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Optical Kerr soliton crystal microcomb source for RF photonic fractional differentiation
Mengxi Tan, Xingyuan Xu, Bill Corcoran, Jiayang Wu, Andreas Boes, Thach G. Nguyen, Sai T. Chu, Brent E. Little, Roberto Morandotti, Arnan Mitchell, David J. Moss
TL;DR
Photonic fractional differentiators have received limited attention, while existing transversal approaches can require many discrete light sources and incur greater size, cost, and complexity. This paper uses a CMOS-compatible Kerr micro-comb, shapes its lines into weighted taps, and directly differentiates RF signals. It demonstrates tunable fractional orders from 0.15 to 0.9 over 15.49 GHz, with measured frequency and Gaussian-pulse responses agreeing well with theory.
Problem
Photonic fractional differentiation has received comparatively little attention, and discrete-source transversal schemes increase size, cost, complexity, and limit available taps.
Method
A CMOS-compatible Kerr micro-comb provides many wavelengths that are programmed and shaped according to calculated tap weights for a transversal RF differentiator.
Results
The differentiator achieves tunable fractional orders from 0.15 to 0.9 and a 15.49 GHz operating bandwidth, with measured frequency and Gaussian-pulse responses agreeing with theory.
Takeaways & Limitations
The demonstrated approach implements high-speed, reconfigurable RF fractional differentiation with broad processing bandwidth and reduced-footprint potential.
Abstract
from arXiv · showhide
We report a photonic radio frequency (RF) fractional differentiator based on an integrated Kerr micro-comb source. The micro-comb source has a free spectral range (FSR) of 49 GHz, generating a large number of comb lines that serve as a high-performance multi-wavelength source for the differentiator. By programming and shaping the comb lines according to calculated tap weights, arbitrary fractional orders ranging from 0.15 to 0.90 are achieved over a broad RF operation bandwidth of 15.49 GHz. We experimentally characterize the frequency-domain RF amplitude and phase responses as well as the temporal responses with a Gaussian pulse input. The experimental results show good agreement with theory, confirming the effectiveness of our approach towards high-performance fractional differentiators featuring broad processing bandwidth, high reconfigurability, and potentially greatly reduced size and cost.
I. INTRODUCTION
Photonic RF processing offers high speed and bandwidth, but photonic fractional differentiation has received comparatively little attention. The paper addresses this gap with a reconfigurable Kerr micro-comb differentiator that directly processes RF signals using many wavelength channels.
- Photonic RF techniques can provide substantially higher speed and bandwidth than electronic signal processors.
- Fractional differentiation generalizes integral differentiation and has applications in image edge detection, control theory, and mechatronics.
- Photonic fractional differentiators have received comparatively little attention despite the broader applications of fractional differentiation.
- Existing approaches can target complex optical-field derivatives rather than pure RF differentiation, while RF-delay-line implementations are limited by delay-line bandwidth.
- Discrete laser-array transversal schemes increase system size, cost, and complexity, limiting available taps and processing performance.
- The proposed differentiator uses a 49 GHz-spaced Kerr micro-comb with up to 80 telecommunications-C-band comb lines and a 15.49 GHz operating bandwidth.
- Programming comb-line powers according to calculated tap weights enables reconfigurable fractional orders from 0.15 to 0.9 with RF amplitude, phase, and Gaussian-pulse characterization.
II. PRINCIPLE OF OPERATION
The differentiator implements a fractional-order transfer function whose amplitude scales with RF frequency magnitude and whose phase varies linearly. A transversal optical filter realizes this response using delayed, weighted replicas whose coefficients are derived from the inverse Fourier transform.
- An Nth-order temporal fractional differentiator has a transfer function proportional to (jω)^N, where N may be fractional or complex.
- The amplitude response scales as |ω|^N, while the phase response is linear with a phase jump of Nπ at null frequencies.
- The reconfigurable transversal approach produces finite delayed and weighted replicas of the input RF signal optically and combines them upon detection.
- The transversal filter uses M taps separated by delay T, with h_k as the kth tap coefficient and discrete impulse response of H_N(ω).
- Tap coefficients are obtained from the inverse Fourier transform of H_N(ω) and temporally windowed with a short cosine bell.
III. EXPERIMENTAL RESULTS
The experiment generates and shapes a CMOS-compatible soliton-crystal Kerr micro-comb to form transversal-filter taps. Increasing tap count broadens operation to 15.49 GHz, while measured frequency and temporal responses closely match theory.
- The integrated microcomb supplies the wavelengths forming the transversal differentiator’s taps through optical parametric oscillation in a CMOS-compatible micro-ring resonator.
- Soliton crystal states are generated by tuning pump-resonator detuning and are identified by a distinctive fingerprint optical spectrum.
- Two optical spectral shapers flatten comb-line differences below 2 dB, apply designed tap coefficients, and use feedback calibration against ideal weights.
- 15.49 GHz of operational bandwidth is reached with 27 taps, occupying more than 91% of the Nyquist band.
- Further increasing tap count requires optimizing optical signal-to-noise ratio beyond 40 dB because amplifier noise constrained the experiment.
- Measured power and phase responses from DC to 15.49 GHz closely match simulated slope coefficients and phase shifts across fractional orders.
- For a Gaussian pulse with approximately 200 ps FWHM, measured differentiated waveforms closely match theoretical counterparts.
IV. CONCLUSION
The paper demonstrates a CMOS-compatible Kerr micro-comb RF fractional differentiator that directly processes RF signals. It provides tunable fractional orders from 0.15 to 0.9, approximately 15.49 GHz bandwidth, and Gaussian-pulse responses agreeing with theory.
- The integrated Kerr micro-comb differentiator directly processes RF signals and provides tunable fractional orders from 0.15 to 0.9.
- The measured RF amplitude and phase responses achieve an operation bandwidth of approximately 15.49 GHz.
- Real-time Gaussian-pulse demonstrations agree well with theory, supporting high-speed reconfigurable fractional differentiation.