Midfield microscope: Exploring the extraordinary

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Stellingen

behorende bij het proefschrift

Midfield microscope: exploring extraordinary transmission Margreet Willemijn DOCTER, Technische Universiteit Delft

Maandag 13 oktober 2008

1. Bij het huidige ontwerp van de midfield microscoop is de versterking van transmissie van ondergeschikt belang.

2. In een midfield microscoop kan de diffractielimiet gebroken worden wanneer er gebruik wordt gemaakt van gestructureerde belichting (zoals in het werk van Gustaffson) in combinatie met een niet-lineaire responsie van het object op licht. 3. Er is nog geen universele theorie over de oorzaak van buitengewone transmissie van licht.

4. Wetenschap en muziek worden beiden pas interessant, als je datgene wat al op papier staat overstijgt.

5. Als je altijd toneelspeelt, dreig je je backstage te verliezen. 6. De moderne geneeskunde heeft de evolutie overwonnen.

7. Net als in het Engels blijkt beleefdheid uit de rest van de zin, en niet uit het gebruik van ‘je’ of ‘u’.

8. Een begeleider op afstand helpt bij het sneller zelfstandig doen van onderzoek (zelf oplossen gaat sneller dan op een antwoord wachten).

9. Jezelf openstellen is een langetermijninvestering.

10. Het onderzoek zou een stuk gemakkelijker maar minder interessant zijn als we in plaats van kwantitatieve, kwalitatieve microscopie doen.

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Propositions with the thesis

Midfield microscope: exploring the extraordinary Margreet Willemijn DOCTER, Delft University of Technology,

Monday 13 October 2008

1. The enhanced transmission is of lesser importance for the current midfield microscope design.

2. The diffraction limit can be broken in the midfield microscope when using super resolution based on structured illumination (as in Gustaffson’s work) in combination with a non-linear response of the object to light.

3. There is no universally accepted theory explaining the cause of extraordinary transmission of light.

4. Science and music both become interesting when you go further than what has already been written.

5. Being on stage forever, means there is no off stage anymore. 6. Modern medicine has conquered evolution.

7. Politeness is expressed in the whole sentence and not from the use of ‘je’ or ‘u’ in Dutch.

8. A supervisor abroad helps to develop independency (doing it yourself is faster than waiting for an answer).

9. Opening yourself to others is a long term investment.

10. Research would have been easier but less interesting if we would have performed qualitative instead of quantitative imaging.

11. It is more regretful to not try things, than to have a non-optimal outcome.

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Midfield microscope: exploring extraordinary transmission

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 13 oktober 2008 om 15.00 uur door

Margreet Willemijn DOCTER

natuurkundig ingenieur geboren te Schiedam

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Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. I.T. Young

Prof. dr. Y. Garini

Samenstelling promotiecommissie:

Rector Magnificus, voorzitter

Prof. dr. I.T. Young, Technische Universiteit Delft promotor Prof. dr. Y. Garini, Bar-Ilan University (Israel) promotor Prof. dr. L. Kuipers, FOM Institute AMOLF

Prof. dr. H. P. Urbach, Technische Universiteit Delft Prof.dr.ir P.M. van den Berg, Technische Universiteit Delft Dr. H.J. Lezec, National Institute of Standards

and Technology ( USA) Dr. S. Stallinga, Philips Research Laboratories

Prof.dr.ir. L.J. van Vliet, Technische Universiteit Delft reservelid

Dit werk werd ondersteund door TNO en het Cyttron Consortium. Dit proefschrift is deels gesponsord door Olympus Nederland B.V.

http://www.library.tudelft.nl/dissertations/

ISBN 978-90-9023442-7

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1 Introduction

This century will become the century of nanotechnology. It all started with the idea that science is down-scalable to the individual atom level [1]. Since the discovery of electron microscopes and scanning tunneling microscopes [2] it is possible to observe at such a small scale. This nanoscale is particularly interesting, because it spans a field of research which totally differs from the more classical, large-scale science. Although the size scales linearly, the physics does not. The properties of metals change; two materials attract each other; a nanometric fluid is laminar; nanoscale Brownian motion is present. Every process in the human body, for example, can be influenced by nanoscale motors, which supports the possibility of making nanoscaled devices.

It is interesting to fantasize about manipulating single atoms. It would be possible to make whatever you want, from small bits for data storage to nano-medicine. Two approaches can be taken to do nano-production. One starts from the bottom with single atoms and construct it to the top, either piece by piece which would take forever before a complex system is constructed, or by self assembly. When starting a ‘top down’ approach from bulk one can peel parts off, but then not every atom is individually controlled. Since we already have gathered lots of information about large-scale objects, one tries to iteratively reduce the scale. An important role in all of this is played by microscopes as instruments for observing structures with improved resolution. As of this writing, objects have been observed with optical microscopes with a resolution of 20 nm [3].

1.1 Microscopy

The ability to “enlarge” objects by observing them through lenses was known in the Roman times [4]; people already used (eye) glasses. It took a while before van Leeuwenhoek used those lenses in an early scientific microscope [5]. Since then continuous improvements have been made to observe ever smaller objects.

1.1.1 Wide-field Microscopy

The quality of the early microscope was poor and aberrations (both spherical and chromatical) limited the ability to observe small objects. By improving the lenses the resolution improved tremendously and the limitation shifted towards the diffraction limit. Imagine a small pinhole, a single point, which diffracts the transmitted light. After imaging this point with a lens the resulting image will be the same point blurred, an Airy disc [6]. This is due to the limited size of the lens, which cannot capture all of the light transmitted through the pinhole. It results in missing higher frequencies and the point will be imaged with a certain point spread function (PSF) like the one shown in Figure 1-1.

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The PSF depends on the numerical aperture (NA) of the lens, which is a measure of the angular cone of light captured by the lens, as well as on the wavelength λ. When imaging a single point, its position can be determined with high accuracy by determining the position of the maximal intensity. Localization problems will occur when trying to image two points that are close to each other, because their PSFs will overlap. The resolution, therefore, depends on the PSF. It is classically defined as Rayleigh’s criterion, which is the shortest distance between two points such that the image reveals two distinguishable points [7] and is given by 0.61/NA. With a typical wavelength of 500 nm and a NA of 1.3, the resolution is around 230 nm. This resolution is sufficient when observing a typical human cell with a diameter of about 10 μm. But it is hard (or impossible) to observe its internal organnels like lysosomes (200 nm), ribosomes and cell membranes (10 nm).

