OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 26 — Dec. 24, 2007
  • pp: 17863–17873
« Show journal navigation

Optical transmission through single subwavelength apertures using prism coupled input of laser light of annular intensity profile

L. Feng and P. Dawson  »View Author Affiliations


Optics Express, Vol. 15, Issue 26, pp. 17863-17873 (2007)
http://dx.doi.org/10.1364/OE.15.017863


View Full Text Article

Acrobat PDF (319 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Light transmission through a single subwavelength aperture in a silver film is examined with a novel input configuration comprising an annular laser beam of variable diameter that is prism-coupled to the back face of the silver. Transmission peaks driven by excitation of the back-face surface plasmon mode or by the aperture resonance itself are separately observed. For both cases, comparison of films with and without a front-face, circular grating implies significantly more efficient coupling from the aperture fields to the front-face surface plasmon than directly to free radiation.

© 2007 Optical Society of America

1. Introduction

The transmission of electromagnetic radiation through sub-wavelength apertures has been a topic of some historical fascination [1

1. H. A. Bethe, “Theory of diffraction by small holes,” Phys, Rev. 66, 163–182 (1944). [CrossRef]

,2

2. C. J. Bouwkamp, “On Bethe’s Theory of Diffraction by Small Holes,” Philips Res. Rep. 5, 321–332 (1950).

]. Researchers wrestled with the practicalities of the issue as various forms of near-field optical microscopy were developed during the 1980’s and 1990’s [3

3. M. A. Paesler and P. J. Moyer, Near field optics: theory, instrumentation and applications (John Wiley & Son, 1996), Chap. 3.

]. However, it was not until the observation of extraordinary transmission of visible wavelength light though a regular array of sub-wavelength holes by Ebbesen et al. [4

4. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

], almost a decade ago, that a significant wave of interest was sparked. Since then there has been considerable activity in both experiment and theory [5

5. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007). [CrossRef] [PubMed]

]; in this development the roles of surface plasmon polaritons (SPPs) on both the input and output faces of the film as well as that of localized surface plasmons (LSPs) associated with the aperture itself have been highlighted. Applications of sub-wavelength holes in basic optical componentry (e.g. filters, light input/output couplers), high resolution lithography and data storage, imaging and spectroscopy are envisaged.

2. Experiment

Since the innovation in this work has much to do with the experimental set-up we present a reasonably detailed description with the aid of Fig. 1. The scheme contrasts with all previously employed set-ups for transmission through sub-wavelength holes in that a planar, thin-film optical coupling arrangement, effectively an Otto coupling configuration [14

14. A. Otto, “Excitation of non-radiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398 (1968). [CrossRef]

], is used on the input (see Fig. 1). In this scheme, light incident through a Weierstrass prism (this is detailed further below) couples to a SPP mode that propagates towards the nanoaperture. This SPP mode is supported on the ‘back’ or input surface (MgF2/Ag interface) of the sample which comprises a Ag film grown on a low-index layer (MgF2) deposited on a high-index substrate (nS=1.840). Moreover, a crucial and novel feature of the design is that, instead of filling the entire input cone with light in the coupling prism, of which only a very small proportion would couple to the SPP, the laser light is formed into an annulus, the diameter of which can be varied, so that it can be selectively fed in at the SPP coupling angle, θSPP. (Note, however, that since the input laser beam is linearly polarized (E-field horizontal) the conditions for SPP excitation vary from optimal to zero, from horizontal to vertical sections through the beam, limiting the overall efficiency for conversion to SPPs to a theoretical maximum of 50%.) Light emerging from the aperture etched in the Ag film is then collected and detected as a function of the internal angle of incidence in the prism. Since SPPs on the Ag/air interface may be excited through coupling with the aperture, use is also made of a circular grating pattern, milled concentrically with the aperture on the ‘front’ or output face of the Ag film, to couple these SPPs to light. This is essentially the beaming arrangement discovered by Lezec et al. [13

13. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002). [CrossRef] [PubMed]

].

Fig. 1. Schematic of experimental set-up to produce laser beam of annular section which is fed to the sample via a focusing lens pair and a hyper-hemispherical or Weierstrass prism. Inset shows detail of prism coupling arrangement to excite the surface plasmon polariton mode on the Ag/MgF2 interface of the sample.

