Amplitude response of a Fabry-Perot interferometer

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
IOP Publishing
Google Scholar
Research Projects
Organizational Units
Journal Issue
The complex reflected and transmitted amplitudes from a Fabry-Perot interferometer are analysed using a phase-space approach, in which the real and imaginary parts of those amplitudes are taken as basic variables. As functions of the optical path length of the cavity, the reflected amplitude describes a circle, whereas the transmitted is given by a hippopede. The system performance can be directly related to the geometrical parameters of these curves.
© 2015 IOP Publishing Ltd.Many of the ideas in this paper originated from a long cooperation with the late Alberto G Barriuso, who unexpectedly passed away before being able to guide this work to completion. This paper is dedicated to his memory. Over the years, these ideas have been further developed and expanded with questions, suggestions, criticism, and advice from many colleagues. Particular thanks for help in various ways goes to G Bjork, J F Carinena, H de Guise, P de la Hoz, A B Klimov, G Leuchs, and J M Montesinos-Amilibia. This work is partially supported by the Spanish MINECO (Grant FIS2011-26786).
[1] Hernández G 1986 Fabry-Perot Interferometers (Cambridge: Cambridge Univ. Press) [2] Vaughan JM1989 The Fabry-Perot Interferometer: History, Theory, Practice, and Applications (Bristol: Adam Hilger) [3] Born M and Wolf E 1999 Principles of Optics (Cambridge: Cambridge Univ. Press) [4] Saleh B A E and Teich M C 2007 Fundamentals of Photonics (New York: Wiley) [5] Chen C T 2012 Linear System Theory and Design (Oxford: Oxford Univ. Press) [6] Yeh P 2005 Optical Waves in Layered Media (New York: Wiley) [7] Sánchez-Soto L L., Monzón J J, Barriuso A G, and Cariñena J 2012 Phys. Rep. 513 191–227 [8] Crawford Jr F S 1968 Waves (Berkeley Physics Course Vol. 3) (New York: MacGraw-Hill) [9] Schleich W P 2001 Quantum Optics in Phase Space (Berlin: Wiley) [10] Braunstein S L and van Loock P 2005 Rev. Mod. Phys. 77 513–577 [11] Lawrence J D 1972 Catalog of Special Plane Curves (New York: Dover) [12] Shikin E V 1995 Handbook and Atlas of Curves (London: CRC) [13] Proclus, 1992 A Commentary on the First Book of Euclid’s Elements. (Princeton: Princeton Univ. Press) [14] Booth J 1877 A Treatise on Some New Geometrical Methods, vol. II (London: Longmans, Green, Reader and Dyer) [15] Ferréol R Enciyclopédie des formes mathématiques remarquables [16] Coffman A National Curve Bank [17] Wassenaar J Mathematical Curves, [18] Brieskorn E and Knörrer H 1986 Plane Algebraic Curves (Basel: Birkhäuser) [19] Degiorgio V 1980 Am. J. Phys. 48, 81–82 [20] Zeilinger A 1981 Am. J. Phys. 49 882–883 [21] Ou Z Y and Mandel L 1989 Am. J. Phys. 57 66–67 [22] Yariv A and Yeh P 2006 Photonics: in Modern Communications 6th edition (Oxfod: Oxford University Press ) [23] Schwelb O 2004 J. Lightwave Technol. 22 1380–1394 [24] Monzón J J, Barriuso A G, Sánchez-Soto L L and Montesinos-Amilibia J M 2011 Phys. Rev. A 84 023830