Surface plasmon polaritons on nanostructured ...

,L *O4 Sept.Int. rcaM,!r lom

Conf. an Mathematical Methods in Electromagnetic Theory

14-17, 2004.

oniepropetrovsk, Ukraine

SURFACE PLASMON POLAFUTONS ON NANOSTRUCTURED SURFACES AND THIN FILMS A. V. Zavats', S. A. Darmanyad, D. Gcrard', L. Salomnn', F. d e Fornel'

' The Queen's University of Belfast, School of Mathematics and Physics, Belfast BT7 INN, United Kingdom 'Institute of Spectroscopy, Russian Academy of Sciences, Troitsk 142092, Moscow region, Russia

Laboratoire de Physique de I'Universitb de Bourgogne, CNRS UMR 5027, B.P. 47870,21078 Dijon, France E-mail: [email protected]

- Surface plasmon polariton behaviour on periodically nanostructured metal surfaces and thin films is discussed. Such metallic nanostructures act as polaritonic crystals for surface polaritons, in analogy to photonic crystals for light waves. In this paper surface polariton Bloch mode spectrum on the structured surfaces and films is overviewed and manifestations of various surface plasmon modes in the optical properties of metallic nanostrnctures are considered. Surface plasmon polaritons m e emerging as a new optical information carrier that enables signal manipulation and processing on the subwavelength scale and development of integrated photonic circuits.

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1. INTaODUCTION

Optical functionality of metallic nanostructures is determined by the interaction of photons with collective excitations of conduction electrons at a metal surface. Surface plasmon polariton (SPP) is an electromagnetic excitation on the surface of good metals that consists of a surface plasmon, itself a collective excitation of electrons close to a metal surface, and a photon. SPPs play a crucial role in optical propelties of randomly rough and artificially structured metal surfaces and films, such as reflection, transmission, scattering, second-harmonic generation, surface enhanced Raman scattering, etc. [I]-[4]. Two-dimensional optics of surface polaritons on metal interfaces has been developed that provides tools to manipulate and direct SPP waves on a surface in analogy to light beams in three-dimensional optics [3]. Very recently, short-wavelength SPPs which exist at optical frequencies have been used to demonstrate nanoscale imaging of surface structures in the far-field, breaking the resolution limits of conventional microscopy [ 5 ] . An important class of metallic systems for optical applications is based on periodically nanostructured metal films. Such metallic nanostmctures have been considered for applications as nanoscale surface-plasmnn-based sensors, for the enhancement of nonlinear optical processes and can lead to the development of all-optical photonic circuits where they can be used as passive as well as active photonic components [3]. Behaviour of surface plasmon polaritons on a periodically structured surface is governed by the same rules as of electron behaviour in a crystalline lattice or photons in a periodic structure such as a photonic crystal. In analogy, a nanostructured metal surface or thin film can be considered as surface-polaritonic crystal. The optical properties of such SPP crystals are determined by surface polariton behaviour in a lattice formed by a nanostructure on a surface. Among the optical phenomena related to SPPs on periodic surface structures are resonant absorption, reflection as well as enhanced transmission of light through metallic films [6]-[10], polarization conversion during couplingtdecoupling of photons to surface polariton modes [I I], nonlinear optical effects at low light intensities [12]. All these phenomena are in one or another way related to the SPP Bloch modes formed on a periodically structured surface. Very recently, analytical descriptions of surface polariton states on periodic surfaces and films were developed [9],[13],[14]. This resulted in understanding of the role of the SPP states related to different branches of the Brillouin zones in photon tunnelling through a metal film. The exact knowledge of the electromagnetic mode structure was used to describe near- and far-field properties of the transmitted light. In this paper surface polariton modes on periodically nanostructured metal surfaces and thin films are overviewed in relation to various optical properties of metallic nanostructures. Surface plasmon polaritons are emerging as a new optical information carrier that enables signal manipulation and processing on the subwavelength scale. This suggests the possibility of building a new class of photonic devices and development of all-optical integrated photonic circuits. Numerous applications can be envisaged in classical and quantum optical information processing and optical communications.

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lotbInt. Conf. an Mathematical Methods in Electromagnetic Theory Sept. 14-17.2004. Dniepropetrovsk, uktaine

11. RESULTS AND DISCUSSION

A . Surface Plasmon Polariton Modes Let us consider a smooth metal film surrounded by dielectric media. Surface polaritons existing on the interfaces of the system have the wavevector kspexceeding the wavevector of light in the adjacent dielectric and cannot be directly excited by conventional illumination of the surface. The SPP dispersion (Fig. I a) on a smooth surface is given by [11,[21

where F, and E, are the dielectric constants of metal and adjacent dielectric, respectively, w is the light frequency and c is the speed of light in vacuum. In order for SPPs to be excited in such a system, the wavevector of the illuminating light must match the wavevector of the electromagnetic surface mode which is greater than that of the incident photons and must have an electric field component parallel to SPP propagation direction or perpendicular to the surface: (E .kspf 0). The latter requirement is due to the fact that SPP has both transverse and longitudinal electric field components.

