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Nanophotonics has the potential to provide novel devices and systems with unique functions based on optical near-field interactions. Here we experimentally demonstrate, for the first time, what we call a quadrupole–dipole transform achieved by optical near-field interactions between engineered nanostructures. We describe its principles, the nanostructure design, fabrication of one- and two-layer gold nanostructures, an experimental demonstration, and optical characterization and analysis.
©2009 Optical Society of America
1. Introduction
Nanophotonics is a novel technology that utilizes light–matter optical near-field interactions occurring locally in the nanometer-regime [1]. The fundamental mechanisms involved, such as energy transfer via optical near-fields [2–4], have been extensively studied. Also, technological vehicles for nanophotonics have seen rapid progress, such as in geometry-controlled quantum dots [5] and metal nanostructures [6]. The well-known merits of nanophotonics include the ability to break though the diffraction limit of light [7] and local field enhancement thanks to the resonances between light and nanostructures [8], which enhances existing performance figures. However, nanophotonics could also achieve novel functions and systems that are unachievable with conventional technologies [9]. In this paper, we experimentally demonstrate what we call a quadrupole–dipole transform, achieved by optical near-field interactions between engineered nanostructures. We begin with the principles of the quadrupole–dipole transform, followed by the shape design on the nanometer-scale, fabrication of one- and two-layer metal nanostructures, and their optical characterization and analysis.
2. Quadrupole–dipole transform
We first explain the principles of the quadrupole–dipole transform. There are several physical implementation methods that can achieve such a transform using optical near-field interactions. One is based on optical excitation transfer between quantum dots via optical near-field interactions [1,10]. For instance, assume two cubic quantum dots whose side lengths L are a and , which we call QDA and QDB, respectively, as shown in Fig. 1(a) . Suppose that the energy eigenvalues for the quantized exciton energy level specified by quantum numbers in a QD with side length L are given by
where EB is the energy of the exciton in a bulk crystal, and M is the effective mass of the exciton. There exists a resonance between the level of quantum number (1,1,1) for QDA and that of quantum number (2,1,1) for QDB. There is an optical near-field interaction, which is denoted by U, due to the steep gradient of the electric field in the vicinity of QDA. Therefore, excitons in QDA can transfer to the (2,1,1) level in QDB. Note that such a transfer is prohibited if based on propagating light since the (2,1,1) level in QDB contains an even number. In other words, a near-field excitation can populate even the antisymmetric states of the coupled system, or the dark states, whereas a far-field excitation can excite only the symmetric states, that is, the bright states [1]. In QDB, the exciton relaxes to the lower energy sublevel (1,1,1) with a time constant Γ, which is faster than the near-field interaction. Therefore, the exciton finally transfers to the (1,1,1) level of QDB. Also, this sublevel relaxation, or energy dissipation, that occurred at QDB guarantees unidirectional energy flow from QDA to QDB. Here we can find a quadrupole–dipole transform in the transition from the (2,1,1) level to the (1,1,1) level in QDB, and such a transform is unachievable without the optical near-field interactions between QDA and QDB, which allow the (2,1,1) level in QDB to be populated with excitons [11,12].
Fig. 1 (a) A quadrupole–dipole transform in the transition from the (2,1,1) level to the (1,1,1) level in QDB. Such a transform is unachievable without the optical near-field interactions between QDA and QDB, which allow the (2,1,1) level in QDB to be populated with excitons. (b) A quadrupole–dipole transform is also achieved through shape-engineered nanostructures and their associated optical near-field interactions.
Another way of realizing a quadrupole–dipole transform is based on shape-engineered metal nanostructures, which are the principal concern of this paper. In previous work, we have numerically shown that two metal nanostructures can be designed to exhibit far-field radiation only when their shapes are appropriately configured and when they are closely stacked [13,14]. As discussed in detail below, here we can also find a quadrupole–dipole transform in the sense that individual single planes of the nanostructures work as quadrupoles, but they behave as a dipole when two planes of the nanostructures are appropriately configured. In the following, we discuss the shape design of the nanostructures and their experimental fabrication, and we describe optical characterization of the quadrupole–dipole transform.
