1. INTRODUCTION

Since many remarkable applications of nanophotonics require cumbersome equipment, integration of nanophotonics with guided optics is a very promising field. The capacity to couple optical nanostructures with input and output waveguides is a necessary condition for the widespread use of nanophotonic devices in various fields, such as biochips [1,2], telecom [3], or quantum optics [4,5]. Previous theoretical papers already addressed this question of waveguide and nanoantenna combination in the optical domain [6–9].

Basically, the wire nanoantenna illuminated by the guided signal will radiate one part of this signal into free space, thus allowing the wave to convert from a guided to a free propagating one. Reciprocally, while in the absence of an object, no propagating light can be coupled into the waveguide because the parallel part of the wave vector is greater in the waveguide than any plane wave in the cladding; the nanowire will allow some coupling into the waveguide. Traditionally, such coupling or decoupling is performed by a grating or by a prism deposited on top of the waveguide. Here we demonstrate that a nanowire allows the same functionality at the nanoscale.

Several applications can result from this far-field/guided-field transducer function, such as laser antennas [10,11] or wireless optical transmission on chip [12]. For instance, our team and collaborators proposed earlier in 2007 the concept of an integrated Fourier transform spectrometer [13,14]. In this device, gold nanowires are used to extract locally the electromagnetic signal from a guided light interferogram and to send it onto an integrated detector or intensity measurement and further numerical treatment. With a total size of only a few centimeters, this device reaches a 10 pm resolution. In this integrated spectrometer, the nanowire transmits information that characterizes the local field intensity in the waveguide. Other information, such as the polarization state, the propagation direction, or the local waveguide dimensions also can be recovered from the waveguide-coupled nanowire radiation pattern.

In addition to this near-field/far-field transducer capability, it is well known that metallic nanoantennas can support localized surface plasmon resonances (LSPRs) due to collective oscillations of the free electron gas in the metal. These resonances lead to enhanced scattering and absorption cross sections, allow antenna gain tuning, and provide strong exaltations of the electrical near-field [15]. Such plasmon resonances are now routinely used in surface-enhanced Raman spectroscopy (SERS) as well as in optical sensing based on LSPR spectroscopy.

In the growing field of biosensors, biochips, or lab-on-chip [16], waveguide-coupled nanoantennas can play an important role. Indeed, the same device allows the excitation of the light-matter interaction effects and the collection in the waveguide of the resulting spectrum for further analysis, allowing, for instance, fully integrated SERS or LSPR sensing [17]. Moreover, it is now well known that a strongly enhanced near-field may also be used to trap or manipulate particles [18,19].

For all these applications, it is important to characterize the properties of the waveguide-coupled nanowire system; in particular, the coupling efficiency, the polarization sensitivity, the shape of the radiation pattern (directivity), the spectral dependence, and the ratio between absorption and scattering should be quantitatively characterized.

In this paper, we study theoretically and experimentally the optical properties of single gold nanowire antennas with a square cross section. The nanowires are fed by a channel ion-exchanged waveguide integrated on a glass substrate. We give a special emphasis on the study of the resulting radiation pattern. Our experimental setup, based on a microscope equipped with a Fourier lens, allows the measurement of the radiation pattern in the superstrate direction, in the spectral range of 450–700 nm, with control of the linear polarization. We also simulate the system using the Fourier modal method (FMM) in guided configuration [20], which is specifically suited for this type of problem.

Measured and calculated radiation patterns present a great variety of shapes, as well as a great sensitivity to a change of parameters, such as linewidth, line height, or wavelength. We present a brief parametric study to provide some guidelines and references concerning the effect on the radiation pattern of the wavelength, the polarization, or the nanowire size. In TM polarization, LSPR excitations are observed in the radiated intensity for a given wavelength. The spectral position of the resonances depends on the wire size and material. We also discuss effects other than the radiated far field, such as the absorption spectrum and the optical near-field topology.

