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2.2 Geometric optics. 2.3 Polarization. 2.4 Diffraction and interference. 3 Astrophysics definitions. ... Cartesian and spherical polar coordinates are used, xy plane ...
The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by φ ∈ [ 0 , 2 π ] {\displaystyle \varphi \in [0,2\pi ]} : it is the angle between the x -axis and the projection of the radial vector onto the xy -plane.
Consider the case of interaction of two perpendicularly polarized waves in nonlinear media with cubic nonlinearity. [1] The equations describing the self phase modulation of the fundamental wave A and the generation of new wave perpendicularly polarized wave B in condition that |B| << |A| (i.e. when the depletion of the fundamental wave is neglected, self and cross phase modulation of wave B ...
The two-dimensional analogue of the vibrating string is the vibrating membrane, with the edges clamped to be motionless. The Helmholtz equation was solved for many basic shapes in the 19th century: the rectangular membrane by Siméon Denis Poisson in 1829, the equilateral triangle by Gabriel Lamé in 1852, and the circular membrane by Alfred Clebsch in 1862.
As a second-order differential operator, the Laplace operator maps C k functions to C k−2 functions for k ≥ 2.It is a linear operator Δ : C k (R n) → C k−2 (R n), or more generally, an operator Δ : C k (Ω) → C k−2 (Ω) for any open set Ω ⊆ R n.
"Negative" uniaxial crystals (e.g., calcite CaCO 3, sapphire Al 2 O 3) have n e < n o so for these crystals, the extraordinary axis (optic axis) is the fast axis, whereas for "positive" uniaxial crystals (e.g., quartz SiO 2, magnesium fluoride MgF 2, rutile TiO 2), n e > n o and thus the extraordinary axis (optic axis) is the slow axis. Other ...