Xunya Jiang

Time Dependent Theory for Random Lasers

A model to simulate the phenomenon of random lasing is presented. It couples Maxwells equations with the rate equations of electronic population in a disordered system. Finite difference time domain methods are used to obtain the field pattern and the spectra of localized lasing modes inside the system. A critical pumping rate P(c)(r) exists for the appearance of the lasing peaks. The number of lasing modes increases with the pumping rate and the length of the system. There is a lasing mode repulsion. This property leads to a saturation of the number of modes for a given size system and a relation between the localization length xi and average mode length L(m).

Extending the bandwidth of electromagnetic cloaks

Using the idea of transformation medium, a cloak can be designed to make a domain invisible for one target frequency. In this article, we examine the possibility to extend the bandwidth of such a cloak. We obtained a constraint of the band width, which is summarized as a simple inequality that states that limits the bandwidth of operation. The constraint originates from causality requirements. We suggest a simple strategy that can get around the constraint.

Photonic crystal Mach-Zehnder interferometer based on self-collimation

The authors design a photonic crystal Mach-Zehnder interferometer by utilizing the self-collimated beams and the bending and splitting mechanisms of line defects. Using this interferometer, they investigate the phase shift of the reflected and transmitted self-collimated beams over the line defects. In addition, on the basis of the intensity-asymmetric unidirectional-output design, they demonstrate that such interferometers can function as an intensity detector or an ultrafast optical switch when the material of photonic crystal is nonlinear.

Mode repulsion and mode coupling in random lasers

We studied experimentally and theoretically the interaction of lasing modes in random media. When optical gain spectrum is inhomogeneously broadened, most lasing modes repel each other in the frequency domain. Some lasing modes are coupled through photon hopping or electron absorption and reemission. Under pulsed pumping, weak coupling of two modes leads to synchronization of their lasing action. Strong coupling of two lasing modes results in antiphased oscillations of their intensities.

Photonic band gaps and localization in the Thue–Morse structures

Both theoretically and experimentally, we demonstrate that the photonic band gaps in Thue–Morse aperiodic systems can be separated into two flavors, the fractal gaps and the traditional gaps, distinguished by the presence or absence of fractal structure, respectively. The origin of two kind gaps is explained by the different interface correlations. This explanation is confirmed by the gap width behaviors. In addition, the eigenstates near the fractal gaps have a cluster-periodic form, while those near the traditional gaps have the Bloch wavelike form. Our detailed study of these differences is essential for understanding the spectra and light localization in aperiodic systems.

The physical picture and the essential elements of the dynamical process for dispersive cloaking structures

We investigate the dynamical process of dispersive cloak by finite-difference time-domain numerical experiments. We find that there is a strong scattering process before achieving the stable state and its time length can be tuned by the dispersive strength. Poynting-vector directions show that the stable cloaking state is constructed locally while an intensity front sweeps through the cloak. Deeper studies demonstrate that the group velocity tangent component Vgθ is the dominant element in the process. This study is helpful not only for clear physical pictures but also for designing better cloaks to defend pulsive radars.

Localized random lasing modes and a path for observing localization

We demonstrate that a knowledge of the density of states and the eigenstates of a random system without gain, in conjunction with the frequency profile of the gain, can accurately predict the mode that will lase first. Its critical pumping rate can also be obtained. It is found that the shape of the wave function of the random system remains unchanged as gain is introduced. These results were obtained by the time-independent transfer matrix method and finite-difference time-domain methods in a one-dimensional model. They can also be analytically understood by generalizing the semiclassical Lamb theory of lasing in random systems. These findings provide a path for observing the localization of light, such as looking for the mobility edge and studying the localized states.

Transmission and reflection studies of periodic and random systems with gain

The transmission ({ital T}) and reflection ({ital R}) coefficients are studied in periodic systems and random systems with gain. For both the periodic electronic tight-binding model and the periodic classical many-layered model, we obtain numerically and theoretically the dependence of {ital T} and {ital R}. The critical length of periodic system L{sub c}{sup 0}, above which {ital T} decreases with the size of the system {ital L} while {ital R} approaches a constant value, is obtained to be inversely proportional to the imaginary part {var_epsilon}{sup {double_prime}} of the dielectric function {var_epsilon}. For the random system, {ital T} and {ital R} also show a nonmonotonic behavior versus {ital L}. For short systems (L{lt}L{sub c}) with gain {l_angle}ln T{r_angle}=(l{sub g}{sup {minus}1}{minus}{xi}{sub 0}{sup {minus}1})L. For large systems (L{gt}L{sub c}) with gain {l_angle}ln T{r_angle}={minus}(l{sub g}{sup {minus}1}+{xi}{sub 0}{sup {minus}1})L. L{sub c}, l{sub g}, and {xi}{sub 0} are the critical, gain, and localization lengths, respectively. The dependence of the critical length L{sub c} on {var_epsilon}{sup {double_prime}} and disorder strength {ital W} are also given. Finally, the probability distribution of the reflection {ital R} for random systems with gain is also examined. Some very interesting behaviors are observed. {copyright} {ital 1999} {ital The American Physical Society}

Symmetry between absorption and amplification in disordered media

We address the issue of whether amplification, like absorption, suppresses wave transmission at large gain, as has been claimed in previous studies of wave propagation in active random media. A closer examination reveals that the paradoxical symmetry between absorption and amplification is an artifact of unphysical solutions from the time-independent wave equation. Solutions from the time-dependent equation demonstrate clearly that when gain is above the threshold, the amplitude of both the transmitted and the reflected wave actually increases with time, apparently without bound. The implications of the current finding is discussed. {copyright} {ital 1999} {ital The American Physical Society}

Surface plasmon coupling enhanced dielectric environment sensitivity in a quasi-three-dimensional metallic nanohole array

An enhanced dielectric environment response is observed in a kind of metallic nanohole arrays which are prepared by metal deposition on a sacrificial two dimensional colloidal crystal template. The periodic metallic structures are composed of interlinked metallic half-shells supported on a planar dielectric substrate. When putting in dielectric matrix of different refractive index, the measured sensitivity of the quasi-three-dimensional metallic nanohole array can reach a value of 1192 nm per refractive index unit which shows a five-fold increase as compared with the metallic structures supported on the template. The observed boost in sensitivity is found to originate from a substantially reduced substrate effect, resulting in a pronounced surface plasmon coupling of which its strength is independent of the dielectric environment, a characteristics absent in conventional planar metallic subwavelength hole arrays. These findings are analyzed theoretically and confirmed by numerical simulations.