Figure 1-1 a) A typical point spread function for λ=561 nm and NA=1.3, the range of the logarithmic grey scale is -2 to 0. The 3D PSF is shown for the x (lateral) and z (axial) coordinate. b) A line profile through z=0 (plane of focus), the inset shows the signal 50 times enhanced, c) line profile through x=0, d) two overlapping PSFs in z=0, which are at the Rayleigh criterion.

1.1.2 Fluorescence microscopy

A common technique in microscopy is the use of fluorescence markers [8]. They are used to localize biological entities which are too small to be distinguished or have too little contrast in transmission or reflection. The whole object can be illuminated but the only contribution to the image originates from the fluorescent markers. These markers absorb light at a certain wavelength λ1, through which electrons are excited from a ground state to an excited state (Figure 1-2). The excited electrons dissipate some of their energy, corresponding to the Stokes shift, after which they fall back into their ground state, while emitting light with a wavelength λ2 (λ2 > λ1). By placing filters in the illumination and detection path, the excitation light includes only the spectral range around the peak of the

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spectral absorption of the fluorochrome. The excitation light is suppressed such that the emission light can be observed.

One drawback of fluorescence is the limited lifetime of the markers, as they will stop fluorescing after some time. In addition the quantum efficiency of the process is low and the ratio between excitation and emission intensity is small.

Figure 1-2 The fluorescence emission occurs after excitation and loss of some energy.

1.1.3 High resolution far-field microscopy

There is a great need for higher-resolution far-field optical microscopes. For biological processes the resolution should be higher and, when using fluorescent labeling in vivo in a far-field microscope, cell-processes can be studied if the resolution is better than the Rayleigh-diffraction limit. There are few ways of improving the far-field resolution. Either the diffraction limit can be improved, by using some sort of structure in the illumination or the diffraction barrier can be broken by using non-linear effects. Both are described in this section.

Improving the diffraction limit

The diffraction limit is not the ultimate limit; the effective PSF can be reduced. The wide-field resolution criterion (section 1.1.1) assumes that the whole wide-field of view is illuminated and detected simultaneously, in a way that the conventional microscopes work. However, there are other ways to perform the optical detection of an object, and the effective resolution criterion strongly depends on that. One way is to use “structured” illumination instead of illuminating the whole sample. If a smaller part of a sample is illuminated and

_{This ratio is the multiplication of the absorption cross section σ}

A, the concentration of molecules and the depth of focus (DOF) [9]. σA is calculated from the molar absorption coefficient λ and the number of Avogadro NA by σA=103log10(λ/NA). Typical values of λ= 1.2·105_{L/mol·cm (for Atto565, Atto-TEC, used in chapter 6), C=50 μM and DOF=}

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imaged, then the expected contribution to the image from regions outside this illuminated region is reduced.

The confocal microscope is the most widely used structured illumination system (Figure 1-3, [10]). A wide-field microscope is modified with two apertures (in conjugate focal planes) that are placed in the illumination and detection paths in order to block the out of focus light. In most current confocal microscopes both detection and illumination are at the same side of the sample, because then the sample does not have to be moved (no deformation in the sample). Since the image is only a blurred point, a scan needs to be performed. In general, mirrors scan the spot along a stationary sample and image the spot on a photo detector. The effective PSF is the PSFlens(λexcitation)·PSFlens(λemission), from now on abbreviated with PSFlens2, because the light passes through the lens twice and two apertures are used. The samples used in the confocal microscope are usually fluorescently labeled.

Figure 1-3 Confocal microscope.

Another approach is to illuminate with a structure shaped like a one dimensional (1D) cosine, in such a way that a kind of Moiré pattern is formed [11]. Such a low frequency pattern results from summing two high frequency patterns. By using structured illumination, higher frequency information is mapped into the lower frequency part of the image. The phase of the pattern is shifted to vary the intensity of the different contributions, allowing separation of these contributions by computation afterwards. The increase in resolution is unlimited if higher order effects are also used. This has been demonstrated for excited state saturation, but the signal to noise ratio limits the visibility of the highest frequency contributions.

Breaking the diffraction barrier

In Stimulated Emission Depletion (STED, [12]) two pulsed laser light sources are used, the first one to illuminate the fluorescence in a single point in the sample, and the second one to deplete most of the excited spot and leave only a small fraction of it undepleted. For that purpose, the first laser light illuminates a typical PSF in the sample and the second laser is triggered a few nanoseconds after the first one. The second pulse’s wavelength is equal to the emission wavelength of the fluorochrome such that stimulated emission occurs which, if the intensity is high enough, quenches all excited fluochromes. The second pulse has a donut-shape, resulting in a reduction of the total spot size. It is still diffraction-limited, but

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luckily depletion is a non-linear process, which means you can only deplete a molecule once, even if you increase the intensity above the depletion level. By tuning the intensity of the second spot, the fluorescent reduction gets saturated and the remaining emitting spot can be reduced in diameter to 20 nm which is an order of magnitude smaller than the diffraction limited spot, since the sum of two diffraction spots is not diffraction limited. Another technique, which should be mentioned, is PhotoActivated Localization Microscopy (PALM, [13]) in which individual molecules are first isolated before imaging by serial photoactivation and subsequent bleaching. As explained in section 1.1.1, the accuracy with which the location of a single molecule is imaged is far beyond the diffraction limit. Molecules with a separation of 10 nm could be seen individually.

1.1.4 Near-field microscopy

A Near-Field Scanning Optical Microscope (NSOM) works with an elongated sharp needle at the end of a glass fiber [14]. A typical tip size (usually it is a hole in the metal coating the fiber core) is around 50 nm, which acts as a pinhole. Light that exits the tip-hole disperses to all angles, resulting in a rapid decrease of intensity and increase of the spot size with the distance between tip and sample. When the tip is brought to a typical work distance of about 20 nm the main detection signal will result from the part of the object that is in very close proximity to the tip. The high resolution is determined by the hole-diameter and can be as small as ~30 nm. Due to its principle, the NSOM can only be used for surface measurements. The needle can be used either for light illumination or light collection. It is controlled and moved in similar way to an AFM or STM [2, 15].

1.2 Enhanced transmission through hole-arrays

In this thesis an alternative approach for the illumination of a microscope is explored, which is the transmission through sub-wavelength metal hole-arrays. The transmission through a periodic hole array has recently been shown to have extraordinary properties, even though for a single sub-wavelength hole the transmission is very low and fully diffracts [16].

