Numerical Analysis of Ridged-Circular Nanoaperture for Near-Field Optical Disk

A ridged-circular nanoaperture is investigated through three-dimensional (finite-difference time-domain) FDTD method. The motion equations of free electrons are inserted to analyze a metallic material. The electromagnetic field distributions of optical near-field around the aperture are investigated. The phase change disk illuminated by a near-field optical light through a ridgedcircular nanoaperture is also analyzed.The far-field scattering patterns from the phase change disk and the crosstalk characteristics between plural marks are studied.


Introduction
The recording density of conventional optical recording systems has an optical diffraction limit.Recently, there has been a lot of interest in the field of optical storage technologies for the recording methods that are based on near-field optical principles.This is because they have the potential to overcome the limitation by using the localized optical nearfield for writing and reading recorded marks.Many types of nanoapertures and nanoantennas have been proposed to achieve the high throughput of the optical near-field [1][2][3][4].This study focuses on a ridged-circular nanoaperture for a near-field optical disk.The analysis is accomplished by the FDTD method into which the motion equations of free electrons are inserted [5][6][7].This method can easily deal with Drude dispersion and it can be applied to the analysis of various plasmonic devices.First, the electromagnetic field distributions of optical near-field around the ridged-circular nano-aperture are analyzed.Next, the scattering characteristics from a phase change disk with the aperture are studied.Finally, the crosstalk characteristics between plural marks are discussed.

FDTD Formulation
In the FDTD method, special handling of the metallic material is required because the permittivity is dispersive and has a negative value in the optical frequency.In this study, the following motion equation is introduced into the FDTD method to evaluate the conducting current: where u is the electron velocity, E is the electric field,  is the elementary electric charge,  is the electron mass, and ] is the collision frequency.The collision frequency is expressed as follows: where  is the angular frequency of a light wave and  1 and  2 are the real and imaginary parts, respectively, of the complex refractive index  of a metallic material ( =  1 −  2 ).Maxwell's equations are expressed as follows by representing the current density using the electron velocity u and the electron density  0 : where H is the magnetic field and  0 and  0 are the electric permittivity and magnetic permeability of free space, respectively.Figure 1 shows the FDTD cell for analysis.The electron velocity components   ,   , and   are introduced and arranged at the same positions as   ,   , and   , respectively.By evaluating the electron velocity components at the same time as the magnetic field components, the finite difference equations corresponding to (1), (3) are expressed as follows: These equations are used for the analysis.The perfectly matched layer (PML) absorbing boundary conditions are applied to truncate the computational domain.

