Generation of "perfect" vortex of variable size and its effect in angular spectrum of the down-converted photons.

M V Jabir,N Apurv Chaitanya,A Aadhi,G K Samanta

doi:10.1038/srep21877

M V Jabir, N Apurv Chaitanya + Show 2 more

Open Access

https://doi.org/10.1038/srep21877

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Abstract

The “perfect” vortex is a new class of optical vortex beam having ring radius independent of its topological charge (order). One of the simplest techniques to generate such beams is the Fourier transformation of the Bessel-Gauss beams. The variation in ring radius of such vortices require Fourier lenses of different focal lengths and or complicated imaging setup. Here we report a novel experimental scheme to generate perfect vortex of any ring radius using a convex lens and an axicon. As a proof of principle, using a lens of focal length f = 200 mm, we have varied the radius of the vortex beam across 0.3–1.18 mm simply by adjusting the separation between the lens and axicon. This is also a simple scheme to measure the apex angle of an axicon with ease. Using such vortices we have studied non-collinear interaction of photons having orbital angular momentum (OAM) in spontaneous parametric down-conversion (SPDC) process and observed that the angular spectrum of the SPDC photons are independent of OAM of the pump photons rather depends on spatial profile of the pump beam. In the presence of spatial walk-off effect in nonlinear crystals, the SPDC photons have asymmetric angular spectrum with reducing asymmetry at increasing vortex radius.

Highlights

Recent development in the field of structured beams have resulted in a special class of optical vortices, known as perfect vortices[11], where the radius of the vortex ring is independent of its order
Where, wg is the beam waist radius of the Gaussian beam confining the BG beam, Il is the lth order modified Bessel function of first kind, and 2wo is the annular width of the perfect vortex of ring radius governed by the relation[13], ρr = f sin((n − 1)α) where, n and α are the refractive index and base angle of the axicon respectively
Pumping a nonlinear crystal using such vortices of different ring radius we have studied the angular spectrum of the down converted photons and experimentally observed that the angular spectrum of the down converted photons is dictated by the spatial profile of the pump but not it’s orbital angular momentum (OAM)

Summary

Results

According to the Fourier transformation theory[20], any object can be Fourier transformed by placing the object behind the lens at any arbitrary distance D from the focal plane. The basic principle of the technique is pictorially represented, where the object (axicon) placed at a distance (f–D) behind the lens of focal length, f , is Fourier transformed into perfect vortex at the back focal plane for input vortex beams. The amplitude distribution of the perfect vortex at the back focal plane is given by il−1exp i kρ2f 2 2D3. In the current system configuration, the width of the perfect modified Bessel function, Il can be approximated to[13] vortex is

For large value of ρr

Methods

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