Home Search Collections Journals About Contact us My IOPscience N-slit interferometer for secure free-space optical communications: 527 m intra interferometric path length This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 J. Opt. 13 035710 (http://iopscience.iop.org/2040-8986/13/3/035710) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 131.84.11.215 The article was downloaded on 08/02/2011 at 01:07 Please note that terms and conditions apply. Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. 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PERFORMING ORGANIZATION Interferometric Optics,, , ,Rochester,NY,14626-0592 REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES This a US Army High Energy Laser Laboratory project funded through a subcontract to BAE Systems. 14. ABSTRACT The N-slit interferometer is demonstrated to function with an intra interferometric propagation path length of 527.33 m. Interferograms representing several interferometric characters, corresponding to N = 2, 3, 4, and 5, were recorded at the interferometric plane located at the end of an open air propagation range. Interferometric computations, based on the application of Dirac?s notation, were successfully used to predict the structure and divergence of the propagating interferograms. These measurements were carried out during an unusual mild-temperature, low-humidity, summer night in northern Alabama. In the laboratory, at an intra interferometric propagation path length of 7.235 m, the N-slit interferometer was also used to successfully detect the intrusion of microscopic fibers into the intra interferometric propagation path. These experiments led to the detection of diffraction patterns superimposed over the interferograms. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF ABSTRACT OF PAGES RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE Public Release 6 unclassified unclassified unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 IOPPUBLISHING JOURNALOFOPTICS J.Opt.13(2011)035710(5pp) doi:10.1088/2040-8978/13/3/035710 N -slit interferometer for secure free-space optical communications: 527 m intra interferometric path length FJDuarte1,2,TSTaylor3,A MBlack3,WEDavenport4 and PGVarmette5 1InterferometricOptics,Rochester,NY14626-0592,USA 2DepartmentofElectricalandComputerEngineering,UniversityofNewMexico, NM87131-0001,USA 3USArmySpaceandMissileDefenseCommand,TechnicalCenter,TechnologyDirectorate, DirectedEnergyDivision,Huntsville,AL35807,USA 4USArmyAviationandMissileCommand,WeaponsSciencesDirectorate,RedstoneArsenal, AL35898,USA 5ScienceApplicationsInternationalCorporation,Huntsville,AL35806,USA Received5November2010,acceptedforpublication30December2010 Published3February2011 Onlineatstacks.iop.org/JOpt/13/035710 Abstract The N-slitinterferometerisdemonstratedtofunctionwithanintrainterferometricpropagation pathlengthof527.33m.Interferogramsrepresentingseveralinterferometriccharacters, correspondingto N =2,3,4,and5,wererecordedattheinterferometricplanelocatedatthe endofanopenairpropagationrange. Interferometriccomputations,basedontheapplicationof Dirac’snotation,weresuccessfullyusedtopredictthestructureanddivergenceofthe propagatinginterferograms. Thesemeasurementswerecarriedoutduringanunusual mild-temperature,low-humidity,summernightinnorthernAlabama. Inthelaboratory,atan intrainterferometricpropagationpathlengthof7.235m,the N-slitinterferometerwasalso usedtosuccessfullydetecttheintrusionofmicroscopicfibersintotheintrainterferometric propagationpath. Theseexperimentsledtothedetectionofdiffractionpatternssuperimposed overtheinterferograms. Keywords: aviation,beamexpansion,clearairturbulence,Diracnotation,free-space, propagation,interferometriccharacter,interferometricimaging, N-slitinterference, N-slit interferometer, N-slitinterferometry,naturalfibers (Somefiguresinthisarticleareincolouronlyintheelectronicversion) 1. Introduction represent a significant development