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. 2024 Oct 8;15(1):8710.
doi: 10.1038/s41467-024-52958-3.

Time-variant parity-time symmetry in frequency-scanning systems

Mingjian Li  1   2   3 , Tengfei Hao  4   5   6 , Guozheng Li  1   2   3 , Anle Wang  7 , Yitang Dai  8 , Wei Li  1   2   3 , José Capmany  9 , Jianping Yao  10 , Ninghua Zhu  1   2   3 , Ming Li  11   12   13
Affiliations

Time-variant parity-time symmetry in frequency-scanning systems

Mingjian Li et al. Nat Commun. .

Abstract

Parity-time (PT) symmetry is an active research area that provides a variety of new opportunities for different systems with novel functionalities. For instance, PT symmetry has been used in lasers and optoelectronic oscillators to achieve single-frequency lasing or oscillation. A single-frequency system is essentially a static PT-symmetric system, whose frequency is time-invariant. Here we investigate time-variant PT symmetry in frequency-scanning systems. Time-variant PT symmetry equations and eigenfrequencies for frequency-scanning systems are developed. We show that time-variant PT symmetry can dynamically narrow the instantaneous linewidth of frequency-scanning systems. The instantaneous linewidth of a produced frequency-modulated continuous-wave (FMCW) waveform is narrowed by a factor of 14 in the experiment. De-chirping and radar imaging results also show that the time-variant PT-symmetric system outperforms a conventional frequency-scanning one. Our study paves the way for a new class of time-variant PT-symmetric systems and shows great promise for applications including FMCW radar and lidar systems.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1. Time-variant PT-symmetric frequency-scanning system.
a Illustration of a time-invariant PT-symmetric single-frequency system (upper) and the produced single-frequency signal (lower). b Illustration of a time-variant PT-symmetric frequency-scanning system (upper) and the produced frequency-scanning signal (lower). c Instantaneous gain-time diagram (left) and net gain at a certain time window (right) for a conventional frequency-scanning system. a.u.: arbitrary units. d Instantaneous gain-time diagram (left) and net gain at a certain time window (right) for the PT-symmetric frequency-scanning system. e Example of the time-variant PT-symmetric frequency-scanning system in practical applications. It can be used as a key signal source to provide the required FMCW waveform for radar and lidar systems.
Fig. 2
Fig. 2. Produced FMCW waveform with narrow instantaneous linewidth.
a Block diagram of a PT-symmetric frequency-scanning FDML OEO that used in the experiment. SLS: Swept light source; PM: phase modulator; EDFA: Erbium-doped fiber amplifier; OC: optical coupler; TOA: tunable optical attenuator; TDL: tunable delay line; PD: photodetector; EC: electrical coupler; EA: electrical amplifier. b Temporal waveform of the generated FMCW waveform. c Instantaneous frequency-time diagram calculated by the short-time Fourier transform of the temporal waveform. d Instantaneous frequency-time diagram obtained based on self-homodyne and the Hilbert transformation. Inset: Zoom-in view showing the instantaneous linewidth of the time-variant PT-symmetric frequency-scanning oscillator. e Instantaneous frequency-time diagram of a FMCW waveform generated by a conventional frequency-scanning oscillator. Inset: Zoom-in view showing the instantaneous linewidth. f Frequency error between an FMCW waveform generated by the time-variant PT-symmetric frequency-scanning oscillator and an ideal linear FMCW waveform. g Frequency error between an FMCW waveform generated by a conventional frequency-scanning oscillator and an ideal linear FMCW waveform.
Fig. 3
Fig. 3. De-chirped signal using the FMCW waveform generated by the time-variant PT-symmetric and conventional FDML OEO.
a Schematic diagram of the de-chirp processing link. Illustrations of the instantaneous frequency-time diagram and de-chirped signal of b the time-variant PT-symmetric FDML OEO and c a conventional FDML OEO. Spectra of the de-chirped signal of d the time-variant PT-symmetric FDML OEO and e a conventional FDML OEO. Insert: Zoom-in view showing the 3-dB bandwidth of the de-chirped signal. Details of the de-chirped signal corresponding to f the time-variant PT-symmetric FDML OEO and g a conventional FDML OEO. RBW: resolution bandwidth.
Fig. 4
Fig. 4. Radar range profiles and point target imaging results.
The results of radar range profiles based on a the time-variant PT-symmetric and b conventional frequency-scanning oscillators, and the point-target imaging results based on c the time-variant PT-symmetric and d conventional frequency-scanning oscillators.
See this image and copyright information in PMC

References

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