Review of photonic Hilbert transformers

Chaotan SIMA; James C. GATES; Michalis N. ZERVAS; Peter G. R. SMITH

doi:10.1007/s12200-012-0299-1

[1] Frederick W K. Hilbert Transforms: Volume 1. Cambridge: Cambridge University Press, 2009, 1: 1-7

[2] Hahn S L, Poularikas A D. The Transforms and Applications Handbook. 2nd ed. Boca Raton: CRC Press, 2000, 7: 1-18

[3] Kastler A. A system of high-contrast diffraction fringes. Review Optik, 1950, 29: 307-314

[4] Wolter H. The minimum beam labelling as a means of increasing the accuracy of optical measurements and as a methodological tool for the replacement of the concept of the beam. Annalen der Physik., 1950, 442(7): 341-368

[5] Hauk D, Lohmann A W. Minimumstrah1ke.nnich- nung bei Gitterspektrographen. Optik (Stuttgart), 1958, 15: 275-281

[6] Lowenthal S, Belvaux Y. Observation of phase objects by optically processed Hilbert transform. Applied Physics Letters, 1967, 11(2): 49-51

[7] Eu J K T, Lohmann A W. Isotropic Hilbert spatial filtering. Optics Communications, 1973, 9(3): 257-262

[8] Brown B R, Lohmann A W. Complex spatial filtering with binary masks. Applied Optics, 1966, 5(6): 967-969

[9] Lohmann A W, Paris D P. Binary fraunhofer holograms, generated by computer. Applied Optics, 1967, 6(10): 1739-1748

[10] Lohmann A W, Mendlovic D, Zalevsky Z. Fractional Hilbert transform. Optics Letters, 1996, 21(4): 281-283

[11] Lohmann AW, Tepichín E, Ramírez J G. Optical implementation of the fractional Hilbert transform for two-dimensional objects. Applied Optics, 1997, 36(26): 6620-6626

[12] Davis J A, McNamara D E, Cottrell D M, Campos J. Image processing with the radial Hilbert transform: theory and experiments. Optics Letters, 2000, 25(2): 99-101

[13] Guo C S, Han Y J, Xu J B, Ding J. Radial Hilbert transform with Laguerre-Gaussian spatial filters. Optics Letters, 2006, 31(10): 1394-1396

[14] Bokor N, Iketaki Y. Laguerre-Gaussian radial Hilbert transform for edge-enhancement Fourier transform X-ray microscopy. Optics Letters, 2009, 17(7): 5533-5539

[15] Takano K, Hanzawa N, Tanji S, Nakagawa K. Experimental demonstration of optically phase-shifted SSB modulation with fiberbased optical Hilbert transformers. In: Proceedings of Optical Fiber Communication and the National Fiber Optic Engineers Conference. 2007, 1-3

[16] Emami H, Sarkhosh N, Bui L A, Mitchell A.Wideband RF photonic in-phase and quadrature-phase generation. Optics Letters, 2008, 33(2): 98-100

[17] Emami H, Sarkhosh N, Bui L A, Mitchell A. Amplitude independent RF instantaneous frequency measurement system using photonic Hilbert transform. Optics Express, 2008, 16(18): 13707-13712

[18] Han Y, Chi H, Zhang X, Yao J. A continuously tunable microwave fractional Hilbert transformer based on a nonuniformly spaced photonic microwave delay-line filter. Journal of Lightwave Technology, 2012, 30(12): 1948-1953

[19] Wang X, Hanawa M, Nakamura K, Takano K, Nakagawa K. Sideband suppression characteristics of optical SSB generation filter with sampled FBG based 4-taps optical Hilbert transformer. In: Proceedings of the 15th Asia-Pacific Conference on Communications. 2009, 622-625

[20] Asghari M H, Aza a J. All-optical Hilbert transformer based on a single phase-shifted fiber Bragg grating: design and analysis. Optics Letters, 2009, 34(3): 334-336

[21] Cuadrado-Laborde C. Proposal and design of a photonic in-fiber fractional Hilbert transformer. IEEE Photonics Technology Letters, 2010, 22(1): 33-35

[22] 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

[23] Li M, Yao J. Experimental demonstration of a wideband photonic temporal Hilbert transformer based on a single fiber Bragg grating. IEEE Photonics Technology Letters, 2010, 22(21): 1559-1561

[24] Ashrafi R, Azana J. Terahertz bandwidth all-optical Hilbert transformers based on long-period gratings. Optics Letters, 2012, 37(13): 2604-2606

[25] Li Z, Chi H, Zhang X, Yao J. Optical single-sideband modulation using a fiber-Bragg-grating-based optical Hilbert transformer. IEEE Photonics Technology Letters, 2011, 23(9): 558-560

[26] Tanaka K, Takano K, Kondo K, Nakagawa K. Improved sideband suppression of optical SSB modulation using all-optical Hilbert transformer. Electronics Letters, 2002, 38(3): 133-134

[27] Sima C, Gates J C, Rogers H L, Holmes C, Zervas M N, Smith P G R. Integrated all-optical SSB modulator using photonic Hilbert transformer with planar Bragg gratings. In: Proceedings of the European Conference on Lasers and Electro-Optics and the XIIth International Quantum Electronics (CLEO-EUROPE). Optical Society of America. 2011, CI4.5

[28] Sima C, Gates J C, Rogers H L, Mennea P, Holmes C, Zervas M N, Smith P G R. Continuously tunable integrated single-sideband modulator with photonic Hilbert transformer and planar Bragg gratings. Optics Letters, under peer review

[29] Zhuang L, Beeker W, Leinse A, Heideman R, Roeloffzen C. Continuously tunable photonic fractional Hilbert transformer using ring resonators for on-chip microwave photonic signal processing. In: Proceedings of 2012 IEEE International Topical Meeting on Microwave Photonics (MWP2012). 2012, 1-4

[30] Zhuang L, Khan M R, Beeker W, Leinse A, Heideman R, Roeloffzen C. Novel microwave photonic fractional Hilbert transformer using a ring resonator-based optical all-pass filter. Optics Express, 2012, 20(24): 26499-26510

[31] Huang T X, Yi X, Minasian R A. Microwave photonic quadrature filter based on an all-optical programmable Hilbert transformer. Optics Letters, 2011, 36(22): 4440-4442

[32] Proakis J G, Manolakis D G. Digital Signal Processing: Principles, Algorithms, and Applications. 4th ed. New Jersey: Prentice Hall, 2007, 654-659

[33] Kashyap R. Fiber Bragg Gratings. 2nd ed. San Diego: Academic Press, 2009

[34] Feced R, Zervas M N. Efficient inverse scattering algorithm for the design of grating-assisted codirectional mode couplers. Journal of the Optical Society of America. A. 2000, 17(9): 1573-1582

[35] Brenne J K, Skaar J. Design of grating-assisted codirectional couplers with discrete inverse-scattering algorithms. Journal of Lightwave Technology, 2003, 21(1): 254-263

[36] Miller S E. Integrated Optics: An Introduction. Bell System Technical Journal, 1969, 48: 2059-2069

[37] Okamoto K. Fundamentals of Optical Waveguides. 2nd ed. San Diego: Academic Press, 2006, 462-467

[38] Emmerson G D, Watts S P, Gawith C B, Albanis V, Riziotis C, Williams R B, Smith P G R. Fabrication of directly UV-written channel waveguides with simultaneously defined integral Bragg gratings. Electronics Letters, 2002, 38(24): 1531-1532