HW
Microsoft Word - EE 5693_MatE5103 HW#5 renamed HW4 for FY20 only did not assign HW#4 EE 5693/MatE 5103 Fall 2021 HW Assignment #4 Due Dec. 3, 2021 Discussion among classmates encouraged but HW submitted must be your own. Copied work results no credit for both parties. When submitting your homework please certify that: My name is:______________________________ I have completed the homework by my own effort. If applicable: I discussed with the following classmate(s): _______________________________________________ 1. Using direct inspection method to show that point group 432 (4‐fold//<001>, 3‐fold//<111>, and 2‐ fold//<110>), although is a non‐centric symmetry group, has no piezoelectric effect. 2. The spontaneous polarization of a single domain single crystal is Ps=26C/cm2 along <111> direction. Estimate the saturation polarization obtainable by poling the polycrystalline ceramic of the same composition as the single crystal, assuming saturated polarization is due to alignment not inversion. The symmetry after poling is described by Curie group ∞m (the polar axis is along the ∞‐fold rotation axis). 3.A transparent pyroelectric ceramic disk is polarized in its thickness direction (thickness t=100 m) with relative dielectric constants 33=40. The sample’s pyroelectric coefficients are: p1=p2=0, p3=230 [C/m2‐K] where K is Kelvin. If periodic infrared radiation causes the pyroelectric sample to increase its temperature by Tmax=0.1 [Kelvin] in one cycle, find (a) The maximum amount of charge generated on the surface of this sample; and (b) the amplitude of open circuit voltage generated across the thickness of this sample. 4. We have a piece of energy harvesting piezo ceramic with piezoelectric d33=500 [pC/N], surface area of 100 mm2, thickness t=5 mm, relative dielectric constant 33=500. If a person of 80kg steps on it (assuming contact area is 100mm2) repeatedly at a frequency of 2Hz, find out how much energy [J] this system can store and what is the power (W) it can generate if the resistance of the load is 10MOhm. 5. If the loss of an optical fiber is =0.5 dB/km and the input power launched into the fiber by a transmitter is PTX=1 mW, calculate the transmitted power after the optical signal propagates 10 km along the fiber. [note in Beer Lambert law ’ has unit [1/km], dB=10log [(OptPowerInput)/(OptPowerTransmitted)]. 6. The drawing followed shows an optical indicatrix for a crystal of 4mm symmetry. The EM wave is propagating in the crystal along vector m, normal to the wavefront, at =30o from the optical axis. a) Mark on the indecatrix the ordinary and extraordinary refractive indices no, ne, dielectric displacement D, electric field E of the plane wave, Poynting vector S (energy flow direction), the refractive indices n’ [(no)2=(n’)2] and n” [ 2222 22 2 sincos )"( oe eo nn nnn ], including their directions when applicable. b) If the wave normal direction ? is at an angle of =55-degree from the Optical Axis, find out the wave propagation speed V’ and V” that correspond to n’ and n”. Given ne=2.298 and no=2.322. no, ne, D, E, S, (n’), (n”). Optical Axis m x z