For the most part, the system was constructed from low-cost optical components and available items of equipment in the laboratory. Nonetheless, the principle of operation of the coupling scheme is conclusively demonstrated, opening up a new means for the examination and exploitation of transmission through sub-wavelength apertures. The set-up is now described from source to sample. The source is a HeNe laser (Melles Griot 05-LHP-121) which gives a plane-polarized output at wavelength, λ=632.8 nm. The laser beam is first passed through a mechanical chopper and then formed into an annulus by reflection from an external (male) and then an internal (female) cone mirror which are concentrically mounted on the optical axis of the system; both cone mirrors have a half-angle of 45°. As shown in Fig. 1 the beam is incident on the external cone mirror (Edmund Optics) through a hole in the centre of the large internal cone mirror. The position of one cone mirror, relative to the other, along the direction of the optical axis, determines the radius of the annulus which, in turn, determines the internal angle of incidence (in the prism) on the sample. Here the angle of incidence is scanned by translating the small cone mirror along the optical axis using a stepper motor stage. The small cone-mirror itself is glued, via a stand-off rod, to an anti-reflection-coated window so that the entire annulus is transmitted, with no segment obscured by a mounting post. Internal cone mirrors are not commercially available, so that used here was machined from a block of brass and fine polished in the university workshops.

The annulus is then focused on to the back of the sample through a set of two lenses, a plano-convex lens and a positive meniscus lens, of focal lengths 85mm and 100 mm respectively and the Weierstrass prism. The focal point of these lenses, denoted as F2 in Fig. 1, is also the secondary focal point of the Weierstrass prism – rays propagating towards F2 in free space will be focused onto the centre of the plane face of the prism at focal point F1 which is a distance (R + R/np) from the point lying at the intersection of the curved surface with the axis of symmetry of the prism, where R is the radius of the basic hemisphere and np is the prism refractive index. The prism, supplied by Gooch and Housego, was formed in LaSFN9 (refractive index, np=1.845 at 632.8 nm). There is one further, important point of refinement to this arrangement which is that the effective Weierstrass prism in fact comprises a hyperhemisphere prism of axial dimension (R + R/np-1.2) mm and a flat SFL57 substrate (6 mm diameter×1.2 mm thick, ns=1.840) with index matching fluid in between. The flat substrate is manipulated relative to the prism by a manually-actuated, kinematic stage (Melles Griot NanoMax-HS) with x-y-z and angular adjustment (roll, tilt and yaw) motion. The advantage to this arrangement is simply that an indefinite number of samples formed on disposable SFL57 substrates may be fabricated and examined using the same hyperhemisphere prism, rather than using a relatively expensive prism as the substrate for each sample. This Weierstrass scheme is essentially that which has been used in the context of SPP microscopy [15

15. J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter, and S. G. Liu, “Wide-field surface plasmon microscopy with solid immersion lens,” Appl. Phys. Lett. 85, 5451 (2004). [CrossRef]

], in preference to the ‘solid immersion lens’ or full Weierstrass prism [16

16. J. Zhang, M. C. Pitter, S. Liu, C. See, and M. G. Somekh, “Surface-plasmon microscopy with a two-piece solid immersion lens: bright and dark fields,” Appl. Opt. 45, 7977 (2006). [CrossRef] [PubMed]

] and for exactly the same reason. The matching fluid is a non sulphur-containing polymer-based liquid, SL5267 from NuSil with a refractive index nmf=1.66(8) (25°C, 632.8 nm). The lack of an exact index match between the fluid and the prism and indeed between the prism and the flat substrates did not prove problematic.

Light emerging from the aperture in the Ag film is collected by a drum lens and input to a silicon photodiode; phase sensitive detection is used. Both components are held, along with the sample, on the manipulator stage. The prism is held and manipulated independently from a mount on the main optical rail. The results are presented in the form of a transmitted intensity signal versus internal angle of incident in the prism which is calculated from the radius of the annular input beam which is calibrated back to the position of the small conical mirror along the optical axis.

Fig. 2. (a) FIB image of a Ag sample with central hole and circular, concentric grating pattern. (A 4-ring sample is shown but the samples used in Figs. 4 and 5 had an 8-ring pattern). b) Cross-sectional sketch of fully structured Ag sample with tAg=180 nm; all dimensions are in nm, unless otherwise indicated.