on this free-space optics communications technique, originally demonstrated in the Recently, we reported on an N-slit interferometer with an laboratory over a propagation distance of only 10 cm and intra interferometric path length of 35 m [1]. In the envisionedprimarilyasaspace-to-spacesecureinterferometric presentexperimentswehaveextendedtheintrainterferometric communicationstechnique[2]. propagationdistanceto527.33m.Theexperimentwascarried Previously,theintegrityofthisfree-space interferometric out,atnight,usingthefullavailablelengthofanexistingopen communications technique has been demonstrated via the air propagation range. These experiments were performed catastrophic collapse of the interferometric characters, or usingseveraltheoreticallypredictedinterferometriccharacters signal,resultingfromattemptstoinsertthinbeamsplittersinto corresponding to a, b, c, d (N = 2, 3, 4, 5, respectively) [2] the propagation path [1–3]. A refinement in the interception under night-time atmospheric conditions. The successful technique consists in the subtle insertion of microscopic completion of these open air propagation experiments fibers into exact positions in the intra interferometric 2040-8978/11/035710+05$33.00 1 ©2011IOPPublishingLtd PrintedintheUK&theUSA J.Opt.13(2011)035710 FJDuarteetal path. Experiments performed in the laboratory, at an intra interferometric distance of D(cid:2)x|j(cid:3) = 7.235 m, demonstrate that the interferograms easily detect the presence of very thin natural fibers, thus upholding the integrity of this interferometricapproach forfree-space communications. The detectionofthefibersoccursviathesuperimpositionofdistinct Figure1.TopviewschematicsoftheN-slitinterferometeras diffractionpatternsovertheinterferometriccharacters. describedin[1]. N slitsareilluminatedatatransmissiongrating(j) So far, N-slit interferometers have been used in various thusallowingthepropagationofanN-slitinterferencesignal,along industrial metrology tasks including microdensitometry, D(cid:2)x|j(cid:3),towardtheinterferometricplanex,atwhichislocatedaCCD microscopy, and optical modulation measurements of thin detectorarray.ForD(cid:2)x|j(cid:3) =527.33m,theCCDdetectorisreplaced byaflatsurfacedeployedatx.TBEisatelescopicbeamexpander film gratings generated from a variety of manufacturing providinganexpansionfactorofM ≈10.TheMPBEisa processes [4]. The present experiments demonstrate that N- one-dimensionalmultiple-prismbeamexpanderwithM ≈5 slitinterferometersarealsoapplicabletosecureterrestrialfree- (from[1]). space optical communications over propagation distances of practicalinterest.Additionalapplicationsincludethedetection of even mild clear air turbulence [1] over various distances of practical interest without fundamental limitations on its 3. Experiments propagationrange. Experimental details describing the N-slit interferometer, shown in figure 1, are given in [1]. It is however necessary 2. Theory to mentionthat the illuminationsource is a single-transverse- As mentioned in [1], light propagation through N-slit arrays mode narrow-linewidth He–Ne laser (λ = 632.8 nm) and was studied by Newton [5] and N-slit diffraction was the two gratings used were: one grating with 570 μm slits discussed by Michelson [6]. In a more contemporaneous separated by 570 μm isles and a grating with 1000 μm setting, Feynman [7] applied Dirac’s quantum notation [8] slits separated by 1000 μm isles. The tolerances in the slit to perform double-slit thought experiments on electrons. dimensions are quoted by the manufacturer as 0.5 μm, with This approach was applied to the N-slit interferometer furtherdetailsgivenin[1]. (see figure 1), for narrow-linewidth laser illumination, thus The 570 μm grating was employed in the experiments yieldingthegeneralized, one-dimensional, N-slit interference designed for the detection of thin natural fibers at D(cid:2)x|j(cid:3) = equation[9,10] 7.235 m, while the 1000 