Multi-bits coding by multi-directional valley pits permitting stamper mass-production and remote direction readout by polarization reflection

: A new concept of high-density memories by arrays of multi-directional V-shape pits and remote polarization readout is proposed. The polarization readout principles are examined by two model experiments. The first experiment with an array of 1 μ m deep V-pits fabricated by FIB on a Si wafer, carried out under polarization microscope observation, confirmed the concept by the expected contrast variation among the pits images. Accuracy of the remote readout was examined by the second experiment configuring total reflection V-pits by a rectangular prism glued underneath a glass plate. Polarization detection sensitivity of the V-pit direction was found to be ± 0.14°, which should easily accommodate 1.4°=180°/128 separation for 7 bits recording at every single V-pit.


Introduction
Current high-density optical recording systems in combination with a blue laser diode and a high numerical aperture (NA) optics have increased the capacity of optical disks to a 20 G-bits level in the Blu-ray system. For further increase of the data storage capacity, technologies such as a holographic data storage [1], a polarization multiplex recording system [2], a multilayer optical disk [3] have now been developed. However, these technologies lose the simplicity enabling mass-production by simple stamper processing available in current recording media of CD and DVD-ROM. In a recent paper [4] and also in a comprehensive report [5], multi-bits configurations of depth controlled single pits enabling stamper reproduction were proposed. These methods, however, require high precision in the pit shape reproduction since the principle is based on the optical multiplexing involving the reflection phase modulation by the pit geometry.
In this work, we propose a new concept of high-density recording based on V-shape pits with a 90° valley carrying multiple bits information in their valley directions. The structure is of single layer geometry compatible to current mass-production by stamping. We call these pits carrying multi-bits information as "V-pits" and the valley direction as the "V-direction" hereafter.
The information readout is done by reflection polarization measurements under illumination of circular polarization. The reflected light after double reflection of 45° at the facet surfaces of a V-pit may appear as elliptically polarized in general. The double reflection at the facets follows "the law of reflection" within the coordinate planes as shown in Fig. 1 by the x-z plane, which is perpendicular to the V-direction of a V-pit. In other words, under the circular polarization illumination, the direction of reflected ellipse follows the V-direction regardless of the V-pit orientation printed on the media.
In the double reflection configuration, total reflection of transparent material such as glass and plastic can be utilized for the highest throughput and signal-to-noise ratio. In addition, the state of polarization has no sensitivity to relative parallel movements between the pits and the detection optics, as far as the angle of incidence is unchanged. Reflectance variation is also of no consequence because the polarization state is defined independent to the light intensity. These may help realizing a variety of high density memory applications with the pit size and detection distance selected in a range from micrometer to sub-kilometer, as in a spinning disk, static memory tags, chips and even in road information display system for car drivers. Reflected polarization ellipse of γ=-45° and ε=8.1° seen from the z-direction as calculated for double total reflection at the rectangular BK7 prism. The azimuthal angle of the reflected ellipse follows the prism direction.

Reflected polarization under illumination of right circular polarization
The ellipse direction of reflection polarization can be measured with high accuracy from 0.01° to 0.001° by conventional ellipsometric techniques [6], polarization imaging modules [7] or an imaging ellipsometer [8]. Obviously, the record density per pit is decided by the resolution achieved in detecting the state of reflected polarization. For theoretical treatment, the ellipticity and the azimuth of the reflected ellipse are readily described by ellipsometry in referring to the plane of incidence, which is perpendicular to the V-direction.
The complex relative amplitude attenuation ρ of a single reflection surface is expressed by the ellipsometric parameters of the relative amplitude attenuation angle ψ and the relative phase difference Δ as; where r p and r s are the Fresnel reflection coefficients for p-and s-components. We assume that the light to and from the pits travels along the z-direction, and the x-direction is taken parallel to the p-direction of the common plane of incidence upon double reflection as shown in Fig. 1.
For the illumination of right circular polarization, the state of polarization after double reflection of 45°.at a V-pit can be calculated by Jones matrix using the complex relative amplitude attenuation in Eq. (1) as follows; where x-axis is perpendicular to the V-direction. In Eq. (2), a normalization factor is ignored.
By using the ellipsometric parameters Ψ double and Δ double of the double reflection polarization, the complex relative amplitude attenuation of the double reflection ρ double can be expressed as; For the following polarization detection, the rotating analyzer method [9] is assumed. When the analyzer is rotated around the reflected light, the transmitted component results a sinusoidal signal to be detected. The intensity we observe as a function of the azimuthal angle A of the analyzer can be expressed with the parameters Ψ double and Δ double as; ( ) By the rotating analyzer method, Ψ double and Δ double are determined to the accuracy comparable to the pre-determined azimuth A of the rotating analyzer. The polarization ellipse, in terms of its ellipticity angle ε and the azimuth γ is given by simple relations: δ α γ where α=90°-Ψ double and δ=360°-Δ double .
Our proposal is verified experimentally by two V-pits configurations, one by standard surface pits by FIB patterning for the proof of concept and the other by a total reflection pit for examination of the detection sensitivity. The latter also simulates remote sensing applications.

