Source: http://aoot.osa.org/josab/abstract.cfm?uri=josab-28-11-2806
Timestamp: 2019-04-22 10:10:30+00:00

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We experimentally study the behavior of orbital angular momentum (OAM) of light in a noncollinear second- harmonic generation process. The experiment is performed by using a Type I BBO crystal under phase-matching conditions with femtosecond pumping fields at 830 nm. Two specular off-axis vortex beams carrying fractional OAM at the fundamental frequency are used. We analyze the behavior of the OAM of the second-harmonic (SH) signal when the optical vortex of each input field at the FF is displaced from the beam’s axis. We obtain different spatial configurations of the SH field, always carrying the same zero angular momentum.
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Fig. 1 Experimental setup of noncollinear SHG. The collimated beam impinges on the SPP, and then it is split and focused on the nonlinear crystal with relative angles of ± 3.5 ° (total 7 ° ). Bottom-left corner, scan of the Gaussian beam performed by moving the SPP in the horizontal direction.
Fig. 2 Noncollinear SHG signal obtained by displacing the SPP along the x axis at y = 0 , for six different x displacement values. (a) Numerically simulated near field; (b) numerically simulated far field; and (c) experimental results.
Fig. 3 Numerically estimated near-field intensity profiles of the FF beams, (a) and (b), and of the noncollinear SH beam; in FF beams the singularity shifts in opposite directions. The SH beam’s profile carries the singularities of both the FF beams, maintaining their original orientation.
Fig. 4 Phase plots of the electric field for the FFs, (a) and (b), and for the SH (c), corresponding to the configuration of fields given in Fig. 3. The phase changes from − π (dark blue), to 0 (light green), to π (dark red).
Fig. 5 Frame of the far-field movie of the SHG signal as a function of the SPP’s displacement; the top frame corresponds to zero displacement ( x = 0 ) (Media 1).
Fig. 6 OAM of pump and SH fields with the SPP’s displacement. As the device is moved from the beam’s axis, both the FF beams [blue (upper) and black (lower) lines] reduce the absolute value of their OAM from the initial values of ± 0.5 . The SH’s OAM [red (middle) line] is always the sum of the other two, that is, zero.
Fig. 7 Transverse Poynting vector of the SH field generated in the case of on-axis SPP. The absence of rotation of the arrows implies that there is no screw dislocation; therefore, there is no OAM.
(4) P = i ε 0 ω ( u ∇ ⊥ u * − u * ∇ ⊥ u ) + 2 k ε 0 ω | u | 2 z .
(5) ℓ = − i ∫ u * ( r , θ ) ∂ u ( r , θ ) ∂ θ r d r d θ ∫ | u ( r , θ ) | 2 r d r d θ .
(6) ℓ = ∑ l = − ∞ ∞ ∑ p = 0 ∞ l | C l p | 2 .

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