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Comptes Rendus Physique

Artificial dispersion of active optical coupled resonator systems

Stéphane Trebaol, Thị Kim Ngân Nguyên, Hervé Tavernier, Laura Ghişa, Yannick Dumeige, Patrice Féron

Published Dec 1, 2009• 4 citations
Publisher

Abstract

We study both theoretically and experimentally the dispersive properties of single or coupled active resonators. In the case of single resonator systems, we present a simple experimental protocol which allows us to obtain in detail its coupling regime and thus their dispersive properties. We show that the active coupled systems offer some degrees of freedom to tailor the high dispersion orders. All the propositions are experimentally tested using a model system made of Er 3 + doped fiber ring resonators. These artificial media could be used as tunable or amplifying compact optical delay lines. We also show that the proposed experimental protocol can be applied to passive whispering gallery mode resonators.

DOI
10.1016/j.crhy.2009.10.014

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Journal of the Physical Society of Japan•Feb 25, 2009•1 citation
We study both theoretically and experimentally the dispersive properties of single or coupled active resonators. In the case of single resonator systems, we present a simple experimental protocol which allows us to obtain in detail its coupling regime and thus their dispersive properties. We show that the active coupled systems offer some degrees of freedom to tailor the high dispersion orders. All the propositions are experimentally tested using a model system made of Er 3 + doped fiber ring resonators. These artificial media could be used as tunable or amplifying compact optical delay lines. We also show that the proposed experimental protocol can be applied to passive whispering gallery mode resonators.
We have proposed and experimentally demonstrated tunable cavity-linewidth narrowing by means of coupled-active-resonator-induced dispersion. We have theoretically studied the coupling-resonator-induced-dispersion phenomenon in the general case of NNN coupled resonators and especially the case of two or three resonators. In the case of two resonators we have experimentally shown that the strong dispersion induced by the coupling of resonators can lead to cavity ringdown effect enhancement. In the case of three resonators, we propose a coupling scheme allowing the quality (Q)(Q)(Q) factor of a critically coupled resonator to be increased and actively modulated by using two additional coupled resonators. We have experimentally tested the feasibility of the proposition by using a model system consisting of Er3+{\mathrm{Er}}^{3+}Er3+-doped fiber coupled resonators. These experimental results demonstrate the possibility of QQQ-factor tailoring by the use of active artificial photonic media.
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
We demonstrate experimentally coupled active-resonator-induced transparency in a fiber system. We show that the use of Er3+{\mathrm{Er}}^{3+}Er3+-doped fibers can compensate for the optical losses leading to a high transparency of the system. Using a Mach-Zehnder fiber interferometer, we measure the dispersion properties of our coupled active resonators under different pumping rates. We show that the active feature of the system allows us to engineer the different orders of its artificial dispersion. This experimental demonstration shows the potential of active coupled resonators for dispersion tailoring and slow-light applications.
Since the proposition of D.D. Smith et al. [Phys. Rev. A 69 pp. 063804, 2004], the experimental demonstration of coupled resonator induced transparency has been made using passive fiber or whispering-gallery-mode microspheres. These demonstrations show that it is possible to integrate delay lines using high quality resonators. The maximal group delay that it can be introduced depends mainly on the relative value of the intrinsic losses with respect to the value of the coupling between the resonators. In this paper we experimentally show that the limit given by the intrinsic losses of the resonators can be circumvented by using active resonators. Our experimental setup consists in two coupled Er3+ doped fiber resonators. Each resonator can be pumped independently. Consequently, the values of the residual losses in the two resonators can also be modified independently. We then show that the transparency of the coupled resonators can be maximized using the right pumping rate in each resonator. By inserting this device into one arm of a fiber Mach-Zehnder interferometer we are able to optically measure the phase shift produced by the coupled resonators as a function of the optical frequency. The group delay can be deduced from this information.
We theoretically study a parallel configuration of two interacting whispering-gallery-mode optical resonators and show a narrowband modal structure as a basis for a widely tunable delay line. For the optimum coupling configuration the system can possess an unusually narrow spectral feature with a much narrower bandwidth than the loaded bandwidth of each individual resonator. The effect has a direct analogy with the phenomenon of electromagnetically induced transparency in quantum systems for which the interference of spontaneous emission results in ultranarrow resonances.
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