This paper investigates the focusing properties by a single lens, based on the optically thinner medium (OTM). The lens
model is of a plano-concave shape, made from the OTM with a refractive index of 0.5 at the wavelength λ=6.328e-4mm,
named the plano-concave OTM thick lens. Any geometrical approximation is not included in the deducing process,
which ensures that the full geometrical aberrations are included. The intensity distribution, in its focal region, can be
calculated by the Huygens-Fresnel integral formula, using the phase and intensity distributions on the reference plane.
The on-axis intensity distribution in the focal region of the plano-convex optically denser medium (ODM) thick lens is
given correctly. The intensity distribution in the focal region of the plano-concave OTM thick lens is plotted in two
dimensions, no symmetry about the focal plane. The plano-concave OTM thick lens has smaller on-axis spherical
aberration than the plano-convex ODM thick lens has, when they have the same aperture radius, equal curvature radius
(not including the sign), and equal medium index difference quantity (not including the sign also) from the
environmental medium air. The radial resolution, around the near end peak in the focal region of the plano-concave
OTM thick lens with its total spherical aberration, breaks down the traditional diffraction limit. Therefore the planoconcave
OTM thick lens will exhibit its practical super resolution abilities, if the diffraction focused spot can be filtered
off, or further more if the energy outside the near end peak can be moved into it.
A new kind of birefringence is found in a two-dimensional (2D) flat perfect photonic crystal (PhC). It is different from
the one in the normal biaxial crystal, but qualitative, and comes from the positive and negative refraction in the 2D flat
perfect PhC. The quantitative relationship between the refractive index and the incident angle are plotted, by the analysis
of the equal-frequent surface (EFS) of the perfect PhC. The plot is consisted of three branches---the main across 0° to
45.53° of the incident angle, the upper across 33.3° to 38.53° and the lower across 38.53° to 45.53°. The upper reveals the
positive refraction; the lower and the main reveal the negative ones. The finite-difference time-domain (FDTD)
simulations are performed, and the relevantly quantitative measurement validates the quantitative relationship by the
analysis of the EFS, but a 2.67° shift to the bigger incident angle.
A novel beam guiding is observed, which is resulted not from the guiding in a defect photonic crystal (PhC) but from the
negative refraction in a two-dimensional (2D) flat perfect PhC slab.
Many changes of various parameters in photonic crystal cause changes of band structure and thus cause changes of light propagation through photonic crystal. The paper is mainly concerned with the study of negative refraction phenomenon dependent on wave guide width in 2D photonic crystal which consists of a hexagonal lattice of circular dielectric rods with Si. It is separately carried on the elaboration from three aspects: along with the accretion of wave guide width in photonic crystal, how the incident light frequency range in which the negative refraction phenomenon presents is changed; under identical incident light frequency, if the negative refraction phenomenon presents, then what the transformation of corresponding negative refractive index is ; if the value of refractive index of -1 is obtained, what the trend of e incident light frequency is.
The paper is mainly concerned with the study of negative refraction phenomenon dependent on the incident light frequency in 2D photonic crystal which consists of a hexagonal lattice of circular dielectric rods with Si. The result indicates that along with the accretion of incident light frequency, the angle of refractive light and negative refractive index in absolute terms become smaller gradually. This law offers an application of differentiating two close incident light frequencies. And a sample has been made successfully to realize negative refraction phenomenon.