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IEEE Photonics Technology Letters

Design of Rare-Earth-Doped Microspheres

Luciano Mescia, Francesco Prudenzano, M. De Sario, Tommaso Palmisano, Maurizio Ferrari, Giancarlo Cesare Righini

Published Jan 20, 2010• 16 citations
Publisher

Abstract

Two original computer codes for the design of rare-earth-doped dielectric microspheres have been ad hoc developed. The former code is based on a finite-difference time-domain algorithm, suitably extended to model the amplification of the whispering-gallery modes propagating into rare-earth-doped microspheres. It takes into account the wavelength dispersion of the microsphere refractive index and the polarization obtained via the density matrix model. The design of an Er3+-doped silica microsphere coupled with a tapered silica fiber is reported. The latter home-made computer code solves the rate equations and the power propagation equations in frequency domain. The results are in excellent agreement.

DOI
10.1109/lpt.2009.2039932

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Journal of the Physical Society of Japan•Feb 25, 2009•1 citation
Two original computer codes for the design of rare-earth-doped dielectric microspheres have been ad hoc developed. The former code is based on a finite-difference time-domain algorithm, suitably extended to model the amplification of the whispering-gallery modes propagating into rare-earth-doped microspheres. It takes into account the wavelength dispersion of the microsphere refractive index and the polarization obtained via the density matrix model. The design of an Er3+-doped silica microsphere coupled with a tapered silica fiber is reported. The latter home-made computer code solves the rate equations and the power propagation equations in frequency domain. The results are in excellent agreement.
Summary form only given, as follows: The high Q whispering gallery modes of silica microspheres are promising for quantum optics and nonlinear optics experiments involving atoms and photons stored in very small volumes. We have developed the technology of these resonators, learning how to couple light in and out through optical fibers, how to obtain and measure record Q factors, and how to probe, by near-field optical microscopy, the electric field distribution immediately outside the sphere. Whispering gallery mode lasers have also been obtained with microspheres made of silica doped with neodymium ions. We describe these experiments and discuss projects involving the coupling of whispering gallery modes to single atoms or ions to perform cavity QED experiments in the optical domain.
Silica microspheres behave as efficient optical microresonators when small-volume whispering-gallery modes (WGMs) are used. We have realized a cryogenic set-up to work with microspheres immersed in a superfluid helium bath. Quality factors up to 109 have been obtained at 2 K. In this environment, we have been able to observe a dispersive bistable behavior of the WGM resonances, due to the weak intrinsic Kerr optical nonlinearity of silica, with a threshold power of 10 (mu) W only. This result opens the way to the realization of thresholdless microlaser, based on a rare-earth doped silica microsphere and to other Cavity-QED projects with microspheres at low temperatures.
We study both theoretically and experimentally the dispersive properties of single whispering gallery mode resonators. We present a simple experimental protocol which allows us to obtain in detail its coupling regime and thus their dispersive properties. We demonstrate a compact optical amplifier with a gain up to 20dB in an Erbium doped fluoride microsphere of 135μm in diameter coupled via a tapered fiber. The model is also applied to analyze the dynamic behavior of the modal coupling between two degenerate resonances of the same cavity. In particular, this can be used to describe the coupling of counterpropagating whispering gallery modes (WGM) by Rayleigh scattering. The theory is successfully compared to experiments carried out in silica microspheres
Silica microspheres have been demonstrated to provide a permanent resonator which combines small mode volumes with the highest observed quality factors (Q>2.10/sup 9/) corresponding to photon storage times of the order of one microsecond. These properties have allowed us to make a very low-threshold laser with Nd-doped silica microspheres (200 nW absorbed pump power, i.e. 10/sup 6/ excited ions/mode). These microlasers are now operated at 2 K to benefit from a smaller homogeneous linewidth. We then expect to reach the "thresholdless" regime with only a few excited ions. These experiments can also be considered as a first step toward Cavity QED experiments in the strong coupling regime with single atoms or molecules coupled to a whispering gallery mode.