1.2.1 Classical description

Light has a finite wavelength; transmission of light through large holes would allow all the light through, with only slight edge effects. If the hole is smaller than the wavelength then only a small amount of the light is transmitted and what does come through is totally diffracted. The dependency of the transmission on the wavelength and hole-diameter d was described by Bethe in 1944 to be (d/λ)4_{[17]. He made several approximations, namely that} there is no field penetrating the sample, the field inside the hole is constant and the metal film is infinitely thin.

1.2.2 Extraordinary transmission

Due to Bethe’s calculations of the low and diffracted transmission through a sub-wavelength hole it was never seriously considered for further applications. In 1998 Ebbesen et al. described a device of a thin metallic film in which holes are positioned on a periodic array with a certain period. It was discovered that a highly unusual spectrum is transmitted [16]. The observed transmission was for certain wavelengths higher than the

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amount of light at that wavelength impinging on the holes. The underlying reason for this unusual phenomenon was related to surface plasmons (SPs) because of the following reasoning. The enhanced transmission was not found with germanium films, where no SPs are present [16]. Also the spectrum split into several peaks when illuminated with varying angles, which is similar to coupling of light to SPs in reflection gratings.

Besides the enhanced transmission and spectral selection, it was also found that the transmission has a narrow angular spread. The zero-order transmission (for wavelengths larger than the period) is highly directional and was found to have a spread of 3 ([18]).

1.3 Midfield microscope

The high directionality described above was measured with a device that has a single hole surrounded by grooves. This is intriguing as one can imagine that the transmission through a complete set of holes in an array must have a combination of low dispersion and periodic structure. Assuming that a metal hole-array should have a transmission with a periodic set of sub-wavelength features, we proposed to use the device as the illumination light source for a new type of high resolution microscope. The transmission pattern has a three-dimensional structure of high-intensity sub-wavelength beams or spots, as we will show later.

As in a confocal setup, we propose to use these beams to scan a sample. It would improve the resolution compared to a wide-field microscope. It would also increase the number of scanning spots that are simultaneously measured compared to a confocal microscope and therefore it would significantly shorten the three-dimensional measurement. As we show in chapter 4, an interference pattern will be formed, such that the intensity patterns consist of lobes of light. An interference pattern is the result of propagating waves, which are dominant in the far-field region, with some contribution from the evanescent waves resulting from the surface plasmons. The described three-dimensional pattern extends for a few micrometers, far beyond the typical near-field regime. As this region exists in between the near and the far-field, it is termed midfield.

Because of the extended region of the transmitted light pattern, the microscope would, however, not be able to work in transmission mode because more than one point in the sample is illuminated simultaneously. This would give the same problem as in the wide-field microscope. Using fluorescent markers overcomes this problem, as they act as a secondary light source, on which the detection can be focused. Structured illumination, which is based on Moiré imaging, is to be used in the midfield microscope resulting in a similar resolution to the confocal microscope [11]. In combination with non-linearity in the object’s response super resolution, meaning resolution beyond the diffraction barrier, can be achieved.

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1.4 Outline

This thesis describes the exploration of a new microscope. Introducing a new microscope, always leads to comparison to current ones. The main research questions are therefore: What are the characteristics of the field pattern of the transmission through a hole array and can it be used for structured light illumination?

What are the characteristic properties of the midfield microscope?

How does the midfield microscope compare with the existing high-resolution microscopy methods?

An important part of the microscope is its illumination that is created by transmission through a hole-array. Although this subject is rather new, a lot of research has already been done. Chapter 2 describes the fundamental research on the transmission of light through arrays with respect to both experimental aspects, as well as theoretical calculations of the transmission properties. It is found that each array is unique due to a few parameters like material and array periodicity. In chapter 3 we describe the manufacturing procedures as well as the characterization methods. In order to understand this experimental outcome, models were required and constructed for calculating the transmitted field patterns. These models are described in chapter 4 and include: 1) an approximate model which starts from the array exit and uses only one setup-specific wavelength, and 2) a rigorous calculation in which a plane wave enters the system and for which the wavelength can be varied along the full visible spectrum.

After characterization of the arrays and modeling of the transmitted field, we built the midfield microscope itself. Its setup and operation are explained in chapter 5. Experiments are done on the transmission measured by fluorescence, first when the array-exit is in focus and later for multiple focal planes in order to verify the modeled transmission. The results are shown in chapter 6. Finally, conclusions and recommendations are given in chapter 7.

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2 Extraordinary transmission

Bethe predicted in 1944 that hardly any light passes through narrow holes [17]. This seemingly definitive study meant that it took a while before research in transmission through such holes was renewed. Interest increased when Ebbesen et al. showed that the zero-order transmission spectrum was unusually high, during his research on the optical properties of submicron cylindrical cavities in metal films [16]. He actually found increased transmission for wavelengths larger than the period, where the intensity should decrease with λ-1_{[7]. It was explained that an array of sub-wavelength holes is an active} device [16].

The beauty of an active device is that it can be manipulated for different applications and a lot of research started involving both theory and experiments. Several theories exist about the physical origin of what has been termed extraordinary transmission (EOT). These theories are examined by observing the effect of various parameters, such as metal type and array-period, on the transmission. In this chapter a literature review is presented. Preliminary experiments are described, theoretical predictions and physical explanations are given and potential applications are discussed.

The interest in measurements started with a single hole surrounded by grooves and evolved into hole-arrays with exotic structures and a broad wavelength range. In this chapter only the experiments and theory closely related to the periodic hole-array in the midfield microscope will be discussed. Therefore the topic is limited to transmission through single holes, holes with surrounding corrugations and hole-arrays. Relatively simple shapes of the hole will be considered, e.g., square, rectangular or circular. The wavelength is assumed to be in the visible regime.

2.1 Far-field measurements

Most of the experiments that were done with hole-arrays used far-field transmission to study either a spectrum or a spatial intensity distribution, the results will be shown separately.

In this section the amount of extraordinary enhancement will be described qualitatively instead of quantitatively. Different methods were used for calculating the enhancement, either by comparing it with the classically predicted transmission based on Bethe [19], comparing it with the measured transmission through a single hole [20], comparing the fraction of light transmitted with the surface area [16] or comparing it to transmission through a random array [21]. All these methods give enhanced transmission but the actual enhancement factor varies from 1x [16, 20, 21] to 103_[19].

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2.1.1 Spectral measurements

One spectral feature for transmission through gratings, which has been known for a long time before EOT is Wood’s anomaly [22]. This is a dip in the spectrum for a wavelength that is diffracted along the surface and fits exactly in the array period.

