On the generality of the Talbot condition for inducing self-imaging effects on periodic objects

Integer and fractional self-imaging effects can be induced on periodic waveforms across the time, frequency, space, or angular frequency domains by imposing a quadratic phase profile along the corresponding Fourier dual domain. This phase must satisfy the well-known "Talbot condition." The...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Optics letters 2016-01, Vol.41 (2), p.340-343
Hauptverfasser: Cortés, Luis Romero, Guillet de Chatellus, Hugues, Azaña, José
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 343
container_issue 2
container_start_page 340
container_title Optics letters
container_volume 41
creator Cortés, Luis Romero
Guillet de Chatellus, Hugues
Azaña, José
description Integer and fractional self-imaging effects can be induced on periodic waveforms across the time, frequency, space, or angular frequency domains by imposing a quadratic phase profile along the corresponding Fourier dual domain. This phase must satisfy the well-known "Talbot condition." The resulting period-divided fractional self-images exhibit deterministic pulse-to-pulse phase variations that arise from the solution of a Gauss sum. In turn, these self-images can be regarded as inducing a Talbot effect in the Fourier dual domain. This suggests the possibility of observing self-imaging effects by imposing phase profiles that are not defined by the Talbot condition. In this Letter, we show otherwise that the phase profiles retrieved from a Gauss sum also satisfy the Talbot condition, which implies that this condition may encompass all possible quadratic phase patterns for inducing self-imaging effects. We establish here the precise relationships between the solutions of Gauss sums and the corresponding Talbot phases, and derive additional properties of Talbot phase patterns of fundamental and practical interest.
doi_str_mv 10.1364/OL.41.000340
format Article
fullrecord <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_01373984v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1864547830</sourcerecordid><originalsourceid>FETCH-LOGICAL-c401t-12d34d19221e74043bb4d31564f5fce72e4603341a74b488a98687b6071137833</originalsourceid><addsrcrecordid>eNqF0c1LwzAYBvAgis6Pm2fJUcHOvM3bpDmK-AWFXeY5pG0yI10zm07Yf2_mpldPIQ8_Hl54CLkENgUu8G5WTRGmjDGO7IBMoOAqQ6nwkEwYoMhUofITchrjRzJCcn5MTnIhhZBMTYie9XR8t3RhezuYzo8bGtxPMjddHUbahL71ow89dWGgvm_Xje8XNNrOZX5pFtuPdc42Y6QJrezgQ-sbGuqPbXZOjpzpor3Yv2fk7elx_vCSVbPn14f7KmuQwZhB3nJsQeU5WIkMeV1jy6EQ6ArXWJlbFIxzBCOxxrI0qhSlrAWTAFyWnJ-Rm13vu-n0akiXDRsdjNcv95XeZiw5rkr8gmSvd3Y1hM-1jaNe-tjYrjO9DeuooRRYYGpl_1MpWKmKdHaitzvaDCHGwbq_M4Dp7VJ6VmkEvVsq8at987pe2vYP_07DvwH_aYsK</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1760895221</pqid></control><display><type>article</type><title>On the generality of the Talbot condition for inducing self-imaging effects on periodic objects</title><source>Optica Publishing Group (OPG)</source><creator>Cortés, Luis Romero ; Guillet de Chatellus, Hugues ; Azaña, José</creator><creatorcontrib>Cortés, Luis Romero ; Guillet de Chatellus, Hugues ; Azaña, José</creatorcontrib><description>Integer and fractional self-imaging effects can be induced on periodic waveforms across the time, frequency, space, or angular frequency domains by imposing a quadratic phase profile along the corresponding Fourier dual domain. This phase must satisfy the well-known "Talbot condition." The resulting period-divided fractional self-images exhibit deterministic pulse-to-pulse phase variations that arise from the solution of a Gauss sum. In turn, these self-images can be regarded as inducing a Talbot effect in the Fourier dual domain. This suggests the possibility of observing self-imaging effects by imposing phase profiles that are not defined by the Talbot condition. In this Letter, we show otherwise that the phase profiles retrieved from a Gauss sum also satisfy the Talbot condition, which implies that this condition may encompass all possible quadratic phase patterns for inducing self-imaging effects. We establish here the precise relationships between the solutions of Gauss sums and the corresponding Talbot phases, and derive additional properties of Talbot phase patterns of fundamental and practical interest.