We study the transmission of fluorescence through periodically modulated metal films. In one-dimensional corrugated films, transmission is mediated by coherent scattering of surface plasmons directly excited by fluorophores on the surface. This scattering is shown to be a two-dimensional problem in that diffraction orders along both axes are obtained with well-defined states of polarization. In films consisting of two-dimensional arrays of sub-wavelength apertures, an additional mechanism exists in the direct transmission of fluorescence through the apertures, which is the dominant mechanism of transmission as shown by measurement of the radiation pattern from these structures.
© 2004 Optical Society of America
Fluorescence transmission through metal films with one-dimensional corrugation was demonstrated in a series of elegant experiments [1, 2], where transmission can be attributed to the fluorescence excitation of surface plasmon modes in the metal by molecules in close proximity , which subsequently couple into transverse radiation at well-defined scattering angles through interaction with the grating. In these experiments, fluorescence transmission was enhanced by the grating-assisted cross-coupling between the surface plasmon modes at each metal interface. Another series of experiments with 1-D metal gratings  demonstrated the emission of fluorescence in reflection and the appearance of frequency gaps. These experiments were later extended to metal surfaces with two-dimensional periodicity with the demonstration of a full photonic bandgap . The enhanced light transmission through metal films modulated with a 2-D array of sub-wavelength apertures  was reported in 1998, which subsequently sparked considerable experimental and theoretical activity in this phenomenon (see  and references therein, for example).
Numerous applications of the phenomenon of light transmission through periodic metal films have been demonstrated in recent years. One class of applications makes use of these “transparent” conductors in electroluminescent devices such as semiconductor LEDs  and VC-SELs  or organic light emitters (OLEDs) [10, 11]. Another class of applications utilizes the enhancement of fluorescence  for real-time molecular detection . In this paper, we study some additional aspects of light transmission through periodic metal films. Using 1-D corrugated metal films, we demonstrate that the transmission of coherent and incoherent (i.e. fluorescence) light is inherently a 2-D coherent scattering phenomenon. In films consisting of two-dimensional arrays of sub-wavelength apertures, an additional mechanism exists in the direct transmission of fluorescence through the apertures, which is the dominant mechanism of transmission as shown by measurement of the radiation pattern from these structures, which exhibits features due to coherent scattering from the lattice and direct incoherent emission from the apertures.
2. Experimental arrangement
Two types of periodic metal structures are used. The first is gold film with a 1-D corrugation. These structures were obtained from HTS Biosystems, and consist of a corrugated polycarbonate substrate upon which an 80 nm layer of gold is deposited. The period of the corrugation is 850 nm and the corrugation depth is 22 nm, as measured by atomic force microscopy. The second type of structure is a 2-D periodic array of apertures in 70 nm thick gold film. These structures were fabricated with e-beam lithography and dry etching , with aperture spacing of 1 µm and aperture diameter of 180 nm. The underlying substrate for these structures is quartz. One example of this structure is shown in Fig. 1, with aperture fill fraction of 2.5%.
The nanostructured metal films were coated on the top surfaces with a fluorescing monolayer, which consists of avidin labeled with Cy-5 dye. Cy-5 has peak absorption near 649 nm and peak emission near 670 nm. A solution of 1 µM avidin in phosphate buffered saline (PBS, pH 7.5, containing 0.02% sodlium azide as a preservative) is labeled with Cy-5, where the ratio of Cy-5 to avidin is 0.95. This solution is then diluted to the desired Cy-5 concentration (10 nM for 1% dye concentration) in 1 µM pure avidin in PBS. The diluted solution is then used to coat the sample surface, which is left for 3 hours at room temperature to allow formation of the labeled monolayer. Then, the unadsorbed species are removed by washing the samples in TE buffer, which contains 10 mM Tris buffer (pH7.4) and 1 mM EDTA. Finally, the samples are dried in vacuum for 1 hour and immediately used.
Figure 1 shows the experimental setup for light transmission measurements. Incident light from a narrow-line tunable diode laser set to 633 nm is p-polarized and attenuated by an OD 3 filter to reduce photobleaching effects during long measurements. The light is spectrally filtered by a 1.5 nm width band-pass filter to suppress broad-band spontaneous emission, and is passed through a chopper before being focused on the sample. A photomultiplier tube (PMT) is mounted on an adjustable-length arm attached to a computer controlled rotation stage, while the sample is mounted at the center of rotation of this stage on a manual rotation stage. With this configuration, the laser incidence angle (θ) and the transmission detection angle (α) can be adjusted either collectively or independently. Transmission of incident laser light is measured in the zeroth-order by a photodetector. For fluorescence transmission measurements, the detector is removed and the fluorescence signal is imaged through a 670 nm band-pass filter onto the PMT. The PMT is connected to a lock-in amplifier, the output of which is read by a computer.
