Optical signal processing based on silicon photonics waveguide Bragg gratings: review

doi:10.1007/s12200-018-0813-1

Front. Optoelectron.

2018, Vol. 11

Issue (2) : 163-188 https://doi.org/10.1007/s12200-018-0813-1

REVIEW ARTICLE

Optical signal processing based on silicon photonics waveguide Bragg gratings: review

Saket KAUSHAL¹, Rui Cheng², Minglei Ma², Ajay Mistry², Maurizio Burla^1,³, Lukas Chrostowski²(

), José Azaña¹(

)

¹. Institut National de la Recherche Scientifique – Centre Energie, Matériaux et Télécommunications (INRS-EMT), Varennes, QC J3X 1S2 Canada
². Department of Electrical and Computer Engineering, University of British Columbia (UBC), Vancouver, British Columbia, V6T 1Z4 Canada
³. Institute of Electromagnetic Fields, ETH Zurich, Gloriastrasse 35, Zurich 8092, Switzerland

Download: PDF(1547 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

This paper reviews the work done by researchers at INRS and UBC in the field of integrated microwave photonics (IMWPs) using silicon based waveguide Bragg gratings (WBGs). The grating design methodology is discussed in detail, including practical device fabrication considerations. On-chip implementations of various fundamental photonic signal processing units, including Fourier transformers, Hilbert transformers, ultrafast pulse shapers etc., are reviewed. Recent progress on WBGs-based IMWP subsystems, such as true time delay elements, phase shifters, real time frequency identification systems, is also discussed.

Keywords silicon photonics ultrafast optical signal processing integrated microwave photonics (IMWPs)

Corresponding Author(s): Lukas Chrostowski,José Azaña

Just Accepted Date: 04 June 2018 Online First Date: 02 July 2018 Issue Date: 04 July 2018

Cite this article:

Saket KAUSHAL,Rui Cheng,Minglei Ma, et al. Optical signal processing based on silicon photonics waveguide Bragg gratings: review[J]. Front. Optoelectron., 2018, 11(2): 163-188.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-018-0813-1
https://academic.hep.com.cn/foe/EN/Y2018/V11/I2/163

Fig.1 (a) Cross-sectional view of silicon-on-insulator (SOI) wafer. (b) Common waveguides in silicon photonics. (Left) Strip waveguide, also known as channel waveguides, photonic wires, or ridge waveguides. (Right) Rib waveguide, also known as ridge waveguide or strip-loaded ridge waveguide; Reproduced from Ref. [¹⁴]

Fig.2 Schematic illustration of a typical side-wall waveguide Bragg grating (WBG). W: waveguide width; ΔW: corrugation width; Λ: grating period; N: number of the periods

Fig.3 A typical design flow of an integrated Bragg grating for a target spectral response

Fig.4 (a) Typical amplitude and phase response of a photonic Hilbert transformer. (b) Corresponding apodization profile of a fiber based Bragg grating, obtained using layer peeling algorithm. Reproduced from Ref. [²⁹]

Fig.5 Schematic of cladding-modulated waveguide Bragg gratings (WBGs). Λ: period of the silicon cylinders; W: diameter of the silicon cylinder; d: distance of the silicon cylinders from the edge of the waveguide

Fig.6 (a) (Left) Schematic of grating duty-cycle modulation and (right) the relationship curve between duty cycle and k. (b) (Left) Schematic of side-wall miss-alignment modulation and (right) the relationship curve between the miss-alignment and k

Fig.7 (a) Schematic flow showing the process of mapping the apodization profile into grating structure, taken from Ref. [³⁵]. (b) Schematic diagram illustrating a typical phase-modulated grating structure. (c) (Blue) Target Gaussian apodization profile and (red) phase modulation amplitude along the grating A(z). (d) Phase modulation profile along the grating. (e) d(i) distribution along the grating position, where the horizontal line represents the level of Λ_G/2 (158 nm)

