Since Allen1 published his paper on discovering that higher-order Laguerre–Gaussian beam with a spiral phase wavefront
Advanced Photonics, Volume. 5, Issue 3, 036002(2023)
Propagation of transverse photonic orbital angular momentum through few-mode fiber On the Cover , Author Presentation
Spatiotemporal optical vortex (STOV) pulses can carry transverse orbital angular momentum (OAM) that is perpendicular to the direction of pulse propagation. For a STOV pulse, its spatiotemporal profile can be significantly distorted due to unbalanced dispersive and diffractive phases. This may limit its use in many research applications, where a long interaction length and a tight confinement of the pulse are needed. The first demonstration of STOV pulse propagation through a few-mode optical fiber is presented. Both numerical and experimental analysis on the propagation of STOV pulse through a commercially available SMF-28 standard telecommunication fiber is performed. The spatiotemporal phase feature of the pulse can be well kept after the pulse propagates a few-meter length through the fiber even with bending. Further propagation of the pulse will result in a breakup of its spatiotemporal spiral phase structure due to an excessive amount of modal group delay dispersion. The stable and robust transmission of transverse photonic OAM through optical fiber may open new opportunities for transverse photonic OAM studies in telecommunications, OAM lasers, and nonlinear fiber-optical research.
1 Introduction
Since Allen1 published his paper on discovering that higher-order Laguerre–Gaussian beam with a spiral phase wavefront
STOV pulse has a spatiotemporally coupled field distribution. Under an unbalanced dispersion and diffraction phase, the STOV pulse can be significantly distorted,15,16 leading to a breakup of the STOV charge and splitting the STOV pulse into multiple lobes in the spatiotemporal domain. This limits the use of the STOV pulse in many applications where a long interaction length and a tight confinement of the pulse are needed. One solution for overcoming this limitation is to generate a STOV pulse in a Bessel form in the spatiotemporal domain so the STOV charge is confined within a tight space-time cross section and the STOV pulse can be nonspreading when it propagates in a dispersive medium.26,27 However, this Bessel STOV approach requires the pulse to be engineered to accommodate the dispersion relationship of the medium, and the resulting nonspreading propagation distance is still limited by the finite spatial and spectral width of the pulse.
Another approach for achieving a long-distance, stable propagation of the STOV pulse is to use a few-mode optical fiber to guide the STOV pulse. A step-index fiber can support multiple guiding modes if the
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To answer these questions, we present here what we believe is the first demonstration of STOV pulse propagation through a few-mode optical fiber. We choose a commercially available, standard telecommunication fiber, SMF-28, as our platform to perform all the studies. We implement both numerical and experimental analysis on propagating the STOV pulse through the fiber. The spatiotemporal spiral phase structure of STOV pulses can be kept well for a considerable length of a few meters. Further propagating the pulse inside the fiber will result in a breakup of its phase structure due to an excessive amount of group delay difference. Nevertheless, our experiment achieved a long-distance, stable, and robust transmission of transverse photonic OAM through the fiber. This will bring new opportunities in utilizing transverse photonic OAM in optical telecommunication, building novel transverse OAM lasers, and studying nonlinear fiber optical phenomena that involve transverse OAM.
2 Theoretical Analysis and Numerical Simulations
The STOV pulse has an annular intensity profile with a spiral phase of
Figure 1.Modal decomposition of STOV pulse and focused STOV pulse in LP modes. (a) Spatiotemporal intensity and phase profile of a STOV pulse (
Figure 1(c) shows the spatiotemporal profile of the STOV pulse with a topological charge of
In the STOV pulses shown in Figs. 1(a) and 1(c), we have assumed that the STOV pulse is already propagating inside the fiber. In practice, a free-space STOV pulse is normally focused into the fiber by an aspherical lens. Figure 1(e) shows the spatiotemporal intensity and phase profile when the STOV pulse is focused. Differing from its free-space form, a focused STOV pulse has two lobes with a
To simulate the STOV pulse propagation inside the fiber, we need to make two assumptions: (1) the STOV pulse is propagating linearly inside the fiber without any loss and (2) there is no cross talk between different LP modes. With these assumptions, the evolution of the STOV pulse is dictated by the propagation constant
|
We now perform numerical simulation of the focused STOV pulse propagation in SMF-28 by setting the virtual fiber length at 100, 200, and 300 cm. The STOV pulse has a topological charge of
Figure 2.Numerical propagation of focused STOV pulse in few-mode fiber. (a) Unchirped focused STOV pulse; (b) unchirped focused STOV pulse with GVM between LP modes set at zero; (c) unchirped focused STOV pulse with GVD of each LP mode set at zero; (d) chirped focused STOV pulse.