Guidance in relation to the thickness of the MgF2 layer was based on modeled reflectance curves for planar structures. Figure 3 shows the reflectance of p-polarized light for the case of the prism separated from optically thick Ag (tAg=180 nm) by different thickness layers of MgF2. A 400 nm thickness of MgF2, yielding close to optimal coupling to the MgF2/Ag SPP mode, was chosen as the standard thickness for all experiments; the s-polarized reflectance curve is also presented for this case. The equivalent reflectance curves for tAg=350 nm effectively overlie those shown for tAg=180 nm.

Fig. 3. Calculated reflectance of p-polarized light versus internal angle of incidence in the prism for planar system, prism/MgF2/Ag (180 nm thick) for various thicknesses of MgF2. Reflectance of s-polarized light for the case of a 400 nm thick layer of MgF2 is also shown.

Considerable care must be taken to align all the components with respect to the optical axis. For samples with an aperture, light was input at θSPP and the sample position finely adjusted with the manipulator in order to optimize the transmitted signal. In order to check the size of the focal spot a Ag sample with a linear array of 9 holes of diameter 300 nm and spacing 100 µm was scanned manually along the line of the holes using the manipulator. The signal from each hole had a spatial diameter of ~10–11 µm (to the 1/e intensity points). This does not correspond to a diffraction limited spot size and is determined by the quality of the input optics, most notably the conical reflectors and the input face of the prism.

3. Results and discussion

In the investigation of Degiron and Ebbesen [12

12. A. Degiron and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694 (2004). [CrossRef] [PubMed]

] on the optical transmission of sub-wavelength apertures in free-standing metal films with a grating pattern on just one or on both sides, the transmission was analyzed in terms of a three-step process – 1) the collection of light on the input face, 2) the transmission of electromagnetic energy through the hole and 3) the outcoupling to free electromagnetic radiation on the output face of the sample. This is a useful initial framework for considering the results presented here. Figures 4 and 5 show graphs of transmitted intensity versus internal angle of incidence for two sets of samples with tAg=180 nm and 350 nm respectively. The first feature to note is the peak at θSPP ~53.5° for the fully structured samples. This corresponds to the excitation of the SPP mode at the MgF2/Ag interface – see Fig. 3. There is a second large peak in the case of the tAg=180 nm sample which we consider to be due to a resonant mode of the hole itself, as discussed later.

Fig. 4. Transmitted signal intensity as a function of internal angle of incidence for various sample structures, as shown. Silver film thickness, tAg=180 nm in all cases, hole diameter, d=300 nm, grating period and depth are 600 nm and 90 nm respectively.
Fig. 5. Transmitted signal intensity as a function of internal angle of incidence for various sample structures, as shown. Silver film thickness, tAg=350 nm in all cases, hole diameter, d=300 nm, grating period and depth are 600 nm and 90 nm respectively.

Focusing first on the tAg=180 nm sample, it is clear that there is significant transmission when the SPP mode on the input face of the Ag film is excited. The baseline for comparison is the planar, unpatterned thin film which shows a small peak in the region of 53.5°; this would appear to indicate a background coupling of the MgF2/Ag SPP mode through the film and subsequent scattering to radiation, possibly due to residual roughness of the film surfaces. With a grating pattern on the outer surface of the film the overall level of transmission is increased, including a small feature at θSPP. The general level of signal increase across the angle range is interpreted as due to a small amount of cross-talk between the sample surfaces since the film is only ~90nm thick at the bottom of the grating grooves. Specifically, at θSPP there is the possibility of grating coupling from the SPP mode at the MgF2/Ag interface directly to radiation on the air side of the sample – light thus scattered will fall comfortably within the detection cone angle. The coupling of electromagnetic energy through the film occurs primarily over the area of the grating surface, ~77 µm2.

With the introduction of only a hole in an otherwise planar Ag film there is a more marked change in the transmission than with just a grating pattern only. The peak at θSPP is ~5 times more intense than that for the planar film and 2–3 times more intense than for the grating-only case. The transmission properties of the hole at θSPP are very evident when relevant areal considerations are taken into account. For the case of the thin, planar film, coupling of energy through the film will take place across the entire area of the focal spot ~95 µm2 and for the grating-only surface the relevant area is ~77 µm2 while for the case of the hole the geometrical area is ~0.07 µm2. The transmission enhancement per unit area for the hole is thus a factor of 5-7×103.

