Calculator Inputs
Example Data Table
| Case | Radius | Gap | Wavelength | Medium index | Polarization |
|---|---|---|---|---|---|
| Gold sensing dimer | 40 nm | 5 nm | 633 nm | 1.33 | Longitudinal |
| Silver narrow gap | 35 nm | 3 nm | 532 nm | 1.00 | Longitudinal |
| Transverse check | 50 nm | 8 nm | 785 nm | 1.50 | Transverse |
Formula Used
The calculator uses a coupled dipole approximation for two equal spherical particles.
Medium permittivity: εm = n²
Complex contrast: C = (εp − εm) / (εp + 2εm)
Center separation: d = 2a + g
Coupled denominator: D = 1 − K a³C / d³
K is 2 for longitudinal polarization. K is −1 for transverse polarization.
Gap field ratio: Egap / E0 = |1 + S a³C / (D x³)|
x equals d / 2. S is 4 for longitudinal mode. S is −2 for transverse mode.
Intensity enhancement: Ienh = |Egap / E0|²
This model is an estimator. Use full wave simulation for final device design.
How to Use This Calculator
- Enter the particle radius in nanometers.
- Enter the physical gap between the two particles.
- Add wavelength and incident electric field amplitude.
- Select a material preset or enter complex permittivity.
- Enter the surrounding medium refractive index.
- Choose longitudinal or transverse polarization.
- Use the correction factor for calibrated adjustments.
- Press Calculate Field and review the result above the form.
- Download CSV or PDF for reporting.
About nanoparticle dimer fields
A nanoparticle dimer is a pair of nearby particles. Light drives charges on both particles. The charges interact across the narrow gap. This interaction can create a strong local field. The strongest region is often called a hot spot. Designers use this effect in sensing, spectroscopy, photothermal work, and nano antenna studies.
What this estimator does
This calculator uses a coupled dipole model. It treats each particle as a small polarizable sphere. The method is useful when particle radius is much smaller than wavelength. It also works best when the gap is not atomic scale. The result is an estimate, not a full electromagnetic simulation. It gives fast guidance before deeper modeling.
Key inputs
Radius controls polarizability. A larger radius usually gives stronger coupling. Gap distance controls the hot spot. Small gaps raise field enhancement quickly. Wavelength and material permittivity set the optical response. The medium index changes the surrounding dielectric constant. Polarization decides whether the dipoles add through the gap or oppose across it.
Reading the output
The field enhancement is the ratio of gap field to incident field. The intensity enhancement is its square. A high coupling parameter means the particles strongly influence each other. A low denominator magnitude signals a possible dimer resonance. The surface charge proxy helps compare cases, but it has arbitrary units.
Practical limits
Real dimers may have faceted shapes, substrate effects, oxide layers, and nonlocal behavior. Quantum tunneling can reduce enhancement in sub nanometer gaps. Heating and damage may also change material values. Use the correction factor when you have calibration data from measurement or simulation. Keep inputs consistent and compare trends carefully.
Useful workflow
Start with measured particle size and gap. Choose a material preset or enter complex permittivity. Run the longitudinal case first. Then compare transverse polarization. Sweep the gap to see sensitivity. Export the table for records. Use the result to choose cases for detailed finite element, FDTD, or boundary element analysis.
Why estimates still help
Early estimates save time. They reveal unsafe field levels, weak designs, and sensitive dimensions. They also expose bad inputs before simulation begins. Document each assumption. Material data can vary by source, film quality, temperature, and particle fabrication method during testing.
FAQs
What is a nanoparticle dimer?
It is a pair of nanoparticles placed close together. Their optical dipoles interact through the gap. This interaction can create a strong local electric field.
What does field enhancement mean?
It is the gap field divided by the incoming field. A value of 20 means the local field estimate is twenty times stronger than the incident field.
Why does the gap matter so much?
The near field changes quickly with distance. Smaller gaps usually increase coupling and hot spot strength. Very tiny gaps may need quantum corrections.
Which polarization should I choose?
Use longitudinal when the electric field points along the dimer axis. Use transverse when it points across the dimer axis.
Can this replace electromagnetic simulation?
No. It is a fast estimator. Use FDTD, FEM, or BEM simulation for final designs, complex shapes, substrates, and very small gaps.
What is complex permittivity?
It describes optical material response. The real part controls storage and resonance. The imaginary part represents loss and absorption.
What is the correction factor?
It scales the estimated gap contribution. Use it when you have calibration data from experiments, trusted simulations, or known geometry corrections.
Why can transverse enhancement be lower?
In transverse mode, dipole fields tend to oppose the gap field. Longitudinal mode usually concentrates charge directly across the gap.