CDEW (Composite Diffracted Evanescent Waves):
New model for enhanced transmission of subwavelength apertures.

H.J. Lezec and T. Thio, Optics Express 12, 3629 (2004)
"Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays"

T Thio, American Scientist 94, 40 (2006)
"A bright future for subwavelength light sources "

What's on this page:
Synopsis of paper (all figure and equation numbers refer to those in the paper)
FAQ (frequently asked questions) on the CDEW model

Synopsis

The extraordinary transmission of subwavelength apertures which are placed in a metal film of which the surface has periodic corrugations, is generally attributed to a resonance with a surface plasmon polariton (SP) mode at the metal surface, leading to very high transmission enhancement (up to factor 1000 quoted).

While the SP model is widely accepted, there are a number of experimental observations, both in the literature (-) and from recent experiments as described in the paper (+) which are inconsistent with the SP model:

• - Enhanced transmission observed in marginally metallic systems (Cr in IR region) and calculated in nonmetallic systems (W in visible).
  
• - Observed peak wavelengths about 15% longer than predicted by SP model; predicted SP positions coincide with transmission minima.
  
• - Very large peak widths inconsistent with very large transmission enhancements reported
  
• + Transmission enhancement spectra of nonmetallic W and amorhous Si identical in shape to that of Ag (Fig. 3).
  
• + Transmission suppression as well as enhancement (Fig. 1).
  
• + Peak enhancement is G<7 when compared to real, single isolated hole in same film.

CDEW model for transmission enhancement and suppression

We have proposed a new model of the transmission enhancement and suppression. The model reconciles the contradictions listed above, and is consistent with all experimental results published in the literature.

Scattering by subwavelength feature on surface:
Incident light (wavevector k₀) is scattered both into radiative modes (k_x<k₀; omitted from figure below for clarity) and evanescent modes (k_x>k₀ and k_z imaginary). For a linear slit or groove, integrating over all the evanescent modes gives a surface wave which we label a composite diffracted evanescent wave (CDEW; red arrows in figure below). The CDEW propagates perpendicular to the slit or groove with a well-defined wave vector k_CDEW=k₀, an amplitude which decays with distance from the groove as 1/x, and a phase which is shifted by f=p/2 compared to the excitation at the source. The theoretical prediction is verified by experimental observations.

Interference
When the CDEW arrives at a neighbouring hole it interferes with the light that is directly hitting that hole, giving rise to electric field enhancement at the aperture entrance when the interference is constructive, or field suppression when the interference is destructive.
The transmission efficiency T_H of the hole itself is independent of whether or not there are surface corrugations in the vicinity of the hole; the latter merely modify the intensity at the aperture entrance, and hence the total intensity at the aperture exit.

CDEW at rear surface
As the light emerges from the aperture on the unilluminated side of the film, again part of it will be diffracted into radiative modes (black arrows in above figure), and part into evanescent modes which make up a CDEW essentially identical to those formed at the illuminated surface (red arrows). Scattering from neighbouring surface features (brown arrows) is observable in the far field in the form of beaming effects.

The total intensity transmitted through the hole and collected by a lens behind the screen is thus given by
        T_C(l) = A₁(l) T_H(l) A₂(l) f_C
where A₁(l) is the field enhancement at the entrance of the aperture, T_H(l) the intrinsic transmission coefficient of the aperture, and A₂(l) the effective collection enhancement due to scattering off the corrugation on the exit side of the film (beaming effects), and f_C is the fraction of the total light emerging from the aperture exit, that is collected by the lens.

Successes of the CDEW model:

• correctly predicts position & width of transmission peaks of hole array (Fig. 8)
• excellent fit to transmission spectrum of single slit with varying number of grooves (Fig. 7)
• naturally includes transmission suppression as well as enhancement
• applicable to nonmetallic systems
• consistent with all experimental observations published in literature
• relevant to large class of systems with periodic surface corrugations, including diffraction gratings and frequency-selective surfaces.

Frequently asked questions about the CDEW model

Q. Where are the surface plasmons?
A. In nonmetallic systems (which do not support SPs) the transmission enhancement and suppression is due solely to CDEW. On metallic surfaces which are corrugated, incident light does excite surface plasmons through grating coupling.
However, in the case of a hole array, the SP wavelengths coincide with minima in the transmission spectra. Even when the geometry (circular symmetry) and material (silver) are optimised for the detection of SPs, we find (see Fig. 9 in the paper) that the SP contribution to the transmission enhancement is negligible compared to the CDEW contribution.

Q. Are the CDEWs not the same as the SPs?
A. They are not:
(1) SPs are guided modes of the metal surface with propagation lengths limited only by surface absorption (e.g. on silver the SP decay exponentially with a characterisic decay length of about 20-30 µm in the visible, and far longer in the IR). In contrast, the composite nature of the CDEW causes it to have a 1/x decay where x is the distance from the scattering centre (Figs. 5,6).
(2) Furthermore, efficient coupling to SPs requires a surface grating with reasonably large area; CDEWs are generated with large efficiency by a single subwavelength surface feature (Fig. 6), and propagate with a charateristic phase shift with respect to the excitation site.
(3) Finally, CDEWs do not require a metal surface.

Q. What about all the calculations that show the importance of SPs?
A. We do not question the validity of the calculations. We trust that they solve the Maxwell equations correctly, and have no quarrel with the numerical results. But we disagree with their surface plasmon interpretation, since our experimental evidence point to the importance of CDEWs which do not require a metal surface. Indeed, Sarrazin's calculations on hole arrays in nonmetallic tungsten and chromium give results very similar to those of silver.

Q. In comparing the transmission of a hole array to a single hole, do you take into account the numerical aperture of the collection optics?
A. We do; see section 2.1. However, we note that for a single aperture with front-surface corrugation (and a smooth back surface; see Figs. 6,7), the enhancement G(l) can be obtained by a straightforward division by the transmission spectrum of a single "bare" hole (which has an identical radiation pattern on the exit side, except for the amplitude).

Q. The CDEW expression you give in Eqs. 1,2 is valid for a slit or a groove. Is it applicable to an array of subwavelength holes?
A. A periodic array of holes can be thought of as a collection of rows of holes. The data of Fig. 5 shows that a linear row of subwavelength holes generates CDEWs very similar to those created by a slit. Indeed, similar experiments on two adjacent slits with varying distance (not shown in the paper) give identical results except that the transmission spectra have additional features due to slit modes.