Perhaps the most remarkable feature is the increase in intensity observed when both a sub-wavelength aperture and a circular grating pattern are present. This amounts to a further factor of almost 5 increase relative to the hole-only case. (This factor is >6 with background subtraction but might be smaller if it is argued that there is strong forward beaming in the case of the hole + grating while in the hole-only case some of the light escapes detection outside the ±45° detection cone angle.) Since the input coupling and transmission of energy via the hole (i.e. steps 1 and 2 in the 3-step process) are the same or very closely similar in the two cases, this implies strong coupling between the fields associated with the hole and the SPP mode on the output surface of the sample. Indeed, it appears that coupling to the front-face SPP is strongly preferred over coupling directly to free radiation and that the bulk of the energy conveyed via the aperture is only effectively radiated in the presence of a grating.

Since the collection and outcoupling conditions (steps 1 and 3) are the same for the tAg=180 nm and tAg=350 nm samples (the MgF2 spacer thickness, hole diameter and grating dimensions are nominally the same in each case) the decrease in transmitted intensity is, in the 3-step model, clearly associated with the transmission function of the aperture itself. If an exponential decay of the signal, I, with sample thickness (taken to be equivalent to hole depth, h) is assumed then the characteristic intensity decay length, ho, is:-

ho=(h2h1)ln(I1I2)135nm
(1)

or, equivalently, the field skin depth, δ, is 270 nm or a factor of >10 greater than the intrinsic skin depth (23.5 nm) of the host material. This assumes peak intensity measurements with background signal subtraction. If the integrated intensity of the peaks is used then the figure for δ drops to ~170 nm on account of the significantly greater width of the thin film peak.

Consider now the transmission peak below 50° for the tAg=180 nm thick sample. This does not correspond to any resonant input of energy (see Fig. 3) and we attribute it to the excitation of a resonant Fabry-Perot-like mode of the aperture itself. While the response of the plain film and grating-only film is flat in this region, there is noticeably more response for the hole-only film and a very significant transmission for the film with hole + grating. The fact that the broad peak for the hole-only sample is at a lower angle than the main peak is probably due simply to a slightly different hole geometry in a different sample. As with the peaks associated with the SPP mediated input, the transmission is greatly enhanced with the presence of the grating on the output surface, again implying significantly stronger coupling of the resonant hole mode with the front-surface SPP than with free radiation. The situation with the tAg=350 nm sample is less clear-cut; while a higher signal is generated in films with a hole there is no clearly defined single peak for θ<50°.

It is thus clear that communication between the two faces of the sample can be established for λ>2d, as was evident in earlier experimental [22

22. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength apertures,” Appl. Phys. Lett. 81, 4327–4329 (2002). [CrossRef]

] and theoretical [23

23. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

] work on hole arrays where particular attention was focused on the h-dependence of the transmission. In fact, two regimes were noted. At higher thickness (h>300 nm) the field skin depth, δ, was of the order of 180 nm (with d=300 nm) in a suspended metal film [22

22. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength apertures,” Appl. Phys. Lett. 81, 4327–4329 (2002). [CrossRef]

]. For h<300 nm approximately, the h-dependence was noted to be very weak and the transmission peaks became broader. This latter regime bears comparison with the case of transmission through a single aperture with d=270 nm where SPP assisted input and output is operative in free standing samples with grating patterns on both faces [12

12. A. Degiron and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694 (2004). [CrossRef] [PubMed]

]; a value of δ~800 nm applies between the h=200 nm and 340nm films of that study. (It was, however, a main claim of ref. [12

12. A. Degiron and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694 (2004). [CrossRef] [PubMed]

] that there was only one exponential regime as a function of h). The comparable value from this study, based on peak transmission values at h=180 and 350nm, is δ=270 nm which lies between the values cited above.