3. Designing nanostructural patterns
We first design two nanostructural patterns, called Shape A and Shape B hereafter. Shape A and Shape B were designed as aligned rectangular units on an xy-plane with constant intervals horizontally (along the x-axis) and vertically (along the y-axis), respectively. When we irradiate Shape A with x-polarized light, surface charges are concentrated at the horizontal edges of each of the rectangular units. The relative phase difference of the oscillating charges between the horizontal edges is π, which is schematically represented by + and – marks in Fig. 1(b). Now, note the y-component of the far-field radiation from Shape A, which is associated with the charge distributions induced in the rectangle. We draw arrows from the + mark to the – mark along the y-axis. We can find that adjacent arrows are always directed oppositely, indicating that the y-component of the far-field radiation is externally small. In other words, Shape A behaves as a quadrupole regarding the y-component of the far-field radiation. It should also be noted that near-field components exist in the vicinity of the units in Shape A. With this fact in mind, we put the other metal nanostructure, Shape B, on top of Shape A. Through the optical near-fields in the vicinity of Shape A, surface charges are induced on Shape B. What should be noted here is that the arrows connecting the + and – marks along the y-axis are now aligned in the same direction, and so the y-component of the far-field radiation appears; that is, the stacked structure of Shape A and Shape B behaves as a dipole. Also, Shape A and Shape B need to be closely located to invoke such effects since the optical near-field interactions between Shape A and Shape B are critical. In other words, a quadrupole–dipole transform is achieved through shape-engineered nanostructures and their associated optical near-field interactions.
In order to verify this mechanism of the quadrupole-dipole transform by shape-engineered nanostructures, we numerically calculated the surface charge distributions induced in the nanostructures and their associated far-field radiation based on a finite-difference time-domain (FDTD) electromagnetic simulator (Poynting for Optics, a product of Fujitsu, Japan).
Figure 2(a) schematically represents the design of (i) Shape A only, (ii) Shape B only, and (iii) a stacked structure of Shape A and Shape B, which consist of arrays of gold rectangular units. The length of each of the rectangular units is 500 nm, and the width and height are 100 nm, identical to the dimensions of the experimental devices discussed in Section 4. As the material, we assumed a Drude model of gold with a refractive index of 0.16 and an extinction ratio of 3.8 at a wavelength of 688 nm [15].
Fig. 2 (a) Specifications of the three types of nanostructures used in numerical evaluation of the conversion efficiency based on the FDTD method: Shape A only, Shape B only, and a stacked structure of Shapes A and B. (b,c) Surface charge density distributions induced in (b) Shape A only and (c) Shape B only. (d) Surface charge density distribution induced in Shape B only when it is stacked on top of Shape A only. (e) Calculated performance figures of the quadrupole–dipole transform, namely, polarization conversion efficiency, with three types of nanostructures. (f) Selective comparison at a wavelength of 690 nm.
When irradiating these three structures with continuous-wave x-polarized input light at a wavelength of 688 nm, Fig. 2(b), 2(c) and 2(d) respectively show the induced surface charge density distributions (simply called surface charge hereafter) by calculating the divergence of the electric fields. For the Shape A only structure (Fig. 2(b)), we can find a local maximum and local minimum of the surface charges, denoted by plus and minus marks. When we draw arrows from plus marks to minus marks between adjacent rectangular units, as discussed in Section 2, we can see that the arrows are always directed oppositely between the adjacent ones, meaning that the Shape A only structure behaves as a quadrupole for the y-components of the far-field radiation. For the Shape B only structure (Fig. 2(c)), the electron charges are concentrated at the horizontal edges of each of the rectangular units, and there are no y-components that could contribute to the far-field radiation. Figure 2(d) shows the surface charge distributions induced in Shape B when it is stacked on top of Shape A. We can clearly see that the electron charges are induced at the vertical edges of each of the rectangular units, and they are arranged in the same directions. In other words, a dipole arrangement is accomplished with respect to the y-component, leading to a drastic increase in the far-field radiation.