Fig.8 (a) Complex spectral response of the designed Hilbert transformer. (b) Required coupling coefficient profile. (c), (d) and (e) are the calculated spectral responses of the gating apodized by the phase modulation method, the side-wall misalignment modulation, and duty cycle modulation, respectively; the spectral calculation is based on the standard transfer matrix method upon the apodized grating structures; the black curves in these figures are the amplitude response of designed Hilbert transformer, shown for comparison

Fig.9 Spectral responses of photonic Hilbert transformers based on waveguide Bragg gratings (WBGs) with different corrugation widths, calculated by the transfer matrix method (TMM) method

Fig.10 (a) Compare of the band structures for uniform medium and 1-D photonic crystal. (b) Schematic illustration of how the band structure is related to the reflection band of a Bragg grating. (c) FDTD band structure analysis in Lumeical FDTD Solutions. (d) Band structure diagram for of a waveguide Bragg grating (WBG) with ΔW of 50 nm. (e) Fourier transform (magnitude) of the time domain signals at the band edge from the FDTD simulation for WBGs with different ΔW; the frequency range between the two peaks corresponds to the band gap width

Fig.11 k versus corrugation width ΔW calculated by the different approaches, with the experimental values of the gratings fabricated by electron-beam lithography included for the comparison

Fig.12 (a) Spectra of WBGs with different degrees of ΔW jitter effects applied. s: standard deviations of ΔW variations. (b) Spectra of WBGs fabricated with different grid sizes when the s of ΔW jitter is (left) 1 nm and (right) 3 nm

Fig.13 Frequency to time conversion using temporal chromatic dispersion. Reproduced from Ref. [⁵³]

Fig.14 Incident (solid red curve) and reflected (dashed green curve) spectra superimposed on the scaled oscilloscope traces of the output temporal waveforms (solid black curve): (a) for in-phase incident pulses and (b) for π-phase-shifted incident pulses. (c) Spectrum (dashed green curve) and the scaled temporal waveform (solid black curve) of the reflected in-phase double pulse signal reconstructed through Fourier transform spectral interferometry (FTSI). (d) Phase of the reflected signal reconstructed through FTSI. Reproduced from Ref. [²¹]

Fig.15 Measured reflection spectral response of the fabricated phase-shifted waveguide Bragg grating (PS-WBG) compared with the ideal fractional Hilbert transformer (FHT) response in (a) magnitude and (b) phase. The top inset shows examples of Gaussian input pulse spectra. Reproduced from Ref. [¹⁸]

Fig.16 Time-domain experimental testing results. The figure shows the measured input pulse (solid line), simulated output pulse obtained by filtering the measured input pulse with an ideal Hilbert transformer (dashed line), and actual output pulse measured using Fourier transform spectral interferometry (FTSI) (circled line), for input pulses with full width at half-maximum (FWHM) durations of (a) 4 ps and (b) 1.5 ps. Reproduced from Ref. [¹⁸]

Fig.17 Schematic of a laterally apodized waveguide Bragg grating (WBG). Reproduced from Ref. [¹⁶]

Fig.18 (a)−(c) Simulated and (d)−(f) measured amplitude and phase spectral responses, (g)−(i) cross-correlation coefficients, and (j)−(l) comparison between the temporal responses of ideal HTs with the response from the fabricated devices to different Gaussian pulses for the integer (two top rows) and fractional (last row) photonic HTs. Reproduced from Ref. [¹⁶]

Fig.19 Pulse shaping by linear filtering: (a) time-domain view; (b) frequency-domain view

