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Frontiers of Optoelectronics

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Front Optoelec    2013, Vol. 6 Issue (1) : 78-88    https://doi.org/10.1007/s12200-012-0299-1
REVIEW ARTICLE
Review of photonic Hilbert transformers
Chaotan SIMA(), James C. GATES, Michalis N. ZERVAS, Peter G. R. SMITH
Optoelectronics Research Centre, University of Southampton, Southampton SO17 1BJ, UK
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Abstract

This paper reviews the demonstrations of photonic Hilbert transformers (PHTs), describing their progress and recent developments. The physical operating principles of PHTs including fractional Hilbert transformers are discussed, together with device applications in all-optical signal processing. Versatile approaches to realize PHTs are discussed, e.g., discrete free space optics, fiber-based schemes and integrated planar geometry. The numerical designs and experimental performances of these PHTs are analyzed in terms of spectral quality, operating bandwidth, system integration, and mechanical and thermal stability. Recent developments of the monolithically integrated photonic Hilbert transform (HT) devices include directional couplers and planar Bragg gratings which allow all-optical single-sideband (SSB) suppression and sideband switching.
Keywords photonic Hilbert transformer (PHT)      Bragg reflectors      direct UV writing      all-optical signal processing     
Corresponding Author(s): SIMA Chaotan,Email:Chaotan.Sima@soton.ac.uk   
Issue Date: 05 March 2013
 Cite this article:   
Chaotan SIMA,James C. GATES,Michalis N. ZERVAS, et al. Review of photonic Hilbert transformers[J]. Front Optoelec, 2013, 6(1): 78-88.
 URL:  
https://academic.hep.com.cn/foe/EN/10.1007/s12200-012-0299-1
https://academic.hep.com.cn/foe/EN/Y2013/V6/I1/78
Fig.1  (a) Theoretical expression of HT (solid line) and FrHT (dashed line) functions; (b) amplitude and (c) phase responses of HT (solid line) and order FrHT (dashed line)
Fig.1  (a) Theoretical expression of HT (solid line) and FrHT (dashed line) functions; (b) amplitude and (c) phase responses of HT (solid line) and order FrHT (dashed line)
Fig.1  (a) Theoretical expression of HT (solid line) and FrHT (dashed line) functions; (b) amplitude and (c) phase responses of HT (solid line) and order FrHT (dashed line)
Fig.1  (a) Theoretical expression of HT (solid line) and FrHT (dashed line) functions; (b) amplitude and (c) phase responses of HT (solid line) and order FrHT (dashed line)
Fig.2  Schematic drawing of (a) amplitude and (b) phase responses of physically realizable HT (solid lines) compared to those of ideal HT (dashed lines) in frequency domain
Fig.2  Schematic drawing of (a) amplitude and (b) phase responses of physically realizable HT (solid lines) compared to those of ideal HT (dashed lines) in frequency domain
Fig.2  Schematic drawing of (a) amplitude and (b) phase responses of physically realizable HT (solid lines) compared to those of ideal HT (dashed lines) in frequency domain
Fig.2  Schematic drawing of (a) amplitude and (b) phase responses of physically realizable HT (solid lines) compared to those of ideal HT (dashed lines) in frequency domain
Fig.3  Block diagram of all-optical SSB modulation system using PHT. DSB: double sideband
Fig.3  Block diagram of all-optical SSB modulation system using PHT. DSB: double sideband
Fig.3  Block diagram of all-optical SSB modulation system using PHT. DSB: double sideband
Fig.3  Block diagram of all-optical SSB modulation system using PHT. DSB: double sideband
Fig.4  Optical setup for performing conventional spatial HT and FrHT (reprinted from Ref. [])
Fig.4  Optical setup for performing conventional spatial HT and FrHT (reprinted from Ref. [])
Fig.4  Optical setup for performing conventional spatial HT and FrHT (reprinted from Ref. [])
Fig.4  Optical setup for performing conventional spatial HT and FrHT (reprinted from Ref. [])
Fig.5  Configuration of non-grating fiber based PHT (a) method combining several fiber-based MZIs to form PHT; (b) impulse response of PHT in (a); (c) experimental setup of optically phase-shifted SSB modulation using (a); (d) SSB signal with 7.8 dB suppression ratio at 10 GHz of system in (c) (reprinted from Ref. [])
Fig.5  Configuration of non-grating fiber based PHT (a) method combining several fiber-based MZIs to form PHT; (b) impulse response of PHT in (a); (c) experimental setup of optically phase-shifted SSB modulation using (a); (d) SSB signal with 7.8 dB suppression ratio at 10 GHz of system in (c) (reprinted from Ref. [])
Fig.5  Configuration of non-grating fiber based PHT (a) method combining several fiber-based MZIs to form PHT; (b) impulse response of PHT in (a); (c) experimental setup of optically phase-shifted SSB modulation using (a); (d) SSB signal with 7.8 dB suppression ratio at 10 GHz of system in (c) (reprinted from Ref. [])
Fig.5  Configuration of non-grating fiber based PHT (a) method combining several fiber-based MZIs to form PHT; (b) impulse response of PHT in (a); (c) experimental setup of optically phase-shifted SSB modulation using (a); (d) SSB signal with 7.8 dB suppression ratio at 10 GHz of system in (c) (reprinted from Ref. [])
Fig.6  (a) System implementation with pre-setting 4 taps weights and spacing; (b) magnitude response; (c) phase response (reprinted from Ref. [])
Fig.6  (a) System implementation with pre-setting 4 taps weights and spacing; (b) magnitude response; (c) phase response (reprinted from Ref. [])
Fig.6  (a) System implementation with pre-setting 4 taps weights and spacing; (b) magnitude response; (c) phase response (reprinted from Ref. [])