Spectral measurements are currently done in order to characterize the array and to validate theoretical models. The simplest model takes only the period into account (see the dispersion curves in paragraph 2.4.1), but as will be shown in this section, such a model is too simple. The spectrum depends on many array properties. A single hole, for example, already has a well-defined spectrum [23]; the geometric arrangement of the holes provides an additional parameter that effects the spectral characteristics.

We first consider the spectral dependence on the geometric arrangement of the holes. If the holes are periodically instead of randomly arranged, the transmission intensity is 3 to 5 times larger [21]. The second harmonic signal is however higher for random arrays. Quasi-periodic arrays [24] or arrays with multiple holes per unit cell [25] show distinct spectral peaks. Increasing the number of holes increases the height and decreases the full width at half maximum of the spectral peak [26], saturation of the spectrum occurs for 19 by 19 holes. If the hole-array has a rectangular grid instead of a square one, the spectrum depends on the polarization direction [27, 28], which implies that the spectrum is period dependent. By adding dimples (grooves) in between the holes, the intensity of spectral peaks, but not their position, can be tuned [20].

The hole-size and shape also have influence on the transmitted spectrum, as was shown for triangular holes [29], rectangular holes [30-32] and elliptical holes [33-35]. Certain elliptical holes, for example, exhibit a spectral peak only for polarization along the short axis [35]. It is not clear what should happen, when the size of the holes increases. It has been reported that the peaks stay at the same position [36], shift to the red for larger holes [37], or shift to the red for narrower holes [38]. In the last case the total hole-area was kept constant, while changing the aspect ratio.

The material type also has an effect on the hole-array properties. This has been shown for different kinds of metals [16, 39]. For gold and silver the transmission is an order of magnitude higher than for nickel. The intensity changes only slightly when using a nickel array covered with a small silver layer instead of a fully silver array [40]. It demonstrates that only the outer layer takes part in the extraordinary transmission and not the bulk of the metal. Varying the supporting medium (glass versus sapphire [41]) or the medium above the array (air versus glycerol [42]) changes the spectrum dramatically. This is expected, as the solution of the electromagnetic field must fulfill the (Maxwell’s equations) boundary conditions that depends on both the metal and the surrounding dielectric medium.

Finally the role of illumination is discussed. The illumination side of the array, which is mostly either metal or the glass supporting it, has no influence on the transmission spectrum but does alter the reflection spectrum [43, 44]. Measuring this reflection spectrum can therefore help in determining which side is influencing which peak. The angle of illumination does change the spectrum; the intensity changes and peaks split up and move apart [16].

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2.1.2 Spatial measurements

From observations of the transmission purely by a CCD, information about beam spread, wavelength and polarization dependency can be gathered. When observing transmission through a single hole in a bull’s eye structure, either captured by CCD or through a moving narrow aperture, the angular spread was found to be limited to 3 beam spread [18]. Even more convincing than the previous far-field experiment, which measured perpendicular to the optical axis, is the measurement in which the beam profile is visualized parallel with the optical axis. This is done by observing the fluorescence of cesium atoms excited by the light transmitted through a single slit surrounded by grooves [45]. Here the beam diameter remained the same for at least 1 mm along the optical axis and a line plot across the beam at 5 mm from the sample-exit reveals that it was still intact. A “confined” beam only occurs for certain wavelengths; color images showed that the transmission occurs in different directions for different wavelengths [46, 47]. When changing the incidence angle away from normal incidence, the position of high intensity light moves from the center to the edge of the array [48].

The polarization dependence of the transmission is observed through a polarizer [49], which reveals that the array only transmits incoming light if the polarization is aligned with the array. Changing the polarization can have a dramatic effect on the transmission and rotating the polarization 6 results in almost complete cancellation of the transmission [50]. A special kind of measurement has been done with a so-called surface plasmon immersion microscope [51], in which surface plasmons (SP, see section 2.4.1) are introduced by total internal reflection on a part of the sample where an immersion droplet is placed. The droplet’s edges act as a SP mirror, confining the SPs to move at the immersion-sample interface. When placing an array in such a configuration, SPs turn back into propagating waves which are imaged in the far-field with a higher resolution that depends on the higher effective refractive index due to the SP and can be improved with a factor 100. Holes in an array with a period of 500 nm can be resolved; the best experimental resolution was 50 nm.

2.2 Measured near-field features

With the far-field measurements, no information is gained about the transmission near the array. Near-field phenomena like evanescent fields, which decay exponentially, are not detected in the far-field. By measuring the near-field, more information can be found about these evanescent waves, including support for the physical mechanism behind the “extraordinary” transmission. However, near-field measurements are not very common for the following reasons.

The first is the relative complexity of the near-field measurements and the availability of suitable equipment. Using a spectrum analyzer is for example much easier than operating a Near-field Scanning Optical Microscope (NSOM) [52]. The second reason is that the NSOM probe is so close to the device that electromagnetic field interactions can take place. In certain cases of Scanning Probe Microscopy, like Scanning Tunneling or Atomic Force Microscopy [2, 15], this is a preferred effect, but it has a disadvantage for measuring the field without perturbing it.

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In this section the few near-field measurements, by either imprint lithography (section 2.2.1) or Near-field Scanning Optical Microscopy (section 2.2.2), are reported.

2.2.1 (Imprint) lithography

Lithography is an iterative two-step process, in which a pattern is transferred onto a resist after which development of the resist takes place. The most frequently used projection lithography starts with writing a pattern by illuminating a mask with light (which now goes to ultra-violet [53]). Instead of light through a mask, direct writing using an electron or ion beam is also possible. The latter is not (yet) suitable for mass production, and is used in research.

For measuring the near-field by lithography, the mask in projection lithography is replaced by a slit- or hole-array. The transmitted light illuminates a resist, which can be positive or negative, meaning that either the illuminated or the non-illuminated part is removed during development.

Lithography usually works with projection and can be characterized as non-contact, independent of the use of masks. However, lithography that uses the near-field transmission through a sub-wavelength hole-array is a (nearly) contact method. This is necessary because the near-field intensity features are small, and the surface waves decay exponentially as one moves away from the surface in the axial direction [54]. Several researchers have succeeded in doing this kind of lithography for making both sub-wavelength lines [55-57] and dots [58]. They all have written features which are beyond the diffraction limit, for example 60 nm dots at 120 nm pitch with 365 nm light [58]. This could not have been written by an equivalent projection lithography system.

Figure 2-1 SEM image of the structures fabricated by the group of prof. S.C. Chen using 3D-SPAN and an 1D grating mask [59]. The scale bar is 2 μm. This figure is reproduced with kind permission of S.C. Chen.

