Exact Analytical Formula for the Excess Noise Factor for Mixed Carrier Injection Avalanche Photodiodes

The well-known analytical formula for the excess noise factor associated with avalanche photodiodes (APDs), developed by R. J. McIntyre in 1966, assumes the injection of either an electron or a hole at the edge of the APD\u27s avalanche region. This formula is based on the statistics of the probabilities of carriers gaining and losing energy subject to high electric fields. However, this analytical formula, is not applicable in cases when photons are absorbed inside the avalanche region (even though the physics of the high field transport remains the same), and its use may severely underestimate or overestimate the actual excess noise factor depending on the absorption profile and the hole-to-electron ionization coefficient ratio, k. Here, an easy-to-use exact analytical formula is derived for the excess noise factor of APDs while taking into account a mixed-carrier initiated avalanche multiplication process, which is triggered by a parent electron-hole pair at an arbitrarily specified location within the multiplication region. The derivation relies on analytically solving a special case of a previously reported recursive integral equations [Hayat et al., IEEE Trans. Electron Devices, vol. 39, no. 3, pp. 546-552, Mar. 1992.], and the result matches the formula reported by McIntyre in 1999 using a different and limited technique. In addition, an expression for the excess noise factor is presented in the case when the location of the parent electron-hole pair within the multiplication region obeys an arbitrary exponential distribution. The results show that in contrast to the case of edge parent-electron injection, when mixed injection is allowed even a small level of hole ionization (e.g., small k ~ 0.0001) causes the excess noise factor to increase dramatically, depending on the absorption profile as it ranges from narrow to flat within the multiplication region. The theoretical results are validated against experimental results for Si APDs

Sensitivity of High-Speed Lightwave System Receivers Using InAlAs Avalanche Photodiodes

Calculations based on a rigorous analytical model are carried out to compare the sensitivity of optical receivers that use InP and In0.52Al0.48As avalanche photodiodes (APDs). The model includes the effects of intersymbol interference, tunneling current, avalanche noise and its correlation with the stochastic avalanche duration, dead space, and transimpedance amplifier noise. For a 10-Gb/s system with a bit-error rate of 10-12, the optimum receiver sensitivity predicted for In0.52Al0.48As and InP APDs is -28.6 and -28.1 dBm, respectively, corresponding to a reduction of 11% in optical signal power for receivers using In0.52Al0.48As APDs. Thus, considering overall receiver sensitivity, the improvement offered by In0.52Al0.48As APDs over InP is modest

Photon-photon correlations and entanglement in doped photonic crystals

We consider a photonic crystal (PC) doped with four-level atoms whose intermediate transition is coupled near-resonantly with a photonic band-gap edge. We show that two photons, each coupled to a different atomic transition in such atoms, can manifest strong phase or amplitude correlations: One photon can induce a large phase shift on the other photon or trigger its absorption and thus operate as an ultrasensitive nonlinear photon-switch. These features allow the creation of entangled two-photon states and have unique advantages over previously considered media: (i) no control lasers are needed; (ii) the system parameters can be chosen to cause full two-photon entanglement via absorption; (iii) a number of PCs can be combined in a network.Comment: Modified, expanded text; added reference

Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A second fourth-order ordinary differential equation for the general Fourier coefficent is derived from an integral representation of the coefficient, and both differential equations are shown to be equivalent. Series solutions for the various Fourier coefficients are also given, mostly in terms of Legendre functions and Bessel/Hankel functions. These are derived from the closed form hypergeometric solutions or an integral representation, or both. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented

Steklov problem on differential forms

In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\Lambda$ is shown to be self-adjoint on the subspace of coclosed forms and to have purely discrete spectrum there.We investigate properies of eigenvalues of $\Lambda$ and prove a Hersch-Payne-Schiffer type inequality relating products of those eigenvalues to eigenvalues of Hodge Laplacian on the boundary. Moreover, non-trivial eigenvalues of $\Lambda$ are always at least as large as eigenvalues of Dirichlet-to-Neumann map defined by Raulot and Savo. Finally, we remark that a particular case of $p$-forms on the boundary of $2p+2$-dimensional manifold shares a lot of important properties with the classical Steklov eigenvalue problem on surfaces.Comment: 18 page

Etched distributed Bragg reflectors as three-dimensional photonic crystals: photonic bands and density of states

The photonic band dispersion and density of states (DOS) are calculated for the three-dimensional (3D) hexagonal structure corresponding to a distributed Bragg reflector patterned with a 2D triangular lattice of circular holes. Results for the Si/SiO$_2$ and GaAs/AlGaAs systems determine the optimal parameters for which a gap in the 2D plane occurs and overlaps the 1D gap of the multilayer. The DOS is considerably reduced in correspondence with the overlap of 2D and 1D gaps. Also, the local density of states (i.e., the DOS weighted with the squared electric field at a given point) has strong variations depending on the position. Both results imply substantial changes of spontaneous emission rates and patterns for a local emitter embedded in the structure and make this system attractive for the fabrication of a 3D photonic crystal with controlled radiative properties.Comment: 8 pages, 5 figures; to appear in Phys. Rev.

Collisionless hydrodynamics for 1D motion of inhomogeneous degenerate electron gases: equivalence of two recent descriptions

Recently I. Tokatly and O. Pankratov (''TP'', Phys. Rev. B 60, 15550 (1999)) used velocity moments of a semiclassical kinetic equation to derive a hydrodynamic description of electron motion in a degenerate electron gas. Independently, the present authors (Theochem 501-502, 327 (2000)) used considerations arising from the Harmonic Potential Theorem (Phys. Rev. Lett. 73, 2244 (1994)) to generate a new form of high-frequency hydrodynamics for inhomogeneous degenerate electron gases (HPT-N3 hydrodynamics). We show here that TP hydrodynamics yields HPT-N3 hydrodynamics when linearized about a Thomas-Fermi groundstate with one-dimensional spatial inhomnogeneity.Comment: 17p

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov's fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current correlation function is found to be integrable in space, in both classical and quantum regimes.Comment: 19 pages, 1 figur

Interference, reduced action, and trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function's trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.Comment: 12 pages text, 5 figures. Typos corrected. Author's final submission. A companion paper to "Welcher Weg? A trajectory representation of a quantum Young's diffraction experiment", quant-ph/0605121. Keywords: interference, nonlocality, trajectory representation, entanglement, dwell time, determinis