135,545 research outputs found
Unusual modes and photonic gaps in a Vicsek waveguide network
We propose a simple model of a waveguide network designed following the
growth rule of a Vicsek fractal. We show, within the framework of real space
renormalization group (RSRG) method, that such a design may lead to the
appearance of unusual electromagnetic modes. Such modes exhibit an extended
character in RSRG sense. However, they lead to a power law decay in the
end-to-end transmission of light across such a network model as the size of the
network increases. This, to our mind, may lead to an observation of power law
localization of light in a fractal waveguide network. The general occurence of
photonic band gaps and their change as a function of the parameters of the
system are also discussed.Comment: 13 pages, 6 figure
On the Economic Value and Price-Responsiveness of Ramp-Constrained Storage
The primary concerns of this paper are twofold: to understand the economic
value of storage in the presence of ramp constraints and exogenous electricity
prices, and to understand the implications of the associated optimal storage
management policy on qualitative and quantitative characteristics of storage
response to real-time prices. We present an analytic characterization of the
optimal policy, along with the associated finite-horizon time-averaged value of
storage. We also derive an analytical upperbound on the infinite-horizon
time-averaged value of storage. This bound is valid for any achievable
realization of prices when the support of the distribution is fixed, and
highlights the dependence of the value of storage on ramp constraints and
storage capacity. While the value of storage is a non-decreasing function of
price volatility, due to the finite ramp rate, the value of storage saturates
quickly as the capacity increases, regardless of volatility. To study the
implications of the optimal policy, we first present computational experiments
that suggest that optimal utilization of storage can, in expectation, induce a
considerable amount of price elasticity near the average price, but little or
no elasticity far from it. We then present a computational framework for
understanding the behavior of storage as a function of price and the amount of
stored energy, and for characterization of the buy/sell phase transition region
in the price-state plane. Finally, we study the impact of market-based
operation of storage on the required reserves, and show that the reserves may
need to be expanded to accommodate market-based storage
Asymmetric Protocols for Scalable High-Rate Measurement-Device-Independent Quantum Key Distribution Networks
Measurement-device-independent quantum key distribution (MDI-QKD) can
eliminate detector side channels and prevent all attacks on detectors. The
future of MDI-QKD is a quantum network that provides service to many users over
untrusted relay nodes. In a real quantum network, the losses of various
channels are different and users are added and deleted over time. To adapt to
these features, we propose a type of protocols that allow users to
independently choose their optimal intensity settings to compensate for
different channel losses. Such protocol enables a scalable high-rate MDI-QKD
network that can easily be applied for channels of different losses and allows
users to be dynamically added/deleted at any time without affecting the
performance of existing users.Comment: Changed the title to better represent the generality of our method,
and added more discussions on its application to alternative protocols (in
Sec. II, the new Table II, and Appendix E with new Fig. 9). Added more
conceptual explanations in Sec. II on the difference between X and Z bases in
MDI-QKD. Added additional discussions on security of the scheme in Sec. II
and Appendix
Dynamics of the Modulational Instability in Microresonator Frequency Combs
A study is made of frequency comb generation described by the driven and
damped nonlinear Schr\"odinger equation on a finite interval. It is shown that
frequency comb generation can be interpreted as a modulational instability of
the continuous wave pump mode, and a linear stability analysis, taking into
account the cavity boundary conditions, is performed. Further, a truncated
three-wave model is derived, which allows one to gain additional insight into
the dynamical behaviour of the comb generation. This formalism describes the
pump mode and the most unstable sideband and is found to connect the coupled
mode theory with the conventional theory of modulational instability. An
in-depth analysis is done of the nonlinear three-wave model. It is demonstrated
that stable frequency comb states can be interpreted as attractive fixed points
of a dynamical system. The possibility of soft and hard excitation states in
both the normal and the anomalous dispersion regime is discussed.
Investigations are made of bistable comb states, and the dependence of the
final state on the way the comb has been generated. The analytical predictions
are verified by means of direct comparison with numerical simulations of the
full equation and the agreement is discussed.Comment: 9 pages, 6 figures, submitted to Phys. Rev.
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