All-optical transistor action with bistable switching in a photonic crystal cross-waveguide geometry

We demonstrate all-optical switching action in a nonlinear photonic crystal cross-waveguide geometry with instantaneous Kerr nonlinearity, in which the transmission of a signal can be reversibly switched on and off by a control input. Our geometry accomplishes both spatial and spectral separation between the signal and the control in the nonlinear regime. The device occupies a small footprint of a few micrometers squared and requires only a few milliwatts of power at a 10-Gbit/s switching rate by use of Kerr nonlinearity in AlGaAs below half the electronic bandgap. We also show that the switching dynamics, as revealed by both coupled-mode theory and finite-difference time domain simulations, exhibits collective behavior that can be exploited to generate high-contrast logic levels and all-optical memory.     

Optical bistability in axially modulated OmniGuide fibers

We demonstrate the feasibility of optical bistability in an axially modulated nonlinear OmniGuide fiber through analytical theory and detailed numerical experiments. At 1.55-microm carrier wavelength, the in-fiber devices that we propose can operate with only a few tens of milliwatts of power, can have a nearly instantaneous response and recovery time, and can be shorter than 100 microm.     

Some results on starlike trees and sunlike graphs

A tree is called starlike if it has exactly one vertex of degree greater than two. In [4] it was proved that two starlike treesG andH are cospectral if and only if they are isomorphic. We prove here that there exist no two non-isomorphic Laplacian cospectral starlike trees. Further, letG be a simple graph of ordern with vertex setV(G)={1,2, …,n} and letH={H ₁,H ₂, ...H _n } be a family of rooted graphs. According to [2], the rooted productG(H) is the graph obtained by identifying the root ofH _i with thei-th vertex ofG. In particular, ifH is the family of the paths $P_{k_1 } , P_{k_2 } , ..., P_{k_n } $ with the rooted vertices of degree one, in this paper the corresponding graphG(H) is called the sunlike graph and is denoted byG(k ₁,k ₂, …,k _n ). For any (x ₁,x ₂, …,x _n ) ∈I _* ⁿ , whereI _*={0,1}, letG(x ₁,x ₂, …,x _n ) be the subgraph ofG which is obtained by deleting the verticesi ₁, i₂, …,i _j ∈ V(G) (0≤j≤n), provided that $x_{i_1 } = x_{i_2 } = ... = x_{i_j } = 0$ . LetG(x ₁,x ₂,…, x _n] be the characteristic polynomial ofG(x ₁,x ₂,…, x _n ), understanding thatG[0, 0, …, 0] ≡ 1. We prove that $$G[k_1 , k_2 ,..., k_n ] = \Sigma _{x \in ^{I_ * ^n } } \left[ {\Pi _{i = 1}^n P_{k_i + x_i - 2} (\lambda )} \right]( - 1)^{n - (\mathop \Sigma \limits_{i = 1}^n x_i )} G[x_1 , x_2 , ..., x_n ]$$ where x=(x ₁,x ₂,…,x _n );G[k ₁,k ₂,…,k _n ] andP _n (γ) denote the characteristic polynomial ofG(k ₁,k ₂,…,k _n ) andP _n , respectively. Besides, ifG is a graph with λ₁(G)≥1 we show that λ₁(G)≤λ₁(G(k ₁,k ₂, ...,k _n )) < for all positive integersk ₁,k ₂,…,k _n , where λ₁ denotes the largest eigenvalue.     

Solid state solvation in amorphous organic thin films

The photoluminescence (PL) of the red laser dye DCM2, doped into blended thin films of polystyrene (PS) and the polar small molecule camphoric anhydride (CA), redshifts as the CA concentration increases. The DCM2 PL peaks at 2.20 eV (lambda=563 nm) for pure PS films and shifts to 2.05 eV (lambda=605 nm) for films with 24.5% CA (by mass). The capacitively measured electronic permittivity also increases from epsilon=2.4 to epsilon=5.6 with CA concentration. These results are consistent with the theory of solvatochromism developed for organic molecules in liquid solvents. To our knowledge, this work is the first application of a quantitative theory of solvation to organic molecules in amorphous thin films with continuously controllable permittivity, and demonstrates that "solid state solvation" can be used to predictably tune exciton energies in organic thin film structures.     

Experimental indications for the response of the spectators to the participant blast

Precise momentum distributions of identified projectile fragments, formed in the reactions 238U+Pb and 238U+Ti at 1A GeV, are measured with a high-resolution magnetic spectrometer. With increasing mass loss, the velocities first decrease as expected from previously established systematics, then level off, and finally increase again. Light fragments are on the average even faster than the projectiles. This finding is interpreted as the response of the spectators to the participant blast. The reacceleration of projectile spectators is sensitive to the nuclear mean field and provides a new tool for investigating the equation of state of nuclear matter.     

Pseudogap Fermi-Bose Kondo model

We consider a magnetic impurity coupled to both fermionic quasiparticles with a pseudogap density of states and bosonic spin fluctuations. Using renormalization group and large-N calculations we investigate the phase diagram of the resulting Fermi-Bose Kondo model. We show that the Kondo temperature is strongly reduced by low-energy spin fluctuations, and make connections to experiments in cuprate superconductors. Furthermore, we derive an exact exponent for the critical behavior of the conduction electron T matrix, and propose our findings to be relevant for certain scenarios of local quantum criticality in heavy-fermion metals.     

Microdischarges Near Metal–Insulator Interfaces

Some statistical features of microdischarges running near the metal-insulator interfaces have been discussed. The study has verified an exponential character of statistical distributions of the time intervals between microdischarge pulses, power-law distribution of voltage peaks of these pulses (height of pulses) and very weak correlation effects among pulses, i.e. weak time-height correlation, time autocorrelation and height autocorrelation. A statistical parameter of the power law distribution of the heights of microdischarge pulses proved to be sensitive to the voltage load of the insulating interface metal-insulator.     

The Proof That the Standard Transformations of E and B Are Not the Lorentz Transformations

In this paper it is exactly proved that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not relativistically correct transformations. Thence the 3D vectors E and B are not well-defined quantities in the 4D space-time and, contrary to the general belief, the usual Maxwell equations with the 3D E and B are not in agreement with the special relativity. The 4-vectors E ^a and B ^a , as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B. The proof is given in the tensor and the Clifford algebra formalisms.     

MV-Algebra Pasting

Z. Rieanová proved that every D-lattice is a set-theoretical union of MV-algebras. These MV-algebras are blocks in the D-lattice. There is a dual question: How can we construct a D-poset from a given collection of MV-algebras. To solve this problem we use the pasting technique. We define an admissible system of MV-algebras and we prove that the pasting of this system is a D-poset.     

Bounded point evaluations and cyclic polynomials on the spaces $$\hat F$$

LetF be aBK space withAK and denote the set of all formal power series with such that ε F for the sequence of coefficients of . We give a necessary and sufficient condition for a point to be a bounded point evaluation on , and for a polynomial to be cyclic in . As special cases, we obtain the results for the space ℓ _p (β) in [7]. Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and, in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8.