Summary form only given: Amplification in rare-earth doped solid state planar optical structures has attracted a lot of interest in recent years due to the fact that the rare earth ions show sharp absorption and emission bands and relatively long luminescence lifetimes. In particular the erbium (Er) ion is very attractive because of its intra 4f-transition from the first excited state to the ground state around 1.53 mum (4I13/2-4I15/2). The main problem of the erbium doped waveguide amplifiers (EDWAs) is that high values of the Er3+concentration are required to reach high gain figures in a compact length, but in this way the concentration quenching effects become very considerable and detrimental to the optical gain, since they reduce the population in the first excited state. A good solution to overcome this dramatic drawback is to consider erbium doped photonic crystal amplifier (EDPCA). In fact the small group velocity of electromagnetic eigenmodes brings about the enhancement of stimulated emission if the photonic crystals are doped by active media as the rare earth ions E3+r or Yt3+. This phenomenon originates from the long interaction time between radiation field and the matter caused by the small group velocity near the edge of the photonic band gap. The efficient confinement of light is achievable not only by tuning the input signal at the band edge of the gap of the photonic crystal but it is also obtainable by introducing local defects inside photonic crystals. The density of electromagnetic states inside a cavity is significantly modified and the spontaneous emission of atoms in a cavity can be either enhanced or inhibited. Erbium doped silica-titania one-dimensional photonic crystal microcavities have been analyzed by solving the erbium rate equations and the Maxwell equations by means of an auxiliary differential equation finite difference time domain technique. Since the performance of optical amplifiers depends on the populations of the energy levels participating in radiative transitions, determined principally by the distribution and concentration of the rare-earth ions and by the pumping conditions, the relations between these parameters and the transmittance of the EDPCMA have been studied
A dielectric microsphere may be considered as an artificial photonic atom. The electromagnetic modes in the microsphere are completely assigned with indexes similar to those used to characterize simple atomic systems. Microsphere modes, as well as microring or microdisk, trap light in circular orbits near the sphere surface and strongly modify the phase of the interacting light, resulting in very steep dispersions. Pulse propagation experiments were performed in a system consisting of a fiber taper coupled with a silica glass microsphere, and it was shown that the light velocity in the system can be largely changed through the control of the coupling strength. Slow light was also demonstrated in a system in which two ultrahigh-Q silica microspheres of different diameters were coupled in tandem to a fiber taper demonstrating classical analog of electromagnetically induced transparency in atomic system. Here, we employed interferometric techniques based on the Mach-Zehnder interferometer for examining extremely steep dispersions induced by whispering gallery modes with a quality factor on the order of Q 1⁄4 10. Such a narrow resonance in the dielectric microsphere is comparable to that in cooled atomic systems. We successfully observed both normal and anomalous dispersions at the resonant frequency, depending on the coupling strength between the sphere and the fiber. Figure 1 shows our experimental system based on an interferometric setup. We used the second harmonics of a single mode ring cavity Nd3þ yttrium aluminum garnet (Nd3þ:YAG) laser with a line width of 1 kHz at 532 nm. The laser frequency was tuned using thermal control of the ring cavity length, over a mode-hop-free range of greater than 10GHz. The reference arm was empty, while the sample arm contained the microsphere-fiber system. Silica microspheres were fabricated from standard telecommunication optical fiber. The end of the etched fiber was fused using a CO2 laser and the microsphere formed due to the surface tension. The experiments were performed with a microsphere 60 mm in diameter. The fiber taper was also fabricated from the same telecommunication fiber. The typical fiber waist diameter at the coupling region was 0.5 mm. A large number of spectrally overlapping resonance modes exist within a microsphere. The fiber taper method is essential for coupling the incident light to a specific whispering gallery mode selectively and efficiently. The microsphere was attached to a translation stage controlled by a piezo actuator. The relative position between the sphere and the fiber were carefully adjusted so that we could observe spectrally isolated whispering gallery modes with proper coupling strength. The optical path length and dispersion were equalized in each arm as completely as possible. The fringe pattern was captured using a charge-coupled device (CCD) camera for each frequency increment. The observed interference patterns appeared as concentric circles due to the interference between the plain reference wave and the spherical wave from the sample arm. A least square fit for each fringe pattern was performed to extract the phase information in the transmitted light. Figures 2(a) and 2(b) show examples of transmission spectra through the microsphere fiber taper coupled system. These spectra were taken in two different whispering gallery modes at different laser frequencies in the mode-hop-free laser tuning range. The transmission dips appear when the incident laser frequencies are resonant at specific whispering gallery modes in the microsphere. The two whispering gallery modes shown in Figs. 2(a) and 2(b) are denoted as WG1 and WG2, respectively. The transmission minimum was Tmin 1⁄4 0:12, and the resonance width was 1⁄4 BS