2. SAMPLE DESIGN AND FABRICATION

The experimentally studied samples consist of single gold nanowires of different widths, deposited on ion-exchanged waveguides. The waveguides were fabricated by surface silver ion-exchanged on glass [21,22]. In the visible spectrum, this technology presents the advantages of low propagation losses, low birefringence, and compatibility with optical fibers. The nanowires were fabricated on the waveguides by using electron-beam lithography. A chromium layer of estimated thickness of 3 nm was used to allow correct adhesion of gold on the glass surface.

In Fig. 1, we display a 3D schematic and scanning electron micrograph of one of the samples. The width of the ion-exchanged waveguide is 1.3 μm, and the gold nanowire width is $50\pm 10\mathrm{nm}$ for the first sample and $150\pm 10\mathrm{nm}$ for the second one. The nanowire thickness was measured by atomic-force microscopy to be $70\pm 5\mathrm{nm}$ for the total thickness (including chromium layer) and the nanowire length is roughly 20 μm (much larger than the waveguide width).

 

Fig. 1. (a) Representation of the waveguide-coupled nanowire antenna. (b) Scanning-electrons micrography of our widest waveguide-coupled gold nanowire (height: 70 nm; width: 150 nm; length: 20 μm) on top of a silver ion-exchanged waveguide (width: 1.4 μm). The waveguide appears as a faint contrast horizontal gray band, and the nanowire is the vertical white line.

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3. MEASUREMENT SETUP AND CALIBRATION

A. Description of the Setup

The purpose of the experimental setup is to quantitatively characterize the radiation pattern of an isolated nanowire coupled to a waveguide, including the ability to study its spectral properties and to control the polarization state of the guided wave.

The light radiated by the nanowire is collected by a high numerical aperture microscope objective (Fig. 2). Unlike the traditional microscope configuration, where the object plane (sample) is conjugated with the detector (camera CCD), our configuration uses an additional lens to conjugate the CCD camera with the Fourier plane of the microscope objective. The intensity distribution as a function of the wave-vector direction is then directly recorded by the CCD detector. This additional Fourier lens is removable in order to allow direct imaging of the sample. We need this direct imaging, particularly during the alignment of the nanowire with the microscope optical axis.

 

Fig. 2. Description of the measurement setup.

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We use a supercontinuum laser white source, filtered through an acousto-optics tunable filter, delivering a quasi-monochromatic signal with an adjustable wavelength in the 450–700 nm spectral range and a 5 nm bandwith. This light is linearly polarized and is delivered to the waveguide by single-mode polarization maintaining fibers. For obtaining a reference signal, a second fiber is used to collect the light at the end of the waveguide. Each fiber is mounted onto a rotating holder to control the polarization direction.

B. Calibration Procedure

For a quantitative characterization of the nanowire radiation pattern, the radiated intensity has to be normalized by the guided light intensity $I_0(\lambda )$ (Fig. 2). However, $I_0(\lambda )$ cannot be obtained by direct measurement. We can only measure the intensities of the light before the coupling $I_{\text{in}}(\lambda )$ and the light that does exit from the waveguide and is recoupled into the second optical fiber $I_{\text{out}}(\lambda )$. These quantities differ from $I_0(\lambda )$ due to the losses that occur either at the coupling between the optical fibers and the waveguide or during the propagation in the waveguide (absorption and scattering losses). Moreover, these losses are strongly wavelength-dependent. For the determination of $I_0(\lambda )$, we perform two series of measurements: one where we couple the light into the waveguide entry $e_1$ and measure the scattered light $S_{e_1}(\lambda )$ and the transmitted light $I_{\text{out},e_1}(\lambda )$, and the other where we couple the light into entry $e_2$ and measure the scattered light $S_{e_2}(\lambda )$ and the transmitted light $I_{\text{out},e_2}(\lambda )$. When coupling from entry $e_1$, we have the relationships

4. MODELING

The numerical results reported in this paper have been obtained using the 2D FMM in guided configuration [20], which is a specific adaptation of the classical FMM (also known as rigorous coupled wave analysis) [23,24] to the case of guiding structures.

