Accurate semiclassical analysis of light propagation on tilted hyperplanes
Patrick Gioia, San Vu Ngoc (IUF, IRMAR)
在 Helmholtz' 方程在 R^1+d 中给出的标量光模型中,我们考虑通过任意的亲和变换(可以将其视为向倾斜的超平面传播)中初始场景(全息图)的变换。 在高频方案中,我们使用微局部和半经典分析来描述传播器是半经典的傅里叶积分运算符,从而从光学中概括了众所周知的Angular Spectrum公式。 然后我们证明新的精确的Egorov定理,包括子原理术语,这表明如何考虑沿几何光学射线的传播。
In the scalar light model given by Helmholtz' equation in R^1+d , we consider the transformation of an initial scene (a hologram) in 0xR^d by an arbitrary affine transformation (which can be viewed as a propagation into a tilted hyperplane). In the high frequency regime, we use microlocal and semiclassical analysis to describe the propagator as a semiclassical Fourier integral operator, thus generalising the well-known Angular Spectrum formula from optics. We then prove new precise Egorov theore...