photon surface plasmon surface polariton

-4xm -2nm 0 2 x l D 4xm kll kii Fig. 1. (a) The dispersion of surface plasmon polaritons on a smooth metal surface (solid line), surface plasmon frequency (dotted line), and photon dispersion in adjacent dielectric (dashed line). @) SPP dispersion on a periodically structured surface (period 0).the dispersion of SPPs on a smooth surface is shown with dotted lines. The light cone is shown by dxhed lines

When a periodic modulation of the refractive index or topographic profile is created on a metal surface of the order of SPP wavelength, a band gap is opened up in the SPP dispersion curve (Fig. 2 b). The SPP propagation through a periodic stmcture leads to the same effects as for electrons propagating through a crystal lattice or photons propagating through a medium with a periodically modulated refractive index, namely, to modification of their dispersion law wsp(ksp) and the band-gap effects [15],[16]. In analogy to photonic crystals, a periodically structured interface can be considered as a surface polaritonic crystal. The SPPs with the wavevector k,,> d n d c being true surface electromagnetic excitations have an infinite lifetime (with respect to decay in photons), while the SPPs with wavevector falling into a light cone are believed to be radiative modes because they can couple to light. Diffiction of light by the periodical structure provides the increased wavevector required for SPP excitation: 0

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D

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+q--uy,

D

where n, is the refractive index of the medium through which the surface is illuminated, Bis the angle of incidence, = I or 0 for p- or s-polarized incident light (with respect to the sample surface), U, and uv are the unit reciprocal lattice vectors of the periodic structure, D is the periodicity (same in both x and y directions) and p and q are integer numbers corresponding to different directions in the SPP Brillouin zone.

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MMf!T*04

10m lnt. Conf. On Mathematical Methods in Electromagnetic Theory

Sept. 14-17, 2004. Oniepropetmvsk,

Ukraine

B. Optical Properties ofMetal Films Related to SPP BIoch Modes In the general case of a finite thickness metal film, the SPP modes can be distinguished hy their origin as film SPP modes: e.g., for symmetric surroundings, the lower energy f mode with the symmetric electric field distribution in a film and the higher energy antisymmetric mode f. Both these modes will he split into the set of the Bloch modes with lower ( 8 3 and higher (g.) frequencies at the edges of the Brillouin zones. If we consider a periodically structured surface illuminated at normal incidence 8= 0, the only SPPs in the vicinity of even-numbered band-gaps (second, forth, etc.) can be excited directly with light (Eq. 2). These SPPs correspond to standing SPP-Bloch waves on a periodic surface. However, conservation of energy and momentum, or in other words, matching the frequencies and wavevecton of SPPs and photons that takes place in the light cone (Fig. 1 b), is not sufficient condition for SPPs to be directly excited by (or converted to) light [9]. There is a very important difference between frequencies of the top and bottom edges of the SPP bands at ksp = 0. For example, in the case of a weak periodic modulation of the refractive index of the film, the frequencies w. corresponding to the top edges of the allowed bands (g+) are complex-valued. In contrast, the frequencies wb corresponding to the bottoms of the allowed hands ( g ) are completely real (if Ohmic losses in metal are neglected) [9]. It means that SPPs at frequencies ob have an infinite life-time and do not interact with light directly. Thus, only SPPs with frequency w. participate in the resonant interaction with the illuminating light at normal incidence. Depending on the origin of the periodic modulation, radiative and non-raditaive SPP Bloch modes can correspond to different Brillouin zones [16]. Such properties of SPP Bloch modes have important consequences for understanding optical properties of periodically structured metal films, since the spectra of the SPP resonances determine the spectral dependencies of absorption, reflection, and transmission of nanostructured metal films [7].

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Fig. 2. Reflection (a), absorption (b), and transmission (c) spectra ofthe periodically nanostructured silver film at different angles of incidence: (black) 0 = O", (dark grey) 9 = lo, (light grey) 0 = 2', (prey) 0 = 4". The srmcfure consists of the silver ridges (h=20 nm,d=250 nm and D=500 nm) on both film interfaces. (let?) Weak coupling regime (film thickness H=100 nm) and (right) strong coupling regime (H=40nm). Let us consider optical properties of a free standing metal film in air with the metal ridges on both film interfaces. Such a system can he numerically modelled using the modified differential method [lO],[17]. Relatively thick films (weak coupling between film SPP modes) exhibit only one peak in reflectiodahsorption in the spectral range corresponding to the lowest (first) dimaction order of light coupling to the SPP modes on the grating, while thinner films (strong SPP coupling) have two different peaks related to the film SPP modes f' and f . At normal incidence these SPP modes are the standing Bloch waves corresponding to the top edge of the second Brillouin zone (g'). For a relatively thick metal film, the interaction between the SPP modes on the opposite film interfaces is weak and the position of the resonances observed in reflection, absorption, and transmission corresponds well to the band-gap edge which lies on the long-wavelength side of the SPP resonance of a smooth single surface (Fig. 2). These numerical simulations confirm that even when the realistic Ohmic losses are taken into account, the g- SPP Bloch mode is only weakly coupled to photons. At oblique illumination, photons can efficiently interact with both branches of the SPP Bloch waves near the hand-gap, and

