1. Introduction

Diffraction limit poses a fundamental restriction on the resolution of traditional optical microscopy, as well as the minimum size of photonic devices. To reduce the size of photonic devices to subwavelength scale and to meet the challenge of nanophotonics[1, 2], it is essential to overcome optical diffraction limit. Recently, metallic nanostructures (nanoparticles, nanoshell, nanogroove, nanohole, and etc.) become attractive to scientists and engineers, since the interaction between electromagnetic waves and metallic nanostructures exhibits fascinate phenomena, like highly localized field enhancement, extraordinarily light transmission[3] and nonlinear optical response[4], via the excitation of surface plasmon resonance[5]. The surface plasmon mode supported by metallic nanostrucutres is evanescent plasmon polariton and provides an approach to overcome the diffraction limit of light. Especially the surface plasmon modes of metallic nanoparticles[6] are being explored for various applications in chemical and biological sensors[7], nanophotonic devices[1], plasmonics[8], etc. By manipulating the localized surface plasmon resonance, local field enhancement, and near-field coupling of nanoparticles, it is promising to be able to focus, to transport, and to interact with light in nano-scale region.

One apparent area of nanophotonic application is high-density optical storage. To achieve high recording density beyond diffraction limit, near-field optical technology has been applied to various high-density optical storage systems. In the near-field optical data storage, the readout signals include not only the propagating diffraction light but also the nonpropagating (or evanescent) light by a fiber probe, a micro-lens, or nanoparticles. The far-field fluorescence microscopy could also achieve super-resolution beyond optical diffraction limit by stimulated emission since scanning with a smaller fluorescent spot signifies increased spatial resolution.[9, 10] In contrast to near-field scanning optical microscopy, this method can produce three-dimensional images and have found applications in three-dimensional optical data storage. In addition to conventional scanning near-field microscopy technology [11] and solid immersion lens[12], the super-resolution near-field structure (super-RENS) which was proposed by Tominaga et al.[13] has overcome the difficulty of near-field distance control and is able to realize high-density near-field optical data storage in a feasible way. Comparing with conventional optical disks, super-RENS disks usually add three-layer structure – a near-field active layer between two protective dielectric layers. The protective dielectric layers avoid abrasion and is responsible for the near-field distance control between the near-field active layer and the phase-change recording layer. The nanostructure in the near-field active layer is the main device to realize super-resolution for the super-RENS disks. There are several types of super-RENS disks. Sb-type super-RENS disks was the first one and then AgO_x-type super-RENS disks appeared as a re-writable media for better performance[14]. The PtO_x-type super-RENS was proposed later[15] for improving signal intensity and readout stability. Recently blue laser based super-RENS disks have been fabricated and measured[16, 17]. The distinguishable record mark size is reduced to 16 nm due to shorter wavelength, but there is no significant increase in carrier-to-noise ratio (CNR).

Compared to the Sb-type super-RENS disk, the light-scattering-center-type super-RENS disk (including AgO_x-type and PtO_x-type super-RENS) has stronger local field enhancement and high CNR[14, 15]. Experimental and simulation results[18, 19, 20, 21, 22, 23, 24, 25] indicate that the main working mechanism of light-scattering-center-type super-RENS based on the photo-dissociated metallic nanoparticles in the AgO_x or PtO_x layer generated by laser beam in readout or write process. The collective effects of local field enhancement around metallic nanoparticles because of localized surface plasmon resonances formed strongly scattering center. These nanoparticles function as the fiber tip of conventional scanning near-field microscope. The evanescent waves from subwavelength structures in the recording layer couple with metallic nanoparticles and is transferred into propagating waves which is detectable in far-field regime[26]. Surface plasmon effects from those randomly distributed metallic nanoparticles further enhance the efficiency of evanescent waves coupling and therefore super-RENS disks can efficiently reach the spatial resolution beyond diffraction limit. There is a wide range of applications associated with super-resolution of super-RENS, including lithography[27] and nano-scale device fabrication[28].

