Microwave and RF non-integral order Hilbert transforms using a 49GHz FSR integrated optical micro-comb source

We report a photonic microwave and RF fractional Hilbert transformer based on an integrated Kerr micro-comb source. The micro-comb source has a free spectral range (FSR) of 50GHz, generating a large number of comb lines that serve as a high-performance multi-wavelength source for the transformer. By programming and shaping the comb lines according to calculated tap weights, we achieve both arbitrary fractional orders and a broad operation bandwidth. We experimentally characterize the RF amplitude and phase response for different fractional orders and perform system demonstrations of real-time fractional Hilbert transforms. We achieve a phase ripple of < 0.15 rad within the 3-dB pass-band, with bandwidths ranging from 5 to 9 octaves, depending on the order. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a new way to implement high-performance fractional Hilbert transformers with broad processing bandwidth, high reconfigurability, and greatly reduced size and complexity.

An introduction to analysis of R\’enyi complexity ratio of quantum states for central potential

R\’enyi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of R\’enyi complexity ratio are proved by Lebesgue measure. Some properties of R\’enyi complexity ratio are demonstrated and investigated for different quantum systems. Exact analytical forms of R\’enyi entropy, R\’enyi complexity ratio, statistical complexities based on R\’enyi entropy for integral order have been presented for solutions of pseudoharmonic and a family of isospectral potentials. Some properties of R\’enyi complexity ratio are verified for six diatomic molecules (CO, NO, N$_2$, CH, H$_2$, and ScH) and for other quantum systems.

Integral order RF and microwave photonic based signal processors using Kerr soliton crystal micro-combs

Soliton crystal micro-combs are powerful tools as sources of multiple wavelength channels for radio frequency (RF) signal processing. They offer a compact device footprint, large numbers of wavelengths, very high versatility, and wide Nyquist bandwidths. Here, we demonstrate integral order RF signal processing functions based on a soliton crystal micro-comb, including a Hilbert transformer and first- to third-order differentiators. We compare and contrast results achieved and the tradeoffs involved with varying comb spacing, tap design methods, as well as shaping methods.

Integral order RF and microwave photonic based signal processors using Kerr soliton crystal micro-combs

Soliton crystal micro-combs are powerful tools as sources of multiple wavelength channels for radio frequency (RF) signal processing. They offer a compact device footprint, large numbers of wavelengths, very high versatility, and wide Nyquist bandwidths. Here, we demonstrate integral order RF signal processing functions based on a soliton crystal micro-comb, including a Hilbert transformer and first- to third-order differentiators. We compare and contrast results achieved and the tradeoffs involved with varying comb spacing, tap design methods, as well as shaping methods.

Photonic RF signal processors with integral order based on Kerr micro-combs

<p>Soliton crystal micro-combs are powerful tools as sources of multiple wavelength channels for radio frequency (RF) signal processing. They offer a compact device footprint, large numbers of wavelengths, very high versatility, and wide Nyquist bandwidths. Here, we demonstrate integral order RF signal processing functions based on a soliton crystal micro-comb, including a Hilbert transformer and first- to third-order differentiators. We compare and contrast results achieved and the tradeoffs involved with varying comb spacing, tap design methods, as well as shaping methods. </p>

Photonic RF signal processors with integral order based on Kerr micro-combs

<p>Soliton crystal micro-combs are powerful tools as sources of multiple wavelength channels for radio frequency (RF) signal processing. They offer a compact device footprint, large numbers of wavelengths, very high versatility, and wide Nyquist bandwidths. Here, we demonstrate integral order RF signal processing functions based on a soliton crystal micro-comb, including a Hilbert transformer and first- to third-order differentiators. We compare and contrast results achieved and the tradeoffs involved with varying comb spacing, tap design methods, as well as shaping methods. </p>

Integral order photonic RF and microwave signal processors based on Kerr micro-combs

Soliton crystal micro-combs are powerful tools as sources of multiple wavelength channels for radio frequency (RF) signal processing. They offer a compact device footprint, large numbers of wavelengths, very high versatility, and wide Nyquist bandwidths. Here, we demonstrate integral order RF signal processing functions based on a soliton crystal micro-comb, including a Hilbert transformer and first- to third-order differentiators. We compare and contrast results achieved and the tradeoffs involved with varying comb spacing, tap design methods, as well as shaping methods.

Integral Order Photonic RF Signal Processors Based on Kerr Micro-combs

Soliton crystal micro-combs are powerful tools as sources of multiple wavelength channels for radio frequency (RF) signal processing. They offer a compact device footprint, large numbers of wavelengths, very high versatility, and wide Nyquist bandwidths. Here, we demonstrate integral order RF signal processing functions based on a soliton crystal micro-comb, including a Hilbert transformer and first- to third-order differentiators. We compare and contrast results achieved and the tradeoffs involved with varying comb spacing, tap design methods, as well as shaping methods.