Fig.20 (a) (i) Spectra of the ultrashort pulse of 7.8 ps pulse width before and after propagation through the fabricated Mach-Zehdner interferometer (MZI) when the pulse carrier wavelength matches one of the MZIs peak transmission wavelengths. (ii) Time-domain intensity profiles of the input pulse, the measured output pulse, and the simulated ideal output. Phase profile of the measured output pulse is also shown. (b) (i) Spectra of the ultrashort pulse of 11 ps pulse width before and after propagation through the fabricated MZI when the pulse carrier wavelength matches one of the MZIs notch transmission wavelengths. (ii) Time-domain intensity profiles of the input pulse, the measured output pulse, and the simulated ideal output. (iii) and (iv) Intensity and phase profiles of the measured output pulse. Reproduced from Ref. [⁶⁵]

Fig.21 (a) Schematic of the proposed pulse shaping device and its principle of operation. (b) Phase coding by tuning the waveguide length in the differential delay lines. (c) Amplitude coding by tuning the coupling length. Reproduced from Ref. [⁶⁶]

Fig.22 Micrographs taken using a camera mounted on a microscope, from part of the fabricated devices with [(a) and (b), respectively] R = 5 µm and 3 µm; (c) and (d), respectively, the simulated and measured amplitude temporal response and power spectral response (PSR) of a device consisting of n = 10 identical cascaded couplers; (e) and (f), respectively, n = 20 identical cascaded couplers; and (g) and (h), respectively, n = 5 identical cascaded couplers with a shorter delay difference. Reproduced from Ref. [⁶⁶]

Fig.23 Dual-phase-shifted waveguide Bragg grating (DPS-WBG) magnitude response (a), operation as phase shifting (PS) (b), and true-time delay (TTD) (c). Reproduced from Ref. [¹⁹]

Fig.24 (a) Complex (magnitude and phase) radio frequency (RF) response for different phase shift values. (b) Complex (magnitude and phase) RF response for different true time delay values. Reproduced from Ref. [¹⁹]

Fig.25 Schematic of the silicon WBG (PS-WBG) employed as a linear-optics frequency discriminator. TX port: transmission port; RX port: reflection port. Reproduced from Ref. [¹⁷]

Fig.26 Simulated (dashed line) and measured (solid line; a) linear optical transmission and (b) reflection spectral responses of the phase-shifted waveguide Bragg grating (PS-WBG); (c) and (d) zoom with overlapped optical single sideband carrier (OSSB+C) spectrum. The optical responses are normalized to the maximum. (e) Radio frequency (RF) response of transmission (TX) and reflection (RX) ports; (f) ACF, obtained from Eq. (10). Reproduced from. [¹⁷]

Fig.27 Estimated frequency (red dots) and corresponding error (blue dots). Reproduced from Ref. [¹⁷]

Fig.28 Experiment of dynamic frequency identification. (a) A radio frequency (RF) signal with unknown frequency content enters the photonic instantaneous frequency measurement (IFM) system. (b) Time-domain signal at the IFM output was amplitude-coded according to the time-varying frequency content of the input signal. (c) Instantaneous power was extracted by self-mixing and low-pass filtering. (d) Using the inverse amplitude comparison function (ACF), the RF frequency content was estimated in a dynamic manner. (e) Spectrogram of the frequency-hopping input sequence is shown for comparison. Reproduced from Ref. [¹⁷]

