Perturbation Methods in a Problem of Waveguide Theory
Perturbation Methods in a Problem of Waveguide Theory
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In our eReader you can find the full English version of the book. Read Perturbation Methods in a Problem of Waveguide Theory Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Perturbation Methods in a Problem of Waveguide Theory
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2. . , —, sm (mjc + arte ) hr . 2 sm qite 29 This expression is clearly bounded, independent of m. Call this bound B. We have < B 3iii _2q_ s > ; r = m _2q_ + 1 2 < ^^^\2 r / m. 2q m = k-, — 3 m Thus, we have shown that the original sum is less than (k_, + k^ + k^ +k, ) — J. 2 5 4 m as m becomes laree. In order to complete the proof of convergence of u • e (eq^uation (35))^ we must demonstrate the absolute convergence of (36) 1 — e m m m=l Each component of the vector e is a coefficient of the Fourier expansion of the field in the aperture. qjt (37) m. 1_ qir m E cos — y dy y q -qrt Inasmuch as E vanishes for qir < |y| < :n:, equation (37) can be written as (58) e = — / E cos — y dy m qn J y q. ^ -^ 30 2rtq. I Jti ■rti dw dz m m — z - — z e'l + e ^ dz We can convert this to a Line integral in the w-plane using the Schwartz-Christoffel mapping given in equation (29). (59) ^^ = 2^i 1 yq e^+1 + q\/e^+l q. dw \/ 2 w _ i/v 7 Vqe+1+ Ve +1 an m (1-a)^ q C 1-q -w l^V q e +1 + /e +1 dw The path of integration^ C, is illustrated in the following sketch: w- plane I I I TTi+log —5 TTi I q +7ri — r— I L TTI I .
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To quickly assess the difficulty of the text, read a short excerpt:
2. . , —, sm (mjc + arte ) hr . 2 sm qite 29 This expression is clearly bounded, independent of m. Call this bound B. We have < B 3iii _2q_ s > ; r = m _2q_ + 1 2 < ^^^\2 r / m. 2q m = k-, — 3 m Thus, we have shown that the original sum is less than (k_, + k^ + k^ +k, ) — J. 2 5 4 m as m becomes laree. In order to complete the proof of convergence of u • e (eq^uation (35))^ we must demonstrate the absolute convergence of (36) 1 — e m m m=l Each component of the vector e is a coefficient of the Fourier expansion of the field in the aperture. qjt (37) m. 1_ qir m E cos — y dy y q -qrt Inasmuch as E vanishes for qir < |y| < :n:, equation (37) can be written as (58) e = — / E cos — y dy m qn J y q. ^ -^ 30 2rtq. I Jti ■rti dw dz m m — z - — z e'l + e ^ dz We can convert this to a Line integral in the w-plane using the Schwartz-Christoffel mapping given in equation (29). (59) ^^ = 2^i 1 yq e^+1 + q\/e^+l q. dw \/ 2 w _ i/v 7 Vqe+1+ Ve +1 an m (1-a)^ q C 1-q -w l^V q e +1 + /e +1 dw The path of integration^ C, is illustrated in the following sketch: w- plane I I I TTi+log —5 TTi I q +7ri — r— I L TTI I .
What to read after Perturbation Methods in a Problem of Waveguide Theory?
You can find similar books in the "Read Also" column, or choose other free books by David Fox to read online
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