Midterm Solutions

Midterm Solutions - Midterm Solutions ECE 162C May 6 2009...

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Unformatted text preview: Midterm Solutions ECE 162C May 6, 2009 Department of Electrical and Computer Engineering University of California, Santa Barbara Name_______________________________________ ` 2 (20 pts) 1. It is desired to put anti-reflection (AR) coatings on a DFB laser chip. It emits at 1550 nm and is composed of an InGaAsP waveguide and active region clad by InP. It is known that the initial power reflection coefficient from the semiconductor-air cleaved facets is 32%. Assuming that the guided mode reflects just like a plane wave, (a) What index of refraction is needed for a perfect single-layer AR coating? (b) What thickness should this layer have? (a) amplitudes of incoming and reflected wave must be the same in order for wave to fully destructively interfere with itself, therefore the reflectivity at each interface must be the same: g G¡¢£¤¥¦ §g ¤¨ g G¡¢£¤¥¦ ©g ¤¨ = g ¤¨ §g ¤ª« g ¤¨ ©g ¤ª« ¬ = .32 = ­ g G¡¢£¤¥¦ §g ¤ª« g G¡¢£¤¥¦ ©g ¤ª« ® ¯ ; n air =1; now solve for ° ±g²³´µ¶ .32 = · ° ±g²³´µ¶ − 1 ° ±g²³´µ¶ + 1 ¸ ¯ ° ±g²³´µ¶ = 3.605 now solve first equation for ° ´¹ º.»¼½§g ¤¨ º.»¼½©g ¤¨ = g ¤¨ §¾ g ¤¨ ©¾ ¿3.605 − ° ´¹ À¿° ´¹ + 1À = ¿° ´¹ − 1À¿3.605 + ° ´¹ À ° ´¹ = Á ° ± g²³´µ¶ ° ´ÂÃ...
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Midterm Solutions - Midterm Solutions ECE 162C May 6 2009...

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