Diffraction of Electromagnetic Waves By a Circular Aperture in An Infinitely Con
Diffraction of Electromagnetic Waves By a Circular Aperture in An Infinitely Con
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To exemplify our procedure, we show how the behavior of V^ is obtained. We begin by assuming that | z/a | < e, where e < r/a is a small positive number. Then we deform the contour near t = in the right member of equation (3-1) into a semi-circle of radius e centered at t = and falling below the real t-axis. On the new contour -- C say — the ratio | z/a | will then be everywhere less than |t|. Then, we observe that the integral representation of V.^ [see equation (3. 1)^ niay ^^ expressed as (3. 16) V. (m) -19- ir\ j expiik R (r, z ;t) ] ^^ R (r, z;t) e 1 dt Vz+iat m 4"^(t)dt, on noting that (3-17) 1 S_ f expji'kR'^) r Sr V p+ ia(z+iat) dt d / eyp(ikR R + integrating by parts m times and finally making use of the "behavior of f|"^''(t) at t = ±1 [see equation (3. 3), and recall that f|™^(t) is oddj . Next, we make use of the fact that exp(ikR )/r = (z+iat) d(exp ikE )/dt, integrate by parts once again and find that , +/ f3 18) V^™^ = - — l—]'^ r expfikR""(r, z;t)] ^^' ' 1 ka Va / I z+iat dt \ z+iat/ m f^"^)(t) -1 expfikE (r, z;t)] R"^(r, z;t) dt V z+iat -im+l f{"^)(t)dt.
What to read after Diffraction of Electromagnetic Waves By a Circular Aperture in An Infinitely Con?
You can find similar books in the "Read Also" column, or choose other free books by Jack Bazer to read online
To quickly assess the difficulty of the text, read a short excerpt:
To exemplify our procedure, we show how the behavior of V^ is obtained. We begin by assuming that | z/a | < e, where e < r/a is a small positive number. Then we deform the contour near t = in the right member of equation (3-1) into a semi-circle of radius e centered at t = and falling below the real t-axis. On the new contour -- C say — the ratio | z/a | will then be everywhere less than |t|. Then, we observe that the integral representation of V.^ [see equation (3. 1)^ niay ^^ expressed as (3. 16) V. (m) -19- ir\ j expiik R (r, z ;t) ] ^^ R (r, z;t) e 1 dt Vz+iat m 4"^(t)dt, on noting that (3-17) 1 S_ f expji'kR'^) r Sr V p+ ia(z+iat) dt d / eyp(ikR R + integrating by parts m times and finally making use of the "behavior of f|"^''(t) at t = ±1 [see equation (3. 3), and recall that f|™^(t) is oddj . Next, we make use of the fact that exp(ikR )/r = (z+iat) d(exp ikE )/dt, integrate by parts once again and find that , +/ f3 18) V^™^ = - — l—]'^ r expfikR""(r, z;t)] ^^' ' 1 ka Va / I z+iat dt \ z+iat/ m f^"^)(t) -1 expfikE (r, z;t)] R"^(r, z;t) dt V z+iat -im+l f{"^)(t)dt.
What to read after Diffraction of Electromagnetic Waves By a Circular Aperture in An Infinitely Con?
You can find similar books in the "Read Also" column, or choose other free books by Jack Bazer to read online
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