</description><identifier>ISSN: 0146-9592</identifier><identifier>EISSN: 1539-4794</identifier><identifier>DOI: 10.1364/OL.41.000340</identifier><identifier>PMID: 26766709</identifier><language>eng</language><publisher>United States: Optical Society of America - OSA Publishing</publisher><subject>Fourier analysis ; Frequency domains ; Integers ; Optics ; Physics ; Sums ; Talbot effect ; Waveforms</subject><ispartof>Optics letters, 2016-01, Vol.41 (2), p.340-343</ispartof><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c401t-12d34d19221e74043bb4d31564f5fce72e4603341a74b488a98687b6071137833</citedby><cites>FETCH-LOGICAL-c401t-12d34d19221e74043bb4d31564f5fce72e4603341a74b488a98687b6071137833</cites><orcidid>0000-0003-2075-4056</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,315,781,785,886,3259,27926,27927</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/26766709$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-01373984$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Cortés, Luis Romero</creatorcontrib><creatorcontrib>Guillet de Chatellus, Hugues</creatorcontrib><creatorcontrib>Azaña, José</creatorcontrib><title>On the generality of the Talbot condition for inducing self-imaging effects on periodic objects</title><title>Optics letters</title><addtitle>Opt Lett</addtitle><description>Integer and fractional self-imaging effects can be induced on periodic waveforms across the time, frequency, space, or angular frequency domains by imposing a quadratic phase profile along the corresponding Fourier dual domain. This phase must satisfy the well-known "Talbot condition." The resulting period-divided fractional self-images exhibit deterministic pulse-to-pulse phase variations that arise from the solution of a Gauss sum. In turn, these self-images can be regarded as inducing a Talbot effect in the Fourier dual domain. This suggests the possibility of observing self-imaging effects by imposing phase profiles that are not defined by the Talbot condition. In this Letter, we show otherwise that the phase profiles retrieved from a Gauss sum also satisfy the Talbot condition, which implies that this condition may encompass all possible quadratic phase patterns for inducing self-imaging effects. We establish here the precise relationships between the solutions of Gauss sums and the corresponding Talbot phases, and derive additional properties of Talbot phase patterns of fundamental and practical interest.</description><subject>Fourier analysis</subject><subject>Frequency domains</subject><subject>Integers</subject><subject>Optics</subject><subject>Physics</subject><subject>Sums</subject><subject>Talbot effect</subject><subject>Waveforms</subject><issn>0146-9592</issn><issn>1539-4794</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNqF0c1LwzAYBvAgis6Pm2fJUcHOvM3bpDmK-AWFXeY5pG0yI10zm07Yf2_mpldPIQ8_Hl54CLkENgUu8G5WTRGmjDGO7IBMoOAqQ6nwkEwYoMhUofITchrjRzJCcn5MTnIhhZBMTYie9XR8t3RhezuYzo8bGtxPMjddHUbahL71ow89dWGgvm_Xje8XNNrOZX5pFtuPdc42Y6QJrezgQ-sbGuqPbXZOjpzpor3Yv2fk7elx_vCSVbPn14f7KmuQwZhB3nJsQeU5WIkMeV1jy6EQ6ArXWJlbFIxzBCOxxrI0qhSlrAWTAFyWnJ-Rm13vu-n0akiXDRsdjNcv95XeZiw5rkr8gmSvd3Y1hM-1jaNe-tjYrjO9DeuooRRYYGpl_1MpWKmKdHaitzvaDCHGwbq_M4Dp7VJ6VmkEvVsq8at987pe2vYP_07DvwH_aYsK</recordid><startdate>20160115</startdate><enddate>20160115</enddate><creator>Cortés, Luis Romero</creator><creator>Guillet de Chatellus, Hugues</creator><creator>Azaña, José</creator><general>Optical Society of America - OSA