Strong amplitude and phase modulation of optical spatial...

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OPTICS Copyright © 2017 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). Strong amplitude and phase modulation of optical spatial coherence with surface plasmon polaritons Dongfang Li and Domenico Pacifici* The degree of optical spatial coherencea fundamental property of light that describes the mutual correla- tions between fluctuating electromagnetic fieldshas been proven challenging to control at the micrometer scale. We use surface plasmon polaritonsevanescent waves excited on both surfaces of a thin metal filmas a means to mix the random fluctuations of the incident electromagnetic fields at the slit locations of a Youngs double-slit interferometer. Strong tunability of the complex degree of spatial coherence of light is achieved by finely varying the separation distance between the two slits. Continuous modulation of the de- gree of spatial coherence with amplitudes ranging from 0 to 80% allows us to transform totally incoherent incident light into highly coherent light and vice versa. These findings pave the way for alternative methods to engineer flat optical elements with multifunctional capabilities beyond conventional refractive- and diffractive- based photonic metasurfaces. INTRODUCTION Control of light propagation and interaction with matter relies upon knowledge of the amplitude and phase of the electromagnetic fields, as well as their mutual temporal and spatial correlations, which are described by the complex degree of coherence (13). Planar metal and dielectric surfaces with subwavelength featuresalso known as metasurfaces (46)have recently been proposed as a way to manip- ulate light by producing abrupt changes in the local amplitude and phase of the incident electromagnetic fields (7). Typically, the incident fields are highly coherent, and the scattered fields originating from the interaction of incident light with the nanostructured surfaces are mu- tually coherent. Then, optical interference effects produce desired changes in beam directionality, polarization, intensity, phase, and spin (8, 9). Optical spatial coherence can provide an alternative, powerful tool to control the flow of light with various degrees of coherence beyond conventional wavefront shaping methods offered by photonic meta- surfaces. From an application standpoint, control of the degree of spatial coherence of light can lead to higher-resolution speckle-free imaging (10, 11), ultimate capability to shape (12) and redirect light beams (1315), and enable novel modulation methods for free-space optical communications and interconnects (16, 17). However, full con- trol of spatial coherence at length scales comparable to the wavelength of light has been proven challenging. Although it has been theoretically suggested that surface plasmon polaritons (SPPs)electromagnetic waves evanescently bound to metal surfacescan, in principle, modulate the degree of spatial coherence (1820), a very few experimental studies have shown this effect, reporting only modest modulation amplitudes (2123). Here, we show, for the first time, large and finely tunable changes in the amplitude and phase of the complex degree of spatial coherence, controllable at the micrometer scale by simply varying the slit-slit sep- aration distance, as well as the wavelength and polarization state of the incident light. For instance, we report how light incident on a Youngs double-slit can be tuned from completely incoherent to partially coher- ent and vice versa, with degrees of coherence continuously variable from ~0% (totally incoherent) to ~80% (almost fully coherent). RESULTS Spatial coherence of optical fields Partially coherent light exiting the two slits placed at points P 1 and P 2 in an opaque film can generate interference fringes when projected onto a far-zone screen, as the result of constructive and destructive interference caused by the difference in the optical paths from each slit to a specific point on the screen (Fig. 1A and fig. S1). The fringe contrast, or visibil- ity, defined as V¼ðI max I min Þ=ðI max þ I min Þ , where I max and I min are the maximum intensity and minimum intensity, respectively, in the in- terference pattern (Fig. 1A), can be used to quantitatively describe the complex mutual correlation function m(P 1 , P 2 )=|m|e if between the electromagnetic fields at the two different points where the slits are lo- cated. It can be proven that the visibility of the interference fringes is equal to the amplitude of the degree of spatial coherence (24), that is, m j j¼V. The phase f can be inferred by looking at the interference con- dition at the center of the screen, with constructive (destructive) inter- ference corresponding to f =0(p). Therefore, Youngs double-slits can be used to directly measure and quantify the changes of the degree of co- herence of incident light at the slit locations, with m = 0 (or 1) corre- sponding to totally incoherent (or coherent) light. Transforming incoherent light into coherent light and vice versa In the absence of SPPs, the degree of coherence of transmitted light is unaffected after interaction with the slitted screen (Fig. 1A), resulting in m in = m out . This condition can be realized by using perfectly opaque screens or very large slit-slit separation distances in real metals or when light is linearly polarized with the electric field direction parallel to the long axis of the slits [transverse electric (TE)polarized]. Under transverse magnetic (TM) illumination (that is, the electric field perpendicular to the long axis of the slits), SPPs are excited and can introduce additional or eliminate existing correlations between the fields at the two slits, which enables strong modulation of the degree of spatial coherence provided that the SPP excitation process is coherent (2527). For example, Fig. 1B shows how SPPs can transform partially coherent light incident onto the slits into fully incoherent light leaving the slits. This is evidenced by the disappearance of the interference fringes that are replaced by a broad, featureless intensity distribution on the projection screen caused by the incoherent sum of two single-slit diffraction patterns (Fig. 1B). School of Engineering and Department of Physics, Brown University, Providence, RI 02912, USA. *Corresponding author. Email: [email protected] SCIENCE ADVANCES | RESEARCH ARTICLE Li and Pacifici Sci. 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School of Engineering and Department of Physics, Brown University, Providence,RI 02912, USA.*Corresponding author. Email: [email protected]

