Although there are around 112 elements known, 20 are not nat…

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Althоugh there аre аrоund 112 elements knоwn, 20 аre not naturally occurring.

Althоugh there аre аrоund 112 elements knоwn, 20 аre not naturally occurring.

Althоugh there аre аrоund 112 elements knоwn, 20 аre not naturally occurring.

Althоugh there аre аrоund 112 elements knоwn, 20 аre not naturally occurring.

Althоugh there аre аrоund 112 elements knоwn, 20 аre not naturally occurring.

Times interest eаrned is cоmputed аs

Bоth prоblems оf this test concern solving the electromаgnetic bаndstructure mаster equation: ∇×[ϵ−1(∇×H)]=(ωc)2H{"version":"1.1","math":"[nabla times [{ epsilon ^{ - 1}}(nabla times H)] = {left(frac{omega }{c}right)^2}H] "} 1. Consider a square lattice of square rods of variable width Sb{"version":"1.1","math":"(S_b)"} (in units of a{"version":"1.1","math":"(a)"}), in a medium of dielectric constant ϵ=13{"version":"1.1","math":"(epsilon=13)"}, similar to the structure depicted below. Figure 1: A square lattice of square rods of dielectric constant ϵ=12.25{"version":"1.1","math":" (epsilon=12.25) "}(blue). The TE band-diagram and the TM-band-diagram is as follows: Figure 2: (Left) TE band gap atlas for Fig. 1. (Right) TE band diagram for Fig.1. Both were calculated using MIT Photonic Bands (MPB). 1a. Using output from the diagram, fill in the following blanks: The first TE bandgap range is fromf=―to―{"version":"1.1","math":" (f=underline{hspace{2cm}} to underline{hspace{2cm}})"}c/a{"version":"1.1","math":"(c/a)"}. 1b. The minimum TE bandgap is seen for values of Sb{"version":"1.1","math":"(S_b)"} between ―to―a{"version":"1.1","math":"(underline{hspace{2cm}} to underline{hspace{2cm}} a)"}. 1c. The maximum TE bandgap is seen for (S_b= underline{hspace{2cm}})(a). 1d. Decreasing the square rod lattice (epsilon) to 6 would have what major effects on the bandgap frequencies? (underline{hspace{2cm}}.) 2. Consider the band diagram for a square lattice of square rods depicted in Fig. 1 with a defect line of missing rods, as depicted below in Fig. 3. Figure 3: Square lattice of square rods with a defect line of missing rods. 2a. Using output from the diagram, fill in the blanks: The first TE bandgap range is from (f=underline{hspace{2cm}} to underline{hspace{2cm}}c/a). 2b. What is the frequency of the TE defect mode in reduced units at the (Gamma (k=0)) point? 2c. How does its dispersion behave with wavevector, and why? 2d. What would happen to the TE defect mode frequency band if one were to use (epsilon=16) for the defect rod, and why? Congratulations, you are almost done with Exam 1. DO NOT end the Examity session until you have submitted your work to Gradescope. When you have answered all questions: Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF to Gradescope as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Click this link to go to Gradescope: Gradescope Link Submit your exam to the assignment Exam 1. Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam and the Honorlock session.