Publishing</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-2075-4056</orcidid></search><sort><creationdate>20160115</creationdate><title>On the generality of the Talbot condition for inducing self-imaging effects on periodic objects</title><author>Cortés, Luis Romero ; Guillet de Chatellus, Hugues ; Azaña, José</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c401t-12d34d19221e74043bb4d31564f5fce72e4603341a74b488a98687b6071137833</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Fourier analysis</topic><topic>Frequency domains</topic><topic>Integers</topic><topic>Optics</topic><topic>Physics</topic><topic>Sums</topic><topic>Talbot effect</topic><topic>Waveforms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cortés, Luis Romero</creatorcontrib><creatorcontrib>Guillet de Chatellus, Hugues</creatorcontrib><creatorcontrib>Azaña, José</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>Electronics &amp; Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Optics letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cortés, Luis Romero</au><au>Guillet de Chatellus, Hugues</au><au>Azaña, José</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the generality of the Talbot condition for inducing self-imaging effects on periodic objects</atitle><jtitle>Optics letters</jtitle><addtitle>Opt Lett</addtitle><date>2016-01-15</date><risdate>2016</risdate><volume>41</volume><issue>2</issue><spage>340</spage><epage>343</epage><pages>340-343</pages><issn>0146-9592</issn><eissn>1539-4794</eissn><abstract>Integer and fractional self-imaging effects can be induced on periodic waveforms across the time, frequency, space, or angular frequency domains by imposing a quadratic phase profile along the corresponding Fourier dual domain. This phase must satisfy the well-known "Talbot condition." The resulting period-divided fractional self-images exhibit deterministic pulse-to-pulse phase variations that arise from the solution of a Gauss sum. In turn, these self-images can be regarded as inducing a Talbot effect in the Fourier dual domain. This suggests the possibility of observing self-imaging effects by imposing phase profiles that are not defined by the Talbot condition. In this Letter, we show otherwise that the phase profiles retrieved from a Gauss sum also satisfy the Talbot condition, which implies that this condition may encompass all possible quadratic phase patterns for inducing self-imaging effects. We establish here the precise relationships between the solutions of Gauss sums and the corresponding Talbot phases, and derive additional properties of Talbot phase patterns of fundamental and practical interest.</abstract><cop>United States</cop><pub>Optical Society of America - OSA Publishing</pub><pmid>26766709</pmid><doi>10.1364/OL.41.000340</doi><tpages>4</tpages><orcidid>https://orcid.org/0000-0003-2075-4056</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 0146-9592
ispartof Optics letters, 2016-01, Vol.41 (2), p.340-343
issn 0146-9592
1539-4794
language eng
recordid cdi_hal_primary_oai_HAL_hal_01373984v1
source Optica Publishing Group (OPG)
subjects Fourier analysis
Frequency domains
Integers
Optics
Physics
Sums
Talbot effect
Waveforms
title On the generality of the Talbot condition for inducing self-imaging effects on periodic objects
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-17T14%3A33%3A18IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20generality%20of%20the%20Talbot%20condition%20for%20inducing%20self-imaging%20effects%20on%20periodic%20objects&rft.jtitle=Optics%20letters&rft.au=Cort%C3%A9s,%20Luis%20Romero&rft.date=2016-01-15&rft.volume=41&rft.issue=2&rft.spage=340&rft.epage=343&rft.pages=340-343&rft.issn=0146-9592&rft.eissn=1539-4794&rft_id=info:doi/10.1364/OL.41.000340&rft_dat=%3Cproquest_hal_p%3E1864547830%3C/proquest_hal_p%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1760895221&rft_id=info:pmid/26766709&rfr_iscdi=true