The two regimes were explained as follows in the context of hole arrays [22

22. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength apertures,” Appl. Phys. Lett. 81, 4327–4329 (2002). [CrossRef]

,23

23. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

]. For the low-h case the SPP modes couple via a resonant aperture mode leading (for a given value of wavevector parallel to the surface) to an energy splitting or lifting of the degeneracy of the SPP modes at each interface. The broader, lower energy mode of the coupled system dominates the transmission spectrum. At resonance this is really a standing wave mode – and in that sense is localized - characterized by strong coupling, a weak h-dependence and thus a large value of δ. (The higher energy mode was not observed [22

22. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength apertures,” Appl. Phys. Lett. 81, 4327–4329 (2002). [CrossRef]

]). This type of symmetrically bounded (suspended) film case was referred to as a “homopolar plasmonic molecule” [23

23. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

]. For large h the SPPs at the two interfaces remain uncoupled with each other and communicate only via exponentially decaying evanescent fields associated with the hole. This is essentially an optical tunneling regime, characterized by exponential decay with increasing h and smaller values of δ, as well as a narrower spectral width, characteristic of the uncoupled SPP single-interface modes.

Consider first the transmission peaks due to the SPP-mediated input in the results presented here. We posit that the peak in the large-h case (Fig. 5) is due to optical tunneling between the SPP modes at each interface as described in refs. [22

22. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength apertures,” Appl. Phys. Lett. 81, 4327–4329 (2002). [CrossRef]

] and [23

23. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

]; this is more clearly evidenced by consideration of the peak width described below. The main contrast concerning the films in this work as opposed to those discussed above [12

12. A. Degiron and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694 (2004). [CrossRef] [PubMed]

,22

22. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength apertures,” Appl. Phys. Lett. 81, 4327–4329 (2002). [CrossRef]

] is that they are supported on a substrate and are thus asymmetric in nature. Although the unperturbed SPP modes on each interface have different energies (for a given value of wavevector) there is, nonetheless, the possibility of coupling for this case also i.e. the “heteropolar plasmonic molecule” of ref. [23

23. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

]. The asymmetric case was treated in some detail, both theoretically and experimentally by Krishnan et al. [24

24. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200, 1–7 (2001). [CrossRef]

]. While they found that there is clear advantage (i.e. the transmission is greatly enhanced) in matching the SPP modes on each interface (symmetric case) the coupling persists towards the asymmetric case. We consider that this phenomenon offers an explanation of the SPP-driven mode observed in the case of the tAg (=h)=180 nm thick film, but suggest that such coupling is established only at lower values of h than for the symmetric film case, which would account for our intermediate value of δ.

The strong transmission peak at ~45° for the hole + grating sample of Fig. 4 is considered due to a resonant mode of the aperture, essentially a Fabry-Perot-like mode, strongly coupled with the front-surface SPP mode, but there is no driver SPP on the back surface; in the language of ref. [23

23. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

] this might be regarded as a dangling bond plasmonic atom. The corollary is that the transmission peak at θSPP actually represents either an off-resonance coupling between the asymmetric SPP modes on each interface, involving the same mode as at ~45° [24

24. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200, 1–7 (2001). [CrossRef]

], or that it involves another mode of the hole. We favor the former scenario since one might expect a somewhat greater intensity with resonant energy input combined with resonant aperture mode coupling.

The physical interpretation presented above, based on a consideration of the angular positions of the transmission peaks and of the field skin depth, δ, is corroborated by a consideration of the widths of the spectral peaks. The transmission peak at 45° is relatively broad (FWHM=2.4°). The aperture mode itself may be of this angular width but there is also required a strong coupling regime – a coupled mode of the system as a whole – to yield the overall angularly broad resonances (at fixed wavelength) of Fig. 4, analogous to the spectrally broad features of refs. [12

12. A. Degiron and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694 (2004). [CrossRef] [PubMed]

] and [22

22. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength apertures,” Appl. Phys. Lett. 81, 4327–4329 (2002). [CrossRef]

] and other work. A simple product of the back-surface collection, hole transmission and front-surface emission functions would yield a width determined predominantly by the function with the smallest angular width – note that the FWHM for the SPP dip of Fig. 3 is 0.6°. Experimentally, a large angular width of the hole resonance may be due to an imperfect, e.g. tapered, hole structure. By contrast, for the tAg=350 nm sample the SPP modes at the interfaces can interact via evanescent fields in the hole (tunneling) but there is no strong cross-coupling and they remain as distinct modes. In this regime, which we suggest onsets at a smaller h-value for asymmetrically bounded samples, a sequential view of the collection, transfer via the hole – with exponential decay of the transmission with increasing h - and re-emission is more appropriate. The transmitted intensity is weaker and the FWHM (0.85°) of the transmission peak is much closer to that of the SPP modes on the interfaces. Indeed, it could be argued that the lack of a distinct low-angle transmission peak due to a Fabry-Perot-like mode and the nature of the SPP-mediated transmission resonance are causally linked. In the tunneling picture the large-h case is associated with single sequential tunneling events where the time to build up a resonant mode of the hole is less than the intrinsic radiative decay time of the single interface SPPs; for low-h the reverse is true and a multiple pass of a trapped photon state in the hole leads to the development of a resonant mode of the hole analogous to resonant electron tunneling [23

23. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

]. The alternative in the large-h case of a coupled mode of the system involving a better-defined, angularly narrow hole resonance seems less plausible [22

22. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength apertures,” Appl. Phys. Lett. 81, 4327–4329 (2002). [CrossRef]

24

24. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200, 1–7 (2001). [CrossRef]

].

A further point in relation to the transmission peak at ~45° in Fig. 4 is the question of how its intensity matches that of the peak at 53.5° for which the energy is fed towards the hole by a SPP excitation. In addition to the coupling issues discussed above, it should be noted that in the planar film calculation of Fig. 3 the high reflectance in the region of 44°–46° is due primarily to the presence of the metal film – the transmission across the substrate/MgF2 interface in this sub-critical-angle range is 0.81 - 0.71 and 0.97 - 0.91 for s- and p-polarized light respectively. The incident light can thus interact significantly with the hole region of the sample. In addition, the input should take place over an area larger than the geometrical footprint of the hole.

4. Summary and conclusions

We have presented a novel scheme for examining the transmission of subwavelength apertures that combines a thin-film planar input geometry with a wavelength-scale diffraction grating and the sub-wavelength aperture element itself. Not only does it constitute a new means for analytical study but it offers a route to optimizing the efficiency of these fascinating, passive nano-optical elements. Firstly, it allows the role of the collection or input stage to be de-convoluted from the rest of the transmission process on a given sample, that is to say the coupling of light into the aperture can be switched from non-resonant input to resonant modes of the input structure simply by varying the angle of incidence. The response of hole-only or hole + front-surface-grating samples can thus be studied under three contrasting input conditions – SPP input, guided wave input (this simply requires a thicker-low index coupling layer (MgF2) than that used here) and non-resonant input – while all other parameters of the system remain identical. In this initial study we have tackled only the SPP case and, by default, non-resonant input conditions. The key feature facilitating this physically transparent situation, an input laser beam of annular profile, is also that which would be critical in optimizing the transmission. The arrangement selectively directs the incident energy into a resonant input mode of the system. Furthermore, if, for example, the input beam were rendered radially polarized then all the input energy would be transferred to a circularly symmetric cascade of SPPs (or TM guided wave modes) impinging on the hole; optimal transmission is envisaged for the case of a mode of the system resulting from strong overlap of a resonant input mode with an aperture resonance.

The main conclusions of the study are as follows. Firstly, the contrast between samples with and without output grating coupling indicates that the coupling between the field system of the aperture to SPPs on the top surface is significantly more efficient than direct coupling to bulk radiation. Secondly, consideration of the position and widths of the transmission peaks indicates their physical assignment as follows:- the lower angle peak for h=180 nm is due to a resonant mode of the aperture, strongly coupled to the front-surface SPP, while the peak of similar width at 53.5° is driven by resonant back-surface SPP input coupled to the front-surface SPP presumably via the off-resonance hole mode; for the transmission peak in the h=350 nm case an optical tunneling mechanism between the input- and output-face SPP modes (they remain essentially uncoupled) is deemed appropriate to account for the lower efficiency and narrower peak width. Thus, as far as the SPP-driven transmission peaks are concerned, the distinction, then, is between a coupled mode of the system as a whole (h=180 nm case) and a tunneling interaction between distinct SPP excitations on the two surfaces. Thirdly, from the transmission peaks with resonant SPP input on the fully structured samples, it was found that the effective 1/e field decay length for hole transmission, δ, is ~270 nm which is an order of magnitude greater than the optical skin depth (23.5 nm) of the surrounding material. This represents an upper bound for δ since we consider that the 180 nm thick sample has crossed over to a strong coupling regime that would be characterized by a somewhat larger value of δ.

Acknowledgments

This research was supported by Nanotec Northern Ireland with funding from the EC administered by Invest Northern Ireland. Lei Feng gratefully acknowledges PhD studentship support provided jointly by the European Social Fund and Queen’s University Belfast.

