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Methodology - Fluorescence Enhancement

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cover_picture_fluorescence_enhancement_small_zoom15This example has been updated. Find the latest version at Fluorescence Enhancement.

 

 

 

 

 

This page discusses the suggested methodology and workflow for fluorescence emission enhancement simulations.

 

Solvers

FDTD

See also

Surface Plasmons

Mie scattering 3D

Fluorescence Enhancement

dipolepower script function

Source - Dipole

Related publications

1.L. Novotny and B. Hecht, "Principles of Nano-Optics", Cambridge University Press, Cambridge, (2006).

2.P. Bharadwaj and L. Novotny, "Spectral dependence of single molecule fluorescence enhancement," Opt. Express 15, 14266-14274 (2007).

3.J. Gersten and A. Nitzan, "Spectroscopic properties of molecules interacting with small dielectric particles", J. Chem. Phys. 75, 1139 (1981).

4.Chowdhury, et al, “Systematic Computational Study of the Effect of Silver Nanoparticle Dimers on the Coupled Emission from Nearby Fluorophores”, J. Phys. Chem. C., 112(30), 11236-11249 (2008).

Acknowledgment

We gratefully acknowledge collaborative development of this example with Joseph Lakowicz and Mustafa Chowdhury at the Center for Fluorescence Spectroscopy, Medical Biotechnology Center, University of Maryland School of Medicine (http://cfs.umbi.umd.edu/jrl/index.html), Stephen Gray at Argonne National Labs (http://anchi8.chm.anl.gov/staff/chem-dyn/gray.html), and discussions with David Ginger at the University of Washington (http://depts.washington.edu/gingerlb/).

sp_fluorescence_screenshot1_zoom70

FDTD simulation approach

In experiment, we may want to enhance the fluorophore’s emission by using some plasmonic structure (eg, nanoparticles) to collect a stronger signal. We can typically consider the enhancement process in two steps:

 

1.Excitation enhancement - An excitation light hits the nanoparticle (NP). This can cause some plasmonic effects and thus be possible to enhance the fields near the NP. This can effectively increase the optical pump rate, ie, excitation enhancement.

2.Fluorescence enhancement - Due to the presence of the NP, it will affect the Quantum Efficiency (QE) of the fluorescence emission rate. If the system is designed properly, it can enhance the emission at the desired range of frequencies.

 

Combining the above two steps, fluorescence emission enhancement can be achieved. However, in FDTD simulations, we are not going to simulate the full system in a single simulation. Instead, we simulate these two different parts of the physical experiment as distinct simulation steps.

FDTD simulation set-up

Part 1 : The excitation enhancement

Here we use a source such as a TFSF source, plane wave or a Gaussian beam, depending on your experimental setup. This source will represent the excitation light source in the experiment. In the simulation region, you should have the plasmoinc structure in place and we will use a frequency monitor to measure the field enhancement. We are typically looking at measuring the local field enhancement at the fluorophore position. This will allow you to determine the increase in excitation rate. The Mie 3D example is a useful reference for this type of simulation to calculate the field enhancement.

 

nano_particle_mie_3d_enhancement_yz_fluores_meth_zoom52

Note:

The fluorophore is not present in part 1. Simulations for part 1 are to find the maximum field enhancement and its location. These locations will be where the fluorophore is placed in simulations for part 2.

 

Part 2 : The fluorescence enhancement

Once the locations for the maximum field enhancement are located in part 1, then we can simulate the enhancement of the QE in part 2. Here we use a dipole source to determine how the decay rate of a fluorophore will change due to the presence of a nearby metal object such as a nanoparticle. To do this, we use some complicated relationships between the quantum decay rate and the classical Maxwell’s equations (worked out in detail in [1]). The results are measured by recording the amount of radiation leaving the system using the trans_box analysis group. The details of the results are located in the Results section on this page.

 

sp_fluorescence_screenshot1_zoom50

 

 

Results

Nanoparticles can be used to enhance fluorescence and there are mainly two contributions - 1. increasing the excitation rate; 2. increasing the quantum efficiency (QE). For a fluorescence system, the two effects can be assumed to be uncorrelated [2],

 

 

 

Fluorescence emission rate. Calculations involving the absolute fluorescence emission rate are not within the scope of an FDTD simulation.

