP-CLU-M-CTP10-00). On-chip grating couplers are used to couple light into/out of the silicon-nitride-loaded LN waveguides (see Supplementary Note S9). We measured the electro-optic tuning of the boundary states at different voltages using a voltage-current source meter (Keithley 2400).
The light is coupled into the topological device using grating couplers. As shown in
The small-signal response measurements are performed using a 110-GHz LCA and a 90-GHz photodiode (XPDV4120R-WFFP). For the raw eye diagram measurements, an AWG with a sampling rate of 120 GS/s (Keysight M8194) and an RF amplifier (SHF S807C, 3-dB bandwidth: 55 GHz) are utilized to generate a pseudorandom bit sequence (PRBS), and the signals are connected to the LN topological modulator by a high-bandwidth GS probe with a driving peak-to-peak voltage of ~2 V. Finally, the modulated light is recorded by an electrical sampling oscilloscope (Keysight N1092). For the ROP sensitivity testing, the details for the experiment and transceiver DSP flow charts are provided in Supplementary Note S8.
This work was supported in part by the Key Technologies Research and Development Program under Grant 2020YFB2206101 and the National Natural Science Foundation of China (NSFC) under Grant 62035016/61975115/61835008. We would like to thank the Center for Advanced Electronic Materials and Devices (AEMD) of Shanghai Jiao Tong University (SJTU) for its support in device fabrication. We would like to acknowledge the National Information Optoelectronics Innovation Center (Wuhan, China) for high-speed measurements.
Y.Z. conceived the idea. J.S., Y.Z., H.W., L.S., L.Z., and J.D. performed the theoretical analysis and numerical simulations. Y.Z., J.S., J.X., M.L., and Y.W. designed and fabricated the topological devices. J.S., J.L., C.F., and Y.Z. performed the measurements. Y.Z. wrote the original draft. Y.S., J.D., and Y.T. reviewed and polished the draft. Y.Z. and Y.S. supervised the project.
The authors declare no competing interests.
Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41377-023-01251-x.
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