Cavity Q, mode volume, and lasing threshold in small diameter AlGaAs microdisks with embedded quantum dots

The quality factor (Q), mode volume (Veff), and room-temperature lasing threshold of microdisk cavities with embedded quantum dots (QDs) are investigated. Finite element method simulations of standing wave modes within the microdisk reveal that Veff can be as small as 2(lambda/n)^3 while maintaining radiation-limited Qs in excess of 10^5. Microdisks of diameter D=2 microns are fabricated in an AlGaAs material containing a single layer of InAs QDs with peak emission at lambda = 1317 nm. For devices with Veff ~2 (lambda/n)^3, Qs as high as 1.2 x 10^5 are measured passively in the 1.4 micron band, using an optical fiber taper waveguide. Optical pumping yields laser emission in the 1.3 micron band, with room temperature, continuous-wave thresholds as low as 1 microWatt of absorbed pump power. Out-coupling of the laser emission is also shown to be significantly enhanced through the use of optical fiber tapers, with laser differential efficiency as high as xi~16% and out-coupling efficiency in excess of 28%.Comment: 6 figure

Single quantum dot spectroscopy using a fiber taper waveguide near-field optic

Photoluminescence spectroscopy of single InAs quantum dots at cryogenic temperatures (~14 K) is performed using a micron-scale optical fiber taper waveguide as a near-field optic. The measured collection efficiency of quantum dot spontaneous emission into the fundamental guided mode of the fiber taper is estimated at 0.1%, and spatially-resolved measurements with ~600 nm resolution are obtained by varying the taper position with respect to the sample and using the fiber taper for both the pump and collection channels.Comment: 4 pages, 3 figure

On a remarkable formula of Ramanujan

A simple proof of Ramanujan's formula for the Fourier transform of the square of the modulus of the Gamma function restricted to a vertical line in the right half-plane is given. The result is extended to vertical lines in the left half-plane by solving an inhomogeneous ODE. We then use it to calculate the jump across the imaginary axis.Comment: To appear in Archiv der Mathemati

Reflections on Euler's reflection formula and an additive analogue of Legendre's duplication formula

In this note, we look at some of the less explored aspects of the gamma function. We provide a new proof of Euler's reflection formula and discuss its significance in the theory of special functions. We also discuss a result of Landau concerning the determination of values of the gamma function using functional identities. We show that his result is sharp and extend it to complex arguments. In 1848, Oskar Schl\"omilch gave an interesting additive analogue of the duplication formula. We prove a generalized version of this formula using the theory of hypergeometric functions

Moving boundary and photoelastic coupling in GaAs optomechanical resonators

Chip-based cavity optomechanical systems are being considered for applications in sensing, metrology, and quantum information science. Critical to their development is an understanding of how the optical and mechanical modes interact, quantified by the coupling rate $g_{0}$. Here, we develop GaAs optomechanical resonators and investigate the moving dielectric boundary and photoelastic contributions to $g_{0}$. First, we consider coupling between the fundamental radial breathing mechanical mode and a 1550 nm band optical whispering gallery mode in microdisks. For decreasing disk radius from $R=5$ $\mu$m to $R=1$ $\mu$m, simulations and measurements show that $g_{0}$ changes from being dominated by the moving boundary contribution to having an equal photoelastic contribution. Next, we design and demonstrate nanobeam optomechanical crystals in which a $2.5$ GHz mechanical breathing mode couples to a 1550 nm optical mode predominantly through the photoelastic effect. We show a significant (30 $\%$) dependence of $g_{0}$ on the device's in-plane orientation, resulting from the difference in GaAs photoelastic coefficients along different crystalline axes, with fabricated devices exhibiting $g_{\text{0}}/2\pi$ as high as 1.1 MHz for orientation along the [110] axis. GaAs nanobeam optomechanical crystals are a promising system which can combine the demonstrated large optomechanical coupling strength with additional functionality, such as piezoelectric actuation and incorporation of optical gain media

Macro-Financial Parameters Influencing Bitcoin Prices: Evidence from Symmetric and Asymmetric ARDL Models

Bitcoins are evolving as a modern class of investment assets and it is crucial for investors to manage their investment risk. This paper examines the impact of macroeconomic-financial indicators on Bitcoin price using symmetric and asymmetric version of autoregressive distributed lag (ARDL) models with structural breaks. The asymmetric long-run association ascertained between Bitcoin prices and the macroeconomic-financial indicators is evident. Our empirical results indicate that the Bitcoin cannot be used to hedge against the inflation, Federal funds rate, stock markets and commodity markets. We further find that Bitcoin can be regarded as a hedging device for the oil prices. Our findings have significant implications for market participants who consider including alternate investment assets in their portfolios