Li and Pacifici Sci. Adv. 2017;3 : e1700133 18 October 2017

Copyright © 2017

The Authors, some

rights reserved;

exclusive licensee

American Association

for the Advancement

of Science. No claim to

original U.S. Government

Works. Distributed

under a Creative

Commons Attribution

NonCommercial

License 4.0 (CC BY-NC).

Strong amplitude and phase modulation of opticalspatial coherence with surface plasmon polaritonsDongfang Li and Domenico Pacifici*

The degree of optical spatial coherence—a fundamental property of light that describes the mutual correla-tions between fluctuating electromagnetic fields—has been proven challenging to control at the micrometerscale. We use surface plasmon polaritons—evanescent waves excited on both surfaces of a thin metal film—as a means to mix the random fluctuations of the incident electromagnetic fields at the slit locations of aYoung’s double-slit interferometer. Strong tunability of the complex degree of spatial coherence of light isachieved by finely varying the separation distance between the two slits. Continuous modulation of the de-gree of spatial coherence with amplitudes ranging from 0 to 80% allows us to transform totally incoherentincident light into highly coherent light and vice versa. These findings pave the way for alternative methodsto engineer flat optical elements with multifunctional capabilities beyond conventional refractive- and diffractive-based photonic metasurfaces.

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INTRODUCTIONControl of light propagation and interaction with matter relies uponknowledge of the amplitude and phase of the electromagnetic fields,as well as their mutual temporal and spatial correlations, which aredescribed by the complex degree of coherence (1–3). Planar metaland dielectric surfaces with subwavelength features—also known asmetasurfaces (4–6)—have recently been proposed as a way to manip-ulate light by producing abrupt changes in the local amplitude andphase of the incident electromagnetic fields (7). Typically, the incidentfields are highly coherent, and the scattered fields originating from theinteraction of incident light with the nanostructured surfaces are mu-tually coherent. Then, optical interference effects produce desired changesin beam directionality, polarization, intensity, phase, and spin (8, 9).

Optical spatial coherence can provide an alternative, powerful toolto control the flow of light with various degrees of coherence beyondconventional wavefront shaping methods offered by photonic meta-surfaces. From an application standpoint, control of the degree ofspatial coherence of light can lead to higher-resolution speckle-freeimaging (10, 11), ultimate capability to shape (12) and redirect lightbeams (13–15), and enable novel modulation methods for free-spaceoptical communications and interconnects (16, 17). However, full con-trol of spatial coherence at length scales comparable to the wavelengthof light has been proven challenging. Although it has been theoreticallysuggested that surface plasmon polaritons (SPPs)—electromagneticwaves evanescently bound tometal surfaces—can, in principle, modulatethe degree of spatial coherence (18–20), a very few experimental studieshave shown this effect, reporting only modest modulation amplitudes(21–23).

Here, we show, for the first time, large and finely tunable changes inthe amplitude and phase of the complex degree of spatial coherence,controllable at the micrometer scale by simply varying the slit-slit sep-aration distance, as well as the wavelength and polarization state of theincident light. For instance, we report how light incident on a Young’sdouble-slit can be tuned from completely incoherent to partially coher-ent and vice versa, with degrees of coherence continuously variable from~0% (totally incoherent) to ~80% (almost fully coherent).