High density memory by array of multi-directional V-shape pits
The proof of the concept experiment was carried out by polarization microscope observation of a set of V-pits patterned on a Si wafer substrate. The V-pits of 1 μm in both radius and depth were coded in the CAD input for computer controlled fabrication by a scanning focused ion beam with a commercial 3D-FIB equipment (EIP-5400, Elionix Co. Ltd.) for nanoimprinting and MEMS application. The resolution of the ion milling positioning is 10 nm, high enough to define the V-pit direction at a desired accuracy. The polarizing photographs of these V-pits were taken by a polarizing optical microscope (BX51, Olympus Co.). Schematic of the optical setup used for microscopic readout by polarization reflection from the V-pits is shown in Fig. 2(a). As shown in Fig. 2(b), V-pits were fabricated at nine V-directions from 0° to 160° in steps of 20°. In this setup, the white light of a halogen lamp passes through a polarizer to fall on the substrate surface and is reflected back at each V-pit by double reflection. When the azimuth of linear polarization is set at 45° to the V-direction, the reflected polarization ellipse is with the ellipticity angle ε =0.132° and the azimuth γ =64.8°, as calculated by Eqs. (1)-(3), (5) and (6) where γ is the angle of the major axis of the ellipse as measured counterclockwise from the V-direction. For the calculation of Eq. (1), the complex refractive index n-ik of Si is assumed to be 3.866-i0.029. According to the azimuth variation of the reflected elliptical polarization with the V-direction, the observed intensity should vary through the analyzer fixed at an azimuth θ. As shown in Figs. 2(c)-2(e) taken at three analyzer angles θ=0°, 45° and -45°, the polarization differences among V-pits are obvious. Figure 2(c) shows V-pits images of a high S/N ratio taken under the Si substrate null condition, which generates a dark-background image expected to be useful for tracking and alignment. The good contrast of these images demonstrates well the detection principle by double-reflection polarization at the facets of the V-pits. Since the polarization detection system tolerates parallel shifts and intensity variation, the authors believe that this result would be a good driving force for implementation to the CD and DVD applications.

Remote polarization readout
For further quantitative evaluation of the detection sensitivity, a rectangular BK7 prism of a=b=5 mm (c=7.1 mm) was used for the V-pit as shown in Fig. 1(a). This configuration also shows another form of media utilizing total reflection in transparent material. In this experiment, the BK7 prism reflects back the incoming right circular polarization as elliptical after double total reflection. Since the total reflection results in the parameter Ψ double being equal to 45°, the azimuth of the double reflected ellipse is fixed at -45.0° from the Vdirection. The ellipticity angle as calculated for the double total reflection is equal to 8.1°, which is independent of the V-direction of the pit as shown in Figs. 1(a) and 1(b). Figure 3 shows the experimental setup schematically. The collimated light of a wavelength of 632.8 nm is fed through a polarizer (P), a mica quarter-wave plate (QWP) and a beam splitter (BS) to illuminate the prism sample (S) at normal incidence. Sheet polarizers of an extinction ratio of 7×10 -3 are used for the polarizer and analyzer (A). With the use of the analyzer, the angular sensitivity of better than (7×10 -3 ) 1/2 =0.08 rad can be expected. To carry out the rotating analyzer method of ellipsometry [9], the analyzer is mounted on an optical rotary encoder of 0.001° resolution. The azimuthal angles of P and QWP are set at proper angles for the right circular polarized illumination after the BS. For the sample (S), the rectangular BK7 prism fixed underneath a 3 mm thick BK7 plate by optical adhesive is set on a rotary stage of 1° angular resolution. In this total reflection configuration, the light passes through the plate except for the prism area where the total internal reflection takes place twice at the interface between prism and the air. Therefore, a high signal to noise ratio can be expected. By replacing the rectangular prism with a corner cube reflector, new systems of remote readout of high density data should be realized.  The elliptical polarization by double total-reflection at the prism is thus evaluated through the BS by recording the detector output signal as a function of the analyzer azimuthal angle. Rotating analyzer output signals from the BK7 prism in the V-direction from 0° to 90° at steps of 15° as a function of the analyzer azimuth sampled at every 5° for 180° rotation are shown in Fig. 4 as the solid circles. The solid sinusoidal curves in Fig. 4 show the best fit curves using the ellipsometric parameters of Ψ double and Δ double determined by Eq. (4). The phase and amplitude of the signal directly correspond to the azimuth of the major axis and the ellipticity of the polarization ellipse, respectively. Although additional relative phase shift was caused by passing through the BS, a linear phase shift of the sinusoidal curve that we predicted was measured as the V-direction. This simulates the practical situation with non-ideal optics causing systematic shift, which is of no consequence as far as the amount is constant. Under illumination of right circular polarization, the azimuth of the ellipse in the reflection polarization precisely follows the prism direction. By the best fit analysis, ψ double and Δ double are respectively determined within the errors of ±0.12° and ±0.45°. It follows that the Vdirection or γ can be read out by the polarization with accuracy of ±0.14° in the present case.
This experimental result shows the high density recording in excess of 7 bits is feasible at this single pit recording, since the 128 directions can be assigned within 180° by 1.4°separation, which is one order of magnitude larger than the achieved accuracy by our trial experiment with standard optics available. In practice, the maximum number of bits achievable would be dependent on the device system designs of media operation (spinning or static) and dimensions.

Summary
We proposed and proved a new concept for high-density recording by imprinting an array of V-shape pits composed of mirror facets of specified directions and slopes on a media surface. Under a circularly polarized illumination, the direction of the facet can be read out by determining the parameters of the reflected polarization ellipse. The principle was successfully demonstrated by 1μm deep V-shape pits of a 90° dihedral angle patterned by FIB on a Si wafer substrate. The rotating analyzer output signals from a rectangular prism under illumination of right circular polarization showed sinusoidal variations resolving the prism direction with accuracy of ±0.14°. It should be noted here that the high accuracy of polarization measurements also suggests a possibility to include the ellipticity angle as an independent parameter of coding. Extension of this will be treated in a separate publication.