Now, one of the performance figures of the quadrupole–dipole transform is
where Ix -IN and Iy -OUT represent the intensities of the x-component of the incident light and the y-component of the radiated light, respectively. We irradiate a short optical pulse with a differential Gaussian form whose width is 0.9 fs, corresponding to a bandwidth of around 200 to 1300 THz. Figure 2(e) shows I conv as a function of the input light wavelength, and Fig. 2(f) compares I conv specifically at 690 nm, which is the wavelength used in the experiment described below. I conv appears strongly with the stacked structure of Shapes A and B, whereas it exhibits a small value with Shape A only and Shape B only. We can clearly see the quadrupole–dipole transform as the change of I conv from the individual single-layer structures to the stacked one.4. Fabrication and demonstration
In the experiments, we fabricated structures consisting of (i) Shape A only, (ii) Shape B only, and (iii) Shape A and Shape B stacked. Although the stacked structure should ideally be provided by combining the individual single layer structures, in the following experiment, the stacked structure was integrated in a single sample as a solid two-layer structure to avoid experimental difficulty in precisely aligning the individual structures mechanically. The fabrication process was as follows.
- (1) Spin coat Espacer 300Z and resist solution 2EP-520A at a thickness of 350 nm on a sapphire substrate to be subjected to electron-beam (EB) lithography.
- (2) Fabricate the first layer (Shape A) by EB lithography, and vacuum-evaporate an Au layer to a thickness of 100 nm.
- (3) Lift-off the Espacer layer and EB resist layer with 2EP-A and acetone. Then sputter an SiO2 layer to a thickness 200 nm to form a gap layer between the first and second layers.
- (4) Fabricate the second layer (Shape B) in a similar manner to the above processes.
Figure 3(a) schematically represents cross-sectional profiles of these fabrication processes, where (i) Shape A-only structures are fabricated in the first layer, (ii) Shape B-only structures are fabricated in the second layer, and (iii) stacked structures have Shapes A and B in the first and second layers, respectively. Figure 3(b) also shows scanning electron microscopy (SEM) images of fabricated samples of (i), (ii), and (iii). Because the stacked structure was fabricated as a single sample, the gap between Shape A and Shape B was fixed at 200 nm.
Fig. 3 (a) Schematic diagram of the fabrication process of the two-layer nanostructure. The stacked structure was integrated in a single sample as a solid two-layer structure to avoid experimental difficulty in precisely aligning the individual structures mechanically. (b) SEM images of each structure.
The performance of the quadrupole–dipole transform, in terms of the polarization conversion efficiency I conv given by Eq. (2), was experimentally evaluated by radiating x-polarized light on each of the areas (i), (ii), and (iii) and measuring the intensity of the y-component in the transmitted light. The light source was a laser diode with an operating wavelength of 690 nm. Two sets of Glan-Thompson prisms (extinction ratio 10−6) were used to extract the x-component for the input light and to extract the y-component in the transmitted light. The intensity was measured by a lock-in controlled photodiode. The position of the sample was controlled by a stepping motor with a step size of 20 μm.
Figure 4(a) shows I conv as a function of the position on the sample, where I conv exhibited a larger value specifically in the areas where the stacked structure of Shapes A and B was located, which agrees well with the calculated result shown in Fig. 2(c).
Fig. 4 (a) Measured conversion efficiency for the three types of nanostructures. Conversion efficiency exhibited a larger value specifically in the areas where the stacked structure of Shapes A and B was located. (b) Conversion efficiency within the area of the stacked structure of Shapes A and B. SEM images are also shown corresponding to the evaluation position. Conversion efficiency exhibited a larger value when the misalignment between Shape A and Shape B was minimized.
