Bertolotti, M.

Hoenders, B.

Mandatori, A.

Sibilia, C.

English

The effects of the coherence properties of light beams propagating through periodic structures are discussed. In particular, spatial coherence may influence the transmitted field. Some 2D structures which give transmittances strongly influenced by the coherence of the incoming field are discussed

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   University of GroningenThe Effect of Coherence in the Propagation through Periodic StructuresBertolotti, M.; Hoenders, B.; Mandatori, A.; Sibilia, C.Published in:2006 International Conference on Transparent Optical NetworksIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2006Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Bertolotti, M., Hoenders, B., Mandatori, A., & Sibilia, C. (2006). The Effect of Coherence in the Propagationthrough Periodic Structures. In 2006 International Conference on Transparent Optical Networks (pp. 30-31). University of Groningen, The Zernike Institute for Advanced Materials.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 06-06-2022Mo.C2.2 30 ICTON 2006 1-4244-0236-0/06/$20.00 ©2006 IEEE The Effect of Coherence in the Propagation through  Periodic Structures M. Bertolotti*, B. Hoenders**, A. Mandatori*, C. Sibilia*  *Dipartimento di Energetica – Università “La Sapienza” di Roma  Via Scarpa 16, 00161, Roma (Italy),+39 06 49941 6542 fax +39 06 442 40 183 , mario.bertolotti@uniroma1.it ** University of Groningen, Centre for Theoretical  Physics & Materials Science Centre Nijenborgh 4, 9747 AG Groningen (The Netherlands)   Tel: +31 50-363413,  Fax: + 31 50-3634947,  B.J.Hoenders@rug.nl  ABSTRACT The effects of the coherence properties of light beams propagating through periodic structures are discussed. In particular, spatial coherence may influence the transmitted field. Some 2D structures which give transmittances strongly influenced by the coherence of the incoming field are discussed.  SUMMARY To investigate the coherence properties of a light beam there are several methods such as the Michelson or the Young interferometers that are very simple methods to determine the time of coherence and coherence area of a beam. All these systems are very useful to determine the coherence properties of a field but unfortunately they are big setup (very big if compared with the wavelength) and so they are very sensible to the perturbations of the external world and difficult to make rugged. It could be interesting to find a system that is very small, comparable with the wavelength of the light we want to investigate, and very compact so to be insensitive to the perturbations of the external world. A filter that put directly on the light beam could give the possibility to find the coherence properties of the field would be very useful.  Fig. 1. Schematic representation of the 2D filter. We discuss here very simple systems that have these properties. A 2D system is shown in Fig. 1. The  wave enters from the left side in the system which contains a grating whose period d has been chosen between the wavelength and two times the wavelength. The output electric field can be written as  nx ni(k x t z)nnE (x,z) T eν∞− +=−∞= ∑  , (1) where  2 2 20 0 0 02, sin .n nx nx i i d xt n k k k n n k nk kdπ ϕ= − = + = +  (2) In the output only three plane waves propagate that generate an interference field on the output plane (z = z0). The input wave is assumed to have some coherence area that we would like to determine by observing the interference in the output. Fig. 2 show some characteristic results obtained for a partial coherent plane wave with a coherence area described by a Gaussian function with variance σ contrasted with the fringes obtained for a fully spatial coherent beam. 1n2n1n2niExz0=z z1E0E1−E3n4n 3n 4nICTON 2006 31 Mo.C2.2   Fig. 2 show that by increasing the distance of the observation plane (z = z0) the visibility of the fringes in the partial coherence case decreases.  Other systems of this kind are described and their properties are discussed. 2E0.2 0.6 101 2 z 500 m= µx( m)µz 1500 m= µ0.2 0.6 10 12 2Ex( m)µz 5000 m= µ0.2 0.6 1 0 122Ex( m)µ0.2 0.6 1 01 2 2Ex( m)µz 1000 m= µFigure. 2. Square modulus of transmitted electric field at several z output planes, the dashed curves refer to a completely coherent input plane wave, the solid lines refer to a partially coherent input plane wave,  with σ = 1000 µm. 

The Effect of Coherence in the Propagation through Periodic Structures

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The Effect of Coherence in the Propagation through Periodic Structures

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