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Most of the structures that are written by lithography with an array as mask are two-dimensional and lack information about the variation in transmitted intensity along the system’s optical axis, the third axial dimension. In contrast, Amarie et al. [60] showed that it is possible to use lithographic resist to map the transmitted intensity. Balloons of resist were formed above single holes (after development) and the size varied with exposure time. A similar technique was used by Shao et al. [59] in order to produce a 3D pattern and is shown in Figure 2-1. During development of the resist, the features of the transmission pattern interconnected resembling an interference pattern. This is an important result to which we will later refer.

2.2.2 NSOM measurements

A Near-Field Scanning Optical Microscope works with an elongated sharp tip at the end of a glass fiber [14]. This ‘needle’ can either be used to illuminate the sample or capture the light; in most of the studies of hole-arrays it is used as a collecting device. A typical diameter of the hole at the tip is 50 nm. It is used in close proximity to an object and scanned in a similar way to an AFM or STM [2, 15].

NSOM measurements on transmission through arrays revealed high intensity above the holes. These studies also showed, in those cases where the hole or slits were separated far enough, a standing wave in between the holes [61-65] with a strong dependence on the polarization of the incident light. These standing waves may be related to surface plasmons, which are usually described as the cause of extraordinary transmission, as will be discussed in section 2.4.1.

In another study, energy transfer was found between two arrays mounted at a certain distance from each other on the same substrate. One array was illuminated and the light coming from the neighboring array on the same foil was measured [66, 67]. The re-emitted light looked similar to the light measured above the illuminated array and the light has been described as the re-emission of surface waves originating from the illuminated array. It would provide more insight, however, if besides the intensity also the direction of the electromagnetic fields could be measured. Lee and co workers [68] managed to map the vector field by connecting a gold nanoparticle to a NSOM needle, the gold particle being elliptic and therefore polarization sensitive. After measuring each point in the image while varying the analyzer polarization 360, the experimental results were that a standing wave was found in between two illuminated arrays.

2.3 Theoretical predictions based on Maxwell’s equations

The existence of the extraordinary transmission [16] faces a theoretical challenge so that it can be explained and further developed. Obviously the earlier reasoning by Bethe [17] that the transmitted intensity depends on d/λ4_{– with wavelength λ and hole diameter d – does} not hold, as the system is different, and a model must take the periodicity of the structure into account.

The physical solution for the EOT should be such that the predicted EM fields from Maxwell’s equations still apply ([69] vol. 2 chapter 18, and section 2.3.1). Modeling, therefore, starts with the EM equations together with the appropriate boundary conditions.

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show different models found in literature which all start from these equations (section 2.3.2).

2.3.1 Maxwell’s equations

The electromagnetic (EM) field obeys Maxwell’s equations, which give the relations between electric and magnetic fields. For a time-harmonic wave we use the format [70] that depends on exp(-it). This negative time dependency is consistent with the formulation in [54] and it implies that the spatial-dependency depends on exp(+ikr). It also influences the signs in equations (2.1) and (2.2).

In these equations E is the electric field, B the magnetic field, H the magnetic field strength, D the electric displacement. All the fields and their strengths are vectorial. ε is the permittivity (dielectric constant), which is the multiplication of the free space parameter ε0 times its complex, relative material-dependent part εR. Free charges and steady state currents have no influence since their time-derivative vanishes. We assume uniform and isotropic media, such that ε and ρ only depend on the material and not the position. The relation between E and D, and between B and H are D= εE and B= μH. Via integral forms, found with help of Gauss’ and Stokes’ laws, the discontinuities across the boundary can be found. The normal components have continuity for μHn and εEn, and the tangential components for Ht and E.

By solving Maxwell’s equations, Bethe [17] found the transmission of monochromatic light through a single hole with a diameter smaller than the wavelength. His result showed that the transmission depends on (d/λ)4_.

2.3.2 Theoretical modeling

Various numerical predictions have been found in the literature in order to explain the empirical observation of EOT, as well as to gain more physical understanding on the phenomenon causing the EOT. In this section some of the numerical calculation techniques are given.

Finite Difference Time Domain (FDTD)

Since the electronic and magnetic fields are dependent on each other in time according to Maxwell’s equations, these two fields can be calculated sequentially on a rectangular, equally spaced, grid [71]. This continues until “the artificial boundary conditions affect the solution”, which is at the time a stable solution is found everywhere in the defined system. Results from FDTD support the experiments described in section 2.1. The transmission is higher for a slit surrounded by grooves than for an isolated slit [72]. Randomly distributed holes transmit less light than periodically ordered ones [73]. The transmission intensity increases with increasing hole size and it decreases when the array-thickness increases [74,

H iE    (2.1) E iH    (2.2) 0 D    (2.3) 0 B    (2.4)

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75]; although this has also been reported to vary periodically with the thickness [76] and period [77]. The transmission intensity does not have such periodic behavior for tungsten as it has for silver [78]. Several works support the formation of a directional beam [79-82]. New ideas, like shaping the hole can be tested “in silico” and perhaps later implemented; according to the simulation the intensity increases when the hole is structured differently from a straight cylinder [83, 84].

Reducing the calculated spatial steps increases the resolution of the solution, which is particularly interesting in the near-field. For certain wavelengths, highly localized fields in the holes or high fields at the surface have been found [85, 86], as well as propagating waves inside the holes [87]. The field at the surface in between the holes reveals interference [88].

Modal expansion, Rigorous Coupled Wave Analysis (RCWA)

In modal or mode expansion, different regions of a system are described by means of their eigenmodes, after which the different regions are matched [89]. The modes inside a hole or slit can be analytically described for a perfect conductor and only numerically for a dielectric. Most modal expansions are, therefore, made for a perfect conductor, which for gold limits the description to the THz regime [90], although it is said to be a good approximation in the visible regime as well [91]. A special case of model methods is the one based on Fourier expansion, also known as the rigorous coupled wave analysis (RCWA). Modal expansions are used to reduce the computation time by going from an enormous amount of individually calculated voxels to a lesser number of waveguide modes which are to be matched at the boundaries. For certain wavelengths (near the SP maximal excitation, paragraph 3.4.1) only the first few modes are required [92].

At widths < 50 nm, the transmission efficiency varies periodically with the diameter, the sample thickness and the wavelength [93-96]. With a decrease of the thickness the spectrum also splits into two peaks which then move away from each other [97].