RESULTSSpatial coherence of optical fieldsPartially coherent light exiting the two slits placed at points P1 and P2 inan opaque film can generate interference fringes when projected onto afar-zone screen, as the result of constructive and destructive interferencecaused by the difference in the optical paths from each slit to a specificpoint on the screen (Fig. 1A and fig. S1). The fringe contrast, or visibil-ity, defined asV ¼ ðImax � IminÞ=ðImax þ IminÞ, where Imax and Imin arethe maximum intensity andminimum intensity, respectively, in the in-terference pattern (Fig. 1A), can be used to quantitatively describe thecomplex mutual correlation function m(P1, P2) = |m|eif between theelectromagnetic fields at the two different points where the slits are lo-cated. It can be proven that the visibility of the interference fringes isequal to the amplitude of the degree of spatial coherence (24), that is,mj j ¼ V. The phase f can be inferred by looking at the interference con-dition at the center of the screen, with constructive (destructive) inter-ference corresponding to f = 0 (p). Therefore, Young’s double-slits canbe used to directly measure and quantify the changes of the degree of co-herence of incident light at the slit locations, with m = 0 (or 1) corre-sponding to totally incoherent (or coherent) light.

Transforming incoherent light into coherent light andvice versaIn the absence of SPPs, the degree of coherence of transmitted light isunaffected after interaction with the slitted screen (Fig. 1A), resulting inmin = mout. This condition can be realized by using perfectly opaquescreens or very large slit-slit separation distances in real metals or whenlight is linearly polarized with the electric field direction parallel to thelong axis of the slits [transverse electric (TE)–polarized].

Under transverse magnetic (TM) illumination (that is, the electricfield perpendicular to the long axis of the slits), SPPs are excited andcan introduce additional or eliminate existing correlations betweenthe fields at the two slits, which enables strongmodulation of the degreeof spatial coherence provided that the SPP excitation process is coherent(25–27). For example, Fig. 1B shows how SPPs can transform partiallycoherent light incident onto the slits into fully incoherent light leavingthe slits. This is evidenced by the disappearance of the interferencefringes that are replaced by a broad, featureless intensity distributionon the projection screen caused by the incoherent sum of two single-slitdiffraction patterns (Fig. 1B).

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Totally incoherent light incident upon the double slits is unable togenerate interference fringes in the far field (Fig. 1C, TE polarization, noSPPs). However, SPPs excited at each slit location and propagatingtoward the other slit can, under proper conditions, mix the initiallyuncorrelated fields and generate partially coherent light with non-zero degree of coherence at the output of the double-slit. Because ofthese SPP-induced correlations introduced by the alternative path thatlight can take in the form of propagating SPPs, totally incoherent lightcan be transformed into partially coherent light, and as a result, thefar-zone fringe visibility is restored (Fig. 1D). Far-zone interferencepatterns can therefore be used to infer the complex degree of spatialcoherence and quantify the changes induced by SPPs (see the Supple-mentary Materials for more details).

Experimental setupFigure 1E shows a schematic of the experimental setup that was specif-ically designed to measure wavelength-resolved Young’s double-slitinterference patterns as a function of slit-slit separation distance dand incident polarization. In particular, double-slits etched in a thinsilver film were illuminated by linearly polarized broadband lightunder Köhler illumination (28). The objective of an inverted micro-scope was purposely defocused to project the interference pattern onto

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the entrancemask of a spectrograph, which disperses the transmitted lightand projects the generated interference patterns onto a two-dimensionalimaging camera.Representativewavelength-resolved interferencepatternsemerging from a Young’s double-slit with d = 5 mm, illuminated withpartially coherent light with two different polarization states (TE andTM; Fig. 1, F and G, respectively), show the marked changes in fringevisibility caused by SPPs. Remarkably, the results reported in the rightinsets of Fig. 1 (F and G) show—now experimentally—that SPPs cantransform incoherent light incident upon the double-slit into partiallycoherent light at the output of the slitted screen (solid lines; l1 = 581 nm),as attested by the increased fringe visibility whenTM-polarized light isused. Vice versa, partially coherent light can be transformed into in-coherent light (dashed lines; l2 = 712 nm), as evidenced by the sup-pressed fringe contrast due to SPP-induced modulation of the mutualcorrelation function (see Materials and Methods for more details).