The conversion efficiency with the Shape B only structure is slightly larger than that with the Shape A only structure, as shown in Fig. 4(a), which exhibits behavior opposite that obtained in the simulation shown in Fig. 2(f). Also, the magnitude of the increase of the conversion efficiency from the stacked structure of Shapes A and B is not drastic compared with that predicted by the simulation in Fig. 2(f). We attribute such effects primarily to the inhomogeneity of the shapes and the layout of the experimental devices, as implied from the SEM images in Fig. 3(b). The slight rotational misalignment between the irradiated light and the device under study and other factors could be involved in this effect.
Although I conv exhibited a larger value at the stacked structure, the signals fluctuated within the corresponding area. This was due to the variance of the misalignment between the first layer (Shape A) and the second layer (Shape B), as observed in the SEM images shown in Fig. 4(b). From Fig. 4(b), we can see that I conv exhibited a larger value when the misalignment between Shape A and Shape B was minimized. The variance of the misalignment was presumably due to drift effects in the lithography process during fabrication.
The alignment tolerances were further analyzed as shown below. From the SEM images in Fig. 4(b), horizontal and vertical misalignments were respectively evaluated as and shown in Fig. 5(a) . Figure 5(b) and 5(c) respectively show I conv as a function of the horizontal and vertical misalignments. Solid lines represent calculated results, and the left-hand axis and right-hand axis represent the conversion efficiency of the experimental and calculated results, respectively. Although the absolute values of the efficiency were different between the experiments and simulations, they showed similar dependence on the misalignment. If we define the alignment tolerance as the maximum misalignment that yields 10% of the maximum efficiency, the horizontal and vertical alignment tolerances are respectively estimated to be about 150 nm and 200 nm.
Fig. 5 (a) Horizontal and vertical misalignments between Shape A and Shape B denoted by and , and (b), (c), their relations to conversion efficiency. (d) Schematic cross-sectional profiles of samples with different gaps. The thickness of the SiO2 gap layer between the first and second layers was set in three steps. (e) The conversion efficiency decreased as the gap increased. The result validates the principle of the quadrupole–dipole transform that requires optical near-field interactions between closely arranged nanostructures.
In order to analyze the gap dependency of the conversion efficiency, other samples were also fabricated. As shown in Fig. 5(d), the thickness of the SiO2 gap layer between the first and second layers was 143 nm, 216 nm, and 363 nm. As shown in Fig. 5(e), the conversion efficiency decreased as the gap between the layers increased, which also validates the principle of the quadrupole–dipole transform that requires optical near-field interactions between closely arranged nanostructures.
5. Conclusion
Finally, we make a few remarks regarding the quadrupole–dipole transform demonstrated in this study. We can further engineer many more degrees-of-freedom on the nanometer-scale while using far-field radiation for straightforward characterization. For practical use, on the other hand, more precise fabrication of nanostructures and more precise alignment between the two layers are necessary. Optical near-field lithography would be one solution for the mass production of large-area nanostructures [16,17]. As for alignment, use of Micro Electro Mechanical Systems (MEMS) technologies [18] would be one option to resolve the alignment difficulties.
From a system perspective, the quadrupole–dipole transform can be regarded as a kind of mutual authentication or certification function of two devices, meaning that the authentication of Device A (with Shape A) and Device B (with Shape B) is achieved through the quadrupole–dipole transform. Because such fine nanostructures are difficult to falsify, the vulnerability of a security system based on this technology is expected to be extremely low.
Another relevant issue is to seek more general theories that account for the relationship between the shapes and layout of nanostructures and their associated hierarchical optical properties at the sub-wavelength scale [19]. Dependence on the internal structures of the materials could be exploited [20]. Also, dependence on operating wavelengths and other physical perspectives [21] could be understood possibly in a unified manner. We will explore these issues more fully in future work.
In summary, we have described a quadrupole–dipole transform based on optical near-field interactions in nanostructures and, for the first time to the best of our knowledge, experimentally demonstrated its operating principle by fabricating and characterizing shape-engineered one- and two-layer gold nanostructures. The performance of the experimental system agreed with numerical estimations.
Acknowledgement
This work was supported by the research project of the New Energy and Industrial Technology Organization, Japan, and Special Coordination Funds for Promoting Science and Technology, Japan.
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