Circular cross section waveguides processed by multi-foci-shaped femtosecond pulses
Zezheng Li, Xiaoyan Li, Feng Yu, Qi‐Dai Chen, Zhen‐Nan Tian, Hong‐Bo Sun
Abstract
We developed a simple multi-foci-shaped femtosecond pulsed (MFSFP) method for processing circular cross section waveguides in transparent materials. With this flexible processing method, the focus energy distribution can be designed freely and arbitrarily, and single-mode waveguides with cross section circularity better than 96.0% were achieved. The mode shape difference (1.93%) of circular waveguides is smaller than the difference (7.01%) of normal elliptical waveguides. The coupling abilities of the two kinds of waveguides were investigated with three-dimensional (3D) directional couplers in both experiments and theoretical simulations. The coupling coefficient difference of circular waveguides in vertical and horizontal coupling directions was <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>∼</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0.01</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , which was smaller than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0.33</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> of normal waveguides. The circular symmetric waveguides will play an important role in large-scale high-intensity 3D photonic integrated circuits.