Effects of spatial coherence of incident lightSeveral wavelength-resolved interference patterns for the same Young’sdouble-slit with d = 5 mmunder varying degrees of spatial coherence ofthe incident light are reported in Fig. 2. Under TE-polarized illumina-tion (no SPPs), the far-zone interference patterns gradually change as afunction of incident wavelength l, at any givenDq (Fig. 2, A to C). Light

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Fig. 1. Schematics of Young’s double-slit experiment with and without SPPs. Simulated interference patterns showing modulation of the degree of spatial coherence ofincident light induced by SPPs. Partially coherent light (A) can be transformed into incoherent light (B), and vice versa, incoherent light (C) can be transformed into partiallycoherent light (D) upon interaction with the slitted screen, when SPPs are excited. Electromagnetic fields with different degrees of spatial coherence incident on the two slits areschematically indicated with arrows filled with different fractions of black and white areas. (E) Schematic of the experimental setup designed to record the far-zone interferencepattern from Young’s double-slit to extract visibility as a function of wavelength. (F and G) Experimental TE (no SPPs) (F) and TM (with SPPs) (G) wavelength-resolved far-zoneinterference patterns originating from a Young’s double-slit with slit-slit separation distance d= 5 mmand subtended illumination angleDq ≈ 6°. Insets (right panels): ExperimentalSPP-induced modulation of interference patterns at two different wavelengths, showing transformation of incoherent light into partially coherent light (solid lines; l1 = 581 nm)and vice versa (dashed lines; l2 = 712 nm), when the polarization state of the incident light is varied from TE to TM.

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with longer wavelength generates interference fringes that are spatiallymore spread out comparedwith shorter wavelengths, as the result of thelonger optical path difference required to achieve the same phase shifton the projection screen. The fringe visibility is greatly reduced whenlight with lower degree of spatial coherence (that is, higher subtendedillumination angle Dq) is used. By rotating the polarization state of theincident light by p/2 (that is, from TE to TM), SPPs from both metal/dielectric interfaces can be turned on, and strong modulation of thefringe visibility is observed as the result of additional beatings betweenthe two SPPmodes (Fig. 2, D to F). Both the amplitude (related to fringevisibility) and phase (related to either constructive or destructive inter-ference at the screen center) of the degree of spatial coherence are stronglymodulated under TM-polarized illumination due to SPP excitation(Fig. 2, E and F) that determines a redistribution of the far-zone lightintensity. Both enhancement and suppression of fringe visibility canbe achieved relative to the respective interference patterns under TEillumination (Fig. 2, B and C, no SPPs).

Theory of optical coherence modulation withsurface plasmonsAn analytical expression for the output fields that includes SPP con-tributions can bewritten as Ei(l, d) = tEi,in(l) + tbEj,in(l), where (i, j) =(1, 2) or (2, 1);Ei,in is the incident scalar field at one slit location; t is thetransmission coefficient through the slit;l is the free-spacewavelengthof light; and b ¼ bte

ikSPP;td þ bbeikSPP;bd , where bt and bb are the SPP

coupling coefficients at the top (that is, glass/Ti/Ag) and bottom (that is,Ag/air) interfaces, respectively, and kSPP,t and kSPP,b are the correspondingSPP complex wave vectors, which account for SPP absorption due toohmic losses in the metal.

By using the definition of cross-spectral density functionWijðlÞ ¼⟨E*

i ðlÞEjðlÞ⟩, where the angle brackets indicate ensemble averaging, thedegree of spatial coherence of light exiting the double-slit can be writtenas (19, 23)

moutðlÞ ¼W12ðlÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

W11ðlÞW22ðlÞp

¼ minðlÞ þ 2ReðbÞþjbj2m*inðlÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1þ bj j2 þ 2Re½bminðlÞ�Þ 1þð jbj2 þ 2Re½bm*inðlÞ�Þ

p

ð1Þ

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where min is the complex degree of spatial coherence of light incident onthe double-slit, which is generally treated as an ad hoc tunable parameter(21–23). Here, min is experimentally tuned using a Köhler illuminationsetup inwhich lightwith varying degrees of spatial coherence is generatedby changing the subtended illumination angle through a variable con-denser aperture. Moreover, a theoretical framework is developed to cal-culate the far-field intensity distribution determined by light diffractionand interference either with orwithout SPP contributions, as described inthe Supplementary Materials.

