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383V_Fall_2010_Lecture-9-11_DFG_and_OPO

# 383V_Fall_2010_Lecture-9-11_DFG_and_OPO - Nonlinear Optics...

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1 N o n l i n e a r O p t i c s EE 383V Prof. Mikhail Belkin Lectures 9 11 Difference frequency Generation and Optical Parametric Amplification Summary of the previous lecture material 1 2 3 d eff Th d + ti i li t l Three waves 1 , 2 , and 3 = 1 2 propagating in a nonlinear crystal. They all interact via sum and difference frequency generation processes and can exchange their power: photons at 1 and 2 may combine and produce a photon at 3 alternatively, a photon at 3 may split into one photon at 1 and one at 2 These processes are all described by coupled wave equations derived earlier: Coupled wave equations (d eff is the same for all equations in case of transparent media)

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2 Difference frequency generation (DFG) and parametric amplification Previously, we considered the case of sum frequency generation: Namely, we had two input waves at 1 and 2 and we had phase matching: k 1 +k 2 =k 3 for a process 1 + 2 = 3 . As a result, 1 and 2 interacted and produced 3 Let’s now consider the case of difference frequency generation: Namely, we now have two input waves at 1 and 3 and we had phase matching: k 3 k 1 =k 2 for a process 3 + 1 = 2 . As a result, 1 and 2 interacted and produced 3 We have already ‘seen’ a DFG process in our calculations of SFG with pump depletion: Remember, when we considered a case of SFG with 2 being ‘strong’ (undepletable) pump and 2 being ‘weak’ pump we got this solution for A 1 and A 3 : Difference frequency generation Consider this experimental situation: We have 3 and 2 as inputs; Are we going to generate 2 = 3 + 1 (SFG) or 2 = 3 1 (DFG)? Answer: we are going to generate both; a process that is phase matched will result in high conversion efficiency and will dominate
3 Coupled-wave equations for DFG Consider now that A 3 (high frequency pump) is very strong and let’s neglect its depletion: z (phase mismatch for DFG) Assume: k=0 ‘Strong pump’ solution Use initial conditions (A 2 =0) to get: The power in strong wave A 3 goes to amplify both A 1 and A 2

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