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Int. Conf. on Mathematical Methods in Electromagnetic Theory MMM ;"*po4 Sept. 14-17. 2004. Dniepropetrovsk. Ukraine

two peaks are observed in the spectra on both sides from the peak that was seen at normal incidence. The same as in the case of normal incidence, at the wavelengths of resonant transmission, the reflection has minimum while the absorption has maximum. The difference in the transmission amplitudes and the peak width at the frequencies of lower and upper SPP Bloch modes at oblique incidence is mainly related to different densities of the SPP states and Ohmic losses at the respective wavelengths. This also explains why the difference in the transmission peak amplitudes associated with different Bloch modes increases with the angle of incidence.

Fig. 3. The magnetic field distribution in the near-field region of the metallic smchlre at the wavelengths correspondingto (a) f g ~ ( I = 493 nm). (b) fg* ( I = 555 nm), (c) fg' - (A. = 527 nm), and (d) fg' ( I = 579 tnn) film SPP Bloch modes around the respective second-band gaps in a strong-couplingregime. Angle of incidence is I3 = 4'. The parametres of the struchlre are the same as in Fig. 2 (right). Geometry of the film is also shown. The field distributions above the structure show that the strongest near-field is related to the edges of the ridges (Fig. 3). The near-field of the g'mode is much stronger close to the surface and has longer extension range in the dielectric compared to the g--mode [17]. This g* SPP mode provides stronger far-field transmission (Fig. 2 c). For both modes the near-field transmission is significant above ridges as well as groves of the grating. For the film SPP Bloch modes in different Brillouin zones, the film mode symmetry is superimposed on the respective Bloch mode symmetries. This can be clearly seen from the near-field distributions in the case of a strong coupling when all 4 SPP modes are significantly separated (Fig. 3, cf. Fig. 2, right). The comparison of the near-field intensities at the resonant wavelengths with the far-field transmission shows the difference in the near-field and far-field transmittance related to the different strength of SPP coupling to photons. For example, the fg' mode provides highest far-field transmission but the strongest near-field is associated with the fgf mode probably due to smaller losses associated with this antisymmetric (in electric field) SPP mode. The symmetry of the near-field distributions corresponds to the symmetries of the film SPP Bloch modes in different Brillouin zones (Fig. 3): the magnetic field is symmetric with respect to the film plane for f-modes (antisymmetric Efield) and antisymmetric for f-modes as should be expected, at the same time for both film SPP modes there is a phase difference between the g- and g' Bloch modes corresponding to different Brillouin zones. In a strong coupling regime, the crossing of film SPP Bloch modes may occur at the certain angle of incidence. The angle of incidence at which the crossing takes place depends on the film thickness and the grating parameters. The crossing leads to the interplay between the two modes of different symmetries and opposite phases so that the outgoing fields are tend to cancel each other, and null far-field transmittance accompanied by the increased absorption is observed at the crossing wavelength (Fig. 2, right, 0 = 2') [14],[17]. With the further increase of the angle of incidence, the states of the SPP Bloch modes become again separated and the related transmission resonances are observed again. In spite of the significant near-field transmission (the field in the vicinity of the interface opposite to the illuminated one) since the SPP modes are efficiently exited on both film interfaces, there is no far-field radiation at the crossing frequency: the field intensity above

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MM($pod 10’”Int. Conf. on Mathematical Methods in ElecfmmagneticTheow ,\\\

Sept. 14-17, 2004. Oniepropetrovsk, Ukraine

the Structure rapidly decays from the surface at the distance shorter than a wavelength. Physically, this can be understood considering opposite phases of the two SPP modes on the interface: each of them is coupled to the outgoing far-field wave, however, due to the difference in the phase, the outgoing fields cancel each other in the far-field region. The intensity distribution across the surface has 2-fold symmetry over the period of the structure confirming that the two competing SPP Bloch modes are completely identical (in the case of non-zero far-field transmittance, the intensity distribution is periodic only with the period of the structure). In the absence of radiative losses, these SPP modes propagate on the surface until converted into heat due to Ohmic losses, thus leading to the increased absorption observed at the crossing frequency. The crossing does not results in the additional band-gap formation (anti-crossing) since the symmetries of the involved SPP modes are different. In the case of a strong coupling regime, the film SPP Bloch modes have different symmetries associated with (i) the branches of the g’ and g- SPP Bloch modes having different field distribution across the surface and (ii) the film SPP modes f and f with symmetric and antisymmetric field distribution in the film. Generally, g’ and gmodes cannot coexist at the same frequency and this is the origin of the band-gap in the SPP spectrum. However, different film SPP Bloch modes characterised by symmetries f g + and f g - can exist at the same frequency because the two Bloch modes are related to different film SPP modes. It should be noted that the lower frequency SPP Bloch mode branch g’ has a negative refraction index (do/dksp