Beatings between surface plasmons excited on both metal/dielectric interfacesTo better quantify and control themodulation of the complex degree ofspatial coherence, SPP contributions from both metal/dielectric inter-faces need to be considered and carefully tailored. These contributionscan be extracted by analyzing the plasmonic interferogram, that is, aplot of the normalized intensity ratio at a given wavelength obtainedby normalizing the light intensity transmitted through each double-slitwith varying separation distance to the reference intensity transmittedthrough the corresponding individual slit (29). Figure 3A shows a repre-sentative plasmonic interferogram measured at l = 600 nm. DiscreteFourier transform analysis applied to this data set (28, 30) shows thedifferent SPP contributions originating frombothAg/air (black arrows)and glass/Ti/Ag interfaces (red arrows) as distinct intensity peaks in theFourier power spectrum amplitude (Fig. 3B). This procedure can be ex-tended to allmeasuredwavelengths, and the resulting data sets are plottedas two-dimensional color maps of plasmonic interferograms (Fig. 3C)and Fourier transform power spectra (Fig. 3D), which reveal the energy-momentum dispersion of SPPs existing on both interfaces. By filteringout thehigher-order SPPcontributions (withm>1), plasmonic interfero-grams with only first-order SPP contributions can be reconstructed (redline inFig. 3A), and the corresponding SPPcoupling coefficientsbt andbbcan be extracted from fits to the filtered data (seeMaterials andMethods).

Strong modulation of spatial coherenceFar-zone interference patterns as a function of slit-slit separation dis-tance can be constructed by scanning all of the fabricated Young’sdouble-slit interferometers with varying separation distances underTE-polarized (Fig. 4, A to C) and TM-polarized (Fig. 4, D to F) illu-mination. The far-zone interference patterns recorded in the pres-ence of SPPs show strong modulation in the fringe contrast and richer

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Fig. 2. Effects of SPPs onwavelength-resolved far-zone interference patterns for incident light with varying degrees of spatial coherence. (A to F) Interference patternsmeasured at the output of a Young’s double-slit interferometer with d = 5 mmas a function of incident wavelength for three values of Köhler subtended illumination angles (Dq ≈3°, 6°, and 10°), corresponding to decreasing spatial coherence, in the absence (TE polarization) (A to C) and in the presence (TMpolarization) (D to F) of SPPs. Strongmodulation offringe visibility induced by SPPs is visible. The color bar refers to normalized interference-fringe intensity on the projection screen.

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Fig. 3. Evidencing SPP contributions supported by bothmetal/dielectric interfaces. (A) Plasmonic interferogram as a function of slit-slit distance measured at l = 600 nm(black line). Reconstructed filtered data (red line) and theoretical fits (blue line) are also reported. The distance between adjacent vertical dashed lines is equal to lSPP,b, that is, theSPP wavelength at the Ag/air interface. (B) Discrete Fourier transform power spectrum calculated from the experimental data in (A), which shows different orders of SPP con-tributions from both glass/Ti(3 nm)/Ag (red arrows) and Ag/air (black arrows) interfaces. Inset: Schematic of SPPs propagating along bothmetal/dielectric interfaces and simulta-neously affecting the output intensity and far-zone interference pattern. (C) Wavelength-resolved plasmonic interferograms obtained by normalizing the transmission spectrathrough double-slit interferometers by the reference transmission spectra through individual slits. (D) Energy-resolved power spectra obtained by applying discrete Fouriertransform to the data in (C). Energy-momentum dispersion curves evidence the presence of SPPs supported by both Ag/dielectric interfaces [bright bands in (D)] and are ingood agreement with calculations (gray lines) based on the dielectric functions of materials.