References and links

1.

H. A. Bethe, “Theory of diffraction by small holes,” Phys, Rev. 66, 163–182 (1944). [CrossRef]

2.

C. J. Bouwkamp, “On Bethe’s Theory of Diffraction by Small Holes,” Philips Res. Rep. 5, 321–332 (1950).

3.

M. A. Paesler and P. J. Moyer, Near field optics: theory, instrumentation and applications (John Wiley & Son, 1996), Chap. 3.

4.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

5.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007). [CrossRef] [PubMed]

6.

C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000). [CrossRef]

7.

M. Mrejen, A. Israel, H. Taha, M. Palchan, and A. Lewis, “Near-field characterisation of extraordinary optical transmission in sub-wavelength aperture arrays,” Opt. Express 15, 9129–9138 (2007). [CrossRef] [PubMed]

8.

L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S.-H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown, and C. W. Kimball, “Surface plasmons at single nanoholes in Au films,” Appl. Phys. Lett. 85, 467–469 (2004). [CrossRef]

9.

A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen, “Optical transmission properties of a single subwavelength aperture in a real metal,” Opt. Commun. 239, 61–66 (2004). [CrossRef]

10.

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, “Enhanced light transmission through a single subwavelength aperture,” Opt. Lett. 26, 1972–1974 (2001). [CrossRef]

11.

T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, “Giant optical transmission of sub-wavelength apertures: physics and applications,” Nanotechnology 13, 429–432 (2002). [CrossRef]

12.

A. Degiron and T. W. Ebbesen, “Analysis of the transmission process through single apertures surrounded by periodic corrugations,” Opt. Express 12, 3694 (2004). [CrossRef] [PubMed]

13.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002). [CrossRef] [PubMed]

14.

A. Otto, “Excitation of non-radiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216, 398 (1968). [CrossRef]

15.

J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter, and S. G. Liu, “Wide-field surface plasmon microscopy with solid immersion lens,” Appl. Phys. Lett. 85, 5451 (2004). [CrossRef]

16.

J. Zhang, M. C. Pitter, S. Liu, C. See, and M. G. Somekh, “Surface-plasmon microscopy with a two-piece solid immersion lens: bright and dark fields,” Appl. Opt. 45, 7977 (2006). [CrossRef] [PubMed]

17.

C. J. T. Rea, Modelling surface plasmons on smooth and periodic multi-layers, Ph.D. thesis (1997), Queen’s University of Belfast.

18.

F. J. Garcia de Abajo, “Light transmission through a single cylindrical hole in a metallic film,” Opt. Express 10, 1475–1484 (2002). [PubMed]

19.

R. Gordon and A. Brolo, “Increased cut-off wavelength for a subwavelength hole in a real metal,” Opt. Express 13, 1933–1938 (2005). [CrossRef] [PubMed]

20.

F. J. Garcia-Vidal, L. Martin-Moreno, E. Moreno, L. K. S. Kumar, and R. Gordon, “Transmission of light through a single rectangular hole in a real metal,” Phys. Rev. B 74, 153411-1-4 (2006). [CrossRef]

21.

K. J. Webb and J. Li, “Analysis of transmission through small apertures in conducting films,” Phys. Rev. B 73, 033401-1-4 (2006). [CrossRef]

22.

A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, “Effects of hole depth on enhanced light transmission through subwavelength apertures,” Appl. Phys. Lett. 81, 4327–4329 (2002). [CrossRef]

23.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

24.

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200, 1–7 (2001). [CrossRef]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(240.6680) Optics at surfaces : Surface plasmons
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Diffraction and Gratings

History
Original Manuscript: October 29, 2007
Revised Manuscript: December 5, 2007
Manuscript Accepted: December 6, 2007
Published: December 14, 2007

Citation
Lei Feng and Paul Dawson, "Optical transmission through single subwavelength apertures using prism coupled input of laser light of annular intensity profile," Opt. Express 15, 17863-17873 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-17863