1	Koenig S, Lopez-Diaz D, Antes J, Boes F, Henneberger R, Leuther A, Tessmann A, Schmogrow R, Hillerkuss D, Palmer R, Zwick T, Koos C, Freude W, Ambacher O, Leuthold J, Kallfass I. Wireless sub-THz communication system with high data rate. Nature Photonics, 2013, 7(12): 977–981 https://doi.org/10.1038/nphoton.2013.275
2	Eyre J, Bier J. The evolution of DSP processors. IEEE Signal Processing Magazine, 2000, 17(2): 43–51 https://doi.org/10.1109/79.826411
3	Kuo S M, Lee B H, Tian W. Real-time Digital Signal Processing: Fundamentals, Implementations and Applications. New York: John Wiley & Sons, 2013
4	Seeds A J, Shams H, Fice M J, Renaud C C.Terahertz photonics for wireless communications. Journal of Lightwave Technology, 2015, 33 (3): 579–587
5	Nagatsuma T, Horiguchi S, Minamikata Y, Yoshimizu Y, Hisatake S, Kuwano S, Yoshimoto N, Terada J, Takahashi H. Terahertz wireless communications based on photonics technologies. Optics Express, 2013, 21(20): 23736–23747 https://doi.org/10.1364/OE.21.023736 pmid: 24104286
6	Seeds A J. Microwave photonics. IEEE Transactions on Microwave Theory and Techniques, 2002, 50(3): 877–887 https://doi.org/10.1109/22.989971
7	Iezekiel S. Microwave Photonics: Devices and Applications. New York: John Wiley & Sons, 2009
8	Capmany J, Novak D. Microwave photonics combines two worlds. Nature Photonics, 2007, 1(6): 319–330 https://doi.org/10.1038/nphoton.2007.89
9	Yao J. Microwave photonics. Journal of Lightwave Technology, 2009, 27(3): 314–335 https://doi.org/10.1109/JLT.2008.2009551
10	Marpaung D, Roeloffzen C, Heideman R, Leinse A, Sales S, Capmany J. Integrated microwave photonics. Laser & Photonics Reviews, 2013, 7(4): 506–538 https://doi.org/10.1002/lpor.201200032
11	Roeloffzen C G, Zhuang L, Taddei C, Leinse A, Heideman R G, van Dijk P W, Oldenbeuving R M, Marpaung D A, Burla M, Boller K J. Silicon nitride microwave photonic circuits. Optics Express, 2013, 21(19): 22937–22961 https://doi.org/10.1364/OE.21.022937 pmid: 24104179
12	Zhang W, Yao J. Silicon-based integrated microwave photonics. IEEE Journal of Quantum Electronics, 2016, 52: 1–12
13	Bogaerts W, De Heyn P, Van Vaerenbergh T, De Vos K, Kumar Selvaraja S, Claes T, Dumon P, Bienstman P, Van Thourhout D, Baets R. Silicon Microring Resonators. Laser & Photonics Reviews, 2012, 6(1): 47–73 https://doi.org/10.1002/lpor.201100017
14	Chrostowski L, Hochberg M.Silicon Photonics Design: From Devices to Systems. Cambridge: Cambridge University Press, 2015
15	Hill K O, Meltz G. Fiber Bragg grating technology fundamentals and overview. Journal of Lightwave Technology, 1997, 15(8): 1263–1276 https://doi.org/10.1109/50.618320
16	Bazargani H P, Burla M, Chrostowski L, Azaña J. Photonic Hilbert transformers based on laterally apodized integrated waveguide Bragg gratings on a SOI wafer. Optics Letters, 2016, 41(21): 5039–5042 https://doi.org/10.1364/OL.41.005039 pmid: 27805680
17	Burla M, Wang X, Li M, Chrostowski L, Azaña J. Wideband dynamic microwave frequency identification system using a low-power ultracompact silicon photonic chip. Nature Communications, 2016, 7: 13004 https://doi.org/10.1038/ncomms13004 pmid: 27687576
18	Burla M, Li M, Cortés L R, Wang X, Fernández-Ruiz M R, Chrostowski L, Azaña J. Terahertz-bandwidth photonic fractional Hilbert transformer based on a phase-shifted waveguide Bragg grating on silicon. Optics Letters, 2014, 39(21): 6241–6244 https://doi.org/10.1364/OL.39.006241 pmid: 25361324
19	Burla M, Cortés L R, Li M, Wang X, Chrostowski L, Azaña J. On-chip programmable ultra-wideband microwave photonic phase shifter and true time delay unit. Optics Letters, 2014, 39(21): 6181–6184 https://doi.org/10.1364/OL.39.006181 pmid: 25361309