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Fig. 4. SPP-enabledamplitudeandphasemodulationof complexdegreeof spatial coherence. (A toF) TE-polarized (A toC) and TM-polarized (D to F) Young’s double-slit far-zoneinterference patterns measured at l = 600 nm as a function of slit-slit distance and for three different Köhler subtended illumination angles (Dq ≈ 3°, 6°, and 10°), corresponding todecreasing spatial coherence length (LC =3.18, 1.47, and 0.93 mm, respectively). The color bar refers to normalized interference-fringe intensity on the projection screen. (G to I) Exper-imental visibility curves extracted from far-zone interference patternsmeasured under TE-polarized (green lines; no SPPs) and TM-polarized (blue lines; with SPPs) illumination, at l = 600nm, and for different values of Dq. The black lines are the theoretical results for TE illumination obtained by fitting the corresponding experimental data to a sinc function (jsincðk0dDq2 Þj),with Dq as the only fitting parameter. The red lines are the theoretical predictions of visibility under TM illumination calculated using Eq. 1 and including SPPs from bothmetal/dielectricinterfaces. Insets in (I) highlight strongmodulation of visibility (and, correspondingly, amplitude of complex degree of spatial coherence) induced by SPPs. (J to L) Experimental TM (bluelines), theoretical TE (gray lines), and theoretical TM (red lines) phase values of complex degrees of spatial coherence for variousDq. For clarity, the red andblue lines are slightly shifted inthe vertical direction. Discrete data points sporadically missing from the blue lines correspond to visibility values V < 0.088 for which the phase cannot be accurately retrieved.

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intensity features, with overall increased number of observable maximaandminima (for instance, compare Fig. 4F with Fig. 4C). The amplitudeand phase of the complex degree of spatial coherence at any given wave-length can be extracted from quantitative inspection of the interferencepatterns. The results of such an exercise are reported in Fig. 4 (G toL), forboth TE and TM illumination, at l = 600 nm. The fringe visibility re-cordedunderTE-polarized (noSPPs) illuminationwithDq =3° graduallydecreases as a function of increasing slit-slit separation distance (greenline in Fig. 4G). Such a change follows the model derived from the vanCittert–Zernike theorem (black line in Fig. 4G). In contrast, the mea-sured visibility under TM illumination (with SPPs) is significantlymod-ulated (blue line in Fig. 4G). Note that for small separation distances(d < 5 mm), interference effects caused by beatings of SPPs supportedby both metal/dielectric interfaces are visible, as evidenced by the non–single-periodic oscillations of the visibility curve. In contrast, for largeseparation distances (d > 5 mm), the SPPs propagating along the glass/Ti/Ag interface are more strongly attenuated compared to the SPPsalong the Ag/air interface and no longer contribute to visibility modu-lation. According to Eq. 1, under TE illumination, mout = min becauseSPPs are not excited (that is, b = 0) and cannot modulate fringe visibility.Thus, the experimental visibility values extracted under TE illuminationare a direct measure of the mutual correlation function of the incidentlight at the slit locations. From this and by using the SPP coupling coeffi-cients obtained from plasmonic interferograms as input parameters inEq. 1, the amplitude and phase of the complex degree of spatial coherenceunder TM illumination can be theoretically predicted (red lines in Fig. 4,G and J). The theoretical values agree well with the experimental resultsover the whole range of visibility, wavelength, and slit-slit separation dis-tance (see the Supplementary Materials for more details).

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DISCUSSIONAs highlighted in the first inset of Fig. 4I, by finely varying the slit-slitseparation distance within a range of only ~ lSPP/2≈ 240 nm, with lSPPas the average SPPwavelength at l = 600 nm, the experimental visibilitycan be varied from~0 (totally incoherent) to ~0.8 (almost fully coherent)under TM illumination. Furthermore, as shown in the second inset ofFig. 4I, by simply changing the polarization state from TE (green lines;no SPPs) to TM (blue lines; with SPPs), fully incoherent incident fieldscan be transformed into highly correlated (f =0) or anticorrelated (f = p)fields with V > 0:4. Compared with a previous work (23), higher SPPcoupling coefficients achieved by tuning the width of each slit enablestronger amplitude modulation of spatial coherence. In addition, thepresence of SPPs on both interfaces can also be used to finely modulatethe phase of the complex degree of spatial coherence, as shown in Fig. 4(K and L).

In principle, dense arrays of nanoslits, nanoholes, or other nano-structures inmetal filmsmay be designed tomodify the spatial coherenceof an entire light beam (20). As an alternative to SPPs supported bycorrugated, lossy metal surfaces, photonic modes in planar waveguidescoupled with dielectric metasurfacesmay also be used to stronglymodifythe spatial coherenceof incident light,which can lead to beam-transformingoptical elements with significantly lower transmission losses.

