Download Optical filter design and analysis: a signal processing by Christi K. Madsen PDF

By Christi K. Madsen

ISBN-10: 0471183733

ISBN-13: 9780471183730

ISBN-10: 0471213756

ISBN-13: 9780471213758

A different, state of the art method of Optical clear out layout With a growing number of info being transmitted over fiber-optic strains, optical filtering has develop into the most important to the complicated performance of ultra-modern communications networks. assisting researchers and engineers retain velocity with this speedily evolving expertise, this booklet offers electronic processing innovations for optical filter out layout. This higher-level strategy makes a speciality of filter out features and allows readers to quick calculate the filter out reaction in addition to take on higher and extra advanced filters. The authors comprise quite a few theoretical and experimental effects from the literature and talk about functions to various systems-including the hot wavelength department multiplexing (WDM) expertise, that's speedy turning into the popular process for method improve and enlargement. certain positive factors of this publication include:
* the speculation underlying a number of architectures which can approximate any filter out function
* filter out layout thoughts appropriate to a extensive diversity of fabrics systems-from silica to fiber to microelectromechanical (MEM) systems
* layout examples appropriate to filters for WDM platforms and planar waveguide devices
* 250 figures in addition to challenge units to be used in graduate-level reports

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Optical filter design and analysis: a signal processing approach

A special, state of the art method of Optical clear out layout With a growing number of info being transmitted over fiber-optic strains, optical filtering has turn into an important to the complex performance of trendy communications networks. supporting researchers and engineers retain velocity with this quickly evolving expertise, this e-book provides electronic processing strategies for optical clear out layout.

Additional resources for Optical filter design and analysis: a signal processing approach

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3. The maximum possible ␤ value is k0n1 beyond which the picture would be unphysical. At ␤ = k0n1, k and ␤ are both along the z direction and the ray in this case is called the central ray. 2 Characteristic Equations for the Slab Waveguide To determine the possible values of the longitudinal wave vector ␤, which characterizes the possible guided waves, we have to apply the proper boundary conditions to the general solutions of Eqs. (93) and (94). Since we are interested in standing waves inside and evanescent fields outside the guiding layer, the transverse electric field amplitudes in the three regions of the slab waveguide can be written as ETE(x) = A cos(␬x – ␾) for 0 < x < h ETE(x) = Be␥1x for x < 0 (100) ETE(x) = Ce–␥2(x–h) for x > h (101) (99) where A, B, and C are amplitude coefficients to be determined and ␥1, ␥2 and ␬ are defined as 2 2 ␥1 = ͙␤ ෆ2ෆ–ෆෆkෆn ෆ2 0ෆ (102) 2 2 ␥2 = ͙␤ ෆ2ෆ–ෆෆkෆn ෆ3 0ෆ (103) ␬1 = ͙kෆ02ෆnෆ21ෆ–ෆ ␤2ෆ (104) 38 FUNDAMENTALS OF DIELECTRIC WAVEGUIDES By applying boundary conditions for the continuous tangential E and H (equivalent to continuous dETE/dx) across each interface, we have, at x = 0 B = A cos(␾) (105) ␥1B = –␬A sin(–␾) (106) ␥1 tan(␾) = ᎏ ␬ (107) which lead to Similarly, by applying the boundary conditions to the x = h interface, we get C = A cos(␬h – ␾) (108) ␥2C = ␬A sin(␬h – ␾) (109) ␥2 tan(␬h – ␾) = ᎏ ␬ (110) and which lead to By using the following trigonometrical indentity tan(A1 – A2) = (tan A1 – tan A2)/(1 + tan A1 tan A2) (111) we can combine Eqs.

185) into Eq.

Equation (13) becomes Ǟ Ǟ Ѩ Ѩ ѨD Ѩ2E Ǟ Ǟ ١ × ١ × E = –␮ ᎏ ١ × H = –␮ ᎏ ᎏ = –␮␧ ᎏ Ѩt Ѩt Ѩt Ѩt2 ΂ ΃ (14) Using the vector identity Ǟ Ǟ Ǟ ١ × ١ × E = ١(١· E) – ١2 E (15) and the fact that Ǟ Ǟ Ǟ Ǟ ١· D = ١·(␧ E) = ١␧ ·E + ␧١· E = 0 (16) or Ǟ E ١· E = – ᎏ ·١␧ Ϸ 0 ␧ Ǟ (17) Ǟ we have the following wave equation for E by combining Eqs. (14), (15) and (17): Ǟ Ѩ2 E Ǟ ١2 E – ␮␧ ᎏ =0 Ѩt2 (18) Ǟ Similarly, we can derive the wave equation for H as Ǟ Ѩ2H =0 ١ H – ␮␧ ᎏ Ѩt2 2 Ǟ (19) 22 FUNDAMENTALS OF DIELECTRIC WAVEGUIDES It should be stressed that the above wave equations are valid for ١␧ Ϸ 0 (for homogeneous or near homogeneous dielectric materials).

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