Since the method is based on Fourier decomposition, an artificial periodization in the real space results from the discretization in the space of spatial frequencies. This artificial periodization of the structure is made in the ($z$) direction, transverse to the waveguide [Fig. 3(a)]. Perfectly matched layers (PMLs) are used to avoid cross-cells interference effects.

 

Fig. 3. (a) Principle of artificial periodization along the $z$ axis of the structure for guided FMM computation. (b) Real part of the magnetic field (TM polarization). (c) Real part of the radiated magnetic field obtained after subtraction of the guided mode. Nanowire cross section $50\mathrm{nm}\times 50\mathrm{nm}$, wavelength 520 nm, TM polarization.

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The complete set of transversal modes of the guiding structure surrounded by the PML is expressed in terms of a Fourier decomposition and is propagated along the waveguide as long as the structure remains unchanged. When a change occurs in the guiding structure (like the presence of the nanowire), a new set of modes are calculated and matched with the preceding one by applying the boundary conditions for the electromagnetic field.

The field distribution as a function of the wave vector $k_x$ is obtained by a Fourier decomposition of the real space ($x$) distribution in an homogeneous region (substrate or superstrate). An effective index method allows us to model the 3D ($xyz$) guiding structure by a 2D ($xz$) approximation, which is well verified for low-contrast waveguides. The absorption of the nanowire is then computed using the following expression:

A typical result of the guided FMM is shown in Figs. 3(b) and 3(c). 1600 harmonics were used for the computation. The nanowire size was set to 50 nm height and 50 nm length. The amplitude of the magnetic field is shown on Fig. 3(b) when TM polarized light is injected at the left input. Figure 3(c) shows the real part of magnetic field radiated by the nanowire. For this purpose, the guided mode has been simply removed from the set of eigenmodes corresponding to the total magnetic field to only observe the radiated modes. This mode manipulation is straightforward when using a computational method based on mode expansion such as the guided FMM. We can also observe the effect of the PMLs characterized by the high decrease of the light in the up and down layers of the window.

All calculations presented here consider a glass substrate with a refractive index of 1.5, a waveguide thickness of 1 μm with an effective refractive index of 1.51, a gold nanowire of rectangular shape section, in contact with the waveguide and a cover layer with refractive index of 1. All refractive indices were taken from [25] and the 3 nm Cr layer was not taken into account [26].

5. RADIATION PATTERN SHAPE AND DIRECTIVITY

A. General Description of the Radiation Pattern

1. Bidimensional Aspect

In Fig. 4(a) we show an example of radiation pattern of a 50 nm width nanowire for TM polarization, obtained by the experimental setup described Fig. 2. The center of the image corresponds to the direction normal to the sample ($z$ axis). The doted circular line corresponds to the limit of the numerical aperture. Vertical direction ($x$ axis) corresponds to the direction parallel to the waveguide and horizontal direction ($y$ axis) to the direction of the nanowire.

 

Fig. 4. (a) Example of a waveguide-coupled nanowire radiation pattern observed with the setup described Fig. 2. The transverse variation ($k_y$) is essentially linked to the Fourier transform of the guided mode, while the longitudinal variation $k_x$ (parallel to the waveguide) varies in a complex manner linked to the nanowire properties (size, shape, material), the field properties (wavelength, polarization), the waveguide depth, and the permittivity of the surrounding media. (b) Radiation pattern divided by its average $k_x$ variation, showing a $k_x$ and $k_y$ independence.

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An important property of the radiation pattern, is a quasi-independence of the $k_x$ and $k_y$ variations. In other words, the bidimensional radiated intensity distribution $I(k_x,k_y)$ is well approximated by the product of two unidimensional functions $I_x(k_x)$ and $I_y(k_y)$

This could be easily demonstrated by dividing the bidimensional variation $I(k_x,k_y)$ by its average $k_x$ variation, showing a result that no longer depends on $k_x$ [Fig. 4(b)].