20	Burla M, Cortés L R, Li M, Wang X, Chrostowski L, Azaña J. Integrated waveguide Bragg gratings for microwave photonics signal processing. Optics Express, 2013, 21(21): 25120–25147 https://doi.org/10.1364/OE.21.025120 pmid: 24150355
21	Dolgaleva K, Malacarne A, Tannouri P, Fernandes L A, Grenier J R, Aitchison J S, Azaña J, Morandotti R, Herman P R, Marques P V. Integrated optical temporal Fourier transformer based on a chirped Bragg grating waveguide. Optics Letters, 2011, 36(22): 4416–4418 https://doi.org/10.1364/OL.36.004416 pmid: 22089582
22	Rutkowska K A, Duchesne D, Strain M J, Morandotti R, Sorel M, Azaña J. Ultrafast all-optical temporal differentiators based on CMOS-compatible integrated-waveguide Bragg gratings. Optics Express, 2011, 19(20): 19514–19522 https://doi.org/10.1364/OE.19.019514 pmid: 21996892
23	Bogaerts W, Selvaraja S K, Dumon P, Brouckaert J, De Vos K, Van Thourhout D, Baets R. Silicon-on-insulator spectral filters fabricated with CMOS technology. IEEE Journal of Selected Topics in Quantum Electronics, 2010, 16(1): 33–44 https://doi.org/10.1109/JSTQE.2009.2039680
24	Othonos A.Fiber Bragg gratings. Review of Scientific Instruments, 1997, 68 (12): 4309–4341
25	Vivien L, Osmond J, Fédéli J M, Marris-Morini D, Crozat P, Damlencourt J F, Cassan E, Lecunff Y, Laval S. 42 GHz p.i.n germanium photodetector integrated in a silicon-on-insulator waveguide. Optics Express, 2009, 17(8): 6252–6257 https://doi.org/10.1364/OE.17.006252 pmid: 19365450
26	Skaar J. Synthesis and Characterization of Fiber Bragg Gratings. Dissertation for the Doctoral Degree. Trondheim, Norway: Norwegian University of Science and Technology, 2000
27	Sima C, Gates J C, Holmes C, Mennea P L, Zervas M N, Smith P G. Terahertz bandwidth photonic Hilbert transformers based on synthesized planar Bragg grating fabrication. Optics Letters, 2013, 38(17): 3448–3451 https://doi.org/10.1364/OL.38.003448 pmid: 23988981
28	Simard A D, Strain M J, Meriggi L, Sorel M, LaRochelle S. Bandpass integrated Bragg gratings in silicon-on-insulator with well-controlled amplitude and phase responses. Optics Letters, 2015, 40(5): 736–739 https://doi.org/10.1364/OL.40.000736 pmid: 25723420
29	Li M, Yao J. All-fiber temporal photonic fractional Hilbert transformer based on a directly designed fiber Bragg grating. Optics Letters, 2010, 35(2): 223–225 https://doi.org/10.1364/OL.35.000223 pmid: 20081975
30	Simard A D, Belhadj N, Painchaud Y, LaRochelle S. Apodized silicon-on-insulator Bragg gratings. IEEE Photonics Technology Letters, 2012, 24(12): 1033–1035 https://doi.org/10.1109/LPT.2012.2194278
31	Wiesmann D, David C, Germann R, Emi D, Bona G. Apodized surface-corrugated gratings with varying duty cycles. IEEE Photonics Technology Letters, 2000, 12(6): 639–641 https://doi.org/10.1109/68.849069
32	Tan D T, Ikeda K, Fainman Y. Cladding-modulated Bragg gratings in silicon waveguides. Optics Letters, 2009, 34(9): 1357–1359 https://doi.org/10.1364/OL.34.001357 pmid: 19412271
33	Hung Y J, Lin K H, Wu C J, Wang C Y, Chen Y J. Narrowband reflection from weakly coupled cladding-modulated Bragg gratings. IEEE Journal of Selected Topics in Quantum Electronics, 2016, 22(6): 218–224 https://doi.org/10.1109/JSTQE.2015.2487878
34	Wang X, Wang Y, Flueckiger J, Bojko R, Liu A, Reid A, Pond J, Jaeger N A, Chrostowski L. Precise control of the coupling coefficient through destructive interference in silicon waveguide Bragg gratings. Optics Letters, 2014, 39(19): 5519–5522 https://doi.org/10.1364/OL.39.005519 pmid: 25360917
35	Cheng R, Chrostowski L. Multichannel photonic Hilbert transformers based on complex modulated integrated Bragg gratings. Optics Letters, 2018, 43(5): 1031–1034 https://doi.org/10.1364/OL.43.001031 pmid: 29489773