μm grating was used to obtain the (cid:2)N (cid:2)N resultswiththe D(cid:2)x|j(cid:3) =527.33mconfiguration. |(cid:2)x|s(cid:3)|2 = (cid:2)(rj) (cid:2)(rm)ei((cid:3)m−(cid:3)j) (1a) As discussed in [2], for both gratings a series of j=1 m=1 interferometric characters were created by illuminating an increasing number of slits. That is, a, b, c, and d, or interferometriccharactersweregeneratedbythecorresponding (cid:2)N (cid:2)N illuminationof N =2,3,4,and5slitsrespectively. |(cid:2)x|s(cid:3)|2 = (cid:2)(rj)2+2 (cid:2)(rj) Asinthepreviousindoorexperiment(at T ≈ 22◦C)the (cid:3) (cid:2)jN=1 j=1 (cid:4) detectorfortheD(cid:2)x|j(cid:3) =7.235mmeasurementsisaPrinceton × (cid:2)(r )cos((cid:3) −(cid:3) ) . (1b) Instrument (Pixis 100) CCD array composed of 1340 pixels m m j each ∼20 μm in width. This CCD array is deployed at the m=j+1 interferometric plane (x). Two types of natural fibers were In either equation, s represents the photon source, j refers used: initially, fine human hair with a diameter of ∼50 μm, to the jth slit in the transmission grating, x represents the and subsequently, a spider web fiber with a diameter in the interference plane, (cid:2)(r ) are wavefunction amplitudes of j 25–30μmrange. ‘ordinary wave optics’ [8, 11], and the term in parenthesis For the experiment on the extended configuration, at represents the phase which describes the exact geometry of the N-slit interferometer [10, 11]. As discussed D(cid:2)x|j(cid:3) = 527.33 m, the interferometric plane (x) was in [1], this equation was originally derived for single- comprised of a calibrated screen and the interferograms were photon propagation, albeit in practice it also applies to an recorded using digital photography. The illumination-grating ensemble of indistinguishable photons [12], as in the case part of the interferometer was mounted on a small optical of narrow-linewidth laser emission. This approach [10, 12] table [1] and deployed at an elevation of 15.17 m, whilst the is consistent with van Kampen’s quantum theorems [13]. interferometric plane was deployed on a small hill at an intra The nexus between the probability distribution |(cid:2)x|s(cid:3)|2 and interferometric distance of D(cid:2)x|j(cid:3) = 527.33 m, as measured measured interferometric profiles is also described in [12]. with a calibrated laser range finder. These experiments were As previously emphasized, an important advantage of this performed during a clear summer night with atmospheric quantuminterferenceequationisthecontinuousdescriptionof conditions characterized by an ambient temperature of T ≈ measuredinterferogramsfromthenear-tothefar-field[10]. 24◦Candahumidityof∼66%. 2 J.Opt.13(2011)035710 FJDuarteetal Figure2.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =527.33m, λ=632.8nm,andN =4(1000μmslitsseparatedby1000μm), recordedinopenairatT ≈24◦Candahumidityof66%.This interferogramcorrespondstotheinterferometriccharacterc.The horizontalscaleatthebaseofthefigureis5cm/div(whilsttheless visibleupperscaleis1cm/div). Figure5.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =7.235m, λ=632.8nm,andN =2(570μmslitsseparatedby570μm)with aspiderwebfiberdeployedorthogonallytothepropagationplane (thatis,paralleltotheslits,orperpendiculartotheplaneoffigure1) atadistanceof15cmfromx.Thediffractionpattern,generatedby Figure3.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =527.33m, thefiber,issuperimposedoverthecentralorderoftheinterferogram. λ=632.8nm,andN =5(1000μmslitsseparatedby1000μm), recordedinopenairatT ≈24◦Candahumidityof66%.This interferogramcorrespondstotheinterferometriccharacterd.The horizontalscaleatthebaseofthefigureis5cm/div(whilsttheless visibleupperscaleis1cm/div). Figure6.