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Both problems of this test concern solving the electromagnetic bandstructure master 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: https://www.gradescope.com/courses/695047 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.  End the Examity session. 

Assume the market for extra-long twin mattresses is in equilibrium. There is a sudden decrease in income throughout the economy. If all else is held constant, we would expect that if extra-long twin mattresses are a(n) ________ good, then the demand curve will shift to the ________, causing the equilibrium price and quantity to ________.

Goods that are necessities are very likely to have

The elasticity of Roger’s All Natural Super Sour Hard Candy is 2.25. If the price increases by 10%, what will happen to the quantity demand?

Match the individual caste with a description of it. 

The Bhagavad Gita which is a section of the Mahabharata details a struggle among the decedents of the King Bharata.  In the Bhagavad Gita a warrior Arjuna encounters the incarnation of the god Vishnu as Krishna. 

Match the following terms with what they mean about the nature of God or Brahman.

Most religions of antiquity are characterized by Polytheism.  What is Polytheism?

There are two categories of written texts in Early Hinduism.  One category are those scriptures that were revealed to the early rishis or sages. The name for these mean “What is heard,” and it was orally recited by priests for centuries before being written down. The other category is literature formed after this and passed down in written form. The name of these mean “What is remembered,” and sometimes are explaining the previous category.  What are the two names of these categories. 

_______ is a practice or discipline that may involve a philosophical system and mental concentration as well as physical postures and exercises. And this is different than  _______ which is an esoteric school which emerged around the fifth century and focused on a number of controversial practices, some being sexual.