36	Agrawal G P, Radic S. Phase-shifted fiber Bragg gratings and their application for wavelength demultiplexing. IEEE Photonics Technology Letters, 1994, 6(8): 995–997 https://doi.org/10.1109/68.313074
37	Katsidis C C, Siapkas D I. General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference. Applied Optics, 2002, 41(19): 3978–3987 https://doi.org/10.1364/AO.41.003978
38	Stoll H, Yariv A. Coupled-mode analysis of periodic dielectric waveguides. Optics Communications, 1973, 8(1): 5–8 https://doi.org/10.1016/0030-4018(73)90168-5
39	Yariv A. Coupled-mode theory for guided-wave optics. IEEE Journal of Quantum Electronics, 1973, 9(9): 919–933 https://doi.org/10.1109/JQE.1973.1077767
40	Streifer W, Scifres D, Burnham R. Coupling coefficients for distributed feedback single-and double-heterostructure diode lasers. IEEE Journal of Quantum Electronics, 1975, 11(11): 867–873 https://doi.org/10.1109/JQE.1975.1068539
41	Zhang Y, Holzwarth N, Williams R. Electronic band structures of the scheelite materials CaMoO4, CaWO4, PbMoO4, and PbWO4. Physical Review B: Condensed Matter and Materials Physics, 1998, 57(20): 12738–12750 https://doi.org/10.1103/PhysRevB.57.12738
42	Lumerical FDTD, 2018
43	Pendry J. Photonic band structures. Journal of Modern Optics, 1994, 41(2): 209–229 https://doi.org/10.1080/09500349414550281
44	Li Z Y, Lin L L. Photonic band structures solved by a plane-wave-based transfer-matrix method. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2003, 67(4 Pt 2): 046607 https://doi.org/10.1103/PhysRevE.67.046607 pmid: 12786509
45	Applied Nanotools Inc., 2018
46	Simard A D, Beaudin G, Aimez V, Painchaud Y, Larochelle S. Characterization and reduction of spectral distortions in silicon-on-insulator integrated Bragg gratings. Optics Express, 2013, 21(20): 23145–23159 https://doi.org/10.1364/OE.21.023145 pmid: 24104229
47	Ayotte N, Simard A D, LaRochelle S. Long integrated Bragg gratings for SOI wafer metrology. IEEE Photonics Technology Letters, 2015, 27(7): 755–758 https://doi.org/10.1109/LPT.2015.2391174
48	Simard A D, Painchaud Y, LaRochelle S. Integrated Bragg gratings in spiral waveguides. Optics Express, 2013, 21(7): 8953–8963 https://doi.org/10.1364/OE.21.008953 pmid: 23571986
49	Wang X, Yun H, Chrostowski L. Integrated Bragg gratings in spiral waveguides. In: Proceedings of Conference on Lasers and Electro-Optics (CLEO). San Jose, California: OSA, 2013, CTh4F.8
50	Ma M, Chen Z, Yun H, Wang Y, Wang X, Jaeger N A F, Chrostowski L. Apodized spiral Bragg grating waveguides in silicon-on-insulator. IEEE Photonics Technology Letters, 2018, 30(1): 111–114 https://doi.org/10.1109/LPT.2017.2777824
51	Simard A D, Ayotte N, Painchaud Y, Bedard S, LaRochelle S. Impact of sidewall roughness on integrated Bragg gratings. Journal of Lightwave Technology, 2011, 29(24): 3693–3704 https://doi.org/10.1109/JLT.2011.2173556
52	Azaña J, Muriel M A. Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings. IEEE Journal of Quantum Electronics, 2000, 36(5): 517–526 https://doi.org/10.1109/3.842092
53	Azaña J, Berger N K, Levit B, Fischer B. Spectral Fraunhofer regime: time-to-frequency conversion by the action of a single time lens on an optical pulse. Applied Optics, 2004, 43(2): 483–490 https://doi.org/10.1364/AO.43.000483 pmid: 14735967
54	Yariv A, Yeh P. Photonics: Optical Electronics in Modern Communications. Oxford: Oxford University Press, 2006
55	Tong Y, Chan L, Tsang H. Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope. Electronics Letters, 1997, 33(11): 983–985 https://doi.org/10.1049/el:19970663
