MidtermECE183.pdf - UCSD Department of Electrical and...

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UCSD Department of Electrical and Computer Engineering ECE 183 Winter 2018 Midterm Assigned: February 1, 2018. Due: February 6, 2018 (start of class). Policies: 1. Read both questions; then, do Question 2 first (Question 1 is harder). You can use the course notes (lecture notes, homeworks, homework solutions), but no other references. 2. Attempt to answer and submit solutions individually. You may not discuss the problems with others. You can email questions to the instructor or TA and we will try our best to answer them. 3. Please either typeset your solutions, or answer them in a bluebook, writing very neatly. 1 Light emission pattern from an LED [3 points] An isotropic point emitter of light at wavelength λ is embedded in a semiconductor of refractive index n s , and radiates as shown towards the air (refractive index n air = 1) interface. Assume that the total power emitted by the LED is P s . Explain why, as a function of the angle Θ as shown and at a given value of r , distance of observer to the virtual image, the intensity as seen by an observer in air is given by: I = P s 4 πr 2 n 2 air n 2 s cos Θ (1) Θ ϕ n_s n_air Point emitter of light d Θ d ϕ virtual image r observer Hint: For a ray at angle ϕ to the normal, the refracted ray is at angle Θ determined by Fresnel’s formula (for simplicity, assume TE polarization). 1
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Note: For full points, derive an equation between the differential (incremental) angles, and impose power conservation. A correct explanation without (correct) mathematics will get only partial credit. 2 A better LED [7 points] A practical way to enhance the performance of light emitting diodes (for some applications) is to surround the diode with an optical resonator, thus forming the RCLED: resonant-cavity light emitting diode. [Ref. N. E. J. Hunt et al. Applied Physics Letters, Vol. 63, p. 2600 (1993), provided in PDF format in the same folder.] 1. Describe what is an RCLED in 2-3 sentences. Draw a simple figure. 2. Justify the following statement: at some wavelengths, an RCLED enhances the emission intensity along the axis of the cavity. (This is a simple question if you have been following the lectures. Dont write too much.) 3. For the maximum benefit, should L (cavity length) be large or small? Should R (the mirror reflectivity) be large (close to 1) or small (close to 0)? What other factors might play a significant role? (Short answers, 1 line each) 4. Is the integrated emission (i.e., over all wavelengths) also enhanced? Justify your answer. 5. Is the angular dependence of the intensity profile always broader than, or always narrower than, the intensity profile in the first problem [ I (Θ) cos Θ]? Or can it be either broader or narrower? SURVEY Optional. Don’t include your name. Turn it in under my door, EBU1 3203 before Feb 6. 1. Please indicate the time spent on these problems: hours.
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  • Winter '08
  • Yu,P
  • Light Emitting Diodes, chromatic dispersion, spectral width, graded-index multimode fiber, RCLEDs

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