Physical Origins of Extreme Cross-Polarization Extinction in Confocal Microscopy

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Physical Origins of Extreme Cross-Polarization Extinction in Confocal Microscopy

Meryem Benelajla, Elena Kammann, Bernhard Urbaszek, and Khaled Karrai

Phys. Rev. X 11, 021007 – Published 7 April 2021

Abstract

Confocal microscopy is an essential imaging tool for biological systems, solid-state physics and nanophotonics. Using confocal microscopes allows performing resonant fluorescence experiments, where the emitted light has the same wavelength as the excitation laser. These challenging experiments are carried out under linear cross-polarization conditions, rejecting laser light from the detector. In this work, we uncover the physical mechanisms that are at the origin of the yet-unexplained high polarization rejection ratio which makes these measurements possible. We show in both experiment and theory that the use of a reflecting surface (i.e., the beam splitter and mirrors) placed between the polarizer and analyzer in combination with a confocal arrangement explains the giant cross-polarization extinction ratio of $10^{8}$ and beyond. We map the modal transformation of the polarized optical Gaussian beam. We find an intensity “hole” in the reflected beam under cross-polarization conditions. We interpret this hole as a manifestation of the Imbert-Fedorov effect, which deviates the beam depending on its polarization helicity. This result implies that this topological effect is amplified here from the usually observed nanometer to the micrometer scale due to our cross-polarization dark-field methods. We confirm these experimental findings for a large variety of commercially available mirrors and polarization components, allowing their practical implementation in many experiments.

Received 29 April 2020
Revised 14 January 2021
Accepted 15 February 2021

DOI:https://doi.org/10.1103/PhysRevX.11.021007

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nanophotonics Polarization of light

Atomic, Molecular & Optical

Authors & Affiliations

Meryem Benelajla ^1,2, Elena Kammann¹, Bernhard Urbaszek ², and Khaled Karrai^1,*

¹attocube systems AG, Eglfinger Weg2, 85540 Haar, Germany
²Université de Toulouse, INSA-CNRS-UPS, LPCNO, Toulouse 31077, France

^*khaled.karrai@attocube.com

Popular Summary

Confocal microscopy is an essential imaging tool for biological systems, solid-state physics, and nanophotonics. Whereas conventional microscopes flood their targets with light, confocal microscopes peer through pinholes at points of illumination to enhance their resolution. The improved resolution has been of great help in studying light-matter interactions via resonant fluorescence experiments, which require a laser to excite light emission in a material. These experiments employ a technique for suppressing the laser light, and yet it is not clear why this technique works. Here, we uncover the physical mechanism that makes this suppression possible.

To reject the laser light, confocal setups employ polarization filters, which, in theory, should reduce the laser brightness by a factor of up to $10 000$ . In practice, they go up to 6 orders of magnitude beyond that. This is, to say the least, surprising. In our experiments, we show that the effect finds its origin in what is known as the Imbert-Fedorov shift, a subtle sideways shift of a polarized beam of light when it is reflected off a smooth surface, such as the beam splitter and mirrors in these setups.

Our work opens the door to a methodical design of sensitive laser resonant fluorescence microscopes with extreme background extinction for a broad range of applications in quantum optics and solid-state physics. The new experimental methods developed for this work can also be used for measuring material optical properties.

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Vol. 11, Iss. 2 — April - June 2021

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Images

Figure 1
(a),(b) Cross-polarization extinction setup in a confocal microscope arrangement setup as described in the text. (c) Measured and modeled linear polarization extinction ratio for both $p$ - and $s$ -polarized beams around cross-polarization conditions obtained by placing the analyzer before (a) and after (b) a protected silver mirror. A giant extinction enhancement of more than 3 orders of magnitude is obtained in configurations $s$ and $p$ with the reflecting surface placed between crossed polarizers. The inset is a magnification of the polarization extinction near maximum for the $s$ polarization. An angular shift of the location of maxima of extinction is systematically found for the $s$ and $p$ polarization with respect to the reference. When the linear polarization is tilted at $\pm 45 °$ from the plane of incidence, the extinction reduces dramatically down to about 41 as shown with the lowest curve and data point.
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Figure 2
Confocal mapping of $s$ (a) and $p$ (b) laser beams in co- and cross-polarization using a scanning mirror (9). The upper and lower rows of the figures are measurements with the analyzer placed before [Fig. 1] and after [Fig. 1] the test reflecting surface, respectively, in $s$ polarization and $p$ polarization [(a) and (b), respectively]. We plot the extinction ratio map by dividing, pixel per pixel, the copolarized with the cross-polarized data. In cross-polarization, a modal splitting along ${\vec{e}}_{y}$ above and below the plane of incidence is observed for both the $s$ and $p$ polarization. The dotted line circle is the $1 / e$ intensity level of the Gaussian distribution resulting from the confocal convolution between the focused spot and the collecting fiber mode. The location of the maxima of the modal splitting lies exactly on that circle. The diameter of this circle gives also the nonconvoluted focal spot waist diameter at $1 / e^{2}$ focused on the collecting fiber end. The vertical white bar represents $5 μ m$ .
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Figure 3
$p$ -polarized beam reflected off a silver mirror. Measured (a) and simulated (b) evolution of the modal confocal imaging mapping through maximum extinction (c) for different analyzer angles $δ α$ as explained in the text. In (d), the positions of the intensity extrema are shown in units of beam waist $ω_{f}$ at focus.
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Figure 4
$s$ -polarized beam reflected off a silver mirror. Measured (a) and simulated (b) evolution of the modal confocal imaging mapping through maximum extinction (c) for different analyzer angles $δ α$ as explained in the text. In (d), the positions of the intensity extrema are shown in units of beam waist $ω_{f}$ at focus.
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Figure 5
Measured (a) and simulated (b) evolution of the modal mapping through maximum extinction for reflectivity from the air side off a glass surface (BK7) for $p$ polarization. (c) Red symbols: extinction ratio for different analyzer angle $α$ shifts as explained in the text. Black symbols: reference measurement with the analyzer placed just after the polarizers. The positions of the intensity extrema are shown in units of beam waist $ω_{f}$ at focus.
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