Problem 1 [15 points] Consider as a very simplified model for the d...

  1. Home
  2. Homework Library
  3. Physics
  4. Physics - Other
  5. Problem 1 [15 points] Consider as a very simplified model for the d...

QuestionQuestion

Transcribed TextTranscribed Text

Problem 1 [15 points] Consider as a very simplified model for the dielectric function E(W) wo2-w (This is the model discussed in lecture in the limit that the damping force vanishes.) Assume wo < Wp. a) Using the dispersion relation k2 = W2E(W)IC2, make a sketch of k vs w for electromagnetic wave propagation. b) Re-draw this sketch as w vs k, and show that for each value of k > 0 there are two allowed values (modes) of W for the electromagnetic waves. Show that at both small k and at large k one of these two modes has a dispersion relation characteristic of an electromagnetic wave in the vacuum, i.e. w = Vpk where Vp is only weakly dependent on k. Show that the other mode has a frequency W that is, to lowest order, independent of k and so like some internal atomic mode of vibration. Show that these two modes exchange their characteristic behavior as one crosses from small k to large k. In this intermediate region the modes have a mixed character and are referred to as "polaritons". c) Show that, at a given value of k, the higher frequency mode has a phase velocity that satisfies Vp > C, while the lower frequency mode satisfies Vp < C. Show that for both modes the group velocity always satisfies Vg < C.

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution1.pdf and Solution2.m.

    $74.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Physics - Other Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats