Modal coupling in traveling-wave resonators

High-Q traveling-wave-resonators can enter a regime in which even minute scattering amplitudes associated with either bulk or surface imperfections can drive the system into the so-called strong modal coupling regime. Resonators that enter this regime have their coupling properties radically altered and can mimic a narrowband reflector. We experimentally confirm recently predicted deviations from criticality in such strongly coupled systems. Observations of resonators that had Q>10^8 and modal coupling parameters as large as 30 were shown to reflect more than 94% of an incoming optical signal within a narrow bandwidth of 40 MHz

IEP Quality: Changes Observed Following A Period Of Staff Training and Form Revision

During the period 1987-1990, a suburban school district implemented an in-service training program as well as several form revisions for the purpose of improving the quality of IEP documents. The purposes of this study were to document what changes, if any, occurred in the levels of legal compliance and internal consistency in a random sample of IEPs over that three year period, to determine whether a significant difference in the levels of compliance and/or internal consistency existed between IEPS of Level 1 and Level 2 students, and to identify areas of strength and weakness in IEPs

Solgel route to erbium-doped microlasers and Raman microlasers on-a-chip

Ultra-high-Q microresonators are fabricated on silicon chips by the solgel technique. Using wafer-based processing and selective reflow, we create toroid-shaped Er-doped microlasers directly from Er-doped solgel layers and Raman microlasers from undoped silica solgel layers

Theoretical and experimental study of stimulated and cascaded Raman scattering in ultra-high-Q optical microcavities

Stimulated Raman scattering (SRS) in ultra-high-Q surface-tension-induced spherical and chip-based toroid microcavities is considered both theoretically and experimentally. These microcavities are fabricated from silica, exhibit small mode volume (typically 1000 $\mu m^{3}$) and possess whispering-gallery type modes with long photon storage times (in the range of 100 ns), significantly reducing the threshold for stimulated nonlinear optical phenomena. Oscillation threshold levels of less than 100 $\mu$% -Watts of launched fiber pump power, in microcavities with quality factors of 100 million are observed. Using a steady state analysis of the coupled-mode equations for the pump and Raman whispering-gallery modes, the threshold, efficiencies and cascading properties of SRS in UHQ devices are derived. The results are experimentally confirmed in the telecommunication band (1550nm) using tapered optical fibers as highly efficient waveguide coupling elements for both pumping and signal extraction. The device performance dependence on coupling, quality factor and modal volume are measured and found to be in good agreement with theory. This includes analysis of the threshold and efficiency for cascaded Raman scattering. The side-by-side study of nonlinear oscillation in both spherical microcavities and toroid microcavities on-a-chip also allows for comparison of their properties. In addition to the benefits of a wafer-scale geometry, including integration with optical, electrical or mechanical functionality, microtoroids on-a-chip exhibit single mode Raman oscillation over a wide range of pump powers.Comment: 12 pages, 15 figure

Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip

Optical microcavities confine light spatially and temporally and find application in a wide range of fundamental and applied studies. In many areas, the microcavity figure of merit is not only determined by photon lifetime (or the equivalent quality-factor, Q), but also by simultaneous achievement of small mode volume V . Here we demonstrate ultra-high Q-factor small mode volume toroid microcavities on-a-chip, which exhibit a Q/V factor of more than $10^{6}(\lambda/n)^{-3}$. These values are the highest reported to date for any chip-based microcavity. A corresponding Purcell factor in excess of 200 000 and a cavity finesse of $2.8\times10^{6}$ is achieved, demonstrating that toroid microcavities are promising candidates for studies of the Purcell effect, cavity QED or biochemical sensingComment: 4 pages, 3 figures, Submitted to Applied Physics Letter

Ultra-high-Q toroid microcavities on a chip

We demonstrate microfabrication of ultra-high-Q microcavities on a chip, exhibiting a novel toroid-shaped geometry. The cavities possess Q-factors in excess of 100 million which constitutes an improvement close to 4 orders-of-magnitude in Q compared to previous work [B. Gayral, et al., 1999]

Understanding Teacher Leadership in Middle School Mathematics: A Collaborative Research Effort

We report findings from a collaborative research effort designed to examine how teachers act as leaders in their schools. We find that teachers educated by the Math in the Middle Institute act as key sources of advice for colleagues within their schools while drawing support from a network consisting of other teachers in the program and university-level advisors. In addition to reporting on our findings, we reflect on our research process, noting some of the practical challenges involved, as well as some of the benefits of collaboration

Fabrication and coupling to planar high-Q silica disk microcavities

Using standard lithographic techniques, we demonstrate fabrication of silica disk microcavities, which exhibit whispering-gallery-type modes having quality factors (Q) in excess of 1 million. Efficient coupling (high extinction at critical coupling and low, nonresonant insertion loss) to and from the disk structure is achieved by the use of tapered optical fibers. The observed high Q is attributed to the wedged-shaped edge of the disk microcavity, which is believed to isolate modes from the disk perimeter and thereby reduce scattering loss. The mode spectrum is measured and the influence of planar confinement on the mode structure is investigated. We analyze the use of these resonators for very low loss devices, such as add/drop filters

Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process

We report high-Q sol–gel microresonators on silicon chips, fabricated directly from a sol–gel layer deposited onto a silicon substrate. Quality factors as high as 2.5×10^7 at 1561 nm were obtained in toroidal microcavities formed of silica sol–gel, which allowed Raman lasing at absorbed pump powers below 1 mW. Additionally, Er3+-doped microlasers were fabricated from Er3+-doped sol–gel layers with control of the laser dynamics possible by varying the erbium concentration of the starting sol–gel material. Continuous lasing with a threshold of 660 nW for erbium-doped microlaser was also obtained