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =7.235m, λ=632.8nm,andN =2(570μmslitsseparatedby570μm)with aspiderwebfiberdeployedorthogonallytothepropagationplane (thatis,paralleltotheslits,orperpendiculartotheplaneoffigure1) atadistanceof15cmfromx.Thediffractionpattern,generatedby Figure4.Controlinterferogramregisteredatx,for bDy(cid:2)x5|j7(cid:3)0=μ7m.2)3a5tTm,≈λ2=2◦6C3.2.T8hnismi,natenrdfeNrog=ra2m(5co7r0reμsmposnlditsstsoetphaerated itnhteefirfbeeror,girsasmu.perimposedovertheouterrightwingofthe interferometriccharactera. bythediffraction pattern superimposedoverthecentral order 4. Results of the interferogram in figure 5. For comparison purposes the fiber is displaced to intersect the outer right wing of A measured interferogram, resulting from the illuminationof the interferogram, as demonstrated by the diffraction pattern N = 4 slits of the 1000 μm grating, at D(cid:2)x|j(cid:3) = 527.33 m, superimposed over the right secondary maximum of the through the open atmosphere at T ≈ 24◦C and a humidity interferograminfigure6. of66%,isshowninfigure2. Thecorrespondingmeasurement under nearly identical propagation conditions, for N = 5, is Ameasuredinterferogram,resultingfromtheillumination showninfigure3. of N = 3slitsofthe570μmgrating,at D(cid:2)x|j(cid:3) = 7.235m,in thelaboratoryand in theabsenceofturbulence at T ≈ 22◦C Ameasuredinterferogram,resultingfromtheillumination of N = 2slitsofthe570μmgrating,at D(cid:2)x|j(cid:3) = 7.235m,in is shown in figure 7. The corresponding measurement under thelaboratoryandintheabsenceofturbulenceat T ≈ 22◦C, identicalpropagationconditions,for N =3,withaspiderweb is shown in figure 4. The corresponding measurement under fiber deployed orthogonally to the propagation plane (that is, identicalpropagationconditions,for N =2,withaspiderweb parallel to the grooves of the grating) is shown in figure 8. fiber deployed orthogonally to the propagation plane (that is, The fiber is positioned 15 cm from the detection plane (x) paralleltothegroovesofthegrating)isshowninfigure5. and intersects the outer right wing of the interferogram, as The fiber is positioned 15 cm from the detection plane demonstratedbythediffractionpatternsuperimposedoverthe (x)andintersectsthemaininterferenceorder,asdemonstrated outerrightwingoftheinterferograminfigure8. 3 J.Opt.13(2011)035710 FJDuarteetal Figure7.Controlinterferogramregisteredatx,for Figure8.Interferogramregisteredatx,forD(cid:2)x|j(cid:3) =7.235m, D(cid:2)x|j(cid:3)=7.235m,λ=632.8nm,andN =3(570μmslitsseparated λ=632.8nm,andN =3(570μmslitsseparatedby570μm)with by570μm)atT ≈22◦C.Thisinterferogramcorrespondstothe aspiderwebfiberdeployedorthogonallytothepropagationplane interferometriccharacterb. (thatis,paralleltotheslits,orperpendiculartotheplaneoffigure1) atadistanceof15cmfromx.Thediffractionpattern,generatedby thefiber,issuperimposedovertheouterrightwingofthe interferogram. 5. Discussion The atmospheric propagation experiments using an intra interferometric path length of D(cid:2)x|j(cid:3) = 527.33 m consisted tells us that any attempt to observe the intra interferometric in propagating the interferometric characters a, b, c, d, signal will distort or destroy the signal. Indeed, the use of corresponding to N = 2, 3, 4, 5, using the 1000 μm ultrathin transparent beam splitters deployed near Brewster’s grating. Therecorded interferograms, for c and d, are shown angle, its least disruptive configuration, causes the collapse in figures 2 and 3. Planning for these experiments was of the propagating interferometric characters [1–3]. In order facilitated by the accurate prediction of the interferograms to empirically investigate the effect of finer methods of via the interferometric equation. Predicted and recorded intersection in these experiments we used spider web fibers. interferograms, in regard to the overall divergence of the Theexperimentswereconductedinthelaboratory,at D(cid:2)x|j(cid:3) = interferometricpatternsandthepositionofthespatialfeatures 7.235m,for N =2,3,4,5. oftheinterferograms,agreewithin1–2%. Improvedaccuracy The results for N = 2, and 3 are shown in figures 5, 6, shouldbeavailablebyreplacingtheinterference planescreen and 