Second-harmonic generation in periodically poled silicon waveguides with lateral p-i-n junctions
Riccardo Franchi, Claudio Castellan, Mher Ghulinyan, Lorenzo Pavesi
Abstract
Electric-field-induced second-harmonic generation is demonstrated in silicon waveguides with reverse biased lateral p-i-n junctions. Phase matching is achieved by periodically poling the applied electric field. Two different poling configurations are compared: in the first, the p- and n-type doped regions of the junctions are on different sides of the waveguide ( simple configuration), while in the second, they are alternated periodically across the waveguide sides ( interdigitated configuration). Both simulations and experiments show that the generation efficiency is increased by 10 times comparing the interdigitated and simple configurations. The effective second-order susceptibility modulation obtained at a reverse bias voltage of 3.5 V is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msubsup> <mml:mi>χ</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">e</mml:mi> <mml:mi mathvariant="normal">f</mml:mi> <mml:mi mathvariant="normal">f</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>S</mml:mi> </mml:mrow> <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:msubsup> <mml:mo>≃</mml:mo> <mml:mn>0.14</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">m</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">V</mml:mi> </mml:mrow> </mml:math> for the simple configuration and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:msubsup> <mml:mi>χ</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">e</mml:mi> <mml:mi mathvariant="normal">f</mml:mi> <mml:mi mathvariant="normal">f</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>I</mml:mi> </mml:mrow> <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:msubsup> <mml:mo>≃</mml:mo> <mml:mn>0.64</mml:mn> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">p</mml:mi> <mml:mi mathvariant="normal">m</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">V</mml:mi> </mml:mrow> </mml:math> for the interdigitated one.