We investigated, both analytically and numerically, the irradiance formation of an asymmetrically located Lambertian light source in hollow straight light pipes with square and circular shapes. The uniform irradiance distribution in a square light pipe and hot-spot localization in a circular light pipe were examined and determined semianalytically. Typical factors of influence, such as light-pipe length, width, and source size, were identified with extensive simulation. When the ratio of light-pipe length and width was less than 0.5, the deviation from uniformity could be more than 20%. But once the source size was large enough (approximately half of the incident port), such that the Lambertian characteristics of the source dominated the irradiance distribution, the uniformity deviation was reduced. Furthermore, a quantity of root-mean-square circular differences was defined in order to identify the shape deformation of the light pipe; it was found that the peak value of the hot spot decreased exponentially with the deformation scale. The influence of nonperfect reflectivity of the pipe wall on irradiance formation was also examined for a square light pipe; when the reflectivity is larger than 90%, the difference in uniformity is less than 10% and uniform irradiance remains, provided that the ratio of light-pipe length and width is larger than 1; even the source is located asymmetrically.
We experimentally investigated the resonance effect of planar metallic split ring resonators (SRRs) in the far-infrared region (FIR) ($10:6 mm). Experimental results indicated that they exhibit resonance around 10.6 mm, implying negative permeability in the FIR region. Furthermore, the ratio of effective dimensions of the SRR cell and the wavelength of the incident beam was around 1 which suggested a wide scale independence. This size tolerance is useful in realizing the meta-materials with negative indices of refraction in the optical wavelength domain.
Abstract— A wedge plate can be used as the screen of a display, and the thickness of the display can be incredibly thin. In this paper, a basic formula for ray tracing in such a wedge plate is deduced. The fundamental limitation on the display quality of a wedge plate is explored, and the formation of a dark zone on the display screen is analyzed and verified numerically. Experimental exploration and confirmation of one 14‐in. acrylic wedge plate with a white‐light‐emitting diode is also provided. Two approaches to eliminate the dark zone are proposed, and the corresponding numerical demonstration of a 52‐in. wedge‐plate display is also shown.
This study shows that by using a wedge plate the incident direction of light propagation can be rotated as desired while still preserving beam polarization. This study also deduces the basic condition of this preservation of polarization. Two typical wedge plates are analyzed for numerical demonstration. Simulation results verify that a collimated beam with a +45 degrees linear polarization can be guided to an expected direction while preserving the state of polarization with a square of the variation of the ellipse ratio of less than 0.0001%. This study also numerically shows that the wedge vertex angle is the most critical issue and that approximately 0.1 degrees accuracy is required to preserve the polarization state.
The aberration characteristics of a wedge-plate display optical system are analyzed. The study shows that a kink-like feature is inherent in the ray-intercept curve due to either the onset of the dark zone in imaging or the coincidence of the ray direction with the vertex. Third-order aberration coefficients are deduced, and the total amount of aberration is investigated to illustrate the basic limitations of image quality in this type of display. The issue of design optimization is also investigated based on the aberration characteristics. A numerical example of a 50 in. display with a 1:10 thickness and a diagonal screen length ratio is also provided.
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