Surface plasmon resonance is usually sensitive to the frequency of incident light. For single silver nanoparticle, strong light absorbing and scattering occurs at plasmon resonance frequency and high local fields were excited around the nanoparticle. However, in a system consisting of randomly distributed metallic nanoparticles, the surface plasmon resonance is considerably broaden and resonant condition is modified for particle-particle interaction. It is necessary to study the frequency-dependent responses of the AgO_x-type super-RENS disk to understand the roles of surface plasmon effect and particle-particle interaction. In this paper, we used finite-difference time-domain (FDTD) method to study the near-field and far-field optical responses of the AgO_x-type super-RENS disk with randomly distributed silver nanoparticles embedded in the AgO_x layer at different frequencies. Near-field enhancement and the resolution of the AgO_x-type super-RENS disks was influenced by the frequency of incident light. The silver nanoparticles in the AgO_x layer with high scattering efficiency increased the intensity of the far-field detectable signal. Our simulation results indicated that the super-resolution capability of the AgO_x-type super-RENS disks was connected with the frequency-dependent scattering cross section of single silver nanoparticle.

2. Simulation model

The complex interaction between electromagnetic wave and dispersive materials was simulated by two-dimensional finite-difference time-domain method (FDTD). FDTD method treats complex materials and geometrical shapes without extra difficulty and is suitable to study the complicated interaction between randomly distributed metallic nanoparticles. The FDTD method directly solves two curl Maxwell’s equations which are discretized directly in time and spatial domains[29]. In our simulation, the computational region was 4800 by 600 nm and the grid size was 1 nm. The permittivity of the silver nanoparticles was set by the bulk experimental optical constant[30] and the dispersion behavior of dispersive materials was simulated by the Lorentz dispersion model [31]. The Lorentz dispersion model consists with the free electron model or Drude model for metallic materials in the limit ω >> ω ₀. Although the imaginary part of permittivity of silver nanoparticles is dependent of particle size [32], however, according to experimental results, the surface contribution in our case is not significant. A TM-mode Gaussian beam (the direction of the electric field was in the plane of incident) illuminated from above. The numerical aperture (NA) of incident Gaussian laser beam was 0.6. To simulate the electromagnetic wave propagating in free space, the uniaxial perfect matched layer (UPML) was used as radiation boundary condition.[33]

 

Fig. 1. Scheme of the AgO_x-type super-RENS disk with random silver nanoparticles.

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The structure of the AgO_x-type super-RENS disk with random distribution of silver nanoparticles embedded in the AgO_x layer and with recording marks of different lengths is shown in Fig. 1. The multilayer structure of the AgO_x-type super-RENS disk is air/ disk substrate/ ZnS-SiO₂ (20 nm)/ AgO_x (15 nm)/ ZnS-SiO₂ (20 nm)/ Ge₂Sb₂Te₅ (15nm)/ air. The ZnS-SiO₂ layers with refractive index about 2.25 are protective dielectric layers to prevent abrasion and to hold the released oxygen from the decomposition reaction of AgO_x. The AgO_x layer is between two ZnS-SiO₂ layers and its refractive index is about 2.8. In our simulation, we set Ge₂Sb₂Te₅ (GST) as phase change recording material. The refractive index of GST depends on frequency of incident light. Here, to maintain a uniform recording efficiency, we assumed the refractive index of GST was 4.45 + 1.65i (amorphous) and 4.01 + 3.16i (crystalline) for all frequency [19]. The silver nanoparticles in the AgO_x layer are possibly generated in two ways: in fabrication process and in photo-dissociation reaction. In the fabrication process, the AgO_x layer is deposited by sputtering technology and the nanoparticles distribute in uniform random distribution. On the other hand, the silver nanoparticles in the AgO_x layer will be dissociated by laser beam in readout and writing processes and the distribution of AgO_x is Gaussian random distribution according to the field intensity distribution of laser beam. In our simulation, there were total 560 silver nanoparticles in AgO_x layer, 500 nanoparticles in uniform random distribution and 60 ones in Gaussian random distribution. The full width at half-maximum (FWHM) of the Gaussian distribution was 424 nm. The far-field signals of the AgO_x-type super-RENS disks were calculated from near fields by near-to-far-field transformation based on equivalence theorem and Green’s theorem.[29, 31]. The method is accurate within the limits of the Kirchhoff approximation. Fourier transformation was applied to the transverse components of near fields close to the boundaries of simulation region to obtain the angular distribution of the radiation in the far-field. The intensities were integrated within the numerical aperture of the objective lens. To simulate the reading process of the super-RENS disk, in which the laser beam focuses on the mark and off the mark alternatively, we took the far-field signal difference between the on-mark state and off-mark state as a representation of the readout signals from the super-RENS disks. The on-mark state and off-mark state means that the laser beam focuses on the recording mark and between two recording mark, respectively. The far-field difference signal indicates the resolution of the super-RENS disk.