This quasi-$k_x$ and $k_y$ independence is explained by the geometry of the problem: in the $y$ direction, the nanowire is almost infinite ($\sim 20\mathrm{\mu m}$) as compared with the width of the guided mode ($\sim 1\mathrm{\mu m}$). Moreover, the relative index variation at the level of the waveguide is very low ($<1\%$) and can be neglected when compared to the gold/glass refractive index ratio. In other words, for the study of the scattering properties, the structure is well approximated by a structure invariant in the $y$ direction, illuminated by a field varying in the $y$ direction, according to the guided mode. With this assumption, we expect the $k_y$ variation of the radiation pattern $E(k_y)$ to be simply the linear superposition of plane waves, resulting from the $E(y)$ field distribution above the waveguide:

2. Radiation in the Substrate and Superstrate

With our experimental setup (Fig. 2), we only measured the radiation pattern in the superstrate. However, we are able to calculate it in both the superstrate and substrate. Figure 5 shows the $k_x$ variation of a calculated radiation pattern in the substrate and superstrate for a 50 nm width and 50 nm height gold nanowire.

 

Fig. 5. Schematic 2D representation of the waveguide-coupled nanowire, superimposed with a calculated radiation pattern. The distribution of scattered light is bigger in the medium with higher refractive index (substrate).

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The main part of the radiated field lies in the medium of higher refractive index [27]. For our sample configuration, since the core of the waveguide has necessarily a higher refractive index than its cladding, most of the field radiated by the nanowire will be in the direction of the waveguide, which also corresponds to the direction of the substrate. We also observe a more complex shape in the substrate, due to multiple interferences effects.

B. Longitudinal Variation

1. Overview

We have measured the radiation patterns in the superstrate for the 50 nm width and 150 nm width gold nanowires, in TE an TM polarization, and for wavelength in the 450–700 nm range. Our results show that the longitudinal variation of the radiation patterns is full of complex and parameter sensitive information. Only electromagnetic modeling or measurements allow an accurate quantitative description of the pattern. Here we give some qualitative properties and comments, based on our measurements and FMM calculations.

Figure 6 illustrates the waveguide-coupled nanowire directivity, for the 50 and 150 nm width nanowires, in TM and TE polarization. Notice that amplitude scale is different for each diagram of Fig. 6 and that measurements are scaled to calculated data (with roughly the same coefficient for each diagram) for an emphasis on directivity. Quantitative evolution of the measured amplitude is given in the next section.

 

Fig. 6. Radiation patterns of a single waveguide-coupled nanowire at 700 nm. Dotted line: measurements; continuous line: theory. Left side: TM polarization (magnetic field parallel to the nanowire); right side: TE polarization. Top: 50 nm width nanowire; bottom: 150 nm width nanowire. Incident guided wave comes from the left. Amplitude scale on the radial axis concerns calculated data.

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Concerning the 50 nm width nanowire, we observe a radiation pattern varying roughly as a $\cos \theta$ in TE polarization. Such variation corresponds to the radiation pattern of a dipole on an interface [17]. At a 700 nm wavelength, for a 50 nm width nanowire, a simple dipole approximation begins to give some useful insights on the situation. Slight oscillations, particularly at grazing angles, are observed in the calculated patterns. These oscillations are not numerical noise but correspond to interference fringes due to multiple reflections in the waveguide. Oscillations observed in the measured radiation pattern are a mix of interference fringes and experimental noise.

In TM polarization, the 50 nm nanowire radiation pattern shows a minimum in the normal direction ($\theta =0$). This behavior can be explained by the fact that, for a small object, the polarization state is essentially maintained by the scattering process. Since in TM polarization the electric field is almost perpendicular to the waveguide top interface and because the field has to be orthogonal to the propagation direction, the scattered intensity is necessarily weak in this direction. It also explains the overall low scattering amplitude for a small nanowire in TM polarization (see amplitude scale on the radial axis). When the size of the scatterer increases, the polarization state is no longer maintained by the scattering process, and the 150 nm width nanowire radiation pattern does not show such local minimum. Moreover it shows a considerably higher integrated scattering intensity ($\times 50$ factor). Resonant effects may also be involved at this wavelength. For this 150 nm nanowire, we can notice that the scattered field is oriented in the backward direction in TM polarization, while it is in the forward direction for TE polarization.

