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从时变媒质中的麦克斯韦方程出发,首先推导出线性、均匀、各向同性的时变媒质中电场和磁场波动方程的一般表达式,然后应用有限差分法,推导出一般情况下电场的时间推进计算公式,计算得到了一种电导率随时间正弦变化:σ(t)=a1+a2sin2πf s t的电场数值解.结果表明,在该电导率时变媒质中传播的电磁波的电场有明显的衰减现象;当电导率的振荡频率等于电磁波的初始频率时,系数a1的增加将导致电场幅度的衰减加快,而系数a2的增加对电场幅度的衰减速度几乎没有明显的影响;当系数a1和a2不变且电导率的振荡频率为10n倍的电磁波的初始频率时,电场衰减速度与电导率的振荡频率呈现非线性的关系,计算结果表明:当电导率的振荡频率f s=2.45×108GHz即10-1倍的电磁波的初始频率时,电场的衰减最快.另外,电场衰减过程中频率没有改变,故在此电导率正弦时变媒质中传播的电磁波不存在“频移现象”.
Starting from Maxwell's equations in time-varying media, the general expressions of electric and magnetic field wave equations in linear, uniform and isotropic medium are deduced firstly. Then, by using the finite difference method, the time advance of the electric field under normal conditions is derived The numerical solution of the electric field with the sinusoid of time is obtained by calculating the formula: σ (t) = a1 + a2sin2πf st The results show that the electric field of the electromagnetic wave propagating in the time-dependent medium has obvious attenuation phenomenon ; When the oscillation frequency of the conductivity is equal to the initial frequency of the electromagnetic wave, the increase of the coefficient a1 will cause the attenuation of the electric field to accelerate, while the increase of the coefficient a2 will have almost no obvious influence on the attenuation rate of the electric field. When the coefficients a1 and a2 remain unchanged And the oscillation frequency of the conductivity is 10n times the initial frequency of the electromagnetic wave, the relationship between the decay rate of the electric field and the oscillation frequency of the conductivity presents a nonlinear relationship. The calculation results show that when the oscillation frequency of the conductivity is fs = 2.45 × 108GHz, When the initial frequency of the electromagnetic wave is doubled, the attenuation of the electric field is the fastest. In addition, the frequency does not change during the attenuation of the electric field, so the propagation of the electric conductivity in the sinusoidal time-varying medium Electromagnetic wave does not exist “frequency shift phenomenon .”