In summary, we have achieved full control of the complex degree ofspatial coherence of light at themicrometer scale using surface plasmon–based interferometers. Strongmodulation of the amplitude and phase ofthe complex degree of coherence is accomplished by engineering thebeatings between the surface plasmons with different wave vectors gen-erated at the two metal/dielectric interfaces. These findings can lead to

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alternative nanoengineered optical flat surfaces that leverage the de-gree of spatial coherence to achieve ultimate control of light flow, whichis beyond conventional refractive- and diffractive-based photonicmetasurfaces.

MATERIALS AND METHODSSample fabricationElectron beam evaporation was used to deposit an approximately200-nm-thick layer of silver (Ag) on one of the two surfaces of a1-mm-thick glass slide that was previously coated with a 3-nm-thicktitanium (Ti) layer to improve film adhesion. Multiple Young’s double-slit interferometers, consisting of two identical ~200-nm-wide, ~200-nm-deep, and ~15-mm-long slits, with variable slit-slit separation distance,were etched on the silver film using focused ion beam milling (fig. S2).The slit width was chosen to provide comparable transmission intensityunder both TE and TM illumination and high SPP coupling coeffi-cients. The separation distance between the two slits ranged from 0.5to 9.525 mm in incremental steps of 25 nm. In total, 362 Young’s double-slit interferometers were etched on the metal film, evenly distributedin two separate columns. A single column containing 181 identical in-dividual slits was also etched on the same silver film to serve as ref-erence for normalizing light transmission through the double-slits.The columns of single- or double-slits were placed 600 mm apart, andadjacent slits along each column were separated by 25 mm to avoidoptical cross-talk during the measurements that could affect the inter-ference patterns and lead to artificially reduced visibility values.

Optical characterizationKöhler illumination was used to achieve variable spatial coherence illu-mination of Young’s double-slit interferometers. The setup consisted ofa xenon arc lamp, coupled to an invertedmicroscope, together with adiffuser, an auxiliary lens, a linear polarizer, a 2-mm-wide slit mask,and a condenser lens system (28). Each interferometer was illuminatedfrom the glass side—that is, from the glass(1mm)/Ti(3 nm)/Ag(200 nm)interface—and the transmitted light intensity was collected with a 20×objective (numerical aperture, 0.75) from the opposite side, that is, fromthe Ag(200 nm)/air interface. The focal plane of the objective lens waslocated ~49 mm below the metal surface containing the double-slit in-terferometers to generate far-zone projections of light intensity onto theimaging plane of a charge-coupled device (CCD) camera. More specif-ically, the interference pattern was projected onto the entrance slit maskof a spectrograph, dispersed by a grating with 150 grooves/mm, andimaged onto a two-dimensional CCD camera to extract the wavelengthdependence of light intensity along the horizontal axis and the spatialintensity distribution along the vertical axis (see Fig. 1). This experimentalsetup allows the detection of wavelength-resolved interference patternstransmitted through eachYoung’s double-slit interferometer, fromwhichthe fringe visibility over several wavelengths can be captured simulta-neously in a single CCD image. By scanning all of the double-slit inter-ferometers with different separation distances using an automatedmicroscope stage, 362 wavelength-resolved interference patterns wereobtained for each subtended angle and for TE (that is, no SPPs) or TM(that is, with SPPs) polarization states of the incident light (fig. S3). Inaddition, a full set of light transmission experiment was also per-formed for all the double-slits and reference single-slits by focusingthe microscope objective directly onto the output metal film surfaceto measure plasmonic interferograms necessary to determine SPP exci-tation, propagation, and coupling coefficients for both top (glass/Ti/Ag)

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and bottom (Ag/air) interfaces as a function of incident wavelength.Note that a Nikon Perfect Focus System was used during the scanningprocess to keep a constant relative distance between themicroscope ob-jective and the bottom sample surface (that is, Ag/air interface). All in-terference patterns (Figs. 1, 2, and 4 and figs. S3 and S6)were normalizedto the correspondingmean intensity value at eachwavelength to removethewavelength-dependent intensity variation introduced by the externallight source.

