Modeling photon pair generation by second-order surface nonlinearity in silica nanofibers
Abderrahim Azzoune, Philippe Delaye, Gilles Pauliat
Abstract
In this paper, we present a design of an all-fiber source of correlated photon pairs based on standard telecommunications tapered fibers. We examine the generation of correlated photon pairs using parametric process <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>χ</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> in silica tapered optical fibers. This nonlinear process is ensured thanks to surface dipole and bulk multipole nonlinearities. The process of photon creation is modeled by taking into account the vector aspect of the propagation of the optical field in a silica nanofiber. The phase matching is provided by propagating the pump field in one spatial mode while generating a photon pair in another spatial mode. The generation efficiency of photon pairs depends on diameter uniformity of the nanofiber after the manufacturing process. We size this nanofiber for a good optimization of photon pair generation efficiency, and we report that the tolerance in diameter uniformity is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> for a generation rate of photon pairs estimated to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext class="MJX-tex-mathit" mathvariant="italic">ph</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>≈</mml:mo> <mml:mn>22</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mn>000</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">r</mml:mi> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:math> , for 1 W power pump and a nanofiber length of 1.1 mm. Deposits on the nanofiber can be used in order to relax the manufacturing constraints on diameter to maximize the generation rate of photon pairs. As an example, the use of polytetrafluoroethylene on the nanofiber applied as a cladding whose thickness is infinite makes it possible to relax the constraints on the nanofiber diameter. For the same <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> , a generation rate of photon pairs estimated to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext class="MJX-tex-mathit" mathvariant="italic">ph</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>≈</mml:mo> <mml:mn>78</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mn>000</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">r</mml:mi> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:math> for 1 W power pump and a nanofiber length of 2.4 mm is predicted.