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We use 3-dimensional finite-difference time-domain method to investigate surface polariton coupling between two nano-recording marks which are of different shapes. The different coupling characteristics and the influence of these coupling effects on read-out reflection signal will be discussed.
©2008 Optical Society of America
1. Introduction
In the field of optical data storage, phase-change materials are used as the recording layer because of the reflection difference between amorphous and crystalline states of these materials [1, 2]. Using a laser light source to heat up the phase-change material, it is possible to write crystalline-state recording marks with different pit lengths in amorphous-state surroundings [3, 4]. These length-modulated recording marks will connote digital information which can be readout by detecting the optical reflection signals. For the purpose of increasing the information storage capacity of an optical disk, reducing the recording mark size is a straightforward and commonly used method to approach this goal. However, when the recording mark size is getting smaller and smaller, the difference of reflection signal from marks and surroundings will become difficult to recognize. In order to improve the reflection signal contrast or carrier-to-noise-ratio (CNR) of an optical disk with sub-wavelength recording marks, many types of super-resolution near-field optical nanostructure disks which using different materials as their active layer (for example, Sb, PtOx, AgOx, ZnO, metal-dielectric composite, or dye etc.) have been proposed recently [5–7]. Roughly speaking, the explanations of super-resolution effect in these disks may be categorized into two mechanisms. One is the interaction between the instant molten or hot region in the active layer with the recorded mark during the readout process (e.g. for PtOx-type near-field optical nanostructure disk) [8–10]. This molten or hot region plays a role of a near-field nano aperture which can enhance signal from a given recording mark while keeping the signal from adjacent neighbors at their normal level (or perhaps even attenuating them). The other mechanism attributed super-resolution effect to the coupling between localized surface plasmon (LSP) resonance of metal nanostructures in the active layer and the recorded marks in the recording layer (e.g. for AgOx- or ZnO-type near-field optical nanostructure disks) [11–13]. The metallic nanostructures play a role of near-field nano probes which coupling effect results in an enhanced reflection or scattering CNR signal of the recording marks. Although the improved CNR signals of sub-wavelength recording marks in these near-field optical nanostructure disks have been demonstrated experimentally, the explanations of super-resolution effect in these disks with different near-field active layers are actually not completely clarified (different mechanisms were proposed for different types of active layer). However, the near-field plasmonic coupling between recording marks in phase-change layer and metallic nanostructures in active layer is generally adopted as one of the key factor to optical super-resolution effects.
Recently, the coupling effect of plasmonic nanostructures have been applied to many nanophotonic applications, such as tuning field enhancement or confinement [14–16], controlling absorption or extinction [14,17], and modulating resonance modes [16,18,19] etc. Since the high density region of a laser focusing spot at focus distributes itself over a spheroid-like region, it is possible to write down two recording marks simultaneously in two vertically separated phase-change material layers. And, these two marks can interact with each other when using another laser focusing spot to read them out. On the basis of using near-field plasmonic coupling mechanism to realize super-resolution effect and the metal-like material property of crystalline-Ge2Sb2Te5 (cr-Ge2Sb2Te5) alloy, we would like to know the influences of near-field surface polariton (SP) coupling between two vertically separated recording marks on optical reflection signals. In this paper, we will numerically investigate the near-field SP coupling effect between two nano-recording marks with different shapes. The characteristics of SP coupling effects and their influence on CNR read-out signal of an optical disk will also be discussed.
2. Model of computation
In the following computations, 3-dimensional finite difference time domain (3-D FDTD) method is used to calculate the near-field optical responses of the system. The spatial grid size and full computation space are set to 5.0 nm×5.0 nm×5.0 nm and 1.6 µm×1.6 µm×0.5 µm, respectively, and a perfect match layer (PML) is used as the simulation boundary condition. A continuous light source with Gaussian profile and wavelength (λ) 658 nm is used as an incident light, which is x-polarized and propagates along the z-direction related to the sample structure.
Figure 1(a) shows the schematic diagram of the sample structure for our computations. Light is incident from the bottom of the sample and, then, passing through the layered structure: ZnS-SiO2 (130 nm)/as-Ge2Sb2Te5 (20 nm)/ZnS-SiO2 (d nm)/as-Ge2Sb2Te5 (20 nm)/ZnS-SiO2 (20 nm). The as-Ge2Sb2Te5 denotes asdeposited-Ge2Sb2Te5 which is an initial state of the phase-change material just after sputtering. The two recording marks depicted in Fig. 1(a) are cr-Ge2Sb2Te5 which may form in different shapes when using different laser power to write down the marks [20]. Figure 1(b) shows some atomic force microscopy (AFM) images recording marks (upper side) under different laser writing powers. The higher (bright) region is cr-Ge2Sb2Te5 and the surrounding is as-Ge2Sb2Te5 which reflectivity is lower than that of recording marks (cr-Ge2Sb2Te5). Because the protuberance of cr-Ge2Sb2Te5 related to surrounding as-Ge2Sb2Te5 is very small, we modeled three types of the recording marks shown in the lower part of Fig. 1(b). The white and gray regions are cr-Ge2Sb2Te5 and as-Ge2Sb2Te5, respectively, and the dark region is just air. The spacer layer, ZnS-SiO2, between two as-Ge2Sb2Te5 layers is used to control the separation distance, d, of the two recording marks and its thickness is varied from 10 nm to 100 nm in our computations.
