Analytical expression of transmission for the orbital angular momentum (OAM) communication using loop antenna arrays and paraboloids is derived to achieve a communication distance of 100 m. With the field distribution of the single “transformed OAM mode” radiated by a loop antenna, the collimated field by the transmitting paraboloid and its diffracted field are analytically derived. Effects of frequencies, sizes of paraboloids, and shifts of transmitting and receiving arrays from the focal planes are included. With the diffracted field distribution on the focal plane of the receiving paraboloid, transmission between the transmitting and receiving loop antennas is analytically estimated. It is shown that the transmission between the antennas with different OAM modes is null, but the transmission between the antennas with the same mode can be reduced. To clarify the mechanism of the reduction, factors of the reduction are quantitatively defined, and the explicit formulae are derived. Based on the analytical results, numerical estimation for a communication distance of 100 m is demonstrated, where the frequency, the focal length, and the size of the paraboloid are 150 GHz, 50 cm and 100 cm, respectively. Where both arrays are located on each focal plane, the transmission for the signal is more than -7.78 dB for eight kinds of OAM modes. The transmission is the least for the highest-order mode. The transmission loss is shown to be mitigated by optimizing the shifts of transmitting and receiving arrays from their focal planes. The loss is made almost even by exploiting the tradeoff of the improvement for the mode orders. The transmission is improved by 5.98 dB, to be more than -1.80 dB, by optimizing the shifts of the arrays.

Unique spatial eigenmodes for the spherical coordinate system are shown to be successfully synthesized by properly allocated combinations of current distributions along θ' and φ' on a spherical conformal array. The allocation ratios are analytically found in a closed form with a matrix that relates the expansion coefficients of the current to its radiated field. The coefficients are obtained by general Fourier expansion of the current and the mode expansion of the field, respectively. The validity of the obtained formulas is numerically confirmed, and important effects of the sphere radius and the degrees of the currents on the radiated fields are numerically explained. The formulas are used to design six current distributions that synthesize six unique eigenmodes. The accuracy of the synthesized fields is quantitatively investigated, and the accuracy is shown to be remarkably improved by more than 27dB with two additional kinds of current distributions.

This paper proposes a simple and efficient method to numerically obtain the mapping degree deg(f, 0, B) of a C1 map f : Rn → Rn at a regular value 0 relative to a bounded open subset B ⊂ Rn. For practical application, this method adopts Aberth's algorithm which does not require computation of derivatives and determinants, and reduces the computational cost with two additional procedures, namely preconditioning using the coordinate transformation and pruning using Krawczyk's method. Numerical examples show that the proposed method gives the mapping degree with 2n+1 operations using interval arithmetic.

This paper presents a novel design procedure for class E oscillator. It is the characteristic of the proposed design procedure that a free-running oscillator is considered as a forced oscillator and the feedback waveform is tuned to the timing of the switching. By using the proposed design procedure, it is possible to design class E oscillator that cannot be designed by the conventional one. By carrying out two circuit experiments, we find that the experimental results agree with the calculated ones quantitatively, and show the validity of the proposed design procedure. One experimental measured power conversion efficiency is 90.7% under 6.8 W output power at an operating frequency 2.02 MHz, the other is 89.7% under 2.8 W output power at an operating frequency 1.97 MHz.

The thermal response of a tunable laser is analyzed by using a mode density method based on a Fourier-Laplace analysis. This method introduces a mode density function for mode distribution of the Fourier-Laplace transform and gives temperature time-dependency in an integral form instead of an infinite weighted summation. When symmetric structures are assumed, the mode density method gives the transient thermal response in a simple form: error functions (spherical-symmetry case) and exponential integral functions (cylindrical-symmetry case). The cylindrical-symmetry analysis was extended to the noncylindrical-symmetry model and the thermal response of the tunable laser was calculated by the mode density method. The result shows good agreement with a Fourier-Laplace analysis (deviation 2%) and experimental results. As a rough estimation, the thermal response of the laser is in proportion to the logarithm of time in some range that depends on the chip and tuning-section size of the laser.

There are so many methods of calculating the cylindrical function Zν(x), but it seems that there is no method of calculating Zν(x) in the region of νx and |ν|»1 with high accuracy. The asymptotic series presented by Watson, et al. are frequently used for the numerical calculation of cylindrical function Zν(x) where νx and |ν|»1. However, the function Bm(εx) included in the m'th term of the asymptotic series is known only for m5. Hence, the asymptotic series can not give sufficiently accurate values of the cylindrical functions. The authors attempt to develop programs for the numerical calculation of the cylindrical functions using this asymptotic series. For this purpose, we must know the function Bm(εx) of arbitrary m. We developed a method of calculating Bm(εx) for arbitrary m, and then succeeded in calculating the cylindrical functions in the region νx with high precision.

Debye's asymptotic series is frequently used for calculation of cylindrical functions. However, it seems that until now this series has not been used in all-purpose programs for numerical calculation of the cylindrical functions. The authors attempt to develop these all-purpose programs. We present some improvements for the numerical calculation. As the results, Debye's series can be used for the all-purpose programs, and it is found out that the series gives sufficient accuracy if some conditions are satisfied.

We show by numerical calculations that a chaotic neuron model driven by a weak sinusoid has resonance. This resonance phenomenon has a peak at a drive frequency similar to that of noise-induced stochastic resonance (SR). This neuron model was proposed from biological studies and shows a chaotic response when a parameter is varied. SR is a noise induced effect in driven nonlinear dynamical systems. The basic SR mechanism can be understood through synchronization and resonance in a bistable system driven by a subthreshold sinusoid plus noise. Therefore, background noise can boost a weak signal using SR. This effect is found in biological sensory neurons and obviously has some useful sensory function. The signal-to-noise ratio (SNR) of the driven chaotic neuron model is improved depending on the drive frequency; especially at low frequencies, the SNR is remarkably promoted. The resonance mechanism in the model is different from the noise-induced SR mechanism. This paper considers the mechanism and proposes possible explanations. Also, the meaning of chaos in biological systems based on the resonance phenomenon is considered.

Calculation Nv(x) of complex order v numerically, we must calculate Df{JN+ε(x)}. When Df{JN+ε(x)} is calculated by the recurrence method, this letter will analyze the error of Df{JN+ε(x)}, and will determine the optimum number of recurrences.

Hankel's asymptotic expansions are frequently used for numerical calculation of cylindrical functions of complex order. We beforehand need to estimate the precisions of the cylindrical functions calculated with Hankel's asymptotic expansions in order to use these expansions. This letter presents comparatively simple expressions for rough estimations of the errors of the cylindrical functions calculated with the asymptotic expansions, and features of the errors are discussed.

The recurrence method is useful for numerical calculation of the Bassel function Jv(x) of complex order v. The necessary total number of the recurrences in this method has been examined for the real order v, but it is known only for limited ranges of the real order v and the variable x, and it is not known for the complex order v. This letter proposes a new algorithm which increases the total number of the recurrences gradually, and which stops the calculation automatically when the approximate Bessel function with a necessary precision is obtained.

We frequently need to calculate the Neumann function Nν(x) of complex order ν numerically in order to solve boundary problems on electromagnetic fields. This paper presents a new method for the numerical calculation of Nν(x) of complex order ν. This method can calculate Nν(x) precisely even when the order ν is close to an integer n, and the algorithm by the method is very simple.

First, the necessity of examining the numerical calculation of the Bessel function Jν(x) of complex order ν is explained. Second, the possibility of the numerical calculation of Jν(x) of arbitrary complex order ν by the use of the recurrence formula is ascertained. The rounding error of Jν(x) calculated by this method is investigated next by means of theory and numerical experiments when the upper limit of recurrence is sufficiently large. As a result, it was known that there is the possibility that the rounding error grows considerably when ν is complex. Counterplans against the growth of the rounding error will be described.