Figure 6 also illustrates the good agreement between the measurements and our calculations for the radiation pattern directivity.

2. Effect of Size, Wavelength, and Polarization on the Longitudinal Variation

Figure 7 presents calculated longitudinal variations of radiation patterns in the superstrate for several sizes of nanowire and wavelength and for both polarizations. These figures have the purpose of providing references and illustrate the wide variety of pattern shapes and parameter sensitivity.

 

Fig. 7. Effects of various parameters on the radiation pattern (simulations). Top: effect of the nanowire width $d$ for a 50 nm height nanowire at a 520 nm wavelength. Middle: effect of the nanowire eight, $h$, for a 50 nm width nanowire at a 520 nm wavelength. Bottom: effect of the wavelength, $\lambda$, for a 50 nm width and 50 nm height nanowire. Right: TM polarization. Left: TE polarization.

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Not surprisingly, Figs. 7(a)–7(d) show a global increase in the scattering amplitude with the nanowire size. Complex variations, high sensitivity to a change of one parameter and wide variety of shapes are observed in TM polarization, while more regular variations and more regular shapes, except for the waveguide interference oscillations, are observed in TE.

The wavelength dependence, in the spectral range 400–1000 nm, is illustrated on Figs. 7(e) and 7(f). We observe that the radiation pattern reaches a maximal scattering amplitude for $\approx 600\mathrm{nm}$ in TM polarization, while in TE polarization the amplitude increases globally with the wavelength.

6. SPECTRAL PROPERTIES AND RESONANCES

A. Scattered Intensity in the Superstrate

If we integrate the radiation pattern intensity [Figs. 7(e) and 7(f)] within the limits of the numerical aperture, $\pm 71.8°$, we obtain the integrated radiated intensity as represented on Fig. 8.

 

Fig. 8. Spectral variations of the integrated radiated intensity in the superstrate for 50 and 150 nm width gold nanowires in TM and TE polarizations. Experimental points are obtained as follows: for each wavelength, a quasi-monochromatic light is coupled in the waveguide, and the radiation pattern is measured, then angularly integrated. The calibration procedure described in Section 3.B is used to correct data from spectral variations from the source and transmission coefficients in the waveguide and fiber. Continuous lines correspond to guided FMM calculations. Vertical scale corresponds to calculations. Each experimental spectrum is multiplied with an arbitrary constant coefficient for visual comparison with calculations.

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When the electric field is parallel to the wire (TE) we observe, for 50 and 150 nm wires, a globally increasing scattering efficiency with the wavelength (Fig. 8). Part of the explanation of this behavior comes from the fact that gold becomes more conductive when the wavelength goes in the infrared region [25] and thus scatters the light more efficiently. The same kind of behavior is observed for other metals in the same spectral region (Fig. 9). On the other hand, the reduction of the ratio scatterer size/wavelength induces a reduction in the scattering efficiency as illustrated in Fig. 9 for a titanium dioxide nanowire (which refractive index is constant in this region). This reduction effect seems to be overcompensated by the refractive index effect in the case of metals.

 

Fig. 9. Other materials than gold. Scattering in the superstrate and absorption for TM and TE polarizations.

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In TM polarization (electric field perpendicular to the wire), 50 and 150 nm width nanowires show LSPR in the radiated intensity. The position of the 150 nm nanowire LSPR ($\approx 670\mathrm{nm}$ for experiments and $\approx 680\mathrm{nm}$ for simulations) is red shifted compared to the 50 nm nanowire ($\approx 580\mathrm{nm}$ for experiments and $\approx 530\mathrm{nm}$ for simulations). Red shifting of the resonance when size increases is a well-known result [17]. For other materials than gold (Fig. 9), LSPR are observed at $\approx 450\mathrm{nm}$ for silver and $\approx 600\mathrm{nm}$ for copper; other metals do not show any LSPR in the 400–1000 nm spectral range.