3. Results and discussion

 

Fig. 2. Movie of the TM-mode near-field distributions of the AgO_x-type super-RENS disk with random silver nanoparticles. The wavelength of incident light is from 400 nm to 827 nm. Front picture presents the case of 650 nm wavelength. The Gaussian beam focused at the recording mark and the size of recording mark was 100 nm. The local fields were enhanced around silver nanoparticles. [Media 1]

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In this work, the near-field and far-field optical responses of the AgO_x-type super-RENS disk with random silver nanoparticles embedded in the AgO_x layer were simulated systematically at different illumination frequencies. The TM-mode near-field distributions in Fig. 2 show that when a Gaussian beam focused on the recording mark, there were highly enhanced local fields around the silver nanoparticles in the AgO_x layer, since localized surface plasmon were excited. With the same distribution of silver nanoparticles, the enhanced local fields around silver nanoparticles varied considerably when they were illuminated by light of different frequencies (wavelengths). Generally, local fields with illumination wavelengths of 400 nm and 690 nm had higher intensity than those of 540 nm and 827 nm. In addition to the wavelength of incident light, the local fields were influenced by particle-particle interaction and exhibited different distributions at different frequencies. Similar phenomenon has been observed in the enhanced local fields of fractal metallic surface.[4] Like the fiber tip of a scanning near-field optical microscope, the silver nanoparticles can transfer the evanescent waves into propagating waves and the local field enhancements around nanoparticles should have a direct influence on the far-field intensity of detectable signals.

 

Fig. 3. Far-field difference signals of the AgO_x-type super-RENS disk with and without silver nanoparticles. The wavelength of incident light was (a) 400 nm, (b) 540 nm, (c) 650 nm, (d) 775 nm.

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The far-field difference signals of the AgO_x-type super-RENS disks with randomly-distributed silver nanoparticles are shown in Fig. 3 to be compared with experimental CNR results. Those results were normalized to the far-field difference signals without any recording mark for each case. If there was no silver nanoparticle in the AgO_x layer, the far-field signals dropped rapidly and became indistinguishable when the size of recording marks was smaller than the optical diffraction limit λ/(4NA). At shorter wavelengths, the minimum distinguishable size of recording marks was smaller. When there were random silver nanoparticles in the AgO_x layer, the far-field difference signals were several magnitudes higher and the recording marks as small as 50 nm were still distinguishable, i.e., recording marks smaller than λ/10 were able to be read. Similar results has been studied from our previous research [23, 25] for illumination wavelength of 650 nm. Here far-field difference signals of the AgO_x-type super-RENS disks with different wavelengths were studied. Unlike those cases without nanoparticles, the far-field difference signals did not decrease monotonously with decreasing recording mark size or increasing incident wavelength. The far-field difference signals with illumination wavelengths of 400 nm and 650 nm had higher intensity than those of 540 nm and 775 nm. The random distribution of embedded silver nanoparticles influenced the near-field enhancements as well as the far-field signals, so the far-field signals had some complex variations, especially for the recording marks smaller than diffraction limit. Comparing with the local fields in Fig. 2, Fig. 3 shows that the intensities of the far-field difference signals were associated to the local-field enhancements at different wavelengths.

 

Fig. 4. Far-field difference signals of the AgO_x-type super-RENS disk with silver nanoparticles as a function of wavelength of incident light. The size of recording marks was larger than diffraction limit of visible light in (a) and smaller than diffraction limit in (b).

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In Fig. 4, the far-field difference signals of each recording mark size were redrawn as a function of illuminating wavelength. In Fig. 4(a), when mark size was larger than diffraction limit of visible light, i.e., around 200 nm for visible wavelength, the far-field difference signals were subject to optical diffraction and became weaker for smaller recording marks. There were two peaks in the far-field signals, one was around 477 nm and another was around 730 nm. There was possibly another peak in the ultraviolet regime. When the mark size was below optical diffraction limit, the far-field signals became complicated and the double-peak feature was also presented in Fig. 4(b). Nonetheless, the peak wavelengths of each smaller recording mark were not the same. The far-field signals of larger mark size were not always stronger than those of smaller mark size in Fig. 4(b). The recording marks of subwavelength size were still distinguishable, since the evanescent light generated by small recording marks was transferred to propagating light by silver nanoparticles. It was noted that the trend of the far-field difference signals was consistent with the trend of the near-field enhancements at different wavelengths.

