专业英语-波动光学 2

Superposition of Waves（波的叠加）
Consider two waves, derived from the same source, but characterized by phase difference Φ. They may be written as
For convenience, we allow them to have the same amplitude. If the waves are superposed, the resultant electric field is
If we multiply both numerator and denominator by b, and define β=kbsinθ/2, we may write
More-proper analysis, based on electromagnetic theory and a twodimensional formulation would include an additional factor of iλ in the expression for E(θ), but the important part is the variable sinβ/β.
The total field at P is the sum of the fields due to individual elements. If the dimension of the slit is b and its center, s=0, this is just the integral where constant terms have been removed from the integral. The integrand is of the form exp(a·s), so the integral is easily evaluated
惠更斯原则：传输波前上每一点（或说无限小一个区 域）会辐射出一个子球面波。这些子球面波传输一小 段距离（实际上是无限小一段距离）后会合成一个" 新的"波前。这个新的波前其实代表的是原波前传播 一小段距离后的位置。
More specifically, Huygen's construction is shown above. The wavefront in this case is a part of a plane wave which has just been allowed to pass through an aperture. The spherical wavelets combine to produce a wavefront lying along their common tangent. The new wavefront is nearly plane and nearly identical with the original wavefront. At the edges, however, it develops some curvature owing to the radiation of the end points away from the axis. Succeeding wavefronts take on more and more curvature, as shown, and eventually the wavefront becomes spherical. We then speak of a diverging wave diffracted by an aperture.
第四章 波动光学
Wave Optics
Wave Optics
4.1 Electromagnetic Waves & Complex Expression Light is a transverse, electromagnetic wave characterized by timevarying electric and magnetic fields. The fields propagate hand in hand; it is usually sufficient to consider either one and ignore the other. It is conventional to retain the electric field, largely because its interaction with matter is in most cases far stronger than that of the magnetic field. It is not generally necessary to retain the vector nature of the field unless polarization effects are specifically known to be important. Thus, we will generally be able to describe light with the scalar equation in complex form,
引起：
Bring about; Give rise to; Cause; Arouse; Stir up; Lead to
4.2.1 Single-Slit Diffraction
The single-slit diffraction is shown in one dimension in Fig. 1. We appeal to Huygen's construction and assume that each element ds of the slit radiates a spherical wavelet. The observing screen is located a distance L away from the aperture, and we seek the intensity of the light diffracted at angle θ to the axis. The center of the aperture is located a distance r from the observation point P. The optical path difference (OPD) between the paths from θ and from the element ds (at s) is s·sinθ, in Fraunhofer approximation. The electric field at P arising from the element is We obtain the r in the denominator by realizing that the element is essentially a point source. We cannot drop it from the phase term k(r+ s·sinθ) because very small changes of s·sinθ cause pronounced changes of the phase of the wave relative to that of another wave.
It is well known that the intensity electromagnetic wave in vacuum is the production of the electric field amplitude and its complex conjugation. We may immediately write
where A is the amplitude, k is the wave vector, ω is the angular frequency and Φ is the phase of light field, respectively.
4.2 Diffraction
Huygen's Principle: each point (or infinitesimal area) on a propagating wavefront itself radiates a small spherical wavelet .The wavelets propagate a short (really, infinitesimal) distance, and their resultant gives rise to a "new" wavefront. The new wavefront represents merely the position of the original wavefront after it has propagated a short distance.
上图是惠更斯原理的一个具体（例子）：一束平面波入 射到一个小孔上，未达小孔时（子波的）波前是平面波的一 部分，即（各点的）子球面波相叠加后产生了一个位于其共 有切线上的（总）波前。而在（孔）边缘处（总波前）出现 了一点弯曲，其由远离光轴的（子波）辐射引起。而如图所 示，之后总波前会越来越弯曲，最终变成球面波。我们称这 种波经过小孔而发散的现象为衍射。
If the viewing screen is the focal plane of a lens, then the first minimum is located a distance
from the center of the pattern, which extends in the direction perpendicular to the edges of the aperture. Over 80% of the diffracted light falls within 2λf'/b of the center of the pattern, and the first secondary maximum is about 5% as intense as the principal maximum. Similar analysis can be carried out with a circular aperture in twodimensions. The result is similar, except that the pattern is a disk, known as the Airy disk, with radius defined by the first zero as