WKB MATCHING CONDITIONS AT GRADUAL INTERFACES. I. WKB MATCHING CONDITIONS AT INTERFACES VARYING AS Xn. II. WKB MATCHING FACTORS FOR A RISING EXPONENTIAL BOUNDARY

Technical Report · Tue May 01 04:00:00 EDT 1962

OSTI ID:4772264

BenDaniel, D J; Hurwitz, H Jr

Reflection coefficients are calculated for the case of a plane wave impinging on a boundary beyond which the dielectric coefficient has a form epsilon /sub o/(1 -- ZX/sup n/) where n is a positive number, Z is a complex constant, and epsilon /sub o/ is the initial dielectric constant. Contour plots of the absolute value of the reflection coefficient are given for n = 0, 1, and 2. The asymptotic form of the solution for large X is obtained and its ratio to the WKB solution is calculated. General formulas for the reflection coefficient and the asymptotic behavior are given for arbitrary positive n and large Z. The development of WKB matching factors previously initiated is extended to the case where epsilon = epsilon /sub o/(1 -- Ze/sup alpha x/), alpha being real and positive. It is shown that the reflection coefficient is a function only of the phase of Z (not its magnitude) and the magnitude of alpha . The ratio of the asymptotic solution for large X to the WKB solution is shown to be a function of alpha alone. (auth)

• Research Organization: General Electric Co. Research Lab., Schenectady, N.Y.
• NSA Number: NSA-16-032469
• OSTI ID: 4772264
• Report Number(s): 62-RL-3011E
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

DIAGRAMS
DIELECTRICS
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC WAVES
PHYSICS
REFLECTION
SURFACES
WKB APPROXIMATION