The optical responses of those randomly distributed silver nanoparticles is complicated, however, one of key points to comprehend those effects is to distinguish the contributions from each nanoparticle and from particle-particle interaction. Here we can compare the far-field signals from random nanoparticles to those from single silver nanoparticle. The scattering efficiency of silver nanoparticles was controllable by particle size, surrounding medium and incident light wavelength, and was important to understand the simulation far-field signals. For single silver spherical nanoparticle, there was one surface plasmon resonance peak in the visible regime. Nevertheless, metallic nanoparticle of different shapes exhibits double (elliptical) or multiple (triangular) surface plasmon resonance. Figure 5 shows that the simulation results of scattering efficiency of single silver nanocylinder in the AgO_x layer. The scattering efficiency with different wavelength exhibited double peaks since the geometric shape of single silver nanoparticle is not perfectly circle in our FDTD numerical simulation and the exact shape of nanoparticle is between a circle and a square. To verify the effect of geometric shape, the scattering efficiency of single silver nanocylinder with increasing diameter was tested. When the diameter of nanocylinder was increased from 3 nm to 10 nm and the shape became closer to a circle, the two peaks graduatedly merged into one peak and the peak wavelength agreed with the theoretical resonant wavelength of a silver nanocylinder.

 

Fig. 5. Scattering efficiency of single silver nanoparticle. The scattering efficiency at different wavelengths exhibited double peaks since the geometric shape of single silver nanoparticle was not perfectly circular in the FDTD numerical simulation.

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Compared with Fig. 4(a), the scattering efficiency results had the same trend as the far-field difference signals of subwavelength marks, but the peak wavelengths in Fig. 6 were around 443 nm and 650 nm, which were considerably shorter than peak wavelengths in Fig. 4(a). The red shift from single particle response to multi-particle response was the contribution from particle-particle interaction. It indicated that the scattering efficiency of silver nanoparticles played an important role in the optical response of far-field signals of the AgO_x-type super-RENS, therefore the super-resolution capability was closely related to the scattering efficiency of silver nanoparticles in the AgO_x layer. Although the FDTD simulation in this work was two-dimensional, it is reasonable to expect three-dimensional super-RENS disks have similar behaviors. There is an opportunity to manipulate the scattering efficiency of silver nanoparticles to improve the super-resolution of the AgO_x-type super-RENS disks. In realistic situation, there are silver nanoparticles in the AgO_x layer with various shapes and sizes and their collective responses tend to smooth out resonant peaks. From sush a random assembly of silver nanoparticles, the CNR of the AgO_x-type super-RENS disk tends to be insensitive to illuminating frequency and it is consistent with the experimental measurements from red laser based and blue laser based super-RENS disks.[17] Recently ferroelectric catastrophe phenomenon in the phase-change recording layer has also been suggested as the mechanism of the super-resolution of super-RENS.[34, 35] However, it is still necessary to have an near-field optical process to overcome diffractrion limit and to distinguish subwavelength recording marks or large phase-changed spots which have only subwavelength displacement. This work provides a theoretical understanding of the near-field optical process.

4. Conclusions

In this paper, the near-field and far-field optical responses of the AgO_x-type super-RENS disks with randomly distributed silver nanoparticles were studied using FDTD simulations. Different near-field distributions of local field enhancement around silver nanoparticles due to localized surface plasmon excitation was observed at different illuminating frequencies. Our results demonstrated that the local-field enhancement of silver nanoparticles in the AgO_x layer directly influenced the super-resolution of subwavelength recording marks. The far-field signals from random silver nanoparticles were closely related to the scattering efficiency of single silver nanoparticle, but the peak wavelengths of random nanoparticles were longer than those of single nanoparticle because of particle-particle interaction. For the close relation with single nanoparticle response, the plasmon resonance condition of random silver nanoparticles can be controllable by particle size, particle density, distributions, surrounding medium and illumination frequency. With such controllability, our research can help us to design a super-RENS with superior resolution. Metal nanoparticle and array of metal nanoparticles have been applied in nanophotonics and plasmonics to pursue optical components of subwavelength size. Super-RENS and random nanoparticles may be used as an alternative approach to near-field optical research, plasmonic devices, and nanophotonic devices.