Thanks for the video. Could you please clarify the units in the degenerate phase matching equation. beta is measured in s^2/m and gama*power is 1/m, how is homogeneity retained?
To clarify, the betas in that equation are spatial frequencies evaluated at four different temporal frequencies. For example, β_u = β(ω_u), which has units of 1/m. They are emphatically NOT group-velocity-dispersion values (i.e. 2nd derivatives of β w.r.t. ω), which have units of s^2/m.
@@yourfavouriteta This is the phase mismatch equation for degenerate FWM 2𝛽𝑝(𝜔𝑝) − 𝛽𝑠(𝜔𝑠 ) + 𝛽𝑖 (𝜔𝑖 ) − 2𝛾𝑃 = 0, IMPLYING balancing GVD, if these betas are the frequencies as u mentioned what is their relation to the respective GVDs? Because after all we are balancing GVDs for PUMP, SIGNAL AND IDLER.
@@muneebfarooq3882 At 11:30 in the video, I explain that 2β(ωb)-β(ωa)-β(ωu) is approximately equal to -Δω^2 * β2(ωb) = -Δω^2 * GVD(ωb) when the difference between three temporal frequencies, ωb, ωa, ωu is small. Note again that "β_b" in my derivation is "the spatial frequency in the medium of an EM wave with a temporal frequency of ω_b". Meanwhile, β_2 = GVD = 2nd derivative of the spatial frequency, β(ω), w.r.t. ω. The point is that phase matching ***in general*** depends on whether the temporal frequencies that are interacting via the nonlinearity (in this case ωb, ωa and ωu) have the correct spatial frequencies and powers for 2β(ωb)-β(ωa)-β(ωu) - 2γP = 0 to be satisfied. In the ***special case***, where the difference between the temporal frequencies is small, this is equivalent to asking if Δω^2 * GVD + 2γP~0.
@@muneebfarooq3882 Well, the range of Δω values where the approximation works depends on how quickly β changes as a function of ω. If β changes a lot, using the full expression is better.
Excellent video on FWM! Really informative and well-explained. Thanks for sharing
You're welcome!
Thanks for the video. Could you please clarify the units in the degenerate phase matching equation. beta is measured in s^2/m and gama*power is 1/m, how is homogeneity retained?
To clarify, the betas in that equation are spatial frequencies evaluated at four different temporal frequencies. For example, β_u = β(ω_u), which has units of 1/m. They are emphatically NOT group-velocity-dispersion values (i.e. 2nd derivatives of β w.r.t. ω), which have units of s^2/m.
@@yourfavouriteta This is the phase mismatch equation for degenerate FWM 2𝛽𝑝(𝜔𝑝) − 𝛽𝑠(𝜔𝑠 ) + 𝛽𝑖 (𝜔𝑖 ) − 2𝛾𝑃 = 0, IMPLYING balancing GVD, if these betas are the frequencies as u mentioned what is their relation to the respective GVDs?
Because after all we are balancing GVDs for PUMP, SIGNAL AND IDLER.
@@muneebfarooq3882 At 11:30 in the video, I explain that 2β(ωb)-β(ωa)-β(ωu) is approximately equal to -Δω^2 * β2(ωb) = -Δω^2 * GVD(ωb) when the difference between three temporal frequencies, ωb, ωa, ωu is small. Note again that "β_b" in my derivation is "the spatial frequency in the medium of an EM wave with a temporal frequency of ω_b". Meanwhile, β_2 = GVD = 2nd derivative of the spatial frequency, β(ω), w.r.t. ω.
The point is that phase matching ***in general*** depends on whether the temporal frequencies that are interacting via the nonlinearity (in this case ωb, ωa and ωu) have the correct spatial frequencies and powers for 2β(ωb)-β(ωa)-β(ωu) - 2γP = 0 to be satisfied. In the ***special case***, where the difference between the temporal frequencies is small, this is equivalent to asking if Δω^2 * GVD + 2γP~0.
@@yourfavouriteta that is right but I think this approximation works only in the linear dispersion regime.
@@muneebfarooq3882 Well, the range of Δω values where the approximation works depends on how quickly β changes as a function of ω. If β changes a lot, using the full expression is better.
Pretty good
Thank you!
Nice lecture, some animation mixing to try better lecture
@@SMITAJAISWAR-nc5lg You're welcome!