Excitation rate. Calculations involving the absolute excitation rate are not within the scope of an FDTD simulation.

Quantum efficiency. Calculations involving the QE are within the scope of an FDTD simulation. See the below for the definition of QE.

"0"

The corresponding free-space quantity.

Fluorescence enhancement. Calculations involving the fluorescence enhancement are within the scope of an FDTD simulation.

Excitation rate enhancement of the emitter (fluorophore). The emitter is typically excited optically. Calculations involving the excitation enhancement are within the scope of an FDTD simulation.

QE enhancement. Typically, the free-space QE is 1. Calculations involving the QE enhancement are within the scope of an FDTD simulation.

 

 

Part 1 : The excitation enhancement (field enhancement)

For an isotropic ensemble of fluorophores, it can be shown that

 

We can use a Mie scattering setup and record at the position of the fluorophore. Only one simulation is needed here to calculate the field enhancement since is 1, by default.

 

Part 2 : The fluorescence enhancement (decay rates and QE)

The analysis of the FDTD results rely on the fact that, for an atomic dipole transition that can only occur through radiation, the quantum mechanical decay rate in an inhomogeneous environment can be related to the classical power radiated by the dipole in the same environment [1]. Specifically, we have the relationship

 

 

where and are the decay rate and radiated power in an inhomogeneous environment (ie, a nanoparticle is near the dipole source), and are the decay rate and power radiated in a homogeneous environment (ie, free-space).

 

This table lists the relationship between the corresponding decay rate and radiated power in FDTD based fluorescence enhancement simulations:

Decay rate

Power in electromagnetic process

(calculated by FDTD)

Description

The decay rate of excitations to photons that can leave the system by radiation. This is an EM process and is typically the decay rate of photons that can be collected in the far field experimentally. Calculations involving the radiated power are within the scope of an FDTD simulation. This can be calculated by using a transmission box around the entire system.

The decay rate of excitations to photons that are absorbed or otherwise lost in the system (eg, photons absorbed by the nanoparticle). This is an EM process and is typically the decay rate of photons that cannot be collected in the far field experimentally. Calculations involving the power loss due to absorption are within the scope of an FDTD simulation.

The total electromangetic decay rate. This can be represented by the total power injected by a dipole source. Calculations involving the total radiated power are within the scope of an FDTD simulation. This can be either calculated by using the dipolepower command or a small transmission box around the dipole source.

N/A

The decay rate of excitations to non-radiative processes. Excitations that decay into phonons (heat) are included in this category. This is not an EM process. Calculations involving the non-radiative decay rate of an emitter are beyond the scope of an FDTD simulation. If you have the information about this quantity, it might be possible to include that in the calculations. Typically, we just assume = 0 in an FDTD simulation.

 

The QE gives the efficiency of the fluorescence process - the ratio of the radiated power measurable in the far field to the total power injected by the fluorophore, defined as,

 

 

We can then use the QE from here, with the results from part 1, for the fluorescence enhancement calculation (ie, ). Note: The free-space QE is typically 1 since the is no NP to absorb light.

 

 

 

Simulation tips

In both parts, mesh can be crucial to the simulation results.

oThe field enhancement can depend on the size of the mesh used. If user is trying to find the max. from a profile monitor, a smaller mesh size can help resolve the peak value.

oFor fluorescence enhancement, the theoretical values of QE are calculated for a dipole distance of d-dx and d+dx. The FDTD result should lie between these two theoretical calculations, since the position of the dipole (and the sphere radius) can only be accurately defined to within about dx.

Optimization

oIt is reasonable to optimize the system (NP size, material, shape, NP-dipole distance, etc) such that the fluorescence emission enhancement is maximized. To do that, it will involve running some distinct simulations and also transferring data between simulation files during the optimization process. It might be a difficult task for the built-in optimization tool. In this case, there could be some advantage to use the a 3rd party driven optimization workflow, such as MATLAB.

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