We experimentally demonstrate the utilization of adaptive optics (AO) to mitigate intragroup power coupling among linearly polarized (LP) modes in a gradedindex fewmode fiber (GI FMF). Generally, in this fiber, the coupling between degenerate modes inside a modal group tends to be stronger than between modes belonging to different groups. In our approach, the coupling inside the
This paper analytically and numerically investigates misalignment and modemismatchinduced power coupling coefficients and losses as a function of Hermite–Gauss (HG) mode order. We show that higherorder HG modes are more susceptible to beam perturbations when, for example, coupling into optical cavities: the misalignment and modemismatchinduced power coupling losses scale linearly and quadratically with respect to the mode indices, respectively. As a result, the modemismatch tolerance for the
 NSFPAR ID:
 10229965
 Publisher / Repository:
 Optical Society of America
 Date Published:
 Journal Name:
 Optics Letters
 Volume:
 46
 Issue:
 11
 ISSN:
 01469592; OPLEDP
 Format(s):
 Medium: X Size: Article No. 2694
 Size(s):
 Article No. 2694
 Sponsoring Org:
 National Science Foundation
More Like this

${\mathrm{L}\mathrm{P}}_{11}$ group can be represented by a combination of orbitalangularmomentum (OAM) modes, such that reducing power coupling in OAM set tends to indicate the capability to reduce the coupling inside the${\mathrm{L}\mathrm{P}}_{11}$ group. We employ two output OAM modes$l=+1$ and$l=<\#comment/>1$ as resultant linear combinations of degenerate${\mathrm{L}\mathrm{P}}_{11\mathrm{a}}$ and${\mathrm{L}\mathrm{P}}_{11\mathrm{b}}$ modes inside the${\mathrm{L}\mathrm{P}}_{11}$ group of a$\sim <\#comment/>0.6\text{}\mathrm{k}\mathrm{m}$ GI FMF. The power coupling is mitigated by shaping the amplitude and phase of the distorted OAM modes. Each OAM mode carries an independent 20, 40, or 100Gbit/s quadraturephaseshiftkeying data stream. We measure the transmission matrix (TM) in the OAM basis within${\mathrm{L}\mathrm{P}}_{11}$ group, which is a subset of the full LP TM of the FMFbased system. An inverse TM is subsequently implemented before the receiver by a spatial light modulator to mitigate the intramodalgroup power coupling. With AO mitigation, the experimental results for$l=+1$ and$l=<\#comment/>1$ modes show, respectively, that (i) intramodalgroup crosstalk is reduced by$><\#comment/>5.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ and$><\#comment/>5.6\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ and (ii) nearerrorfree biterrorrate performance is achieved with a penalty of$\sim <\#comment/>0.6\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ and$\sim <\#comment/>3.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ , respectively. 
We experimentally demonstrate simultaneous turbulence mitigation and channel demultiplexing in a 200 Gbit/s orbitalangularmomentum (OAM) multiplexed link by adaptive wavefront shaping and diffusing (WSD) the light beams. Different realizations of two emulated turbulence strengths (the Fried parameter
${r}_{0}=0.4,\phantom{\rule{thinmathspace}{0ex}}1.0\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{m}$ ) are mitigated. The experimental results show the following. (1) Crosstalk between OAM$l=+1$ and$l=<\#comment/>1$ modes can be reduced by$><\#comment/>10.0$ and$><\#comment/>5.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ , respectively, under the weaker turbulence (${r}_{0}=1.0\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{m}$ ); crosstalk is further improved by$><\#comment/>17.7$ and$><\#comment/>19.4\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ , respectively, under most realizations in the stronger turbulence (${r}_{0}=0.4\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{m}$ ). (2) The optical signaltonoise ratio penalties for the bit error rate performance are measured to be$\sim <\#comment/>0.7$ and$\sim <\#comment/>1.6\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ under weaker turbulence, while measured to be$\sim <\#comment/>3.2$ and$\sim <\#comment/>1.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ under stronger turbulence for OAM$l=+1$ and$l=<\#comment/>1$ mode, respectively. 
