scholarly journals Tunable Broadband RF Photonic Fractional Hilbert Transformer Based on a Soliton Crystal Microcomb

2021 ◽  
Author(s):  
Mengxi Tan ◽  
Xingyuan Xu ◽  
David Moss
Keyword(s):  
Computer System ◽  
Fractional Order ◽  
Spectral Range ◽  
Free Spectral Range ◽  
Hilbert Transformer ◽  
University Of Technology ◽  
E Mail ◽  
Fractional Orders ◽  
Variable Center ◽  
Good Agreement

We demonstrate an RF photonic fractional Hilbert transformer based on an integrated Kerr micro-comb source featuring a record low free spectral range of 49 GHz. By programming and shaping the comb lines according to calculated tap weights for up to 39 wavelengths across the C-band, we achieve tunable bandwidths ranging from 1.2 to 15.3 GHz as well as variable center frequencies from baseband to 9.5 GHz, for both standard integral and arbitrary fractional orders. We experimentally characterize the RF amplitude and phase response of the tunable bandpass and lowpass Hilbert transformers with 90 and 45-degree phase shifts. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a powerful way to implement standard and fractional order Hilbert transformers with broad and variable bandwidths and center frequencies, with high reconfigurability and greatly reduced size and complexity. Tan, and D. J. Moss are with the Optical Sciences Centre, Swinburne University of Technology, Hawthorn, VIC 3122, Australia. (Corresponding e-mail: [email protected]). Xu is with the Electro-Photonics Laboratory, Department of Electrical and Computer System Engineering, Monash University, Clayton, 3800 VIC, Australia

scholarly journals Tunable and adjustable broadband RF photonic fractional Hilbert transformer based on a Kerr soliton crystal optical microcomb  

2021 ◽  
Author(s):  
Mengxi Tan ◽  
Xingyuan Xu ◽  
David Moss
Keyword(s):  
Fractional Order ◽  
Spectral Range ◽  
Free Spectral Range ◽  
Phase Shifts ◽  
Phase Response ◽  
Experimental Results ◽  
Hilbert Transformer ◽  
Fractional Orders ◽  
Variable Center ◽  
Good Agreement

Abstract We demonstrate an RF photonic fractional Hilbert transformer based on an integrated Kerr micro-comb source featuring a record low free spectral range of 49 GHz. By programming and shaping the comb lines according to calculated tap weights for up to 39 wavelengths across the C-band, we achieve tunable bandwidths ranging from 1.2 to 15.3 GHz as well as variable center frequencies from baseband to 9.5 GHz, for both standard integral and arbitrary fractional orders. We experimentally characterize the RF amplitude and phase response of the tunable bandpass and lowpass Hilbert transformers with 90 and 45-degree phase shifts. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a powerful way to implement standard and fractional order Hilbert transformers with broad and variable bandwidths and center frequencies, with high reconfigurability and greatly reduced size and complexity.

scholarly journals Adjustable RF photonic fractional Hilbert transformer based on Kerr microcombs

2021 ◽  
Author(s):  
David Moss
Keyword(s):  
Fractional Order ◽  
Spectral Range ◽  
Free Spectral Range ◽  
Phase Shifts ◽  
Phase Response ◽  
Experimental Results ◽  
Hilbert Transformer ◽  
Fractional Orders ◽  
Variable Center ◽  
Good Agreement

<p>We demonstrate an RF photonic fractional Hilbert transformer based on an integrated Kerr micro-comb source featuring a record low free spectral range of 49 GHz. By programming and shaping the comb lines according to calculated tap weights for up to 39 wavelengths across the C-band, we achieve tunable bandwidths ranging from 1.2 to 15.3 GHz as well as variable center frequencies from baseband to 9.5 GHz, for both standard integral and arbitrary fractional orders. We experimentally characterize the RF amplitude and phase response of the tunable bandpass and lowpass Hilbert transformers with 90 and 45-degree phase shifts. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a powerful way to implement standard and fractional order Hilbert transformers with broad and variable bandwidths and center frequencies, with high reconfigurability and greatly reduced size and complexity.</p>

scholarly journals Tunable and adjustable broadband RF photonic fractional Hilbert transformer based on a Kerr soliton crystal optical microcomb

2021 ◽  
Author(s):  
David Moss
Keyword(s):  
Fractional Order ◽  
Spectral Range ◽  
Free Spectral Range ◽  
Phase Shifts ◽  
Phase Response ◽  
Experimental Results ◽  
Hilbert Transformer ◽  
Fractional Orders ◽  
Variable Center ◽  
Good Agreement

We demonstrate an RF photonic fractional Hilbert transformer based on an integrated Kerr micro-comb source featuring a record low free spectral range of 49 GHz. By programming and shaping the comb lines according to calculated tap weights for up to 39 wavelengths across the C-band, we achieve tunable bandwidths ranging from 1.2 to 15.3 GHz as well as variable center frequencies from baseband to 9.5 GHz, for both standard integral and arbitrary fractional orders. We experimentally characterize the RF amplitude and phase response of the tunable bandpass and lowpass Hilbert transformers with 90 and 45-degree phase shifts. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a powerful way to implement standard and fractional order Hilbert transformers with broad and variable bandwidths and center frequencies, with high reconfigurability and greatly reduced size and complexity.

scholarly journals Adjustable RF photonic fractional Hilbert transformer based on Kerr microcombs

2021 ◽  
Author(s):  
David Moss
Keyword(s):  
Fractional Order ◽  
Spectral Range ◽  
Free Spectral Range ◽  
Phase Shifts ◽  
Phase Response ◽  
Experimental Results ◽  
Hilbert Transformer ◽  
Fractional Orders ◽  
Variable Center ◽  
Good Agreement

<p>We demonstrate an RF photonic fractional Hilbert transformer based on an integrated Kerr micro-comb source featuring a record low free spectral range of 49 GHz. By programming and shaping the comb lines according to calculated tap weights for up to 39 wavelengths across the C-band, we achieve tunable bandwidths ranging from 1.2 to 15.3 GHz as well as variable center frequencies from baseband to 9.5 GHz, for both standard integral and arbitrary fractional orders. We experimentally characterize the RF amplitude and phase response of the tunable bandpass and lowpass Hilbert transformers with 90 and 45-degree phase shifts. The experimental results show good agreement with theory, confirming the effectiveness of our approach as a powerful way to implement standard and fractional order Hilbert transformers with broad and variable bandwidths and center frequencies, with high reconfigurability and greatly reduced size and complexity.</p>

scholarly journals hilbert

2020 ◽  
Author(s):  
David Moss
Keyword(s):  
Real Time ◽  
Spectral Range ◽  
High Performance ◽  
Free Spectral Range ◽  
Phase Response ◽  
Pass Band ◽  
Hilbert Transforms ◽  
Multi Wavelength ◽  
Fractional Orders ◽  
Good Agreement

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 &lt; 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.

scholarly journals RF and microwave fractional differentiation with transversal filters using a soliton crystal microcomb multiwavelength source

2020 ◽  
Author(s):  
David Moss ◽  
Arnan Mitchell ◽  
Roberto Morandotti ◽  
xingyuan xu
Keyword(s):  
High Performance ◽  
Free Spectral Range ◽  
Fractional Differentiation ◽  
Temporal Response ◽  
Pulse Input ◽  
Transversal Filters ◽  
Multi Wavelength ◽  
Fractional Orders ◽  
Fractional Differentiator ◽  
Good Agreement

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 response as well as the temporal response 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 reduced sized and cost.

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

2021 ◽  
Author(s):  
mengxi tan ◽  
xingyuan xu ◽  
David Moss
Keyword(s):  
Real Time ◽  
High Performance ◽  
Free Spectral Range ◽  
Pass Band ◽  
Hilbert Transforms ◽  
Integrated Optical ◽  
Multi Wavelength ◽  
Fractional Orders ◽  
Integral Order ◽  
Good Agreement

Abstract 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.

scholarly journals Microwave and radio frequency fractional differentiation with a 49GHz Kerr soliton crystal microcomb source

2021 ◽  
Author(s):  
David Moss
Keyword(s):  
Radio Frequency ◽  
High Performance ◽  
Free Spectral Range ◽  
Fractional Differentiation ◽  
Temporal Response ◽  
Pulse Input ◽  
Multi Wavelength ◽  
Fractional Orders ◽  
Fractional Differentiator ◽  
Good Agreement

Abstract 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 response as well as the temporal response 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 reduced sized and cost.

scholarly journals RF and microwave fractional differentiation with transversal filters using a soliton crystal microcomb multiwavelength source

2020 ◽  
Author(s):  
David Moss ◽  
Arnan Mitchell ◽  
Roberto Morandotti ◽  
xingyuan xu
Keyword(s):  
High Performance ◽  
Free Spectral Range ◽  
Fractional Differentiation ◽  
Temporal Response ◽  
Pulse Input ◽  
Transversal Filters ◽  
Multi Wavelength ◽  
Fractional Orders ◽  
Fractional Differentiator ◽  
Good Agreement

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 response as well as the temporal response 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 reduced sized and cost.

scholarly journals A fractional order epidemic model for the simulation of outbreaks of Ebola

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Safdar Ali
Keyword(s):  
Numerical Solution ◽  
Root Mean Square ◽  
Fractional Order ◽  
Relative Error ◽  
Numerical Solutions ◽  
Real Data ◽  
Mean Square ◽  
Order Model ◽  
The Real ◽  
Fractional Orders

AbstractThe Ebola outbreak in 2014 caused many infections and deaths. Some literature works have proposed some models to study Ebola virus, such as SIR, SIS, SEIR, etc. It is proved that the fractional order model can describe epidemic dynamics better than the integer order model. In this paper, we propose a fractional order Ebola system and analyze the nonnegative solution, the basic reproduction number $R_{0}$ R 0 , and the stabilities of equilibrium points for the system firstly. In many studies, the numerical solutions of some models cannot fit very well with the real data. Thus, to show the dynamics of the Ebola epidemic, the Gorenflo–Mainardi–Moretti–Paradisi scheme (GMMP) is taken to get the numerical solution of the SEIR fractional order Ebola system and the modified grid approximation method (MGAM) is used to acquire the parameters of the SEIR fractional order Ebola system. We consider that the GMMP method may lead to absurd numerical solutions, so its stability and convergence are given. Then, the new fractional orders, parameters, and the root-mean-square relative error $g(U^{*})=0.4146$ g ( U ∗ ) = 0.4146 are obtained. With the new fractional orders and parameters, the numerical solution of the SEIR fractional order Ebola system is closer to the real data than those models in other literature works. Meanwhile, we find that most of the fractional order Ebola systems have the same order. Hence, the fractional order Ebola system with different orders using the Caputo derivatives is also studied. We also adopt the MGAM algorithm to obtain the new orders, parameters, and the root-mean-square relative error which is $g(U^{*})=0.2744$ g ( U ∗ ) = 0.2744 . With the new parameters and orders, the fractional order Ebola systems with different orders fit very well with the real data.

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