Random Lasing Modes Research Articles

Linear dispersive effect on random lasing modes

A model, by combining Maxwell's equations with all-parameters of Sellmeier's fitting equations and four-level rate equations, is built to investigate linear dispersive effect on the property of random lasing modes. Computed results show that the first excited modes for both dispersive and non-dispersive scattering cases have almost the same resonant frequency but the spectral intensity for dispersive case is lower than that for non-dispersive case, and there exist more modes in the whole spectra for dispersive case. Further analysis demonstrates that threshold of random lasing in dispersive case is higher than that of the non-dispersive case.

Modes of random lasers

In conventional lasers, the optical cavity that confines the photons also determines essential characteristics of the lasing modes such as wavelength, emission pattern, directivity, and polarization. In random lasers, which do not have mirrors or a well-defined cavity, light is confined within the gain medium by means of multiple scattering. The sharp peaks in the emission spectra of semiconductor powders, first observed in 1999, has therefore lead to an intense debate about the nature of the lasing modes in these so-called lasers with resonant feedback. We review numerical and theoretical studies aimed at clarifying the nature of the lasing modes in disordered scattering systems with gain. The past decade has witnessed the emergence of the idea that even the low-Q resonances of such open systems could play a role similar to the cavity modes of a conventional laser and produce sharp lasing peaks. We focus here on the near-threshold single-mode lasing regime where nonlinear effects associated with gain saturation and mode competition can be neglected. We discuss in particular the link between random laser modes near threshold and the resonances or quasi-bound (QB) states of the passive system without gain. For random lasers in the localized (strong scattering) regime, QB states and threshold lasing modes were found to be nearly identical within the scattering medium. These studies were later extended to the case of more lossy systems such as random systems in the diffusive regime, where it was observed that increasing the openness of such systems eventually resulted in measurable and increasing differences between quasi-bound states and lasing modes. Very recently, a theory able to treat lasers with arbitrarily complex and open cavities such as random lasers established that the threshold lasing modes are in fact distinct from QB states of the passive system and are better described in terms of a new class of states, the so-called constant-flux states. The correspondence between QB states and lasing modes is found to improve in the strong scattering limit, confirming the validity of initial work in the strong scattering limit.

Experimental studies on the mode structure of random lasers

We investigate the mode structure of a random laser consisting of a porous semiconductor matrix infiltrated with and surrounded by laser dye. The experimental parameters that influence the types of lasing that are observed are identified. The spatial structure of random laser modes is accessed experimentally by a spatially and spectrally selective detection scheme. We show that random laser modes are distinct from laser speckle.

Directional and controllable edge-emitting ZnO ultraviolet random laser diodes

Room-temperature ultraviolet random lasing action is demonstrated from a p-GaN/annealed i-ZnO:Al(3%)/n-ZnO:Al(5%) buried heterojunction diode with a 2 μm rib waveguide. Excellent electrical-to-optical conversion efficiency is achieved by strong electrical and optical confinement of a buried heterojunction rib waveguide structure. Hence, emission intensity (threshold current) can be enhanced (reduced) by ∼9 times (∼40%). Directional emission as well as controllability on the number of the random lasing modes can also be achieved.

Monte Carlo calculations of spectral features in random lasing

Continuing our ongoing investigations of random lasing, we used the Monte Carlo method to simulate random walks of photons within a multiply scattering medium. By initially applying this technique to calculate pulse-stretching in a passive disordered medium, we elucidated its agreement with analytical diffusion theory. Thereafter, we introduced conditions of optical amplification, and reproduced the experimentally observed spectral features like spectral narrowing, intensity enhancement, bichromaticity, mode competition, etc., in a random laser. After investigating diffusive and sub-diffusive regimes of scattering, we formulated our results in terms of a gain subvolume, the functioning of which depends upon local gain conditions. We then used a modified approach of this technique to study ultranarrow random lasing modes, and successfully reproduced these modes observed in a random laser. Based on our simulations, we were able to explain the origins of ultra-narrow lasing modes as excessively amplified extended modes.

LASER ACTION IN DYE DOPED LIQUID CRYSTALS: FROM PERIODIC STRUCTURES TO RANDOM MEDIA

The birefringence and natural ability to form periodic structures make cholesteric liquid crystalline (CLC — chiral nematics) materials particularly attractive as 1D photonic band gap systems. If a CLC is doped with dye fluorescent molecules, in such a way that the maximum peak of fluorescence matches one of the edges of the selective stop band, laser action is expected at that spectral position. By confining the helical super-structure of chiral liquid crystals in polymeric micro-cavity channels, a tunable microcavity laser array was achieved. In multiple scattering systems, the propagation of the light waves is quite different, as optical scattering may induce a phase transition in the photon transport behavior. Beyond a critical scattering level, the system makes a transition into a strongly localized state and light transmission is inhibited. This effect can be used as a photon trapping mechanism to obtain laser action in the presence of a gain medium. Random lasing modes come from interference effects which survive in disordered systems and open a particular chapter in the study of the interplay between localization and amplification. Here, experiments performed on systems having different order degree and confinement are presented and possible technological implications are discussed.