In practice, the input STOV pulse may be chirped. Here, we perform another set of simulations by sending a positively chirped STOV pulse into the fiber. It is positively chirped to have 7 times the pulse duration of its transform-limited form. The results are shown in Fig. 2(d). Similar to the unchirped STOV pulse situation [Fig. 2(a)], an initially chirped STOV pulse can preserve its spatiotemporal spiral phase feature for a propagation distance of 100 and 200 cm. Further propagating, the pulse will cause its phase singularity to merge with other singularities, resulting in the breakup of the STOV charge.
3 Experimental Results and Discussions
In the laboratory, we use a home-built Yb:fiber laser system as our master laser to perform all the experiments. Figure 3 illustrates the schematic of the experimental setup for generating, transmitting, and measuring the STOV pulse through a few-mode optical fiber. The setup has a Mach–Zehnder interferometer configuration. The output of the mode-locked Yb:fiber laser is split into two replicas. (1) One replica that goes in the upper direction in Fig. 3 is phase modulated in its spatial-spectral (
Figure 3.Schematic for transmitting and measuring STOV pulse through few-mode optical fiber. The system is pumped by a home-built Yb:fiber laser system. One replica of the laser output is spatiotemporally modulated to a STOV pulse. It is then coupled into a few-mode fiber (SMF-28) by a high-NA aspherical lens mounted on a 3D translation stage. Another replica of the laser output is compressed and delay-controlled to serve as a probe pulse to measure the transmitted STOV pulse.
The STOV pulse is generated by applying a spatial–spectral spiral phase
Figure 4.3D measurement results for positively chirped STOV pulse transmitted by few-mode optical fiber. (a) Topological charge
4 Conclusions and Outlook
We present the first demonstration of STOV pulse propagation through a step-index, few-mode optical fiber. We perform both numerical and experimental analysis on the propagation dynamics of the STOV pulse inside the fiber. The spatiotemporal spiral phase feature of the pulse can be well kept for a few-meter propagation distance inside the fiber. Further propagating the pulse will break up the STOV phase singularity structure due to an excessive amount of modal group delay difference accumulated from the GVM between LP modes. Changing the fiber to a graded-index fiber with less GVM may extend the maximum transmission length of the STOV pulse. In addition, the interference between LP modes inside the fiber may generate spatiotemporal structures that greatly resemble STOV pulses generated by a partially temporally coherent source,22 which may be a new approach for producing transverse photonic OAM sources. Further investigation of transmission of transverse photonic OAM through optical fiber may open new avenues for optical telecommunication, building novel transverse OAM lasers, and studying nonlinear fiber optical phenomena that involve transverse OAM.
Qian Cao received his PhD in physics from the Universität Hamburg. He is currently a postdoctoral researcher at the University of Shanghai for Science and Technology (USST). His research interests include novel spatiotemporal optical fields, ultrafast optics, and nonlinear optics.
Andy Chong received his PhD in applied physics from Cornell University. He is currently an associate professor at Pusan National University (PNU).
Qiwen Zhan received his PhD in electrical and computer engineering from the University of Minnesota. He is currently the principal investigator of Nano-photonics Research Group at USST.
Biographies of other authors are not available.
[28] A. W. Snyder, J. D. Love. Optical Waveguide Theory(1983).
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Qian Cao, Zhuo Chen, Chong Zhang, Andy Chong, Qiwen Zhan, "Propagation of transverse photonic orbital angular momentum through few-mode fiber," Adv. Photon. 5, 036002 (2023)
Category: Research Articles
Received: Feb. 7, 2023
Accepted: Mar. 27, 2023
Posted: Mar. 27, 2023
Published Online: Apr. 19, 2023
The Author Email: Qiwen Zhan (qwzhan@usst.edu.cn)