Extraction of SPP coupling coefficients fromplasmonic interferogramsThe light spectra transmitted through the double-slits (IDS) andreference single-slits (ISS) were measured by focusing the objective ontothe nanoapertures. The scalar field transmitted through the single-slit(ESS) and double-slit (EDS) can be expressed as follows

ESSðlÞ ¼ tEinðlÞ ð2Þ

EDSðl; dÞ ¼ tEinðlÞ þ tbEinðlÞ ð3Þ

where the field incident on each slit is assumed to be the same (Ein), andthe two incident fields on the slits can be considered fully coherent up toa 5-mm separation distance under the subtended illumination angle Dq≈ 3 ° (corresponding to min ≥ 0.7). Accordingly, the normalized inten-sity ratio of the transmitted intensity through the double-slit andreference single-slit can be written as

Inðl; dÞ ¼ IDSðl; dÞ2ISSðlÞ ¼ ⟨E�

DSEDS⟩

⟨E�SSESS⟩

¼ 1þ bj j2

¼ j1þ bteikSPP;td þ bbe

ikSPP;bd 2�� ð4Þ

where the factor 2 in the denominator arises from the fact that the twoslits in the Young’s double-slit interferometer can be fully distinguishedby the optical setup; therefore, the intensity (rather than the fields) canbe summed up when the two slits are directly imaged.

A representative plasmonic interferogramat l =600nm is plotted inFig. 3A (black line). Thewavelength-resolved plasmonic interferogramsare shown inFig. 3C.By applyingdiscrete Fourier transform toplasmonicinterferograms, different orders of SPP contributions can be deconvolved(28, 30), as shown by the peaks and bright bands in Fig. 3 (B and D),which are in good agreementwith the calculatedwave vectors of differentorders of SPP (gray lines in Fig. 3D). SPP contributions from both inter-faces (black versus red labels) were evident. After filtering out higher-order SPP contributions (that is, with m > 1), plasmonic interferogramsthat only originate from first-order SPPs can be reconstructed (red line inFig. 3A). By fitting the reconstructed plasmonic interferograms (with dranging from 1 to 5 mm) to Eq. 4, SPP coupling coefficients bt(l) and bb(l) can be extracted (see fig. S7). Thus, themodulation of the visibility inFig. 4 can be theoretically predicted using Eq. 1, provided that the vis-ibility of the incident fields is known.

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/10/e1700133/DC1Supplementary Textfig. S1. Role of angle of incidence and subtended angle in Young’s double-slit interferencepatterns under Köhler illumination.fig. S2. Scanning electron microscopy images of Young’s double-slit interferometers.

Li and Pacifici Sci. Adv. 2017;3 : e1700133 18 October 2017

fig. S3. Experimental, wavelength-resolved interference patterns for representative Young’sdouble-slit interferometers and subtended illumination angles at two different polarizations.fig. S4. Estimate of effective optical width of individual slits.fig. S5. Comparison between visibility curves obtained using numerical integration andanalytical expressions.fig. S6. Comparison between theoretical and experimental Young’s double-slit interferencepatterns for micrometer-scale slit-slit separation distances.fig. S7. Coupling coefficients of SPPs excited along both metal/dielectric interfaces.fig. S8. Representative visibility curves.fig. S9. Experimental SPP energy-momentum dispersion curves.fig. S10. Fourier transform analysis.References (31, 32)

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AcknowledgmentsFunding: This work was supported by the NSF (grant no. CMMI1530547). Authorcontributions: D.L. and D.P. conceived the experiment, discussed and analyzed the data, and

Li and Pacifici Sci. Adv. 2017;3 : e1700133 18 October 2017

wrote the manuscript. D.L. fabricated the sample and performed the experiment.D.P. supervised the project. Competing interests: The authors declare that they have nocompeting interests. Data and materials availability: All data needed to evaluate theconclusions in the paper are present in the paper and/or the Supplementary Materials.Additional data related to this paper may be requested from the authors.

Submitted 12 January 2017Accepted 27 September 2017Published 18 October 201710.1126/sciadv.1700133

Citation: D. Li, D. Pacifici, Strong amplitude and phase modulation of optical spatial coherencewith surface plasmon polaritons. Sci. Adv. 3, e1700133 (2017).

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polaritonsStrong amplitude and phase modulation of optical spatial coherence with surface plasmon

Dongfang Li and Domenico Pacifici

DOI: 10.1126/sciadv.1700133 (10), e1700133.3Sci Adv 

ARTICLE TOOLS http://advances.sciencemag.org/content/3/10/e1700133

MATERIALSSUPPLEMENTARY http://advances.sciencemag.org/content/suppl/2017/10/16/3.10.e1700133.DC1

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