Corrugations at the input surface, and not the output, contribute to intensity, filling these corrugations can increase intensity further [98]. Again, as with FDTD, surface resonances and propagating modes localized in the hole have been predicted [99, 100]. The reflection has also been examined, a dip has been found at angles which depend on the array-period [101].

(Semi) analytical modeling

In analytical methods, assumptions are often made on the basis of a presumed physical explanation and may limit the range of possible solutions.

When the array is approximated as infinite, such that a periodic solution must be found which satisfies Maxwell’s equations, the solution consists of multiple Bloch waves [102] which are periodic with the unit cell of the hole-array. If only one surface wave is assumed, the situation simplifies and solutions above and below the array can be easily matched, although perfect conductance must be assumed to get a field solution at all [103, 104]. A single wave assumption has also been used for analyzing the counter-intuitive increasing cut-off frequency for a decreasing (single) hole-size [105] and for explaining the interference between two slits [106].

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Applying Babinet’s principal on a perfect conductor array, implies that the transmission through a hole-array is the same as the reflection from an array of discs. This leads to the use of dipoles located in the holes [107-109]. This principle gives a similar transmission as predicted by Bethe [17], but it is still based on the use of a perfect conductor [107] which is not true for most hole-arrays. Therefore, Babinet’s principle cannot be used for real (non-perfectly conducting) metals.

Other types of modeling

Other types of modeling have also been used, but with some drawbacks. In the leaky wave antenna model the analogy with antennas in the microwave regime has been sought [110]. This is legitimate except for taking the metal to be ideal, which is not true for the visible wavelength range.

Dynamic diffraction uses all wavelengths. For some wavelengths Bloch modes exist and the combination of all these modes gives the transmitted field [111]. It is assumed that the metal is highly conductive and only a single waveguide mode contributes while others are damped [112].

Diffraction in the reciprocal lattice can be used to determine the spectrum [113]. By using Sommerfeld’s theorem (Green’s function) together with a standing wave solution at the corrugated array exit (conventional scalar theory), a large agreement for holes of 250 nm between this and FDTD have been found [114]. This has also been done, using Huygens’s principal [115, 116].

The multiple multipole technique is a semi-analytical technique, in which many multipoles with known analytical fields (singular at their basis) are positioned in such way and with such intensity that the boundary conditions are approximated [117]. One remarkable result is an extraordinary transmission for a slit-array when the ‘wrong’ polarization is used (E along the slits) if a supporting dielectric layer is placed on top of the perfect metal film. [118]. When using E in the exit-plane perpendicular to the holes, a high intensity at the exit-surface is expected and found [119].

The finite element method (FEM) is used in the case where the field around or in a complex shaped structure has to be calculated. Because of the complexity of the shape, the grid cannot be equally spaced as with FTDT, simple eigenmodes can not be used. Instead the solution is approximated at a varying (often rectangular) grid unit. The beauty of this approach is that the shape of the holes can be varied, and it should necessarily be a cylindrical hole. For example, it may have a sand-watch shape which was shown to increase the transmission intensity [120]. This method is applied later in this thesis.

In the rigorous scattering approach, the field is split into a background and a disturbance [121, 122]. This disturbance, which in our case is the holes, can be characterized by a collection of scatterers. Using a Green’s tensor, the influence of one field point on all others can be calculated. The results found by this technique either puts the classical double slit theory in a new light (interference now occurs at the slits instead of the detector, [123]) or reveals optical vortices near the transmitting hole [124].

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2.4 Theoretical predictions and their physical origin

Sometimes the modeling based on Maxwell’s equations is already overshadowed by interpretations of physical origin, as revealed in section 2.3.2. Some studies found consistency between the transmission spectrum and Fabry Perot resonances [112], which exist only for certain wavelengths that constructively interfere after multiple internal reflections. In the entrance or exit plane some interference can also occur, which is then called Bragg diffraction [125].

The most common explanation, however, is by means of surface plasmon waves (SPs, section 2.4.1). Light can couple to SPs if a periodic grid (array) is present with transmission spectral characteristics similar to those described in [16]. Some authors of that paper raised the idea that not only SP waves, but also other diffracted light, may influence the transmission, suggesting a new model called Coupled Diffraction Evanescent Waves [26]. This we will discuss this in section 2.4.2.

2.4.1 Surface Plasmons, dispersion curve

Figure 2-2 Dispersion curve of light and plasmons calculated according to [126].

Surface plasmons are surface waves which can be seen as disturbances of the surface electron density [54]. They are bound to the surface and their intensity decays exponentially along the axial direction from the surface; they are a near-field evanescent

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wave phenomenon. They can turn back into propagating waves, when scattered at surface roughness sites like corners or holes. The momentum of SPs is higher than for free light because SPs are bound to the surface [126], as can be seen from the lack of overlap between the photon and surface plasmon curve in Figure 2-2. Because of this momentum mismatch, light cannot directly couple to surface plasmons. It requires either a different refractive medium (like the prism used in Total Internal Reflection Microscopy) or a grating.

For a grating or in our case hole-array as shown in Figure 2-3, the surface plasmons give the wave vector k, and the grating constants GX and GY take care of the periodicity [127]:

Figure 2-3 Schematic drawing of the hole-array, coordinates and parameters.

Here kx is the wave number parallel to the surface, ω is the wave number, c the speed of light and ε1,2 are the wavelength-dependent dielectric constants of the array and surrounding material. The above equation gives a relation between the transmitted wavelength (/c=2/λ) and the angle of incidence (kx,photon=2/λ sin(α)), as shown in Figure 2-4. When Ebbesen et al. measured the transmission to be incident angle dependent and comparable to the shown dispersion curve, it was a logical choice to use surface plasmons as the explanation [16].

Note that in this thesis the term surface plasmons (SPs) is always used while elsewhere the term “surface plasmon polaritons (SPPs)” also appears. The latter originates from the interaction between photons and metal, which is the case for all hole-arrays.

The main reason for supporting EOT with SP is the similarity between the dispersion curve (see Figure 2-4) of surface plasmons and the measured transmission spectra. Ghaemi et al.

1 2 , , 1 2 , 2 ; , 1, 2,...; SP x photon x y x y x y k k iG jG i j G c a               (2.5)

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showed that both Wood’s anomalies (see section 2.1.1) and dispersion curve predictions match directly with the measured dispersion curves [19]. Furthermore, when the theoretical calculations are based on Maxwell’s equations, surface plasmons are automatically incorporated [128].

