Growth of Sharp Narrow Microwave Pulses due to Magnetostatic Wave Envelope Solitons

采用液相外延技术在钆镓石榴石（GGG）衬底上生长了高质量的钇铁石榴石（YIG）薄膜。由于YIG的损耗，即使我们使用高质量的YIG样品，观察到静磁波（MSW）孤子传播的路径长度也至多为10毫米。为了产生单孤子脉冲，需要提供比非线性薛定谔方程（NLSE）所确定的功率更高的微波输入功率。NLSE已被数值求解。数值结果表明，如果YIG的损耗可以忽略，那么我们总是可以周期性地呼吸脉冲，并且脉冲在某个时刻变得非常尖锐和狭窄。然而，我们考虑到损失，矩形脉冲被压缩成脉冲压缩比约为3的脉冲。我们发现，如果输入脉冲的波形选择适当，例如抛物线或余弦脉冲，脉冲压缩比可以达到几十倍。在YIG薄膜中使用所谓的孤子效应已被证明是一种有前途的技术，用于产生宽度至少为1 ns的MSW脉冲。为了验证这一点，我们提出了一种利用非均匀传输线设计波形剪裁滤波器的方法。该方法是基于解决一个逆Zakharov-Shabat问题（IZSP）在有限的时间间隔。特性阻抗的分布可以从反射系数和透射系数中找到。该方法是基于变形积分。在实际应用中，传输线的长度是有限的，所以间隔的有限性是很重要的。提出了两种求解IZSP的方法，一种是需要迭代的方法，另一种是不需要迭代的方法。后一种方法被发现可以节省计算时间。此外，它可以应用于广泛的潜力。

High quality yttrium iron garnet (YIG) films have been grown on gadolinium gallium garnet (GGG) substrates by liquid phase epitaxial technology. The path length, where the propagation of magnetostatic wave (MSW) solitons is observed, is at most ten millimeters due to the loss of YIG even if we use a high quality YIG sample. To generate a 1-soliton pulse, we should supply higher power of microwave input than the value determined from the nonlinear Schrodinger equation (NLSE).Rectangular pulses are usually used as input in the MSW soliton experiments. The NLSE has been solved numerically. The numerical results show that if the loss of YIG is negligible, then we can always periodical breathing of pulses and that the pulses have become very sharp and narrow at some instant. However we take into accounts of the loss, the rectangular pulse is compressed into a pulse of which the pulse compression ratio is about three. We found that the pulse compression ratio become as large as a few tens if the wave form of input pulse is chosen appropriately, for example, parabolic or cosine pulse.The use of so-called soliton effects in a YIG film has been shown to be a promising technique for production of MSW pulses with at least as short width as 1 ns.To check this experimentally, we have proposed a method for designing wave form tailoring filters by using nonuniform transmission lines. The method is based on solving an inverse Zakharov-Shabat problem (IZSP) over a finite interval. The distribution of the characteristic impedance can be found from the reflection and transmission coefficients. The method is based on the deformation integrals. In practice, the length of transmission line is finite so the finiteness of interval is important. We proposed two methods for solving the IZSP.One method requires iteration, and the other solves the IZSP without iteration. The latter method is found to save computation time. Furthermore, it can be be applied to a wide range of potentials.