3. Light transmission through a 1-D metallic grating
Figure 2 shows the transmission of excitation light as a function of incidence angle along both the x and y axes for the 1-D corrugated pattern. Well-defined transmission resonances are observed at incidence angles corresponding to the excitation of surface plasmon polaritons on the metal surface; for angles along the x-axis, the transmission is maximized for p-polarized incident light, while for the peak in transmission along the y-axis, the transmission is maximized for incident light polarized at roughly ±45° with respect to the x-axis. The fact that light transmission resonance through a 1-D corrugation can be produced at an angle of incidence along the direction perpendicular to the corrugation (i.e. the y-axis) has not been widely reported to our knowledge. However, this phenomenon can be described by treating the coupling between surface plasmons and free-space incident radiation as a two-dimensional momentum-matching problem:
is the transverse wave-vector of the incident light, K is the x-directed momentum of the grating, and k⃗sp is the wave-vector of the surface plasmon, with magnitude ksp given by
where the effect of periodicity on the surface plasmon dispersion properties  has been neglected under the assumption of weak modulation. Here, ω is the optical (radial) frequency, εm is the complex relative dielectric constant of the metal, and ε is the relative dielectric constant of the material at either interface. Solutions to Eq. (1) are plotted in Fig. 2 for the metal-air interface, parameterized by the integer coupling order |n|. The surface plasmon dispersion relation ksp was calculated using the complex dielectric properties of a smooth gold film deposited on a silicon substrate, as measured via spectroscopic ellipsometry. As shown by the coupling curves of constant order, light transmission can be obtained over a continuous range of incidence angles. The measured data correspond closely to the intersections of these curves with the x and y axes, where the incident light is p-polarized for coupling along the x-axis and 45°-polarized for coupling along the y-axis (for which the measurement was made by simply rotating the sample 90° about the z-axis and rotating the incident polarization). The measured data (along the x-axis) also clearly illustrate that transmission for the n=1 order is greater than for the n=-2 order.
An interesting effect occurs near θx=0, where the +1 and -1 diffraction orders cross. With the 1-D system, this will always occur when K≤ksp. Under the condition that θx=0 (i.e. kt,x=0), we have ksp,x=nK and , providing that |kt,y|<ω/c. In Fig. 2, the only solution exists for n=±1, with surface plasmons propagating at ±45°, which are the states of polarization of the incident light for maximum coupling. In order to demonstrate the crossing of these two coupling orders, we also measured the transmission of incident light along the y-axis with a few degree tilt along the x-axis so that the two orders can be angularly resolved. This result is shown in Fig. 3 for both 45° and -45° incident polarization.
The transmission measurements of Fig. 2 were performed with coherent light. Incoherent light can also transmit through the corrugated film at well-defined angles, owing to the near-field coupling between the fluorophores and the surface plasmon modes of the metal . These surface plasmon modes propagate in all directions in the plane of the film and coherently scatter off the grating. Again, calculation of the scattering angles is a 2-D problem as determined by Eq. (1), where now
is the transverse wavenumber of the scattered light on the transmission side of the metal film, and
is the surface plasmon wave-vector. The propagation of the surface plasmon in the x-y plane is described by the azimuthal angle ϕ, measured with respect to the x-axis, which is allowed to vary uniformly between 0 and 2π for each order n. The peak emission wavelength of Cy-5 (i.e. 670 nm) is used to calculate ksp. Figure 4 shows the calculated coupling curves and measured fluorescence emission, demonstrating excellent agreement. In the measurements, the excitation light was incident normal to the sample, and the PMT arm rotated at an angle αx or αy to the sample normal; along the y-axis, the fluorescence peak contains both +45° and -45° polarizations. The half-angle of the light collection cone of the imaging optics was roughly 2°.
4. Fluorescence transmission through a 2-D array of sub-wavelength apertures
In the 2-D periodic metallic structure, coupling between radiation modes and surface plasmons is described by
where n and m are integers. Because we use a square lattice, the coupling angles along the x and y axes are identical and the coupling curves of constant order (given by |n|+|m|) are symmetric about a 45° line. The measurement of fluorescence emission from the 2-D pattern is shown in Fig. 5. Because of the symmetry of diffraction from the 2-D structure, the fluroescence emission pattern is only measured for angles along the x axis. The emission pattern exhibits a broad background with isolated peaks at angles corresponding to the calculated scattering angles using Eq. (6) and (5) in a similar manner as fluorescence emission through the 1-D films. When measured through an s-oriented analyzer, the emission pattern consists only of the broad background, as the p-polarized scattered fluorescence is blocked, as shown in the upper left plot. The broad background pattern in the measurements is therefore due to direct fluorescence emission from the apertures (in addition to a much weaker contibution due to the direct transmission of fluorescence through the metal), which is the dominant transmission mechanism. Emission from the apertures is incoherent in that there is no correlation from one aperture to another; the collective emission pattern is therefore representative of the emission from a single aperture under far-field measurement.
In summary, we have presented transmission measurements of both coherent and incoherent light through 1-D and 2-D periodic metal films as mediated by surface plasmon excitation. Even in the case of 1-D modulation in the form of a corrugation, light transmission must be treated as a 2-D problem such that coupling into and scattering from surface plasmon modes can occur along directions parallel and perpendicular to the direction of modulation. In the case of 2-D modulation consisting of an array of sub-wavelength apertures, the transmission of fluorescence is dominated by the direct contribution from the apertures.
The authors wish to thank J.-J. Greffet and A. Nahata for useful discussions. This research was sponsored in part by NSF grants NIRT DMR-0102964 and CAREER ECS-0134548 and by NIH grant 1R21EB000481-01.
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