In this letter, a new analytical method is presented to calculate of the semiconductor optical gain coefficient. This method is particularly suitable for theoretical analyses to determine the dependence of semiconduct...In this letter, a new analytical method is presented to calculate of the semiconductor optical gain coefficient. This method is particularly suitable for theoretical analyses to determine the dependence of semiconductor gain on the total carrier density and temperature in the semiconductor lasers. Also, the optical gain functions for semiconductor optical gain coefficient are presented analytically. The analytical evaluation is verified with numerical methods, which illustrates the accuracy of these obtained analytical expressions.展开更多
An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma funct...An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.展开更多
A new analytical approach to the computation of the Fermi-Dirac （FD） functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem these functions a...A new analytical approach to the computation of the Fermi-Dirac （FD） functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.展开更多
By use of complete orthonormal sets of ψα exponential-type orbitals (ψα-ETOs, α = 1, 0,-1,-2, ...) the series expansion formulas for the noninteger n* Slater-type orbitals (NISTOs) in terms of integer n Slater-ty...By use of complete orthonormal sets of ψα exponential-type orbitals (ψα-ETOs, α = 1, 0,-1,-2, ...) the series expansion formulas for the noninteger n* Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals(ISTOs) are derived. These formulas enable us to express the overlap integrals with NISTOs through the overlap integrals over ISTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NISTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.展开更多
文摘In this letter, a new analytical method is presented to calculate of the semiconductor optical gain coefficient. This method is particularly suitable for theoretical analyses to determine the dependence of semiconductor gain on the total carrier density and temperature in the semiconductor lasers. Also, the optical gain functions for semiconductor optical gain coefficient are presented analytically. The analytical evaluation is verified with numerical methods, which illustrates the accuracy of these obtained analytical expressions.
文摘An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.
文摘A new analytical approach to the computation of the Fermi-Dirac （FD） functions is presented, which was suggested by previous experience with various algorithms. Using the binomial expansion theorem these functions are expressed through the binomial coefficients and familiar incomplete Gamma functions. This simplification and the use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speedier calculation, should such limits be required in practice. Some numerical results are presented for significant mapping examples and they are briefly discussed.
文摘By use of complete orthonormal sets of ψα exponential-type orbitals (ψα-ETOs, α = 1, 0,-1,-2, ...) the series expansion formulas for the noninteger n* Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals(ISTOs) are derived. These formulas enable us to express the overlap integrals with NISTOs through the overlap integrals over ISTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NISTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.
