Propagating 292 orbital angular momentum modes over a photonic crystal fiber with high mode quality and low nonlinear coefficient

Abstract A double-ring photonic crystal fiber (DRPCF) with two high refractive index ring is proposed to support and improve the stable transmission of more orbital angular momentum (OAM) mode beams. The proposed DRPCF mainly consists of an outer core ring (OCR) and an inner core ring (ICR), where the OCR has two layers and is prepared from two different materials (SF11 for inner layer and SSK2 for out layer). A finite element method is used to analyze the designed DRPCF. The calculated results show that the proposed DRPCF can support the stable transmission of 292 OAM modes from 1500 to 1600 nm, where the OCR can transmit 198 OAM modes and the ICR can transmit 94 OAM modes, representing the highest number reported to date for a single photonic crystal fiber (PCF). In the OCR/ICR, the effective mode areas and mode quality (MQ), chromatic dispersion (CD), confinement loss (CL) of all supported vector modes by the proposed DRPCF are greater than 161/53 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">μ</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> , greater than 94.4/94.6%, less than 474/668 ps nm −1 km −1 , less than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>11</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo stretchy="true">/</mml:mo> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:mspace width="0.5em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">dBm</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> , respectively. The lower CLs can be achieved in both the ICR and OCR, which facilitate high-quality transmission of OAM modes. Moreover, the 10ps walk-off lengths of most of supported modes are within the range of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mn>5</mml:mn> </mml:msup> </mml:math> m, which are beneficial for long-distance transmission of OAM modes. Additionally, the nonlinear coefficients of the OCR and ICR are also calculated, and the results show that the nonlinear coefficients of all supported modes in the OCR and ICR are below 0.42 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">W</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">km</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> and 1.32 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">W</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">km</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> , respectively, which is beneficial for increasing the transmission distance and capacity of an OAM-based MDM system. Therefore, the proposed DRPCF has significant application value in long-distance communication, optical sensing, ultra-low loss transmission, and other fields.