56	Muriel M A, Azaña J, Carballar A. Real-time Fourier transformer based on fiber gratings. Optics Letters, 1999, 24(1): 1–3 https://doi.org/10.1364/OL.24.000001 pmid: 18071388
57	Coppinger F, Bhushan A, Jalali B. Photonic time stretch and its application to analog-to-digital conversion. IEEE Transactions on Microwave Theory and Techniques, 1999, 47(7): 1309–1314 https://doi.org/10.1109/22.775471
58	Chou J, Han Y, Jalali B. Adaptive RF-photonic arbitrary waveform generator. IEEE Photonics Technology Letters, 2003, 15(4): 581–583 https://doi.org/10.1109/LPT.2003.809309
59	Solli D, Chou J, Jalali B. Amplified wavelength–time transformation for real-time spectroscopy. Nature Photonics, 2008, 2(1): 48–51 https://doi.org/10.1038/nphoton.2007.253
60	Ouellette F. Dispersion cancellation using linearly chirped Bragg grating filters in optical waveguides. Optics Letters, 1987, 12(10): 847–849 https://doi.org/10.1364/OL.12.000847 pmid: 19741893
61	Lepetit L, Chériaux G, Joffre M. Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy. Journal of the Optical Society of America B, 1995, 12(12): 2467–2474 https://doi.org/10.1364/JOSAB.12.002467
62	Weiner A. Ultrafast Optics, volume 72. New York: John Wiley & Sons, 2011
63	Rivas L M, Strain M J, Duchesne D, Carballar A, Sorel M, Morandotti R, Azaña J. Picosecond linear optical pulse shapers based on integrated waveguide Bragg gratings. Optics Letters, 2008, 33(21): 2425–2427 https://doi.org/10.1364/OL.33.002425 pmid: 18978875
64	Ashrafi R, Li M, Belhadj N, Dastmalchi M, LaRochelle S, Azaña J. Experimental demonstration of superluminal space-to-time mapping in long period gratings. Optics Letters, 2013, 38(9): 1419–1421 https://doi.org/10.1364/OL.38.001419 PMID:23632504
65	Li M, Dumais P, Ashrafi R, Bazargani H P, Quelene J B, Callender C, Azana J. Ultrashort flat-top pulse generation using on-chip CMOS-compatible Mach–Zehnder interferometers. IEEE Photonics Technology Letters, 2012, 24(16): 1387–1389 https://doi.org/10.1109/LPT.2012.2203335
66	Bazargani H P, Burla M, Azaña J. Experimental demonstration of sub-picosecond optical pulse shaping in silicon based on discrete space-to-time mapping. Optics Letters, 2015, 40(23): 5423–5426 https://doi.org/10.1364/OL.40.005423 PMID:26625016
67	Bazargani H P, Azaña J. Optical pulse shaping based on discrete space-to-time mapping in cascaded co-directional couplers. Optics Express, 2015, 23(18): 23450–23461 https://doi.org/10.1364/OE.23.023450 PMID:26368445
68	Bazargani H, Burla M, Chen Z, Zhang F, Chrostowski L, Azana J. Long-duration optical pulse shaping and complex coding on SOI. IEEE Photonics Journal, 2016, 8(4): 1–7 https://doi.org/10.1109/JPHOT.2016.2594705
69	Deng N, Liu Z, Wang X, Fu T, Xie W, Dong Y. Distribution of a phase-stabilized 100.02 GHz millimeter-wave signal over a 160 km optical fiber with 4.1 × 10−17 instability. Optics Express, 2018, 26(1): 339–346 https://doi.org/10.1364/OE.26.000339 PMID:29328310
70	Liu Y, Marpaung D, Choudhary A, Eggleton B J. Highly selective and reconfigurable Si3N4 RF photonic notch filter with negligible RF losses. In: Proceedings of Lasers and Electro-Optics (CLEO). San Jose, CA, USA: IEEE, 2017, paper SM1O.7
71	Fandiño J SMuñoz PDoménech D, Capmany J. A monolithic integrated photonic microwave filter. Nature Photonics, 2017, 11(2): 124–129 https://doi.org/10.1038/nphoton.2016.233
72	Zhuang L, Roeloffzen C G, Hoekman M, Boller K J, Lowery A J. Programmable photonic signal processor chip for radio frequency applications. Optica, 2015, 2(10): 854–859 https://doi.org/10.1364/OPTICA.2.000854
73	Capmany J, Gasulla I, Pérez D. The programmable processor. Nature Photonics, 2016, 10: 6–8 https://doi.org/10.1038/nphoton.2015.254