Figure 2-4 Dispersion curve for the gold-air interface of an array with an infinite number of holes, a pitch of 600 nm and a hole diameter of 150 nm [129]. The characters Γ, M and X stand for the following values of (kX,kY) which is k-vector of the incoming light

parallel to the array-plan: (0,0), (π/a,0) and (π/a, π/a), as shown below the curve.

Different explanations have been given about various ways in which surface plasmons contribute to the transmission. Experimental results of transmission through samples

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sides. This can be explained as having three sequential steps, namely coupling of light with the first surface, aperture transmission, and coupling out [130]. The standing SP wave exhibits two modes, being either symmetric or anti-symmetric around the hole [131]. The relevant mode can be fine-tuned by the depth of the surrounding corrugations.

More specificly, surface plasmons have been studied to understand their nature. A localized SP (LSP) is more confined and depends strongly on the hole-diameter and inter-hole distance [132, 133]. A high correspondence between the array transmission and LSP in golden discs, points at the LSPs. Here Babinet’s principle, as used in [107], is applied, which allows inversion of discs and holes having similar diffraction and, as it appears here, similar SP characteristics as well. Delocalized Bragg and localized Mie plasmons have been considered [134], the latter being the (earlier mentioned) localized plasmons trapped inside the holes. Bragg plasmons can be seen as plasmons which interfere constructively only in certain directions, depending on the positioning of the holes. They form traveling Bloch waves, similar to [135], meaning that each unit cell has the same periodic solution. Besides the SP wave, a creeping wave also seems to have some influence, not in the visible range but for longer infrared wavelengths [136]. The creeping wave is a near-field wave with a clear 1/√x dependence (x=distance in plane), similar to a free space radiation of a line source (for a point source this would be 1/x).

The importance of surface plasmons for EOT is still under debate. Gordon et al. reason that SPs are not needed in order to observe a near-field interference effect in a double slit experiment [137]. They calculated the transmission through a perfect electronic conductor (PEC) which does not support surface plasmons, and the spectrum was found to be similar to that of early measurements where SPs were used to explain the transmission [123]. Pendry et al. confirmed these results theoretically; following from Maxwell equations [138]. SP look-a-likes, which are surface bound states in case of a PEC, cause the enhancement.

SPs may not provide the full explanation for the enhanced transmission. Using Fano analysis, two parts in the transmission process - the resonant surface plasmons and the non-resonant direct transmission ([95, 139]) - are taken into account as well as the interference between them. Shifts in the spectrum based on simple SP theory (as in Figure 2-4) can be explained by this analysis.

2.4.2 Composite Diffracted Evanescent Wave model

Continuing doubts about whether surface plasmons are the only or at least the main contributors to EOT, have led to a new theory which includes all diffracted waves [26]. Besides enhanced transmission through metallic arrays (end of section 2.3.2), non-metallic beaming effects [140] also give convincing evidence that the SP model is not sufficient. Note that only a small part of the total power is coupled to SPs; the rest goes into the evanescent waves. In the Composite Diffractive Evanescent Wave model (CDEW), all in-plane waves are taken into account, resulting in a composite evanescent wave. This wave can be characterized by a phase shift with respect to the inducing light, an amplitude that is decaying with distance, and a well-defined wave vector. This is in contrast to SPs which have the same phase as the source and a constant amplitude (at least over the same measured distance) that depends on a power of the inverse distance.

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Measurements were found to be in an excellent agreement with CDEW, and the CDEW model can explain both the transmission suppression and spectral peaks for non-metallic arrays by interference between CDEW and directly transmitted light, while the SP model cannot. However, the model is only useful in the lateral in-plane region within 3-4 μm of the aperture in plane [141], because there the CDEW has enough intensity. Beyond that region the surface plasmons are dominating.

Gay et al. [142] found experimental evidence supporting the CDEW model from far-field measurements of the intensity transmitted through a slit or holes with a groove on the illumination side. The intensity oscillated with the distance between the slit and groove. The reduction of the intensity could be explained by both models, but the SP parameters calculated from the measurements were not consistent with the SP model. The phase shift, which was known to vary due to the quality of the hole, was better explained by CDEW than the SP model. Further, Li et al. [143] who used dielectric bars instead of grooves and Min et al. [144] who varied the input and output surfaces to be metallic or not, could not use the SP model to explain their numerical FTDT simulation results, but could do this with the CDEW model.

Although some of the features, which cannot be explained by the SP model, are explained by the CDEW model, the latter is not well-accepted. One counterargument is given by Visser [128]. He refers to the numerical calculations on the creeping waves [136], which are similar to Gay’s et al. [145], and were explained by the SP model together with the effect of silver oxidization (which was not there according to Gay et al. [146]). Visser recognizes still a lot cannot be explained, but the CDEW is not correct because 1) it is based on an approximate scalar model (and not Maxwell’s vectorial equations), 2) Kirchhoff’s assumption of an incoming plane wave is used, which is not true for this hole size, and 3) the film is assumed to be opaque, while in this wavelength range it should be partly transparent.

2.5 Possible Applications of hole-arrays

As shown in the previous sections, the phenomenon of extraordinary transmission is not yet fully understood, but a lot of promising results have been found which form a solid ground for both device manufacturing and applications development. The drive behind the research, besides from the physical understanding, is the possible new applications based on the EOT.

2.5.1 Lithography

In section 2.2.1 lithography was described as a way of measuring the near-field of transmission of the array [59, 60]. It was shown that small dots can be written, by using the EOT though a metallic array. To keep the dots as narrow as possible, one should carefully choose the illumination intensity. If this intensity is too high, then the field on the metal in between holes due to SP excitation [147] will become too high, which can possibly ruin the highly confined structures [148]. The distance between sample and mask can be varied; according to [149] it can be increased from 50 to 150 nm.

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The most important question is, can EOT be seen as a useful way to improve lithography? The ability to write an arbitrary pattern is important for applications in the computer chip industry. For doing this, either the illumination should be blocked or the holes themselves must be blocked. If the array is illuminated through reflection at a programmable array mirror, light can be deflected away from the hole.

The holes themselves can be statically blocked, in the production process one hole of the total array is not made. This was unintentionally done by Shao et al. in his three-dimensional surface-plasmon-assisted nanolithography (3D-SPAN) technique [59]. Besides revealing a way how to write in 3D (Figure 2-1), Shao et al. showed that for an array the defects are in the form of blocked holes. The transmission responds only locally (above the defect) and two or three holes later the pattern ‘restored itself’. Another way of blocking holes might be to fill them with a nonlinear Kerr media, for which the dielectric constant varies non-linearly with the illumination intensity [150] or by applying an external magnetic field [151].

