Recent content by EmilyRuck

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    Rearranging the equation for the cutoff condition in optical fibers

    The first expression, which is correct, is written using formula (A4) of the linked document: $$\frac{J'_{\nu} (u)}{u J_{\nu}(u)} = \frac{J_{\nu - 1} (u)}{u J_{\nu}(u)} - \frac{\nu}{u^2} = \xi_1(u) - \frac{\nu}{u^2}$$ Formula (A6), used for the second expression, is wrong. It should be...
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    Rearranging the equation for the cutoff condition in optical fibers

    Temporarily putting aside the ##\frac{k_1^2 + k_2^2}{k_1^2}## terms signs, consider the part which should be ##0##. The first 4 terms come from the espansion of the LHS (which involves ##\xi_1##, ##\xi_2##) of the original characteristic equation. The last 3 terms directly come from the RHS of...
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    Rearranging the equation for the cutoff condition in optical fibers

    Hello! In Optical fibers, let ##k_1## and ##k_2## be respectively the propagation constants in core and cladding, ##\beta## the propagation costant of a mode along the direction ##z##, ##a## the radius of the fiber. Using the normalized quantities ##u=a \sqrt{k_1^2 − \beta^2}## and ##w=a...
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    TE and TM modes in optical fibers

    Yes, it is not a good starting point. I have read about the dielectric slab, for example, where modes are much simpler and immediate. My problem is not about modes themselves, but about some unclear information on what modes actually propagate in optical fibers (refer to the quote I just posted...
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    TE and TM modes in optical fibers

    Ok! My doubt arouse because of sentences like: from this document, page 6. However, if I correctly understood what you state, TE and TM modes are, at least conceptually, valid and existing modes, and they are able to propagate by their own. Yes, of course. This depends on the frequency of...
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    TE and TM modes in optical fibers

    Ok, thank you so much! Oh, I don't deal with this, but it is great.
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    TE and TM modes in optical fibers

    Yes, I get it. Sorry, I don't know them. If I correctly understood, yes, modes somehow represent the spectrum of the optical fiber. Any real field propagating in this structure can be described as a composition of modes. But my post was about a slightly different scope: are all these modes...
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    TE and TM modes in optical fibers

    In a step-index optical fiber, considering Bessel functions of order ##\nu = 0## and no ##\phi## dependence, it is possible to obtain two separate sets of components, which generate respectively TE and TM modes. In the former case, only ##E_{\phi}##, ##H_r##, ##H_z## are involved; in the latter...
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    How can the electric field of optical fibers be visualized?

    Hello! For dielectric slab waveguides, starting from the field expressions, it is possible to draw the Electric field corresponding to a specific mode, showing its (possible) zeros inside the core and its exponential decay in the cladding: A Google search can provide plenty of images like...
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    Frequency and energy of EM radiation

    If you can, please, give a quantitative description with some examples, like the cosinusoidal functions in my post. Also the introduction of the exact name for each quantity (transferred energy, available power, reactive power, etc.) surely would be another help to understand.
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    Frequency and energy of EM radiation

    Dear ZapperZ, what you say can intuitively make sense, but it surprises me as well as Chandra Prayaga, maybe because we are lacking some mechanical waves concepts and using a different perspective. When for example Electro-magnetic waves are introduced in a classical approach, the Electric field...
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    Modes of Optical Fiber propagation

    If you are interested in modes, in this page the mode field expressions are obtained for a dielectric slab waveguide. It starts from Maxwell's equations and then uses boundary conditions (after introducing refraction and some basic concepts). Modes in optical fibers are obtained through a...
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    Modes of Optical Fiber propagation

    There is of course a purely mathematical answer to this question (the Wikipedia pages can contain it), but it's not the only one. As regards (metallic, dielectric, ...) waveguides: a mode is a field configuration which is a solution of Maxwell's equations and satisfies the boundary conditions...
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    I Dispersion: expansion of wavenumber as function of omega

    Ok! However, as regards the first derivative, d\omega / dk = v_g and dk/d\omega = 1/v_g, so they are exactly reciprocal. If you take the unit measures, they are reciprocal too. So, here is still my doubt.
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    I Dispersion: expansion of wavenumber as function of omega

    Considering the simplest case, the one regarding plane waves, k = \omega / v with v constant. d\omega/dk = v = v_g is the group velocity and dk/d\omega = 1/v = 1/v_g is the reciprocal of the group velocity. d^2 \omega/dk^2 = \alpha = 0 is the group velocity dispersion; so, the reciprocal of...
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