8. The beautiful diffraction patterns superimposed over with tiled CCD detectors, which for this class of intra the interferometric characters a and b, either at the central interferometricdistance shouldprovidea40–50 cm detection orderoroutlyingpositions,clearlydemonstratethatfree-space width. communications using N-slit interferometry can detect even Digital movie recordings of the interferograms reveal verysubtlemethodsofintrusion. mainly slight variations in the intensity domain of the inter- ferograms, which are consistent with incipient atmospheric 6. Conclusion turbulence conditions[1, 4], mostlikely due to amild breeze present during the experiments, even though the temperature (T ≈ 24◦C) and humidity (∼66%) were very favorable for In this paper we report on the N-slit interferometer unperturbed propagation. Previously [1], slight variations in with the largest intra interferometric path length to date, theinterferograms, for D(cid:2)x|j(cid:3) = 35 m, were detected even in D(cid:2)x|j(cid:3) = 527.33 m. Thus, we have proven that the anenclosedenvironmentatT ≈30◦C. N-slit interferometer is a viable interferometric tool over The results disclosed in this paper, with D(cid:2)x|j(cid:3) = long free-space propagation paths under fair atmospheric 527.33 m, represent a significant advance in interferometric conditions. It has also been demonstrated, in a laboratory free-space optics communications, which were initially environment, that even very subtle attempts to intercept the demonstrated in the laboratory over a propagation distance interferometric characters, using microscopic natural fibers, of only 10 cm and mainly envisioned as a space-to-space arereadilydetected viatheobservationofdiffractionpatterns secure optics communications alternative [2]. Certainly, superimposed over the interferometric signal. This is a new the propagation path demonstrated here opens the realm interferometric effect, which to our knowledge has not been of application for free-space interferometric communications previouslyreported. via the terrestrial atmosphere over propagation distances of These experimental observations, plus the data collected practical interest. Further applications include the detection in previous experiments [1–3], lead us to conclude that N- of even mild clear air turbulence [1] over various distances slitinterferometerswithlargeintrainterferometricpathlengths applicabletocommercialaviationrunways. are ready for the next stage of development into practical In previous publications [1–3] it has been indicated that configurations, either for secure free-space communication the integrity of the interferometric characters is protected systemsor interferometric detection of clear air turbulence in by the fundamental physics of interference [2, 7], which airfields. 4 J.Opt.13(2011)035710 FJDuarteetal Acknowledgment [3] DuarteFJ2005J.Opt.A:PureAppl.Opt.773 [4] DuarteFJ2009TunableLaserApplications2ndedn, ThisaUSArmyHighEnergyLaserLaboratoryprojectfunded edFJDuarte(NewYork:CRC)chapter12 throughasubcontracttoBAESystems. [5] NewtonI1704Opticks(London:RoyalSociety) [6] MichelsonAA1927StudiesinOptics(Chicago:The UniversityofChicago) Note added in proof. The interferograms with superimposed diffraction [7] FeynmanRP,LeightonRBandSandsM1965TheFeynman patterns, as in figures 5, 6, and 8, can betheoretically described using the LecturesonPhysicsvol3(Reading,MA:AddisonWesley) methoddisclosedin[10]thatallowsthecharacterizationofinterferenceviaa [8] DiracPAM1978ThePrinciplesofQuantumMechanics seriesofN-slitarraysalongthepropagationaxis[10]. 4thedn(Oxford:OxfordUniversityPress) [9] DuarteFJ1991HighPowerDyeLasersedFJDuarte(Berlin: References Springer)chapter2 [10] DuarteFJ1993Opt.Commun.1038 [1] DuarteFJ,TaylorTS,ClarkABandDavenportWE2010 [11] DuarteFJ1997Am.J.Phys.65637 J.Opt.12015705 [12] DuarteFJ2004Eur.J.Phys.25L57 [2] DuarteFJ2002Opt.Commun.205313 [13] vanKampenNG1988PhysicaA15397 5