2.5.2 Microscopy

Constructing a microscope that is based on illumination through a hole-array as a main building block is rather new, but constitutes an idea similar to that used in the SP immersion microscope [51]. Since the intensity features in the transmission are so small, it should be possible to increase resolution with it. This idea was the basis for this thesis project. In the “midfield microscope” [152] small illumination spots formed by extraordinary transmission will illuminate a sample; the detection will be done in far-field. The next chapters will focus on different aspects of this microscope.

That EOT can aid in increased confined illumination is demonstrated numerically. Sun et

al. [153] designed metallic array lenses by varying the thickness of the array. The beam

shape shows even a lower diffraction than the already confined beam from a “flat” array. Goto et al. [154] used the array to increase throughput through a vertical cavity surface emitting laser (VCSEL) and micro lens arrays; the EOT produced a 500 times increase in intensity. Shi et al. [155] showed that by using a varying period within one array, it is possible to create a highly defined spot (270 nm FWHM at 1.5 micron above the array). For the same optical scanning purpose, Guo et al. [156] finally showed by numerical calculations that a somewhat larger probe spot with high confinement can be made by an array with constant period. The spot is located at 1.5–2.5 μm above the slit with a FWHM of 350 nm and the enhancement is around 30 times.

2.5.3 Fluorescence

There are several reasons for using EOT through arrays for fluorescence. Brolo et al. used the transmission and the presence of the arrays to gain intensity for quantum dot experiments [157] and sensitivity in fluorescent measurements (change in signal versus change in dye concentration) [158].

A second reason is the spectral sensitivity. The dielectric constant of a surface changes when (fluorescent) molecules bind to the surface, which result in a spectral shift [159, 160]. This was also demonstrated by using a photo-isomerizatable layer, which changes configuration under UV illumination [161].

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If the fluorescence influences the excitation spectrum which characterizes the EOT, a variation in period should only result in a variation in emission intensity and not in the spectrum. This is consistent with the spectral results of Kim using two different periods (400 and 600 nm) that shows little difference [162], while the white light transmission spectrum changes drastically. But as Dintinger et al. [161] already mentioned, the fluorescent intensity depends in a complicated way on the absorption characteristics of the molecule itself and its interaction with the metal.

Arrays have been integrated into a fluidic chip [163, 164] to allow parallel detection at different wavelengths corresponding to arrays with different periods. Such a fluidic chip is even possible with a stack of arrays resulting in a quasi 3D crystal [165, 166].

The third reason is the high confinement of the reactions. Piciu et al. are developing a sensitive micro-fluidic device, with the difference that we will monitor chemical reactions only inside the hole which will serve as smallest reaction chambers with sizes on the order of attoliters [167].

In fluorescence not only the intensity and the spectrum, but also the lifetime gives opportunities for discrimination between fluorescent markers and characterization of biochemical environment. Papers that studied the effect of EOT’s on the fluorescence lifetime showed contradicting results; Garrett et al. found a minor change of 2.1-2.5 ns in lifetime [168] while Lenne et al. report on lifetime changes of 0.9 to 3.7 ns in only a single aperture [169]. While it is unclear how an array changes the lifetime and whether this can be used for discriminating chemical reactions, it is reasonable to expect that the fluorescence produced with sub-wavelength hole-arrays will offer new opportunities for (bio) molecular studies.

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3 Production and characterization of periodic slit-

and hole-arrays

Transmission through hole-arrays is ascribed to a surface wave phenomenon (chapter 2). A clear explanation is not yet available but, whenever these surface waves are better supported, higher transmission intensity is expected. The dielectric constant, given by

ε=ε’+iε”, is a measure of this support. Materials with a large negative ε’ and a small ε”,

like silver and gold, have low absorption [170]. We choose to use gold, because of its slow oxidation rate and shown high transmission [39].

The gold foils are either freestanding or supported by glass. The latter is chosen since in the eventual microscope (chapter 5) the sample will be in contact with the hole-array and a freestanding foil might not be rigid enough. The freestanding foils are better for testing a theory (chapter 4) since, at both the entrance and the exit, the same refractive medium (air) is present. The arrays are characterized by observing their transmission in far-field, giving both spatial and spectral results. The characteristics of the image, spectrum and transmission divergence are found to depend on the details of the illumination, choice of foil, production method, dimensions of hole-diameter and period, aperture form (slit or hole), polarization and incidence angle.

3.1 Production

The main production strategies for making slit- and hole-arrays are as follows. A first approach depends on electron beam patterning in resist after which lift-off takes place. Only glass-supported foils can be made, since the process of making the foil and the holes is interwoven. A second strategy uses ion beams which directly mill structures in already existing foils; these can be either glass-supported or freestanding. Other methods like stamping [171, 172] or nanosphere lithography [173, 174] are not used, because of the high mask costs or the limited flexibility of sample parameters.

3.1.1 Electron beam patterning in resist + lift-off

The production of foils and arrays by using electron patterning [175] in resist and liftoff is shown in Figure 3-1 and is described in detail in [167]. It starts with a clean glass slide on which Chromium is sputtered. This Chromium is not only required as an adhesion layer for the later metal film, but also as a reflective layer for focusing the electron beam. Then a positive resist for near ultraviolet light and a negative resist for the electron beam are deposited. First the electron beam patterns the holes (Leica EBPG). After resist development, pillars are formed by using reactive ion etching. A metal (gold or gold/palladium) is then evaporated and the pillars are removed by lift-off.

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possible, since the technique only depends on the wavelength and incidence angles. With e-beam patterning the kind of distribution, period, hole-diameter and hole-shape can be varied.

Figure 3-1 Production by electron beam lithography of glass-supported foils with hole-arrays, a) double layer resist scheme; b) e-beam exposure and development; c) reactive ion etching of the HPR-504 resist; d) metal e-gun evaporation; e) HPR-504 lift-off.

Figure 3-2 Production of a free-standing foil, a) Nitride-doped Silicon, b) after etching and c) after gold evaporation the remaining SiN is milled and holes are made by Focused Ion Beam.

3.1.2 Production of free-standing foils

A free-standing foil without holes also requires several processing steps, see Figure 3-2. First, silicon is doped with nitride forming a protective layer, after which a positive resist is deposited. The resist is developed and the SiN and Si are etched, the latter along its crystal lattice at 54.7. Gold is evaporated on the etched Si such that a thin layer of gold is formed, supported by SiN.

With a Focused Ion Beam (FEI, Technai) the layer of SiN is locally removed. To avoid charging of the sample, which results in deflection of the ion beam, conductive carbon