M ar 2 01 4 High-cooperativity nanofiber laser

Cavity-free efficient coupling between emitters and guided modes is of great current interest for nonlinear quantum optics as well as efficient and scalable quantum information processing. In this work, we extend these activities to the coupling of organic dye molecules to a highly confined mode of a nanofiber, allowing mirrorless and low-threshold laser action in an effective mode volume of less than 100 femtoliters. We model this laser system based on semi-classical rate equations and present an analytic compact form of the laser output intensity. Despite the lack of a cavity structure, we achieve a coupling efficiency of the spontaneous emission to the waveguide mode of β = 0.07 ± 0.01, in agreement with our calculations. In a further experiment, we also demonstrate the use of a plasmonic nanoparticle as a dispersive output coupler. Our laser architecture is promising for a number of applications in optofluidics and provides a fundamental model system for studying nonresonant feedback stimulated emission. PACS numbers: 42.55. -f, 42.55. Zz, 42.82. Et, , 42.60. Da High-cooperativity nanofiber laser 2 Miniature light sources that can be integrated in chip-scale devices are one of the fundamental building blocks of photonics circuits. Among these, micro and nanolasers are particularly attractive because they offer a high degree of coherence, tunability, directionality, and efficiency. However, reducing the size of the gain medium often compromises the laser threshold and output stability. A customary strategy to counter these undesirable effects is to improve the resonator quality factor [1, 2, 3]. An alternative solution is to maximize the so-called β-factor or cooperativity, which is defined as the fraction of the spontaneous emission into the optical mode that hosts the laser radiation relative to the total emission [4, 5, 6]. As β approaches unity, the laser threshold is expected to vanish [4]. Many efforts have been pursued to increase β via concepts from cavity quantum electrodynamics based on the modification of the density of states in resonant structures [4, 7], but the realization of suitable microcavity geometries often confronts limitations imposed by the choice of material and fabrication technologies [3]. Recently, we have shown that unity coupling efficiency between light and matter can be achieved for propagating photons in a cavity-free single-pass geometry if the spatial mode of the photons and the emission pattern of the atoms are matched [8]. Considering that the emission associated with a typical optical transition follows the radiation pattern of an electric dipole, this means that the photons have to be produced in a dipolar mode. Although the overlap between a tightly-focused light beam and a dipolar radiation mode is very high [9], achieving unity efficiency in this strategy is nontrivial. As an alternative, however, one can engineer the near-field optical interactions to funnel the radiation of point-like emitters into more conventional directed light beams. Some of the avenues discussed in literature either use planar metallo-dielectric antennas [10], or linearly extended architectures such as co-axial [7], photonic crystal [11], or slot [12] waveguides, or plasmonic nanowires [13], or simply nanofibers [14, 15]. In the current work, we choose the latter geometry, which has been experimentally explored by coupling tapered fibers to atoms, molecules, or quantum dots [16, 17, 18]. The β-factor in such waveguiding systems depends on the refractive index contrast and dimensions of the fiber as well as the coordinates of the emitter relative to the mode. Interestingly, lasing from a short semiconductor nanowire with substantial feedback from its endfacets has also been reported about a decade ago although the key issues of its operation were not explained [19]. In this article, we propose and examine the coupling of a gain medium to a nanofiber without an explicit use of any cavity geometry. As a flexible fabrication platform we use glass nanocapillaries, which can be easily filled with organic dye molecules, quantum dots, or other optically active materials. By choosing a filling medium with an index of refraction higher than glass, we can achieve a tightly-confined mode of the waveguide, which yields a maximum β of 0.12 for emitters on the axis of the core. Furthermore, we show that individual gold nanoparticles can serve as efficient dispersive outcouplers. We discuss the theoretical and experimental performance of our nanofiber laser and its connection to nonresonant feedback laser (nRFL) action [20], commonly referred to High-cooperativity nanofiber laser 3 as random laser [21]. Two of the central features of this lasing regime are intrinsic multimode operation and lack of well-defined cavity geometry. These have rendered a quantitative understanding of the laser operation both a theoretical and an experimental challenge. Reduction of the geometry to one dimension and single transverse lasing operation can substantially simplify the system. We compare our measurements with a simplified model based on semi-classical rate equations. Using an explicit and compact formula for the output laser power as a function of pump rate we can extract the β-factor from a direct fit to our measured data. Finally, our work has important implications for enhancing the performance of optofluidic fiber lasers, where β-factors have been typically very low either due to the large mode area in the waveguide or the presence of multiple transverse modes [22, 23, 24]. 1. Experimental methods Our laser architecture consists of a fused-silica glass capillary with an inner diameter of 710 nm filled with phenol and rhodomine-6G as gain medium. To fill the capillary, a short piece is immersed into a 4.7 mM dye solution kept in the liquid form at T = 50◦C. The solution rises inside the capillary for about 30 mm within 100 seconds. The capillary is then taken out and the excess material on the outer surfaces is wiped off with ethanol. Meanwhile, the phenol inside the capillary solidifies at room temperature. A 3-mm piece of the filled nanocapillary is cleaved and glued vertically on a glass cover slip with ultraviolet-curable glue (NOA61, Norland Optical Adhesives). The refractive index of this glue (n = 1.54) is matched with that of phenol. We determined the absorption length of the gain medium to be 37 μm by measuring, perpendicular to the fiber axis, the decay of the red-shifted fluorescence along the core, while exciting the guided mode with continuous-wave light at 532 nm at one end. The experimental setup is sketched in Fig. 1(a). Since the gain medium extends further than its absorption length, any emission produced at the bottom end does not interact with the upper end of the active material. On the lower side, the medium is largely index-matched so that reflections from the capillary end should amount to less than 10. Furthermore, because the output of the nanocapillary mode with a numerical aperture of 0.46 is very divergent, reflections from secondary interfaces farther away are negligible so that we can consider the external feedback to the system to be very small. To pump the medium for laser action, light from a frequency-doubled Q-switched Nd-YAG laser with 10 Hz repetition rate and pulse duration of 7 ns was attenuated and focused on the end of the nanocapillary through a high-NA immersion objective. The red-shifted emission was collected via the same microscope objective and directed to a spectrograph and a digital camera in parallel. Figure 1(b) shows the lower end facet of the capillary. High-cooperativity nanofiber laser 4 0.5 1.0 1.5 2.0 0.00 0.05 0.10 M od e be ta fa ct or Core diameter ( m) 0 1 Fu nd am en ta l m od e ar ea ( m 2 ) Objective 1.05 N.A. (a) (b) Pulsed laser 532 nm 10 Hz 7 ns