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 rO 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 tl 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
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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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4 Compare ‘strong pump’ solutions for SFG DFG and Exponential growth Linear growth, followed by saturation and decrease as the weaker of two pumps is depleted Exponential growth, is equivalent to gain (g) Optical parametric oscillator (OPO) Suppose we A
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This note was uploaded on 10/21/2010 for the course EE 315 taught by Professor Borismurmann during the Spring '09 term at Stanford.

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

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