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. A. Bethe, "Theory of diffraction by small holes," Phys, Rev. 66, 163-182 (1944). [CrossRef]
  2. C. J. Bouwkamp, "On Bethe’s Theory of Diffraction by Small Holes," Philips Res. Rep. 5, 321-332 (1950).
  3. M. A. Paesler and P. J. Moyer, Near field optics: theory, instrumentation and applications (John Wiley & Son, 1996), Chap. 3.
  4. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998). [CrossRef]
  5. C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature 445, 39-46 (2007). [CrossRef] [PubMed]
  6. C. Sönnichsen, A. C. Duch, G. Steininger, M. Koch, G. von Plessen and J. Feldmann, "Launching surface plasmons into nanoholes in metal films," Appl. Phys. Lett. 76, 140-142 (2000). [CrossRef]
  7. M. Mrejen, A. Israel, H. Taha, M. Palchan and A. Lewis, "Near-field characterisation of extraordinary optical transmission in sub-wavelength aperture arrays," Opt. Express 15, 9129-9138 (2007). [CrossRef] [PubMed]
  8. L. Yin, V. K. Vlasko-Vlasov, A. Rydh, J. Pearson, U. Welp, S.-H. Chang, S. K. Gray, G. C. Schatz, D. B. Brown and C. W. Kimball, "Surface plasmons at single nanoholes in Au films," Appl. Phys. Lett. 85, 467-469 (2004). [CrossRef]
  9. A. Degiron, H.J. Lezec, N. Yamamoto, and T.W. Ebbesen, "Optical transmission properties of a single subwavelength aperture in a real metal," Opt. Commun. 239, 61-66 (2004). [CrossRef]
  10. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, "Enhanced light transmission through a single subwavelength aperture," Opt. Lett. 26, 1972-1974 (2001). [CrossRef]
  11. T. Thio, H. J. Lezec, T. W. Ebbesen, K. M. Pellerin, G. D. Lewen, A. Nahata, and R. A. Linke, "Giant optical transmission of sub-wavelength apertures: physics and applications," Nanotechnology 13, 429-432 (2002). [CrossRef]
  12. A. Degiron and T. W. Ebbesen, "Analysis of the transmission process through single apertures surrounded by periodic corrugations," Opt. Express 12, 3694 (2004). [CrossRef] [PubMed]
  13. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002). [CrossRef] [PubMed]
  14. A. Otto, "Excitation of non-radiative surface plasma waves in silver by the method of frustrated total reflection," Z. Phys. 216, 398 (1968). [CrossRef]
  15. J. Zhang, C. W. See, M. G. Somekh, M. C. Pitter and S. G. Liu, "Wide-field surface plasmon microscopy with solid immersion lens," Appl. Phys. Lett. 85, 5451 (2004). [CrossRef]
  16. J. Zhang, M. C. Pitter, S. Liu, C. See and M. G. Somekh, "Surface-plasmon microscopy with a two-piece solid immersion lens: bright and dark fields," Appl. Opt. 45, 7977 (2006). [CrossRef] [PubMed]
  17. C. J. T. Rea, Modelling surface plasmons on smooth and periodic multi-layers, Ph.D. thesis (1997), Queen’s University of Belfast.
  18. F. J. Garcia de Abajo, "Light transmission through a single cylindrical hole in a metallic film," Opt. Express 10, 1475-1484 (2002). [PubMed]
  19. R. Gordon and A. Brolo, "Increased cut-off wavelength for a subwavelength hole in a real metal," Opt. Express 13, 1933-1938 (2005). [CrossRef] [PubMed]
  20. F. J. Garcia-Vidal, L. Martin-Moreno, E. Moreno, L. K. S. Kumar and R. Gordon, "Transmission of light through a single rectangular hole in a real metal," Phys. Rev. B 74, 153411-1-4 (2006). [CrossRef]
  21. K. J. Webb and J. Li, "Analysis of transmission through small apertures in conducting films," Phys. Rev. B 73, 033401-1-4 (2006). [CrossRef]
  22. A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, "Effects of hole depth on enhanced light transmission through subwavelength apertures," Appl. Phys. Lett. 81, 4327-4329 (2002). [CrossRef]
  23. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry and T. W. Ebbesen, "Theory of extraordinary optical transmission through subwavelength hole arrays," Phys. Rev. Lett. 86, 1114-1117 (2001). [CrossRef] [PubMed]
  24. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martín-Moreno, and F. J. García-Vidal, "Evanescently coupled resonance in surface plasmon enhanced transmission," Opt. Commun. 200, 1-7 (2001). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited