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Surface plasmon coupling of a TM polarized free space incident beam by means of the + 1st or the −2nd order of a smooth corrugation grating at a metal surface causes the cancellation of the diffracted −1st order free space beam and a maximum of the 0th order Fresnel reflection whereas the converse occurs midway between these two conditions. This implies that angular tilting of the element or wavelength scanning provokes the switching between the −1st and 0th reflected orders. This plasmon-mediated effect on propagating free-space beams exhibits remarkably low absorption losses.
© 2014 Optical Society of America
1. Introduction
Grating coupling of a TM-polarized incident free space beam to the non-localized plasmon wave propagating along a metal surface by means of the + 1st or −1st order shows as a deep and broad dip of the angular and wavelength Fresnel reflection spectra caused by the absorption of the surface plasmon. This characteristic is used in a number of sensor applications. The mesurement of the location of the dip at fixed incidence in the wavelength spectrum or at fixed wavelength in the angular spectrum is currently used to monitor a biological reaction taking place at the metal surface in biosensors [1]. Angularly dependent reflection upon tilting a corrugated metallized element in a light field can also be used to encode a security feature [2]. What is actually used in most applications of grating plasmon coupling is the strong absorption of the associated collective oscillation of surface electrons. In contrast with the common use of plasmon resonance at a single metal-dielectric interface, a new effect is presented here whereby plasmon coupling only acts as a very low loss trigger in a switching effect between two free space waves diffracted by the very same coupling grating: the 0th and the −1st reflected orders. No phenomenological explanation of this plasmon-mediated switching effect is available yet, but convincing experimental results supported by exact modeling confirm its existence and permit to describe its characteristics. This is what the present paper undertakes. The modeling of the effect (Section 2) is made on the basis of a corrugated silver substrate to best visualize the switching properties whereas the experimental demonstration (Section 3) was made on a larger loss undulated aluminum surface as currently used in the application domain of security elements.
2. Occurrence conditions of plasmon-triggered switching
The effect shows when the 0th and −1st order of the grating both have a propagative character which sets the following condition on the incidence angle θ, the wavelength λ and the grating period Λ if the dielectric above the metal surface is air or vacuum:
Figure 1(a) illustrates a simple structure cross-section which consists of a corrugated metal-dielectric interface of sinusoidal profile. Figure 1(b) represents the Ewald circle at fixed wavelength with the k-vectors involved: the cirle radius , the grating spatial frequency , the incident wave, the propagating −1st order, and the two propagation constants of the forward- and backward- propagating surface plasmons. ne is their effective index usually given at a planar air-metal interface as where εm is the complex permittivity of the metal. When the interface is undulated, ne decreases slightly with increasing grating depth as the exact code of Lyndin’s MC grating package [3] based on the coordinate transform Chandezon method shows [4].
Fig. 1 Cross-section of the corrugated metal substrate supporting a plasmon-triggered switching effect. a) Optogeometrical definitions, b) Corresponding representation in the reciprocal space.
The range of optogeometrical parameters defined by Eq. (1) is not favorable for plasmon coupling per se since the existence of a propagative −1st order represents a loss of optical power which does not contribute in the resonance. This is why it has not been the subject of much attention. Let us however try and make a scan of the incidence angle at fixed wavelength in this region considering a moderate sinusoidal grating depth, e.g. Λ/20. Figure 2(a) gives the angular spectra from normal TM incidence to 45° of the reflected 0th and −1st orders (curves A and B respectively) in a sinusoidally corrugated air-silver interface characterized by a 844 nm period, a fixed wavelength of 633 nm and a corrugation depth of 40 nm. There is nothing remarkable except two narrow complementary kinks on the spectra at two locations at the angles 16.4° and 27.8° which happen to exactly correspond to the coupling synchronism conditions for plasmon excitation in this specific structure by means of the −2nd and + 1st grating orders respectively. The 0th order reflection spectrum of curve A differs strikingly from the 0th order reflection spectrum of a −1st order plasmon coupling by a grating having the same depth at the same wavelength, the same metal substrate and a 460 nm period shown by the thick black curve A of Fig. 2(b). There is a deep reflection dip corresponding to high plasmon absorption as illustrated by the balance spectrum of the thin black curve C which represents the total optical power (i.e. unit power of the incident wave minus absorption). The balance curve and the 0th order reflection curve overlap up to the incidence angle where the −1st order starts propagating (blue curve B). Plasmon excitation provokes an absorption loss as large as 80% whereas the off-resonance absorption is in the range of 12%.
Fig. 2 Angular diffraction spectra (for λ = 633 nm) of a corrugated metal substrate at moderate grating depth of 40 nm. a) 0th (curve A) and −1st (curve B) reflected orders under the condition of expression (1). b) Fresnel reflection in the neighborhood of −1st plasmon coupling (curve A), propagating −1st order (curve B), and balance spectrum (curve C).
Increasing now the grating depth, keeping all other quantities unchanged leads to a major alteration of the optical function from the minor artifacts on the spectra of Fig. 2(a) to a definite coupled wave phenomenon of high contrast as illustrates in Fig. 3(a) to Fig. 3(d) with the sinusoidal grating depth d as a parameter. It is at the depth of about 240 nm (Fig. 3(d)) that the 0th and −1st order coupling reaches its highest contrast (curves A and B respectively). Interestingly, the maxima of Fresnel reflection (curves A) exactly correspond to the synchronism conditions of −2nd and + 1st order plasmon coupling at the angles θ-2 and θ+1 whereas the −1st order maximum occurs midway between the two plasmon coupling conditions in the reciprocal space, at 22°, i.e., exactly at the −1st order Littrow θL angle at the wavelength of 633 nm (curves B). This means that by tilting the metal grating plane in the field of an incident plane wave there is a high contrast switching between the free space 0th and −1st diffraction order triggered by plasmon resonance excitation.
Fig. 3 Alteration of the angular reflection spectra with grating depth d as a parameter: a) d = 90 nm, b) d = 140 nm, c) d = 190 nm, d) d = 240 nm. Curves A, B and C correspond to the reflected 0th and −1st orders and to the balance respectively.
It is useful at this stage to write up the equations relating the three phase matching conditions of + 1st order and −2nd order plasmon coupling and the −1st order Littrow condition:
where and ne(λi) are the wave number and plasmon effective index at the coupling wavelength λi and θi the incidence angle in air at the coupling condition i = + 1, −2 and L.Applying conditions of Eq. (2) to Eq. (4) to the fixed wavelength angular scan of Fig. 3, curves A and B, gives k0+1 = k0-2 = k0L = k0 and ne(λ+1) = ne(λ-2) = ne, and provides the interesting relationships between coupling angles:
which means that the sinus of the plasmon coupling angles (i.e., the angle for maximum 0th order and nul −1st order) are equally distant from the sinus of the Littrow angle.Figure 4 shows curves A and B of Fig. 3(d) again with icons representing the state in the k-vector reciprocal space of each remarkable event of this plasmon-mediated coupling phenomenon. Very intriguing is the balance spectrum of curve C showing that, against expectation, the maximum absorption loss does not occur where the plasmon coupling condition is satisfied, but where it is not, i.e. at the maximum of the −1st diffraction order. That resonant plasmon coupling does occur at the angles of maximum 0th order is confirmed by the fact that the phase of the transverse magnetic field amplitude of the −1st order exhibits the π characteristical jump of a cross-over of a modal resonance at the angles of 16.4° and 27.8° whereas there is no trace of resonance at 22°. This quasi-lossless plasmon coupling feature raises interrogations which a planned coupled wave formalism will hopefully elucidate. Interestingly, curves C of Fig. 3(a) to Fig. 3(d) reveal that the absorption loss spectrum in the neighborhood of the + 1st order plasmon coupling transforms from the usual plasmon coupling loss maximum to the disappearance of the dip in the balance curve as the grating depth increases. Worth noting is the fact that the substitution of silver by aluminium shows the same switching effect with lower maxima, but the balance spectrum exhibits distinct dips (i.e. absorption maxima) where the + 1st and −2nd order plasmon coupling condition is satisfied (i.e. at the maxima of the 0th reflected order).
Fig. 4 Angular spectra of 0th (curve A) and −1st order (curve B) in the highest contrast structure (d = 240 nm) with corresponding icons in the reciprocal space. Curve C: balance spectrum.
If this switching effect occurs in the angular spectrum at constant wavelength as designed above, it also occurs in the wavelength spectrum at constant incidence angle θ0. This is illustrated for the same structure and the incidence angle of maximum 0th and −1st order diffraction efficiencies of 16.4°, 27.8° and 22° respectively in Fig. 5 (the 0th order amplitudes only are shown for sake of clarity) with the icons in the reciprocal space to identify the diffraction conditions in the spectral neighborhood of 633 nm wavelength. At the short wavelength side the spectra do not reveal any distinct feature since more diffraction orders propagate than the sole 0th and −1st orders according to Eq. (1). At 633 nm wavelength the 0th order is maximum at both plasmon coupling angles whereas in the Littrow condition at 22° incidence the 0th order is close to zero. All 0th order amplitudes tend to zero (consequently the −1st order tends to its maximum) at the long wavelength side; there is a sudden jump to 1 at a longer wavelength beyond the cutoff of the −1st order. Design rules can be derived from Eq. (2) to Eq. (4) in the case of a fixed incidence angle θ0 and a broad wavelength range in the following form:
Equation (7) and (8) are implicit equations for λ+1 and λ-2 since the effective index depends on the wavelength as the metal permittivity εm is strongly wavelength dependent. However, the wavelength dependance of ne is very weak and ne very close to 1 (about 1.03 in the case of silver in the structure designed above) which implies that an approximate spectral position of the 0th and −1st order maxima/minima can be safely obtained by setting ne = 1 in (7) and (8) (or nc if the incident medium has the refractive index nc).Fig. 5 Wavelength spectra of the 0th order under 16.4°, 22° and 27.8° incidence with corresponding icons in the reciprocal space.
3. Experimental demonstration
Whereas the description and design of the plasmon-triggered switching effect between 0th and −1st reflected orders was made above on the basis of a low-absorption metal to best reveal its characteristics, its experimental demonstration was made on the basis of aluminum instead of silver because it can be deposited by means of the roll to roll technology currently used in the application domain of security features. In addition, the operation point was shifted from the red to the blue spectral region for reason of application interest; the period and the depth of the grating were decreased accordingly. As a result, the expectable amplitude of the 0th and −1st orders is notably smaller: whereas the silver grating leads to maxima larger than 80%, aluminum reduces the maxima to less than 60%. The experimental structure was fabricated by printing an interferogram in a photoresist layer in its linear regime followed by the deposition of an aluminum layer of about 40 nm thickness. This thickness is large enough to prevent the occurrence of resonant transmission which in the visible range takes place between 15 and 20 nm thickness [5]. Figure 6 shows the AFM scan of the resulting metal grating of 500 nm period and 191 nm depth.
The measurement bench consists of a collimated wide spectrum source incident on the metallic grating at an incidence angle θ0 = 40° in air. Using expressions (7) to (9), and assuming ne = 1, gives the wavelengths at which the 0th and −1st order extrema are expected: λ+1 = 178 nm, λL = 643 nm, and λ-2 = 410 nm. It is clear that the + 1st order coupling must be discarded: with so large an incidence angle and so large a grating k-vector, the coupling can only be achieved with a very large Ewald circle radius, i.e., at so short a wavelength that the plasmon mode does not exist any more. As the measurement of the −1st order is difficult in the neighborhood of the Littrow condition, and its direction changes during the wavelength scan, it was decided to use the 0th order reflection of the TE polarization as a reference. The 0th order TE reflection does not exhibit any plasmonic effect. Its amplitude increases monotonically whereas the −1st order efficiency decreases as a consequence of the decrease of the depth/wavelength ratio. A polarizer was therefore introduced between the source and the grating allowing the variation of the polarization from TE to TM. A spectrometer measures the 0th and −1st orders in the wavelength range. Whereas the analysis of the plasmon-triggered switching effect was made in the angular spectrum at fixed wavelength, it was preferred to make the experimental demonstration in the wavelength spectrum at fixed incidence angle corresponding to the design Fig. 5 since the application aimed at is a security element of level 1 readable under white light. Fig. 7 gives the measured TE and TM spectra in the visible from 380 to 780 nm under 40° incidence.
Fig. 7 Measured and simulated 0th order spectra in the neighborhood of the −2nd order plasmon coupling. The −1st order maximum is expected at 643 nm wavelength. Grating depth is 190 nm and the period is 500 nm.
The measured TM maximum is present close to where it was expected; it is about 20% lower and broader than that expected theoretically. This is attributed to the light scattering resulting from the aluminium surface roughness as evaporated in industrial conditions.
Figure 8 presents different illustrations of the switching phenomenon in the wavelength spectrum which pertains to the domain of security features.
Fig. 8 Pictures of the plasmon-triggered switching effect in real color. a) TE-polarized reflected spot, b) TE-Polarized −1st diffraction order, c) TM-polarized reflected “blue” spot and d) TM-polarized −1st diffraction order.
The pictures of Fig. 8(a) and Fig. 8(b) show the 0th order reflection and the −1st order diffraction of the TE polarization respectively. Both spectra are monotonic and no trace of a switching effect between orders is observed. However the pictures Fig. 8(c) and Fig. 8(d) showing the reflection and the diffraction of the TM polarization exhibit a definite switching effect with the appearance of a blue “spot” on the reflection resulting from the −2nd order plasmon coupling in the blue part of the spectrum (see Fig. 7). One observes simultaneously the vanishing of the blue part of the −1st order diffraction spectrum.
4. Conclusion
The described and demonstrated switching effect between diffracted free-space waves triggered by plasmon coupling is interesting from several points of view. First, from a physical stand point, it is a very low-loss phenomenon although the surface plasmon coupling plays here a key-role. Secondly, the structure is very simple and easy to fabricate by industrial manufacturing technologies using sinusoidal grating hot- or UV-embossing followed by uniform metal deposition. Thirdly, it exhibits a high contrast between switched diffracted waves which implies that it is clearly visible by naked eye which opens to a wide range of applications in the field of security features. Fourthly, its spectral resolution of a few tens of nanometers due to the diffraction strength of the relatively deep grating makes it well adapted to white light processing and to LED light sources.
The designed and experimental structure has an air superstrate. In case the superstrate is a dielectric such as for instance a polymer overlay, the same phenomenon occurs. The same design rules apply in the Ewald circle where the k-vectors are simply multiplied by the superstrate index. Larger absorption losses are however expected since the plasmon absorption scales with the 3rd power of the overlay index.
A big issue remains: it is that of the interpretation of the effect on a the basis of a phenomenological model, first for sake of understanding how surface modes and diffraction orders couple, but also to have at one’s disposal a simplified but efficient mental tool for the design of further useful triggered optical functions. The development of a coupled mode formalism is in progress and will be reported once the phenomenological parameters it uses have been shown to remain relatively constant over a broad range of optogeometrical parameters.
References and links
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2. J. Sauvage-Vincent and V. Petiton, “Optical security component having a reflective effect, manufacture of said component, and secured document provided with such a component,” U.S. patent WO2013060817 A1 (Oct. 26, 2012).
3. MC grating softwarehttp://www.mcgrating.com/
4. L. Li, J. Chandezon, G. Granet, and J. P. Plumey, “Rigorous and efficient grating-analysis method made easy for optical engineers,” Appl. Opt. 38(2), 304–313 (1999). [CrossRef] [PubMed]
5. Y. Jourlin, S. Tonchev, A. V. Tishchenko, C. Pedri, C. Veillas, O. Parriaux, A. Last, and Y. Lacroute, “Spatially and polarization resolved plasmon mediated transmission through continuous metal films,” Opt. Express 17(14), 12155–12166 (2009). [CrossRef] [PubMed]