The midIR spectroscopic properties of
${\mathrm{E}\mathrm{r}}^{3+}$ doped lowphonon${\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{l}}_{3}$ and${\mathrm{C}\mathrm{s}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_{3}$ crystals grown by the Bridgman technique have been investigated. Using optical excitations at$\sim <\#comment/>800\phantom{\rule{thickmathspace}{0ex}}\mathrm{n}\mathrm{m}$ and$\sim <\#comment/>660\phantom{\rule{thickmathspace}{0ex}}\mathrm{n}\mathrm{m}$ , both crystals exhibited IR emissions at$\sim <\#comment/>1.55$ ,$\sim <\#comment/>2.75$ ,$\sim <\#comment/>3.5$ , and$\sim <\#comment/>4.5\phantom{\rule{thickmathspace}{0ex}}\text{\xb5<\#comment/>}\mathrm{m}$ at room temperature. The midIR emission at 4.5 µm, originating from the${}^{4}{\mathrm{I}}_{9/2}\phantom{\rule{thickmathspace}{0ex}}\to <\#comment/>{\phantom{\rule{thickmathspace}{0ex}}}^{4}{\mathrm{I}}_{11/2}$ transition, showed a long emission lifetime of$\sim <\#comment/>11.6\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{s}$ for${\mathrm{E}\mathrm{r}}^{3+}$ doped${\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{l}}_{3}$ , whereas${\mathrm{E}\mathrm{r}}^{3+}$ doped${\mathrm{C}\mathrm{s}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_{3}$ exhibited a shorter lifetime of$\sim <\#comment/>1.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{s}$ . The measured emission lifetimes of the${}^{4}{\mathrm{I}}_{9/2}$ state were nearly independent of the temperature, indicating a negligibly small nonradiative decay rate through multiphonon relaxation, as predicted by the energygap law for lowmaximumphonon energy hosts. The room temperature stimulated emission cross sections for the${}^{4}{\mathrm{I}}_{9/2}\to <\#comment/>{}^{4}{\mathrm{I}}_{11/2}$ transition in${\mathrm{E}\mathrm{r}}^{3+}$ doped${\mathrm{C}\mathrm{s}\mathrm{C}\mathrm{d}\mathrm{C}\mathrm{l}}_{3}$ and${\mathrm{C}\mathrm{s}\mathrm{P}\mathrm{b}\mathrm{C}\mathrm{l}}_{3}$ were determined to be$\sim <\#comment/>0.14\times <\#comment/>{10}^{<\#comment/>20}\phantom{\rule{thickmathspace}{0ex}}{\mathrm{c}\mathrm{m}}^{2}$ and$\sim <\#comment/>0.41\times <\#comment/>{10}^{<\#comment/>20}\phantom{\rule{thickmathspace}{0ex}}{\mathrm{c}\mathrm{m}}^{2}$ , respectively. The results of Judd–Ofelt analysis are presented and discussed. 
Electrooptic quantum coherent interfaces map the amplitude and phase of a quantum signal directly to the phase or intensity of a probe beam. At terahertz frequencies, a fundamental challenge is not only to sense such weak signals (due to a weak coupling with a probe in the nearinfrared) but also to resolve them in the time domain. Cavity confinement of both light fields can increase the interaction and achieve strong coupling. Using this approach, current realizations are limited to low microwave frequencies. Alternatively, in bulk crystals, electrooptic sampling was shown to reach quantumlevel sensitivity of terahertz waves. Yet, the coupling strength was extremely weak. Here, we propose an onchip architecture that concomitantly provides subcycle temporal resolution and an extreme sensitivity to sense terahertz intracavity fields below 20 V/m. We use guided femtosecond pulses in the nearinfrared and a confinement of the terahertz wave to a volume of
${V}_{\mathrm{T}\mathrm{H}\mathrm{z}}\sim <\#comment/>{10}^{<\#comment/>9}({\mathrm{\lambda <\#comment/>}}_{\mathrm{T}\mathrm{H}\mathrm{z}}/2{)}^{3}$ in combination with ultraperformant organic molecules (${r}_{33}=170\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{p}\mathrm{m}/\mathrm{V}$ ) and accomplish a recordhigh singlephoton electrooptic coupling rate of${g}_{\phantom{\rule{negativethinmathspace}{0ex}}\mathrm{e}\mathrm{o}}=2\mathrm{\pi <\#comment/>}\times <\#comment/>0.043\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{G}\mathrm{H}\mathrm{z}$ , 10,000 times higher than in recent reports of sensing vacuum field fluctuations in bulk media. Via homodyne detection implemented directly on chip, the interaction results into an intensity modulation of the femtosecond pulses. The singlephoton cooperativity is${C}_{0}=1.6\times <\#comment/>{10}^{<\#comment/>8}$ , and the multiphoton cooperativity is$C=0.002$ at room temperature. We show$><\#comment/>70\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ dynamic range in intensity at 500 ms integration under irradiation with a weak coherent terahertz field. Similar devices could be employed in future measurements of quantum states in the terahertz at the standard quantum limit, or for entanglement of subsystems on subcycle temporal scales, such as terahertz and nearinfrared quantum bits. 
We utilize aperture diversity combined with multiplemode receivers and multipleinputmultipleoutput (MIMO) digital signal processing (DSP) to demonstrate enhanced tolerance to atmospheric turbulence and spatial misalignment in a 10 Gbit/s quadraturephaseshiftkeyed (QPSK) freespace optical (FSO) link. Turbulence and misalignment could cause power coupling from the fundamental Gaussian mode into higherorder modes. Therefore, we detect power from multiple modes and use MIMO DSP to enhance the recovery of the original data. In our approach, (a) each of multiple transmitter apertures transmits a single fundamental Gaussian beam carrying the same data stream, (b) each of multiple receiver apertures detects the signals that are coupled from the fundamental Gaussian beams to multiple orbital angular momentum (OAM) modes, and (c) MIMO DSP is used to recover the data over multiple modes and receivers. Our simulation shows that the outage probability could be reduced from
$><\#comment/>0.1$ to$<<\#comment/>0.01$ . Moreover, we experimentally demonstrate the scheme by transmitting two fundamental Gaussian beams carrying the same data stream and recovering the signals on OAM modes 0 and$+1$ at each receiver aperture. We measure an up to$\sim <\#comment/>10\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ powerpenalty reduction for a bit error rate (BER) at the 7% forward error correction limit for a 10 Gbit/s QPSK signal.