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Problem 1 (30 points) Consider the following cavity bounded…
Problem 1 (30 points) Consider the following cavity bounded by two mirrors and containing an optical element T whose ABCD matrix is shown. Assume there are no spaces between the mirrors and the optical element. (a) [10 points] Sketch the unit cell for the cavity starting with mirror R. Indicate the unit cell boundaries clearly! (b) [10 points] Determine the ABCD matrix for the unit cell from part a. (c) [10 points] If R→∞, for what values of α would the cavity be stable? Problem 2 (30 points) Consider the following traveling wave cavity. The space between the reflectors is filled with air, and λ0 is 0.6 μm. (a) [10 points] What is the linewidth, Δυ1/2, of the transmission peak from this cavity? (b) [10 points] What is the quality factor of this cavity? (c) [10 points] What is the photon lifetime for this cavity? Problem 3 (40 points) Consider a TEM0,0 Gaussian beam propagating in the +z direction as shown below. The wavelength of the beam is λ0=0.6 μm. A beam waist occurs at position z1 = 30 cm in front of the lens with a beam waist w01 = 0.25 mm. The beam interacts with a thin lens at position z2 whose focal length is f = 10 cm. A second beam waist occurs a distance d2 to the right of the lens. Find numeric values for d2 (e.g. at position z3) and the beam waist w02 at that position. Congratulations, you are almost done with this exam. DO NOT end the Honorlock session until you have submitted your work. 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 as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Click this link to go to Gradescope: Midterm Exam Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.
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