Results and Discussion
Figures 2(a) and 2(b) show the side view and cross section, respectively, of a ridged-circular nano-aperture.Silver, which has a complex refractive index  = 0.07-4.2and a thickness  = 150 nm, is assumed to be the metallic material used.The plane wave with a wavelength  = 650 nm, whose electric field is polarized in the  direction, is illuminated vertically to the aperture.In the FDTD analysis, the 5 nm cubic cells are used.The near-field electric intensity when  = 100 nm (circular aperture) and 30 nm is shown in Figures 3(a) and 3(b), respectively.The near-field is observed on the plane 15 nm below the bottom surface of the aperture as shown in Figure 2(a).The intensity is normalized by the maximum value of the circular nano-aperture shown in Figure 3(a).It is understood that the higher intensity and the smaller spot size can be obtained by using the ridged aperture.
The maximum intensity and full-width half-maximum (FWHM) as a function of  are shown in Figures 4(a value when the gap  is about 30 nm as shown in Figure 4(a).It is understood from Figure 4(b) that the FWHM becomes smaller when using the smaller gap.
Figure 5 shows the structure of a near-field optical disk that consists of a metallic nano-aperture, a phase change disk, two protective films, and a substrate.Here, the ridged-circular nano-aperture shown in Figure 2(b) is used.The refractive index of the phase change disk is 4.6-4.2(crystalline) and the center of the phase change disk is assumed to be the cylindrical recorded mark with a diameter of   , a thickness of 15 nm, and a refractive index of 4.2-1.9(amorphous).The refractive indexes of the protective films and the substrate are assumed to be 2.2 and 1.5, respectively.The numerical aperture of the objective lens NA is assumed to be 0.6.The incident light is a Gaussian beam polarized in the  direction whose electromagnetic field components in the frequency domain are expressed as follows when the focus plane is  =  0 and the center of the light beam is ( 0 ,  0 ) [8]: where , (), (), and () are written as Here, the wavelength  is 650 nm, and  (= 2/) and 2 0 (= 4/() ≅ 1.06) are the wave number and the spot size of the light beam, respectively.In this analysis, the focus plane is set on the upper plane of the metallic film shown in Figure 5, and the center of the light beam is equal to that of the aperture.
Figures 6(a) and 6(b) show the far-field scattering patterns of the transmitted wave from the phase change disk in the  and  planes, respectively.In these figures, the solid and dashed lines show the results when   = 100 and 0 nm (nonrecorded mark), respectively, and they are normalized by using the maximum value in the  plane when   = 100 nm.Here, the transmitted wave is shown because the reflected farfield barely changes when varying the recorded-mark size.It is understood that the light beam, whose electric field is polarized in the  direction, is scattered more widely in the  direction.
Next, the crosstalk characteristics between plural marks are evaluated.Figures 7(a) and 7(b) show the arrangements of three neighboring recorded marks along the  and  axes, respectively.Here, the ridged-circular nano-aperture ( = 30 nm) was used.The diameters of the recorded marks are equally 100 nm and the distances between the marks (  ,   ) are the parameters.
Figures 8(a) and 8(b) show the normalized output as a function of   and   , respectively.The sum-signal output ( sum ) was calculated as follows and normalized with the output of the single nonrecorded mark: where  is the angle from the positive  axis in the  plane,  is the one from the positive  asis, and  far  and  far  are  and  components, respectively, of the far-zone transmitted electric field in the spherical coordinate.Here,  is calculated as where  sub is the refractive index of the substrate ( sub = 1.5).
The arrangements of the three neighboring marks are denoted by m-m-m, n-m-m, m-n-m, and n-n-m, where "m" and "n" represent the recorded and nonrecorded marks, respectively.Along the  axis the influence of the neighboring marks exists when   is much larger than the recorded-mark size.On the other hand, the variation in output with regard to   is smaller.

Conclusion
The ridged-circular nanoaperture for a near-field optical disk was analyzed by using the FDTD method into which the motion equations of free electrons were inserted.The near-field characteristics of the aperture were investigated.The phase change disk illuminated by the optical near-field through a ridged-circular nano-aperture was also analyzed and the crosstalk characteristics between the plural marks were shown.

Figure 2 :Figure 3 :
Figures2(a) and 2(b) show the side view and cross section, respectively, of a ridged-circular nano-aperture.Silver, which has a complex refractive index  = 0.07-4.2and a thickness  = 150 nm, is assumed to be the metallic material used.The plane wave with a wavelength  = 650 nm, whose electric field is polarized in the  direction, is illuminated vertically to the aperture.In the FDTD analysis, the 5 nm cubic cells are used.The near-field electric intensity when  = 100 nm (circular aperture) and 30 nm is shown in Figures3(a) and 3(b), respectively.The near-field is observed on the plane 15 nm below the bottom surface of the aperture as shown in Figure2(a).The intensity is normalized by the maximum value of the circular nano-aperture shown in Figure3(a).It is understood that the higher intensity and the smaller spot size can be obtained by using the ridged aperture.The maximum intensity and full-width half-maximum (FWHM) as a function of  are shown in Figures4(a) and 4(b), respectively.The maximum intensity has the highest

Figure 4 :
Figure 4: Near-field characteristics as a function of  (a) maximum intensity and (b) FWHM.