Research ArticleOPTICS

Strong amplitude and phase modulation of optical spatial coherence with surface plasmon polaritons

See allHide authors and affiliations

Science Advances  18 Oct 2017:
Vol. 3, no. 10, e1700133
DOI: 10.1126/sciadv.1700133
  • Fig. 1 Schematics of Young’s double-slit experiment with and without SPPs.

    Simulated interference patterns showing modulation of the degree of spatial coherence of incident 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 partially coherent 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 are schematically indicated with arrows filled with different fractions of black and white areas. (E) Schematic of the experimental setup designed to record the far-zone interference pattern 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-zone interference patterns originating from a Young’s double-slit with slit-slit separation distance d = 5 μm and subtended illumination angle Δθ ≈ 6°. Insets (right panels): Experimental SPP-induced modulation of interference patterns at two different wavelengths, showing transformation of incoherent light into partially coherent light (solid lines; λ1 = 581 nm) and vice versa (dashed lines; λ2 = 712 nm), when the polarization state of the incident light is varied from TE to TM.

  • Fig. 2 Effects of SPPs on wavelength-resolved far-zone interference patterns for incident light with varying degrees of spatial coherence.

    (A to F) Interference patterns measured at the output of a Young’s double-slit interferometer with d = 5 μm as a function of incident wavelength for three values of Köhler subtended illumination angles (Δθ ≈ 3°, 6°, and 10°), corresponding to decreasing spatial coherence, in the absence (TE polarization) (A to C) and in the presence (TM polarization) (D to F) of SPPs. Strong modulation of fringe visibility induced by SPPs is visible. The color bar refers to normalized interference-fringe intensity on the projection screen.

  • Fig. 3 Evidencing SPP contributions supported by both metal/dielectric interfaces.

    (A) Plasmonic interferogram as a function of slit-slit distance measured at λ = 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 λSPP,b, that is, the SPP 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 contributions from both glass/Ti(3 nm)/Ag (red arrows) and Ag/air (black arrows) interfaces. Inset: Schematic of SPPs propagating along both metal/dielectric interfaces and simultaneously affecting the output intensity and far-zone interference pattern. (C) Wavelength-resolved plasmonic interferograms obtained by normalizing the transmission spectra through double-slit interferometers by the reference transmission spectra through individual slits. (D) Energy-resolved power spectra obtained by applying discrete Fourier transform 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 in good agreement with calculations (gray lines) based on the dielectric functions of materials.

  • Fig. 4 SPP-enabled amplitude and phase modulation of complex degree of spatial coherence.

    (A to F) TE-polarized (A to C) and TM-polarized (D to F) Young’s double-slit far-zone interference patterns measured at λ = 600 nm as a function of slit-slit distance and for three different Köhler subtended illumination angles (Δθ ≈ 3°, 6°, and 10°), corresponding to decreasing spatial coherence length (LC =3.18, 1.47, and 0.93 μm, respectively). The color bar refers to normalized interference-fringe intensity on the projection screen. (G to I) Experimental visibility curves extracted from far-zone interference patterns measured under TE-polarized (green lines; no SPPs) and TM-polarized (blue lines; with SPPs) illumination, at λ = 600 nm, and for different values of Δθ. The black lines are the theoretical results for TE illumination obtained by fitting the corresponding experimental data to a sinc function (Embedded Image), with Δθ 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 both metal/dielectric interfaces. Insets in (I) highlight strong modulation of visibility (and, correspondingly, amplitude of complex degree of spatial coherence) induced by SPPs. (J to L) Experimental TM (blue lines), theoretical TE (gray lines), and theoretical TM (red lines) phase values of complex degrees of spatial coherence for various Δθ. For clarity, the red and blue lines are slightly shifted in the 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.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/10/e1700133/DC1

    Supplementary Text

    fig. S1. Role of angle of incidence and subtended angle in Young’s double-slit interference patterns under Köhler illumination.

    fig. S2. Scanning electron microscopy images of Young’s double-slit interferometers.

    fig. S3. Experimental, wavelength-resolved interference patterns for representative Young’s double-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 and analytical expressions.

    fig. S6. Comparison between theoretical and experimental Young’s double-slit interference patterns 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)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • fig. S1. Role of angle of incidence and subtended angle in Young’s double-slit interference patterns under Köhler illumination.
    • fig. S2. Scanning electron microscopy images of Young’s double-slit interferometers.
    • fig. S3. Experimental, wavelength-resolved interference patterns for representative Young’s double-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 and analytical expressions.
    • fig. S6. Comparison between theoretical and experimental Young’s double-slit interference patterns 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)

    Download PDF

    Files in this Data Supplement: