Theoretical investigation of confocal microscopy using an elliptically polarized cylindrical vector laser beam: Visualization of quantum emitters near interfaces

We theoretically study laser-scanning confocal fluorescence microscopy using elliptically polarized cylindrical vector excitation light as a tool for visualization of arbitrarily oriented single quantum dipole emitters located (1) near planar surfaces enhancing fluorescence, (2) in a thin supported polymer film, (3) in a freestanding polymer film, and (4) in a dielectric planar microcavity. It is shown analytically that by using a tightly focused azimuthally polarized beam, it is possible to exclude completely the orientational dependence of the image intensity maximum of a quantum emitter that absorbs light as a pair of incoherent independent linear dipoles. For linear dipole quantum emitters, the orientational independence degree higher than 0.9 can normally be achieved (this quantity equal to 1 corresponds to completely excluded orientational dependence) if the collection efficiency of the microscope objective and the emitter's total quantum yield are not strongly orientationally dependent. Thus, the visualization of arbitrarily oriented single quantum emitters by means of the studied technique can be performed quite efficiently.

Figure 1

The sketch of a LSCF microscope system. A collimated linearly polarized laser beam is directed onto a polarization converter (PC), then it is reflected by a dichroic mirror (DM) and focused by a microscope objective (O) onto a sample (S). The sample is assumed to be a transparent solid matrix doped with single quantum fluorescent emitters (SQEs). The emitters are excited by a focused laser beam and the emitted fluorescence is collected by the objective. The collected emission is passed through the dichroic mirror, directed by a mirror (M) onto a filter (F) to reject residual laser excitation light, then it is focused by a lens (L) onto a detector (D) through a pinhole (P).

Figure 2

Geometrical models of (a) the linear dipole SQE and (b) the 2D dipole SQE.

Figure 3

The generalized structure of a layered medium under consideration.

Figure 4

The longitudinal position of a SQE in the layered medium. Optical properties of a layered medium are described by the transmission and reflection coefficients.

Figure 5

The explanation to the approach of comparing the dimmest and the brightest orientations.

Figure 6

An example of calculated excitation laser focal field components. The field is focused 20 nm below the polymer–air interface.

Figure 7

Simulated LSCFM images of 2D dipole SQEs located in a polymer film ($n=1.5$) 20 nm below the polymer–air interface; ${\phi }_a={17}^{\circ }$. The numbers in the corners of the images represent the angle ${\theta }_a$ (deg).

Figure 8

The sketch of the layered plasmonic structure. The microscope objective is supposed to be located under the glass substrate.

Figure 9

The product $\eta Q$ of SQEs in a polymer film on a glass surface as a function of the distance from air–polymer interface at different intrinsic quantum yields $q_i$. Vertical and horizontal arrows are related to $z$-oriented and in-plane TDMs, respectively. The low-$q_i$ curves are normalized to $q_i$.

Figure 10

Maximums of the intensities $I_{\rho }, I_{\phi }$, and $I_z$ as functions of the distance from the air–polymer interface $h$.

Figure 11

The orientational independence degree as a function of a cover film thickness for SQEs with different intrinsic quantum yields. The upper indices near $\varepsilon$'s denote the type of beam and the lower indices express SQEs' intrinsic quantum yield.

Figure 12

The orientational independence degree as a function of the film thickness. SQEs are dispersed in the film. The upper indices near $\varepsilon$'s denote the type of beam and the lower indices express SQEs' intrinsic quantum yield.

Figure 13

The dependence of the product $\eta Q$ on the distance between the polymer–air interface and an emitter for 2D dipole SQEs with different intrinsic quantum yields $q_i$. The arrows are related to the emitters' orientations. The low-$q_i$ curves are normalized to $q_i$.

Figure 14

The degree of orientational independence as a function of the cover film thickness for a 2D dipole SQE. The upper indices near $\varepsilon$'s denote the type of beam and the lower indices express SQEs' intrinsic quantum yield.

Figure 15

The dependence of the degree of orientational independence on the thickness of a polymer film for a 2D dipole SQE. The emitters are dispersed in the film.

Figure 16

The variation of the ratio of the intensity of the longitudinal focal-region light field component to the intensity of the azimuthal component as a function of the geometrical focus position.

Figure 17

The variation of the ratio of the intensity of the longitudinal focal-region light field component to the intensity of the azimuthal component as a function of the geometrical focus position: the local minimum.

Figure 18

Maximums of the intensities of the focal-region light field components at the geometrical focus position 660 nm above the polymer–air interface. $I_n$ is the normalized intensity.

Figure 19

The focal-region light field components in the middle of the film ($z=50$ nm) for the geometrical focus position 0.66 $\mu \mathrm{m}$ above the polymer–air interface.

Figure 20

The orientational independence degree as a function of a polymer film thickness for linear dipole SQEs. The emitters are dispersed in the film. The focus position is located 0.66 $\mu \mathrm{m}$ above the polymer–air interface.

Figure 21

The orientational independence degree as a function of a polymer film thickness for 2D dipole SQEs. The emitters are dispersed in the film. The focus position is located 0.66 $\mu \mathrm{m}$ above the polymer–air interface.