We find a renormalized "time-dependent diffusion coefficient," Dt, for pulsed excitation of a nominally diffusive sample by solving the Bethe-Salpeter equation with recurrent scattering. We observe a crossover in dynamics in the transformation from a quasi-1D to a slab geometry implemented by varying the ratio of the radius, R, to the length, L, of the cylindrical sample with reflecting side walls and open ends. Immediately after the peak of the transmitted pulse, Dtfalls linearly with a nonuniversal slope that approaches an asymptotic value for R/L→1. The value of Dtextrapolated to t→0 depends only upon the dimensionless conductance g for R/L→1 and only upon k '0 for R/L 1, where kis the wave vector and '0 is the bare mean free path.

Negative refraction of acoustic waves in two-dimensional phononic crystals has been demonstrated through both analysis and exact numerical simulation. The methods to achieve this behavior have been discussed. A microsuperlens for acoustic waves has also been designed. It is shown that refractive devices based on phononic crystals behave in a manner similar to that of optical systems. Therefore, a negative square root of the effective density or negative refraction index for acoustic waves can be introduced to describe this phenomena very well as the case of electromagnetic waves in the photonic crystals.

We propose a simple, systematic, and efficient method to enlarge the gap of a photonic crystal. In this method, we add a small fraction of a third component into the existing photonic crystal. The dielectric property of the third component as well as its insertion position in a unit cell are chosen according to the field-energy distribution of two Bloch states at the band edges. The method is very general. It can be applied to any microstructure and is independent of the dimensionality of the original photonic crystal. Thus, it opens up a way to engineer photonic band gaps. Here, we demonstrate the validity of this method explicitly in two dimensions for both s and p waves. We show that, for certain microstructures, absolute gaps can be signifi-cantly enlarged. The method is also demonstrated in microwave experiments.

Based on the two-band model, we present a transfer-matrix treatment of the tunnel conductance and magnetoresistance for tunneling through ferromagnet/insulator (semiconductor) single junctions and double junctions subject to a dc bias. Our results are qualitatively in agreement with the experimental measurements for the single junction. For the double junction, we find that there exists, spin-polarized resonant tunneling and giant tunnel magnetoresistance. The highest value of the magnetoresistance in a double junction can reach 90%. We anticipate that our results will stimulate some interest in experimental efforts in designing spinpolarized resonant-tunneling devices.

We propose a simple and efficient method to engineer absolute negative refraction for both polarizations of electromagnetic wave in two-dimensional photonic crystal by adding an additional component to the existing photonic crystal. The dielectric property of the additional component, as well as its insertion position in a unit cell, are chosen according to the field-energy distribution of Bloch states at the band edges. According to our design, the non-near-field focus and images for both polarized waves at the same structure and parameters, explicitly following the well-known wave-beam negative refraction law, can be realized.

It is shown that the transmission resonance of acoustic waves for an incident wavelength larger than the period of the grating exists in acoustic gratings with very narrow slits similar to that of optical subwavelength systems. The results are obtained by multiple-scattering numerical simulations. The physical origin for such an acoustic transmission resonance is also analyzed.

Recently, negative refraction of electromagnetic waves in photonic crystals was demonstrated experimentally and subwavelength images were observed. However, these investigations all focused on the periodic structure. Here, we report a new theoretical and experimental finding that negative refraction can appear in some transparent quasicrystalline photonic structures. The photonic quasicrystals (PQCs) exhibit an effective refractive index close to 1 in a certain frequency window. The index shows small spatial dispersion, consistent with the nearly homogeneous geometry of the quasicrystal. More interestingly, a superlens based on the 2D PQCs can form a non-near-field subwavelength image whose position varies with the source distance. These properties make PQCs promising for application in a range of optical devices.

The field distributions of reflected speckles arising from localized states inside the gap of disordered photonic crystals in two dimensions were studied through numerical simulations using the multiple-scattering method. The statistics of the Lyapunov exponent of the transmitted waves were also studied. Similar to the case of disordered photonic crystals in one dimension, two types of localized states were found depending on the degree of disorder and the frequency inside the gap. Our simulation results indicate that the reflection statistics depend on whether or not the localized states are of the normal type. They also depend on whether the reflected angles are in the Bragg direction or not. For the non-Bragg angles, we found that the intensity distribution arising from the normal-type localized states follows Rayleigh statistics, in agreement with random matrix theory. However, deviations from Rayleigh statistics were found for second type of localized states. The crossover behavior from non-Rayleigh to Rayleigh statistics was studied as a function of the degree of disorder. By separating the field into coherent and diffuse parts, we have studied the statistics of field and phase distributions for both diffuse and total fields as well as their speckle contrasts. It is found that the crossover behavior is very similar to behavior in ballistic to diffusive wave propagation for the transmited waves and can be described by the random-phasor-sum model (RPS). For the Bragg angle, non-Rayleigh statistics were found for both kinds of localized states. The statisics are sensitive to the degree of disorder. It is found that both the RPS and K distribution have limited ranges of validity in this case.

Coherent backscattering (CBS) of light in a strong localization regime is studied with absorption/ amplification included. The CBS cones arising from strongly localized states inside the complete gaps of disordered photonic crystals have been observed by numerical simulations in two dimensions. The structure of the CBS cones can be described well by a theory that incorporates mean free paths, localization length, amplification/absorption length, and single-particle scattering anisotropy. The excellent agreement between theory and simulations without any adjustable parameters makes it ossible to determine the localization length from a measured CBS cone, even in an absorbing medium.

A recent publication [Nature (London) 404, 740 (2000)] claimed that absolute photonic gaps can be realized in 12-fold quasicrystalline arrangement of small airholes in a matrix of silicon nitride or glass. The result is rather surprising since silicon nitride (n52.02) and in particular, glass (n51.45) have rather low refractive index. In this work, we have studied the transmission properties of the same systems by using the multiplescattering method. We found that the 12-fold triangle-square tiling is indeed very good for the realization of photonic gaps and we found absolute gaps in systems with airholes in dielectric, dielectric cylinders in air, and metal cylinders in air. However, for the case of air-holes in a dielectric background, absolute gaps appear only when the dielectric contrast is sufficiently high, and both silicon nitride and glass have refractive indices below the threshold.