Photonic nanojets generated by single microspheres of various sizes illuminated by resonant and non-resonant focused Gaussian beams of different waists

Abstract

We report theoretical simulations on the photonic nanojet (PNJ) of single dielectric microspheres of various sizes illuminated by focused Gaussian beams (FGBs), using analytical theory developed by Gouesbet et al. based on the Bromwich formalism. The radius of the microsphere ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>R</mml:mi> </mml:math> ) is varied from 1 to 45 µm. The effect of the beam waist ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> ) on characteristic parameters such as maximum electric field enhancement ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>η</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">x</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) of the PNJ, the focal length of the microsphere ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>f</mml:mi> </mml:math> ), effective length, and width of the PNJ is studied in detail. The effect of the refractive index of the microsphere ( <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:mi>p</mml:mi> </mml:msub> </mml:mrow> </mml:math> ) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>R</mml:mi> </mml:math> on the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>η</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">x</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> for different values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>ω</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> is studied. The dependence of (i) the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>f</mml:mi> </mml:math> value on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>R</mml:mi> </mml:math> and (ii) the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>η</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">x</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> value on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>λ</mml:mi> </mml:math> is investigated systematically.

Topics & Concepts