Proposal of mosaic-based 2 × 2 3-dB couplers for prospective on-chip communication in mid-infrared wavelengths around 2.1  µm (2022)

We propose two types of mosaic-based <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> <mml:mo>×</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> </mml:math> 3-dB couplers for wavelengths around 2.1 µm. For type I, the proposed device provides excess loss of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>&lt;</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0.22</mml:mn> </mml:mrow> </mml:math> dB and imbalance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>&lt;</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>±</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>.</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>07</mml:mn> </mml:mrow> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">d</mml:mi> <mml:mi mathvariant="normal">B</mml:mi> </mml:mrow> </mml:math> over the wavelength range from 2.06 to 2.14 µm. Compared with the standard multimode-interference-based <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> <mml:mo>×</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> </mml:math> 3-dB coupler, the imbalance is improved by <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>0.4</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">d</mml:mi> <mml:mi mathvariant="normal">B</mml:mi> </mml:mrow> </mml:mrow> </mml:math> . For type II, coupling length in the multimode-interference region is about three times shorter than the one based on multimode-interference theory. It provides excess loss of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>&lt;</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>0.49</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">d</mml:mi> <mml:mi mathvariant="normal">B</mml:mi> </mml:mrow> </mml:mrow> </mml:math> and imbalance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>&lt;</mml:mo> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>±</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:mo>.</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>23</mml:mn> </mml:mrow> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">d</mml:mi> <mml:mi mathvariant="normal">B</mml:mi> </mml:mrow> </mml:mrow> </mml:math> over the wavelength range from 2.06 to 2.14 µm. Both proposed devices show high fabrication tolerance to hole diameter variation. Especially for type II, the fabrication-tolerant direct binary search was effective to obtain such a structure. These mosaic-based <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> <mml:mo>×</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>2</mml:mn> </mml:mrow> </mml:mrow> </mml:math> 3-dB couplers will play an important role in highly integrated photonic circuits.