[1]	Yong ZHANG, Yu HE, Qingming ZHU, Xinhong JIANG, Xuhan Guo, Ciyuan QIU, Yikai SU. On-chip silicon polarization and mode handling devices[J]. Front. Optoelectron., 2018, 11(1): 77-91.
[2]	Mengying HE,Shasha LIAO,Li LIU,Jianji DONG. Theoretical analysis for optomechanical all-optical transistor[J]. Front. Optoelectron., 2016, 9(3): 406-411.
[3]	Xinlun CAI,Michael STRAIN,Siyuan YU,Marc SOREL. Photonic integrated devices for exploiting the orbital angular momentum of light in optical communications[J]. Front. Optoelectron., 2016, 9(3): 518-525.
[4]	Daoxin DAI,Shipeng WANG. Asymmetric directional couplers based on silicon nanophotonic waveguides and applications[J]. Front. Optoelectron., 2016, 9(3): 450-465.
[5]	Charles CAER,Xavier LE ROUX,Samuel SERNA,Weiwei ZHANG,Laurent VIVIEN,Eric CASSAN. Large group-index bandwidth product empty core slow light photonic crystal waveguides for hybrid silicon photonics[J]. Front. Optoelectron., 2014, 7(3): 376-384.
[6]	Zhiyong LI, Liang ZHOU, Xi XIAO, Tao CHU, Yude YU, Jinzhong YU. Improved extinction ratio of Mach-Zehnder based optical modulators on CMOS platform[J]. Front Optoelec, 2012, 5(1): 90-93.
[7]	Guangzhao RAN, Hongqiang LI, Chong WANG. On-chip silicon light source: from photonics to plasmonics[J]. Front Optoelec, 2012, 5(1): 3-6.
[8]	Eric CASSAN, Xavier LE ROUX, Charles CAER, Ran HAO, Damien BERNIER, Delphine MARRIS-MORINI, Laurent VIVIEN. Silicon slow light photonic crystals structures: present achievements and future trends[J]. Front Optoelec Chin, 2011, 4(3): 243-253.

Viewed

Full text

Abstract

Cited

Shared

Discussed