The concept of ‘random lasing’ (RL) has attracted much attention over the past decade.1–4 Conventional laser systems are composed of a laser-gain medium and reflectors that provide coherent, positive feedback to the gain medium. RL operates without reflectors but instead takes advantage of strong multiple scattering in the gain medium (see Figure 1). If a material's refractive index has a random spatial profile, light waves are scattered in multiple directions. If scattering is so strong that a photon's mean free path is shorter than its wavelength, the scattered wave is strongly confined to a small area (as a standing wave), which is known as ‘Anderson localization.’5 In practice, this small area serves as a laser resonator.
Because of the significant advantages associated with RL, particularly its small size constraints, ease of manufacturing, low cost, and mode selectivity facilitated by the host material's randomness, we expect that RL will be applied in smart light-emitting sources1 and sensing devices.2 To realize such applications, however, we must know how to induce the kinds of modes desired, and how to strongly confine them. Despite a number of relevant past studies, the systematics of the modal characteristics are not yet completely understood.3,4
In our research, we assume that the material's structure consists of closely packed nanoparticles, a commonly used RL medium,4 which will also be used for future smart RL devices. We use a finite-difference time-domain (FDTD) approach to analyze the dynamics of the electromagnetic waves confined within this structure, and have investigated the types and quality (Q) factors of the localized modes. We selected the particle's packing conditions as design parameters: diameter, spatial density, and refractive index of the particles as well as system size of the entire medium.
Figure 1. Concepts showing the differences between conventional and random lasing.
Figure 2. Conceptual diagram of a 2D (x,y) random scattering system. PML: Perfectly matched layer, En(t): Electric-field amplitude of the nth observation point as a function of time, t.
We distributed many particles with a refractive index of 2.2 in a spatially random fashion on a 2D background matrix of refractive index 1. After impulse irradiation by an optical point source, the temporal amplitude dependence of the scattered waves is sampled at different observation points (see Figure 2). We then performed discrete Fourier transformation on the sampled amplitudes to obtain a frequency spectrum (provided that a sufficiently long sampling time interval had passed). Frequency components matching the localization modes remain present as standing waves and are associated with strong spectral signals. Nonmatching components leak from the system, and their signals decrease to zero. Hence, we can distinguish the localized modes using frequency spectra.
We performed our calculations by changing the particle diameters (using 100, 140, and 200nm) and their spatial density (from 14 to 45%). Figure 3 shows the electric-field amplitude observed 1.3ps after irradiation, which confirms that the waves are localized in a small area and behave like standing waves. Figure 4 shows the resulting spectrum for a particle diameter of 100nm and a spatial density of 45%. Localized modes only exist as ‘groups’ of several frequency components. We show the central frequencies of groups A and B as a function of diameter and spatial density in Figure 4. The modes are either red- or blueshifted with increasing diameter and/or spatial density. Finally, we changed the refractive index only and found that localized modes are redshifted with increasing index of refraction.
Figure 3. Spatial profile of the localized modes.
Figure 4. (left) Frequency spectrum of the localized modes in arbitrary units (a.u.). (right) Spectral shifts as a function of particle diameter and spatial density.
We subsequently simulated a system in which the particles were inserted in a circular region. We changed the radius of the circular region only and kept the other system parameters constant. The resulting spectra show that localized modes appear suddenly when the system reaches a certain size (see Figure 5). We measured the dependence on the system's radius of the Q factors of the major localized modes (see Figure 5). The Q factors increase significantly with the onset of localization beyond a given threshold size, which depends on the individual frequency groups.
Figure 5. (left) Frequency spectra and (right) Q factors as a function of the system's radius, R.
We have thus shown that an aggregation of randomly packed particles serves as a laser resonator. We can tune the frequencies and confinement strength of the localized modes by changing the diameter, spatial density, and refractive index of the particles, and the system size of the entire medium. By adjusting these parameters correctly, we will be able to acquire the RL spectrum required for future devices. As our next steps, we will fabricate random structures—including for the laser-gain medium—and hope to realize the oscillation-mode tuning discussed here.
This work is supported in part by a Grant-in-Aid to the Global Center of Excellence for High-Level Global Cooperation for a Leading-Edge Platform on Access Spaces from the Japanese Ministry of Education, Culture, Sport, Science, and Technology.
Seiji Takeda, Minoru Obara
Department of Electronics and Electrical Engineering
Seiji Takeda is a PhD student. He has been investigating RL oscillation dynamics through theoretical development of unique model calculations. He is currently studying the properties of Anderson localized modes using an FDTD approach.
Minoru Obara is a professor. He has worked on femtosecond lasers, nanoplasmonics, pulsed-laser deposition, RL, and medical laser applications. He is a fellow of the Institute of Electrical and Electronics Engineers, the Optical Society of America, and the Japan Society of Applied Physics.