ECEN4813 Spring 2004 Final Exam: Optically Pumped Laser Design, Exams of Electrical and Electronics Engineering

Download ECEN4813 Spring 2004 Final Exam: Optically Pumped Laser Design and more Exams Electrical and Electronics Engineering in PDF only on Docsity! ECEN4813 Final Exam: Spring 2004 Name:________________________________ • You will not get a copy of these pages when you take the test, so bring them to the test with you! • Please staple your answer pages to this test. If the entire test is not turned in you will receive a grade of zero. • Underline or put a box around your answers. • Problems which are not legible will not be graded. • Writing on the back of a page will be ignored. This exam will be graded using the following criteria: • 50% of each problem is based on a clear line of reasoning (either mathematical or explanatory) of how you solved the problem. • 20% is based on obtaining a nearly or completely correct answer. • 20% is using a correct approach to solving the problem • 10% is based on using correct units, labeling axes on graphs, and clear organization. Lifelines: You will be given three “lifelines”. At any point in the exam you may raise your hand and receive a clue on how to do a problem. If you receive a lifeline 50% of the points for that problem will be deducted. The clue is not an answer, and there is no guarantee it will help you solve the problem. You have just received a new laser crystal in the mail from a research laboratory in China. They would like you to develop an optically pumped laser based on the crystal. With the crystal you have received a substantial amount of data that will help you to design the laser. Laser Crystal Data: • Refractive index n = 2.0. Group index ng = 2.0. • There are four energy levels. • The degeneracies of all energy levels are equal g0 = g1 = g2 = g3. • The faces of the crystal are AR (antireflection) coated with reflectance of 0.1% • Dimensions of laser crystal are 0.3×0.3×0.5 cm in length. • The doping density of the lasing ions in the crystal is 3×1019 cm-3 The absorption coefficient as a function of wavelength, α(λ),of the crystal has been measured in China and sent along with the crystal. Each of the transitions in the four level crystal is labeled. The width of each lineshape is limited by the resolution of the measurement technique The crystal growers have measured the exact wavelengths of each peak as well as the width of each peak in Hz. They are given in this table: λ01 579.0552 nm 34.5 GHz λ02 352.6885 nm 26.9 GHz λ03 208.3849 nm 71.4 GHz λ12 902.1916 nm 12.6 GHz λ13 325.5355 nm 85.1 GHz λ23 509.3077 nm 44.7 GHz Similarly the lifetimes of each state have been measured by looking at decay of the fluorescence. 200 300 400 500 Wavelength (nm) α (λ ) ( cm -1 ) 1 2 3 4 600 700 800 900 0→20→3 1→21→3 2→3 0→1 α (λ ) ( cm -1 ) 1 2 3 4 Time (µs) 1 2 3 4 5 6 Ι( t) (a rb . u ni ts ) 1 1/e 1→0 3→03→13→2 2→0, .05 ms 2→1 Ι( t) (a rb . u ni ts )