Fig.6  (a) System implementation with pre-setting 4 taps weights and spacing; (b) magnitude response; (c) phase response (reprinted from Ref. [])
Fig.7  (a) Sampled FBG design; (b) schematic of optical SSB generation filter; (c) reflection spectral of both arms; (d) sideband suppression characteristic of optical SSB generation (reprinted from Ref. [])
Fig.7  (a) Sampled FBG design; (b) schematic of optical SSB generation filter; (c) reflection spectral of both arms; (d) sideband suppression characteristic of optical SSB generation (reprinted from Ref. [])
Fig.7  (a) Sampled FBG design; (b) schematic of optical SSB generation filter; (c) reflection spectral of both arms; (d) sideband suppression characteristic of optical SSB generation (reprinted from Ref. [])
Fig.7  (a) Sampled FBG design; (b) schematic of optical SSB generation filter; (c) reflection spectral of both arms; (d) sideband suppression characteristic of optical SSB generation (reprinted from Ref. [])
Fig.8  (a) Example of FBG design using inverse scattering method; (b) reflected power of the fabricated PHT; (c) phase response of the fabricated PHT; (d) SSB signal generation system; (e) generated signals (reprinted from Refs. [,])
Fig.8  (a) Example of FBG design using inverse scattering method; (b) reflected power of the fabricated PHT; (c) phase response of the fabricated PHT; (d) SSB signal generation system; (e) generated signals (reprinted from Refs. [,])
Fig.8  (a) Example of FBG design using inverse scattering method; (b) reflected power of the fabricated PHT; (c) phase response of the fabricated PHT; (d) SSB signal generation system; (e) generated signals (reprinted from Refs. [,])
Fig.8  (a) Example of FBG design using inverse scattering method; (b) reflected power of the fabricated PHT; (c) phase response of the fabricated PHT; (d) SSB signal generation system; (e) generated signals (reprinted from Refs. [,])
Fig.9  (a) Schematic of one ORR with MZI; (b) impulse response of ORR; (c) phase response and (d) power transfer of FrHT using one ORR and another FrHT using two cascaded ORR. ρ indicates the fractional order (reprinted from Ref. [])
Fig.9  (a) Schematic of one ORR with MZI; (b) impulse response of ORR; (c) phase response and (d) power transfer of FrHT using one ORR and another FrHT using two cascaded ORR. ρ indicates the fractional order (reprinted from Ref. [])
Fig.9  (a) Schematic of one ORR with MZI; (b) impulse response of ORR; (c) phase response and (d) power transfer of FrHT using one ORR and another FrHT using two cascaded ORR. ρ indicates the fractional order (reprinted from Ref. [])
Fig.9  (a) Schematic of one ORR with MZI; (b) impulse response of ORR; (c) phase response and (d) power transfer of FrHT using one ORR and another FrHT using two cascaded ORR. ρ indicates the fractional order (reprinted from Ref. [])
Fig.10  Schematic of proposed integrated SSB modulation device with planar Bragg grating based PHT, located in single silica-on-silicon chip
Fig.10  Schematic of proposed integrated SSB modulation device with planar Bragg grating based PHT, located in single silica-on-silicon chip
Fig.10  Schematic of proposed integrated SSB modulation device with planar Bragg grating based PHT, located in single silica-on-silicon chip
Fig.10  Schematic of proposed integrated SSB modulation device with planar Bragg grating based PHT, located in single silica-on-silicon chip
Fig.11  (a) Grating refractive index modulation profile; (b) reflectivity spectrum of initial PHT grating; (c) relative group delay response of initial PHT grating []; (d) amplitude responses of another improved PHT grating (blue) and sinc-apodized flat top reflector (red); (e) all-optical SSB generation and switching, compared with double sideband (DSB) signal []. LSB: lower sideband, USB: upper sideband
Fig.11  (a) Grating refractive index modulation profile; (b) reflectivity spectrum of initial PHT grating; (c) relative group delay response of initial PHT grating []; (d) amplitude responses of another improved PHT grating (blue) and sinc-apodized flat top reflector (red); (e) all-optical SSB generation and switching, compared with double sideband (DSB) signal []. LSB: lower sideband, USB: upper sideband
Fig.11  (a) Grating refractive index modulation profile; (b) reflectivity spectrum of initial PHT grating; (c) relative group delay response of initial PHT grating []; (d) amplitude responses of another improved PHT grating (blue) and sinc-apodized flat top reflector (red); (e) all-optical SSB generation and switching, compared with double sideband (DSB) signal []. LSB: lower sideband, USB: upper sideband
Fig.11  (a) Grating refractive index modulation profile; (b) reflectivity spectrum of initial PHT grating; (c) relative group delay response of initial PHT grating []; (d) amplitude responses of another improved PHT grating (blue) and sinc-apodized flat top reflector (red); (e) all-optical SSB generation and switching, compared with double sideband (DSB) signal []. LSB: lower sideband, USB: upper sideband
researchersoperation principledevice response qualitydevice operation bandwidth /GHzfabrication simplicitysystem stabilityapplication
Takano et al.MZI+ delay line√10√√SSB ratio: 7.8 dB
Emami et al.transversal filter+ coarse WDM coupler√20√√frequency measurements
Hanawa et al.sampled FBGs√√15√√SSB ratio:>10 dB
Huang et al.FDOP+ photodiodes√√√100N.A.√quadrature RF signal generation
Yao et al.photonic microwave delay line filters√√24√√√√differentiator
Yao et al.single FBG√√100√√√SSB ratio:≤20 dB
Zhuang et al.MZI+ optical ring resonator√√√10√√√√quadrature RF signal generation
Sima et al.integrated planar Bragg grating√√√200√√√√√√SSB ratio:≥12 dB
Tab.1  Comparisons between current PHT implementations
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