Abstract
Azimuthal Walsh filters, derived from radially invariant azimuthal Walsh functions, can be used as an effective tool for producing 2D and 3D light structures near the focal plane of a rotationally symmetric imaging system by manipulating the far-field diffraction characteristics when used as pupil filters. Starting with the definition of azimuthal Walsh functions and using the scalar diffraction theory, this research work reports the possibility of modifying the beam structure around the far-field plane by diffraction characteristics of azimuthal Walsh filters placed on the exit pupil plane when computed analytically. The asymmetrical beam produced due to the inherent phase asymmetries introduced by azimuthal Walsh filters may find many important applications in micro- and nano-photonics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
J.L. Walsh, A closed set of normal orthogonal functions. Am. J. Math. 45(1), 5–24 (1923)
H.F. Harmuth, Transmission of Information by Orthogonal Functions (Springer, Berlin, 1972), p. 31
L.N. Hazra, Walsh filters in tailoring of resolution in microscopic imaging. Micron 38(2), 129–135 (2007)
I. Bhattacharya, L.N. Hazra, Study of imaging characteristics of azimuthal Walsh filters. Am. J. Electron. Commun. (AJECT) 1(2), 50–54 (2014)
I. Chattopadhyay, Far-field diffraction characteristics of azimuthal Walsh filters: a veritable potpourri of 2D and 3D light structures, Ph.D. Thesis, 8 June, 2018
A.I. Mahan, C.V. Bitterli, S.M. Cannon, Far-field diffraction patterns of single and multiple apertures bounded by arcs and radii of concentric circles. J. Opt. Soc. Am. A 54(6), 721–732 (1964)
R.A. Lessard, S.C. Som, Imaging properties of sector-shaped apertures. App. Opt. II(4), 811–817 (1972)
T. Vierke, J. Jahns, Diffraction theory for azimuthally structured Fresnel zone plate. J. Opt. Soc. Am. A 31(2), 363–372 (2014)
I. Bhattacharya, A. Saha, L.N. Hazra, Asymmetrical PSF by Azimuthal Walsh filters, in Advances in Optical Science and Engineering Silicon Photonics II: Proceedings of 2015 Second International Conference on Opto-Electronics and Applied Optics, ed. by V. Lakshminarayanan, I. Bhattacharya (IEEE Xplore Digital Library, at University of British Columbia, Vancouver, Canada, 2015)
S. Mukhopadhyay, S. Sarkar, K. Bhattacharya, L.N. Hazra, Polarisation phase shifting interferometric technique for phase calibration of a reflective phase spatial light modulator. Opt. Eng. 52(3), 035602-1–035602-6 (2013)
K.Y. Bliokh, A.Y. Bekshaev, F. Nori, Extraordinary momentum and spin in evanescent waves. Nature Commun. 5, 330 (2014)
D. Pal, I. Bhattacharya, A. Banerjee et al., Spin momentum locking in a tightly focused Gaussian beam, in OSI-ICO International Symposium on Optics (OSI-ICO), 18–22 Sept 2019 (IIT Kanpur, India, 2018)
B. Roy et al., Control transportation of mesoscopic particles by enhanced spin-orbit interaction of light in an optical trap. Phys. Rev. A 87, 043823 (2013)
S.D. Gupta, N. Ghosh, A. Banerjee, Wave Optics: Basic Concepts and Contemporary Trends (CRC Press, 2015)
A. Ashkin, Acceleration and trapping of particles by radiation pressure. Phy. Rev. Lett. 24(4), 156–159 (1970)
Acknowledgments
The author acknowledges the support of Department of Applied Optics and Photonics, University of Calcutta, India for this research work.
Special acknowledgment to Prof. Dr. Ayan Banerjee, Group Leader of Light–Matter Interactions Lab under the Department of Physical Sciences, Indian Institute of Science Education and Research (IISER), Kolkata, India for supporting further extension of the research work in the field of optical micro-manipulation.
The author would like to thank Science and Engineering Research Board, SERB of Department of Science and Technology, DST, Govt. of India to support the travel grant to Cancun, Mexico.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Bhattacharya, I., Hazra, L. (2019). Azimuthal Walsh Filters: An Interesting Tool to Produce 2D and 3D Light Structures. In: MartÃnez-GarcÃa, A., Bhattacharya, I., Otani, Y., Tutsch, R. (eds) Progress in Optomechatronic Technologies . Springer Proceedings in Physics, vol 233. Springer, Singapore. https://doi.org/10.1007/978-981-32-9632-9_2
Download citation
DOI: https://doi.org/10.1007/978-981-32-9632-9_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-32-9631-2
Online ISBN: 978-981-32-9632-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)