Fig. 1. (a). Schematic diagram of the sample structure for numerical investigation. (b) AFM images of recording mark with disk-, ring- and ring-sphere-shapes which are produced by illuminating different laser writing powers on phase-change material.
The optical constants (refraction index, n, and extinction coefficient, κ) of each material used in our computations are listed in Table 1. These optical constants are measured experimentally by an ellipsometer except that the dielectric constants of cr-Ge2Sb2Te5 are referred to Ref. [21]. Here, εR and εI represent the real and imaginary parts of material dielectric constant, respectively. We see that the dielectric constant of cr-Ge2Sb2Te5 has negative value in its real part. Therefore, it may have analogous optical properties to a metallic nanostructure and localized surface plasmons can be excited at the surface of the cr-Ge2Sb2Te5 in our sample structure. However, because the imaginary part of the dielectric constant of cr-Ge2Sb2Te5 is also large, one can imagine that the energy absorption effect will relatively large to that of noble metals.
Table 1. Optical Constants and Dielectric Constants for Thin Films of Materials (for λ=658 nm)
3. Results and discussions
3.1 Disk-shaped recording marks
We first discuss the cases of sample structure with two disk-shaped recording marks whose diameter, D, are changed from 50 nm to 300 nm. The electric field distributions around the recording marks and reflected light fields at the imaging plane (as depicted in Fig. 1(a)) are recorded. Figures 2(a) and 2(b) shows the variations of maximum field intensity ratio and full width at half maximum (FWHM) ratio of reflected light at the imaging plane when the thickness of spacer, d, is changed. In order to emphasize the coupling effect of the nano-recording marks, the values of field intensities and FWHMs are normalized by the corresponding values when there is no recording mark in each as-Ge2Sb2Te5 layer. It is seen that the reflection signal is getting stronger when the size of recording mark is increasing. This is simply due to the larger high reflectivity region of recording marks. On the other hand, the major trend of reflection signal ratio increases as the spacer thickness increases until the spacer thickness is larger than 55 nm. Also, from the variation tendency of each curve in Fig. 2, we may probably sort the coupling behavior of the two recording marks into four categories (with respected to spacer thickness): (1) d lies in between 10 nm and 30 nm, (2) d lies in between 35 nm and 50 nm, (3) d lies in between 55 nm and 85 nm, and (4) d is larger than 90 nm.
Fig. 2. The spacing-thickness dependence of (a) maximum field intensity ratio and (b) FWHM ratio of reflected light at the imaging plane (disk-shaped marks with different mark sizes).
In order to see what happens in the near-field, we show some distributions of near-field intensity ratio around the two recording marks at different spacer thickness (Fig. 3). The intensity ratio here means that the distributed field intensity is divided by the corresponding values when there are not any marks in the sample structure. Firstly, these figures show that the field intensities are concentrated at the edges of the recording marks. It is resulted from the field localization and enhancement effects of the SP oscillations in the recording marks. When the separation of the two recording marks is small, d=30 nm or 35 nm for example, the SP coupling between these two marks is strong and the field distribution of the two marks are highly correlated to each other (Figs. 3(a) to 3(d)). The arrows in each picture of Fig. 3 represent the electric field vectors (including only x- and z-components) which are averaged over the time duration for passing half a wavelength. From the behavior of these field vectors, we infer that the induced SP coupling of the two recording marks resulted in an anti-symmetric SP oscillating behavior in them. This vertical coupling effect may lead to the two individual marks seems optically like a bigger one whose light-matter interaction “optical volume” is extended along z-direction. Therefore, the reflection signal of the system increases as the separation of the two marks increases. However, when the separation distance lies in between 35 nm and 50 nm, we see that the field intensity is highly trapped in the edge region between the two recording marks. This ultra strong SP coupling and field localization effect lead to slightly decreasing in optical reflection signal. Continuously, when the separation distance of the two recording marks is larger than 60 nm, the near-field intensity distribution begins to split into two separated regions around each mark and, otherwise, light intensity trapped at lower surface of the rear recording mark will gradually increased (Fig. 3(e) and 3(f)). These two individual marks seem no more like an optically bigger one due to the weak SP coupling between them, so that, the reflection signal of the system decreases as the separation of the two marks increases.
Fig. 3. Near-field intensity ratio (arbitrary unit) distributions of disk-shaped recording marks in x-z cross-section for different spacer thickness when mark size D=100 nm. (a) d=30 nm, (b)=35 nm, (c) d=45 nm, (d) d=55 nm, (e) d=70 nm and (f) d=90 nm.
Finally, Fig. 2(a) shows that the maximum reflection signal appears at d=55 nm and the corresponding near-field intensity distribution is shown in Fig. 3(d). At this separation distance, the SP coupling effect of the two recording marks leads to a single large near-field “optical volume” and the light field is more concentrated at the front recording mark instead of being trapped between the two marks (see Fig. 3(d)). These two conditions result in the maximum reflection signal of the system.
3.2 Recording marks of different shapes
We also calculated the cases of ring-shaped and ring-sphere-shaped recording marks (as depicted in Fig. 1(b)) to investigate their SP coupling behavior and resulted reflection signals. Similar to previous disk-shaped cases, the outer diameter, D, of ring-shaped recording marks is varied from 50 nm to 300nm, and the inner diameter of the ring is 0.6D. For the ring-sphere- shaped marks, only the case of D=100 nm with a sphere (30 nm in diameter) located at the center of the ring is calculated. Figures 4(a) and 4(b) show the variations of maximum field intensity ratio and FWHM ratio of reflected light at the imaging plane for all the three different types of recording marks with D=100 nm.
Fig. 4. The spacing-thickness dependence of (a) maximum field intensity ratio and (b) FWHM ratio of reflected light at the imaging plane for different mark shapes with D=100 nm.
We can see that the ring-shaped and ring-sphere-shaped recording marks behave similarly in reflection signals when changing the separation distance of the two marks. This result implies that their near-field SP coupling might analogous to each other at least in small mark-size case. On the other hand, in comparison with the cases of ring-shaped and disk-shaped recording marks, the former exhibited both smaller intensity and FWHM in reflected light. These phenomena can be explained by the near-field intensity distributions of ring-shaped recording marks shown in Fig. 5. Because the SP coupling of ring-shaped marks results in higher field localization or trapping at the inner edges of the marks, the reflected light intensity is therefore weaker than that of disk-shaped cases. Also, because of the more spatially concentrated field distribution of the SP coupling in this case, the reflected light fields exhibit smaller FWHMs than that of disk-shaped cases.
The variation tendency of reflection intensity ratio with the separation distance of the two marks can be elucidated by the same arguments discussed in disk-shaped recording marks. It can be seen in Fig. 5 that when d=45 nm, SP coupling of the two marks leads to an optically larger one whose light-matter interaction “optical volume” is largest extended along z-direction, and the light field is more concentrated around the front mark in this condition. Therefore, the reflection signal of ring-shaped recording marks in Fig. 4(a) reaches a maximum value at d=45 nm. Finally, considering the behavior of field vectors in Fig. 5, it can be found that induced SP oscillation at the inner edge of the two recording marks is symmetric, which is different from that of disk-shaped case (that is, anti-symmetric). So that, the vertical coupling distance of the two ring-shaped marks will be smaller than that of disk-shaped marks. This discrepancy behavior of SP oscillations between ring-shaped and diskshaped cases can be used to explain why the maximum reflection signal of the former appears at a smaller separation distance.
Although our calculated results clarify how the SP coupling of two recording marks can have positive influence on reflection read-out signal of an optical disk, the reflection intensity ratio seems only slightly improved even at optimization condition. It may be due to the large extinction coefficients of the cr-Ge2Sb2Te5 alloy so that light energy is more consumed instead of enhanced in these nanostructures when trapped by SP coupling.
Fig. 5. Near-field intensity ratio distributions of ring-shaped recording marks in x-z cross-section for different spacer thickness when mark size D=100 nm. (a) d=30 nm, (b) d=35 nm, (c) d=45 nm, (d) d=55 nm, (e) d=70 nm and (f) d=90 nm.
4. Conclusion
We have investigated the SP coupling between two recording marks and their influences on optical reflection signal in this paper. The characteristics of near-field SP coupling phenomenon which depends on either separation distance or geometrical shape of the recording marks is discussed. From the results of reflection signals and near-field intensity distributions, we may sort the SP coupling into four categories associated to separation distance of the two marks.
Our results demonstrated that the SP oscillations of two vertically separated marks not only can trap light energy around the marks, their coupling effect can also make the two individual marks optically correlated to each other. In suitable conditions, the latter effect may result in an extended light-matter interaction “optical volume” in the near-field region, which will increase reflection signal contrast from the recording marks. This phenomenon is helpful to recognize a sub-wavelength recording mark in an optical disk. Although the simplified structure model (single recording mark in each phase-change material layer) used in our computations is not the same as the real system (periodic mark train in each phase-change material layer), it can give us a clear insight into the relation between vertically coupling of the two recording marks and the variation of reflection contrast signal of the sample structure. This reflection contrast enhancement can somewhat improve the CNR signals in real experimental measurement. According to the calculated results, the maximum reflected field intensity ratio appears at d=55 nm and d=45 nm for disk-shaped and ring-shaped recording marks, respectively. The above discrepancy in d may due major to the different induced SP oscillation types of disk-shaped and ring-shaped marks.
Acknowledgments
The authors are grateful for the research support from the National Science Council of Taiwan, R.O.C., under project number NSC-97-2120-M-002-013- and NSC-96-2923-M-002-002-MY3, respectively. And, we are grateful to the National Center for High-performance Computing for computer time and facilities. We also thank the Computer and Information Networking Center, National Taiwan University for the supporting of high-performance computing facilities. D. P. Tsai thanks the support of National Center for Theoretical Sciences, Taipei Office.
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