For all experimental plots of Fig. 8, oscillations with a noisy aspect can be observed for $\lambda \lesssim 500\mathrm{nm}$. These oscillations are the results of mode beatings in the waveguide, which becomes single-mode only after roughly 500 nm.

B. Absorption, Materials Dispersion, and Near-Field Distribution

Although the main subject of this paper is the study of the radiated far-field field, we discuss here some other important physical effects in order to have a full figure of the problem.

From the viewpoint of the guided signal, scattering mainly corresponds to losses. The other significant factor of the losses is absorption by the nanowire. In Figs. 9(c) and 9(d), calculated absorption losses are presented for a $50\mathrm{nm}\times 50\mathrm{nm}$ five-waveguide-coupled nanowire for different materials.

In TM polarization, we observe a strong absorption peak related to the excitation of LSPR for gold, silver, and copper nanowires. They are related to maxima slightly redshifted in the radiation spectrum. This is a well-known property of LSPR on nanoparticles [28]. The strongest LSPR is obtained for a silver nanowire. Compared to gold, the silver nanowire’s LSPR is blueshifted, whereas it is slightly redshifted for the copper nanowire. While absorption is globally higher than radiated intensity in the superstrate (Fig. 9), it is of the same order of magnitude when we consider the sum of scattered light in the substrate and in the superstrate.

In TE polarization, it is noticeable that the chromium nanowire absorbs more than the other metals and that absorption for a silver nanowire remains very weak and quasi-constant over the entire spectrum. In addition, resonances in the absorption spectrum for gold, copper, and aluminum are clearly visible; they are related to electronic interband transitions between holes and electrons in the conduction band near the Fermi surface [29]. This absorption peak occurs around 470 nm [30] for gold, around 600 nm for copper [31], and around 830 nm for aluminum [32]. Moreover, it is clearly noticeable that the interband transitions are also visible in the radiation spectra [Fig. 9(d)] where they produce local minima in the radiated intensity, slightly redshifted (around 500 nm for gold) from their spectral position in the absorption spectra.

Finally, the near-field amplitude maps calculated for both TE and TM polarization at wavelength of 520 nm for a $50\mathrm{nm}\times 50\mathrm{nm}$ gold nanowire are shown in Fig. 10. This wavelength corresponds to the maximum of scattering efficiency seen in Fig. 8 and is related to the excitation of the LSPR expected in TM polarization. As clearly observed, there is actually a significant change in the field repartition when comparing the two maps. The main difference lies in a local enhancement of the field amplitude in TM at the four corners of the wire. Moreover, it can be seen that the field is further enhanced around the lower corners, just at the interface with the waveguide.

 

Fig. 10. Maps of the electric field amplitude calculated for the wavelength corresponding to the LSP mode resonance of Fig. 8 at a wavelength of 520 nm: (left) TE polarization and (right) TM polarization.

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7. CONCLUSION

Coupling a nanowire with a waveguide is one of the simplest ways to locally connect the waveguide with a far-field propagating signal. The radiation pattern resulting from this coupling is quite complex and carries information on the guided signal, such as intensity, polarization, or propagation direction. The radiation pattern shape can be tuned by adjusting the dimensions of the nanowire in order to respond to a given purpose in term of directivity or coupling efficiency. The coupling efficiency is also easily tuned by adjusting the distance between the nanowire and the waveguide.

Gold nanowires clearly show experimental evidence of LSPR effects when the electric field is perpendicular to the wire. These resonances are characterized in the far field by a maximum in the scattering efficiency and in the near field by a strong local field enhancement. Exploitation of these plasmonic effects in a completely integrated way should be possible with these types of components, as long as the coupling between the waveguide and the nanowire is sufficient to ensure a good signal-to-noise ratio at the waveguide output.