We present the effect of structural randomness on the formation of Anderson localization (AL) in random photonic
crystals (RPCs) by using a two-dimensional FDTD (Finite-Difference Time-Domain) computational method. The RPC
consists of a silicon substrate with an array of air holes aligned in a triangular lattice shape. The structural randomness is
introduced by randomly dislocating the positions of air holes. By investigating impulse response of the system, we
obtained frequency spectra and Q-factors of long-lived modes. The modal characteristics of the modes as a function of
structural randomness in RPCs and optimization of the structural randomness to achieve high photon confinement
efficiency are achieved.
KEYWORDS: Photonic crystals, Near field scanning optical microscopy, Light scattering, Laser crystals, Scattering, Finite-difference time-domain method, Multiple scattering, Near field optics, Photons, Near field
Anderson localization (AL), the localization phenomenon of waves in random media, was theoretically predicted for
electrons in a random potential in 1958 and still has been a recondite puzzle today. Stemming from interferences of
multiply scattered waves, the principle is applicable to whole quantum as well as classical waves. Although experimental
attempts toward AL of light had been performed in fully random structures such as aggregates of fine grains, it had been
difficult to achieve because it demands materials with both extremely high scattering strength and low absorption losses.
It was predicted in 1987 that localization may be more achievable in a randomized photonic crystal which supports a
wide photonic band gap. However, AL of light is not yet experimentally exhibited except by far-field indirect
observations in one- and two-dimensional structures. Here we show the first direct near-field observation of two-dimensional
AL in random photonic crystal lasers by use of SNOM (Scanning Near-field Optical Microscope). We
fabricated two-dimensional random photonic crystal lasers to which structural randomness is introduced by dislocating
the positions of air holes to random directions. We show that only slight amount of randomness induces the extended
Slow Bloch Modes to be Anderson localized, but too much randomness releases the light confinement. In addition, by
performing FDTD computational method we confirm the experimental results to be consistent with theoretical prospects.
Our results directly expose the detailed appearance of two-dimensional Anderson localized light first time ever.
The effect of structural randomness introduction into ordered photonic crystals on the behavior of the Bloch-mode and
defect mode is presented. In order to induce strong localization of optical waves in nanostructures, there are two kinds of
schemes: to utilize the defect mode in photonic crystals and Anderson localization modes in random structures. Recently,
the intermediate state between the two above structures has been remarkably noticed. Despite its potential advantage,
however, the modal characteristic of these merged structures, random photonic crystals, has not been revealed
systematically yet. The aim is to figure out the appropriate degree of randomness to induce highly localized modes. We
investigate an impulse response of the random photonic crystals by 2D FDTD method. We array air holes with triangular
lattice shape into silicon substrate based material, and set a defect area in the center. The randomness is introduced into
the structure by randomly dislocating the positions of the air holes. After the impulse illumination, we acquire the
temporal evolution of the electric amplitudes over the system. By employing DFT on the sampled signals, we achieve the
frequency spectrum and Q factors of the modes. We confirmed the optical phase transition of the system: with the
increase of the randomness, the propagating Bloch-modes become localized and achieve higher Q factors. Slight
spectrum shifts are also confirmed. The confinement efficiency of optical waves in the photonic crystals is greatly
improved as well.
We report on the tuneabilities of Anderson localized light in random scattering systems and its lasing characteristics. By
use of FDTD method, we investigated the impulse response of two-dimensional scattering systems consisting of closely
packed dielectric particles, and analyzed the localized modes. We revealed the frequencies of the localized modes to be
capable of being tuned by changing the structural parameters of the system: diameter, filling factor, and refractive index
of the particles. It was also found to be able to tune the Q (quality) factors of the localized modes by changing the system
size of the entire medium. Furthermore, by combining Maxwell's equations with rate equations for electron's system, we
also theoretically demonstrate how the localized area serves as a laser "resonator" and random lasing is induced.
We demonstrate the selective modal oscillation behavior of Random Lasing (RL) by using a one-dimensional RL model.
This calculation model consists of "one-dimensional scattering model", rate equations, and "cavity term". Using this
model, we investigate how the number and the kinds of modes change as the "randomness" of the medium changes.
Calculation results indicate that there exists the region of "randomness" where the dynamics of emission spectrum shows
selective modal oscillations: certain modes strongly oscillate and shape of the emission spectrum drastically changes.
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