Experimental mitigation of the effects of the limited size aperture or misalignment by singular-value-decomposition-based beam orthogonalization in a free-space optical link using Laguerre–Gaussian modes
Kai Pang, Haoqian Song, Xinzhou Su, Kaiheng Zou, Zhe Zhao, Hao Song, Ahmed Almaiman, Runzhou Zhang, Cong Liu, Nanzhe Hu, Shlomo Zach, Nadav Cohen, Brittany Lynn, Andreas F. Molisch, Robert W. Boyd, Moshe Tur, Alan E. Willner
Abstract
Limited-size receiver (Rx) apertures and transmitter–Rx (Tx–Rx) misalignments could induce power loss and modal crosstalk in a mode-multiplexed free-space link. We experimentally demonstrate the mitigation of these impairments in a 400 Gbit/s four-data-channel free-space optical link. To mitigate the above degradations, our approach of singular-value-decomposition-based (SVD-based) beam orthogonalization includes (1) measuring the transmission matrix <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mtext>H</mml:mtext> </mml:math> for the link given a limited-size aperture or misalignment; (2) performing SVD on the transmission matrix to find the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mtext>U</mml:mtext> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Σ</mml:mi> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mtext>V</mml:mtext> </mml:math> complex matrices; (3) transmitting each data channel on a beam that is a combination of Laguerre–Gaussian modes with complex weights according to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mtext>V</mml:mtext> </mml:math> matrix; and (4) applying the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mtext>U</mml:mtext> </mml:math> matrix to the channel demultiplexer at the Rx. Compared with the case of transmitting each channel on a beam using a single mode, our experimental results when transmitting multi-mode beams show that (a) with a limited-size aperture, the power loss and crosstalk could be reduced 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>8</mml:mn> </mml:mrow> </mml:math> and <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>23</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mtext>dB</mml:mtext> </mml:math> , respectively; and (b) with misalignment, the power loss and crosstalk could be reduced 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>15</mml:mn> </mml:mrow> </mml:math> and <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>40</mml:mn> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mtext>dB</mml:mtext> </mml:math> , respectively.