Exact extreme value statistics at mixed order transitions

We study extreme value statistics (EVS) for spatially extended models exhibiting mixed order phase transitions (MOT). These are phase transitions which exhibit features common to both first order (discontinuity of the order parameter) and second order (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising (TIDSI) model which is a prototypical model exhibiting MOT, and study analytically the extreme value statistics of the domain lengths. The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size $L$. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length $l_{\max}$ converges, in the large $L$ limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of $l_{\max}$ are governed by novel distributions which we compute exactly. Our main analytical results are verified by numerical simulations.Comment: 25 pages, 6 figures, 1 tabl

Monolithic optoelectronic integration of a GaAlAs laser, a field-effect transistor, and a photodiode

A low threshold buried heterostructure laser, a metal-semiconductor field-effect transistor, and a p-i-n photodiode have been integrated on a semi-insulating GaAs substrate. The circuit was operated as a rudimentary optical repeater. The gain bandwidth product of the repeater was measured to be 178 MHz

Gallium Aluminum Arsenide/Gallium Arsenide Integrated Optical Repeater

A low threshold buried heterostructure laser, a metal-semiconductor field effect transistor (MESFET), and a photodiode, have for the first time, been monolithically integrated on a semi-insulating GaAs substrate. This integrated optoelectronic circuit (IOEC) was operated as a rudimentary optical repeater. The incident optical signal is detected by the photodiode, amplified by the MESFET, and converted back to light by the laser. The gain bandwidth product of the repeater was measured to be 178 MHz

High-speed GaAlAs/GaAs p-i-n photodiode on a semi-insulating GaAs substrate

A high-speed, high-responsivity GaAlAs/GaAs p-i-n photodiode has been fabricated on a GaAs semi-insulating substrate. The 75-µm-diam photodiode has a 3-dB bandwidth of 2.5 GHz and responsivity of 0.45 A/W at 8400 Å (external quantum efficiency of 65%). The diode is suitable for monolithic integration with other optoelectronic devices

Fast Structuring of Radio Networks for Multi-Message Communications

We introduce collision free layerings as a powerful way to structure radio networks. These layerings can replace hard-to-compute BFS-trees in many contexts while having an efficient randomized distributed construction. We demonstrate their versatility by using them to provide near optimal distributed algorithms for several multi-message communication primitives. Designing efficient communication primitives for radio networks has a rich history that began 25 years ago when Bar-Yehuda et al. introduced fast randomized algorithms for broadcasting and for constructing BFS-trees. Their BFS-tree construction time was $O(D \log^2 n)$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. Since then, the complexity of a broadcast has been resolved to be $T_{BC} = \Theta(D \log \frac{n}{D} + \log^2 n)$ rounds. On the other hand, BFS-trees have been used as a crucial building block for many communication primitives and their construction time remained a bottleneck for these primitives. We introduce collision free layerings that can be used in place of BFS-trees and we give a randomized construction of these layerings that runs in nearly broadcast time, that is, w.h.p. in $T_{Lay} = O(D \log \frac{n}{D} + \log^{2+\epsilon} n)$ rounds for any constant $\epsilon>0$. We then use these layerings to obtain: (1) A randomized algorithm for gathering $k$ messages running w.h.p. in $O(T_{Lay} + k)$ rounds. (2) A randomized $k$-message broadcast algorithm running w.h.p. in $O(T_{Lay} + k \log n)$ rounds. These algorithms are optimal up to the small difference in the additive poly-logarithmic term between $T_{BC}$ and $T_{Lay}$. Moreover, they imply the first optimal $O(n \log n)$ round randomized gossip algorithm

Combined High Power and High Frequency Operation of InGaAsP/InP Lasers at 1.3μm

A simultaneous operation of a semiconductor laser at high power and high speed was demonstrated in a buried crescent laser on a P-InP substrate. In a cavity length of 300μm, a maximum CW power of 130mW at room temperature was obtained in a junction-up mounting configuration. A 3dB bandwidth in excess of 12GHz at an output power of 52mW was observed

Gallium Arsenide Monolithic Optoelectronic Circuits

The optical properties of GaAs make it a very useful material for the fabrication of optical emitters and detectors. GaAs also possesses electronic properties which allow the fabrication of high speed electronic devices which are superior to conventional silicon devices. Monolithic optoelectronic circuits are formed by the integration of optical and electronic devices on a single GaAs substrate. Integration of many devices is most easily accomplished on a semi-insulating (SI) sub-strate. Several laser structures have been fabricated on SI GaAs substrates. Some of these lasers have been integrated with Gunn diodes and with metal semiconductor field effect transistors (MESFETs). An integrated optical repeater has been demonstrated in which MESFETs are used for optical detection and electronic amplification, and a laser is used to regenerate the optical signal. Monolithic optoelectronic circuits have also been constructed on conducting substrates. A heterojunction bipolar transistor driver has been integrated with a laser on an n-type GaAs substrate

Whispering gallery lasers on semi-insulating GaAs substrates

Double heterostructure lasers are described in which light is guided by total internal reflection along a dielectric interface formed by the perimeter of an etched mesa. By means of the crowding effect, injection current is restricted to a narrow strip adjacent to the edge of the mesa. This results in the preferential excitation of optical modes which are localized in the vicinity of the dielectric interface. Both half-ring lasers formed at a single cleaved facet and quarter-ring lasers formed at a cleaved corner were fabricated