Co-existence of strongly and weakly localized random laser modes

Recent theoretical work on random lasing predicts that the occurrence of narrow lasing spikes can be caused by both localized and extended modes of light1,2,3. Typical random lasing spikes have been observed in powders of zinc oxide nanoparticles4, but identifying the possible degrees of localization of such modes has until now been an open issue5. In this Letter we present an experimental procedure that directly extracts the area of localization of the modes. This method relies on the investigation of micro-structured fields of zinc oxide powder, which also allows direct correlation to the local structural properties of the ensemble of subwavelength particles by scanning electron microscopy. We find that lasing from both localized and extended modes can be observed simultaneously. Our observation also corroborates the prediction that localized modes have a lower loss rate than that of extended modes5. Whether the electromagnetic fields in random lasers are localized or extended is a topic of ongoing debate. Now, the localization of modes in micro-structured ZnO powder is experimentally determined and lasing from both kinds of modes (localized and extended) shown to exist simultaneously.

Suppression of Random Lasing Modes in Polycrystalline ZnO Thin-Film by Using Distributed Bragg Reflector

Formation of vertical-cavity random laser by using a polycrystalline ZnO thin-film optically coupled to 11.5 pairs of Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> -ZnO multilayer distributed Bragg reflector (DBR) is proposed. Lasing characteristics of the laser observed from the surface of the polycrystalline ZnO thin film are studied without and with the presence of DBR. It is found that the corresponding spectral linewidth can be limited to about 4 nm at high excitation intensity under the influence of DBR.

Statistics of random lasing modes in weakly scattering systems

We investigated the statistics of random lasing modes in colloidal solutions with local pumping. The ensemble-averaged spectral correlation function of single-shot emission spectra exhibits regular oscillations. The statistical distribution of laser emission intensity follows a power-law decay, in comparison with an exponential decay of the statistical distribution of amplified spontaneous emission (ASE) intensity. The dramatic difference between the statistics of lasing peaks and that of the stochastic ASE spikes illustrates their distinct mechanisms.

Effect of local pumping on random laser modes in one dimension

We have developed a numerical method based on the transfer matrix to calculate the quasimodes and lasing modes in one-dimensional random systems. Depending on the relative magnitude of the localization length versus the system size, there are two regimes in which the quasimodes are distinct in spatial profile and frequency distribution. In the presence of uniform gain, the lasing modes have one-to-one correspondence to the quasimodes in both regimes. Local excitation may enhance the weight of a mode within the gain region due to local amplification, especially in a weakly scattering system.

Excitation of localized modes and mechanism of random lasing forming in random media

Laser phenomena in random media have been studied based on the localized theory for lightwave in random media. The relationship between random lasing modes and localized modes has been investigated by directly solving Maxwell equations numerically via the finite difference time domain method. The spatial distribution and the spectra of localized modes are obtained for both passive and active random media. The results show that random lasing modes directly originate from the localized modes inside the random medium. In the presence of gain, any one of the localized modes can be amplified and can serve as random lasing mode.

Polarization dependence of lasing modes in two-dimensional random lasers

The time dependent theory of random laser is developed from transverse magnetic field to transverse electric field. Polarization dependence of random lasing phenomenon is investigated by considering both fields in two-dimensional random media via numerically solving Maxwell's equations coupled with rate equations of a four-level atom system. Results show that the field pattern, emission spectrum and total power density are polarization dependent. By comparison, transverse magnetic fields have lower loss and could oscillate preferentially in random media.

Optics of nanostructured dielectrics

We discuss the optical transport properties of complex photonic structures ranging from ordered photonic crystals to disordered strongly-scattering materials, with particular focus on the intermediate regime between complete order and disorder. We start by giving an overview of the field and explain the important analogies between the transport of optical waves in complex photonic materials and the transport of electrons in solids. We then discuss amplifying disordered materials that exhibit random laser action and show how liquid crystal infiltration can be used to control the scattering strength of random structures. Also we discuss the occurrence of narrow emission modes in random lasers. Liquid crystals are discussed as an example of a partially ordered system and particular attention is dedicated to quasi-crystalline materials. One-dimensional quasi-crystals can be realized by controlled etching of multi-layer structures in silicon. Transmission spectra of Fibonacci type quasi-crystals are reported and the (self-similar) light distributions of the transmission modes at the Fibonacci band edge are calculated and discussed.

Amplified extended modes in random lasers.

We report on a new random laser phenomenon that gives rise to narrow emission modes without requiring optical cavities. Sharp emission peaks are observed experimentally over a broad range of scattering strengths and analyzed in numerical calculations. We find that the introduction of exponential gain in a multiple light scattering process strongly increases the importance of very long light paths. Such long paths are rare and often neglected in passive disordered materials but we show that they can dominate the emission spectrum from an amplifying disordered system.

Coupling, competition, and stability of modes in random lasers

We studied analytically and numerically the complex properties of random lasing modes. Mode repulsion in frequency domain for inhomogeneously broadened gain media was confirmed by our numerical results. We constructed a coupled-mode model to explain the synchronized lasing behavior for modes whose frequency difference is less than the homogeneous gain width. The stability of coupled modes was investigated. The effective competition coefficient Ce for two modes with both gain competition and field coupling is obtained analytically. In our numerical experiments, we also found the coupled oscillations of two lasing modes. From the analytical derivation, we demonstrated that such oscillations could reveal the field-coupling strength between the random modes.

Emission properties of organic random lasers

We report on random lasing in a neat film of substituted quinquethienyl S,S-dioxide. Despite the absence of intentionally introduced scatterers random lasing with 5 A Full Width at Half Maximum is observed. The angular distribution of random lasing modes is studied through angle resolved emission measurements demonstrating that random lasing emission is directional with a 8° divergence but different individual emission direction. The origin of the feedback is investigated through Atomic Force Microscopy demonstrating that random lasing is observed only when 50 nm diameter holes are present in the film. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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.