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Due May 6, 2022 You may not discuss the problems with anyone other the instructor until after you hand in the exam. Show all of your algebra!! Use Mathcad for any numerical calculations or plotting. Z (20) Consider second harmonic generation in LiNbO3 in which two ordinary polarized photons at w (pump beam) are converted to a single photon at 20 (signal beam). For this problem, the pump beam wavelength is Tp= 1500 nm and the crystal length is 5.0 mm. no (w) E (20) EZ pm E (w) (20 х (w Problem 1 ne n a) (35 pts.) Starting with the un-depleted pump approximation results discussed in class (whiteboard notes 4-19-2022), show that the intensity of the second harmonic beam can be expressed as (Δk(Θ). sin 2 I(20,0) 1W12W AkOL 2 (Ak@4

Z (20) По Consider second harmonic generation in LiNbO3 in which two ordinary polarized photons at w (pump beam) are converted to a single photon at 2w (signal beam). For this problem, the pump beam wavelength is 1p= 1500 nm and the crystal length is 5.0 mm. EO Opm (20) X (20) (w) Problem 1 no a) (35 pts.) Starting with the un-depleted pump approximation results discussed in class (whiteboard notes 4-19-2022), show that the intensity of the second harmonic beam can be expressed as (AkOL sin 2 I(20,0) « 1(w)l2(W) (Ak(O) ()