Mie Scattering Electric Field Calculator

Calculator

Vacuum wavelength

Particle radius

Medium refractive index

Particle index real part

Particle absorption index

Detector distance

Incident electric field

V/m

Scattering angle

deg

Analyzer angle

deg

Series terms

Use 0 for automatic order selection.

Particle count

Coherence factor

Use 0 for random phases and 1 for coherent addition.

Reported field basis

Example Data Table

Case	Wavelength	Radius	Particle index	Angle	Use case
Fine aerosol analog	532 nm	120 nm	1.55 + 0.01i	90°	Side scatter estimate
Small dust sphere	650 nm	250 nm	1.48 + 0.00i	45°	Forward scatter check
Absorbing pigment	405 nm	80 nm	1.70 + 0.08i	135°	Back scatter comparison

Formula Used

The size parameter is:

x = 2π n_ma / λ₀

The medium wave number is:

k = 2π n_m / λ₀

The relative complex index is:

m = (n_p + iκ_p) / n_m

The Mie coefficients are evaluated with Riccati-Bessel functions:

a_n = [mψ_n(mx)ψ′_n(x) - ψ_n(x)ψ′_n(mx)] / [mψ_n(mx)ξ′_n(x) - ξ_n(x)ψ′_n(mx)]

b_n = [ψ_n(mx)ψ′_n(x) - mψ_n(x)ψ′_n(mx)] / [ψ_n(mx)ξ′_n(x) - mξ_n(x)ψ′_n(mx)]

The amplitude functions are:

S₁ = Σ [(2n + 1) / n(n + 1)] [a_nπ_n + b_nτ_n]

S₂ = Σ [(2n + 1) / n(n + 1)] [a_nτ_n + b_nπ_n]

The far-field scattered electric amplitude is estimated as:

|E_s| = |E₀S| / (kr)

The ensemble field uses:

E_ensemble = E_single √[N(1 - c) + N²c]

How To Use This Calculator

Enter the vacuum wavelength in nanometers.
Enter the spherical particle radius in nanometers.
Add the medium refractive index.
Enter the particle real index and absorption index.
Set detector distance and incident electric field.
Choose the scattering angle and analyzer angle.
Use automatic terms first, then refine if needed.
Press Calculate Field to view results above the form.
Use CSV or PDF buttons to save the same calculation.

Understanding The Calculator

Mie theory predicts how a spherical particle scatters an incoming electromagnetic wave. This calculator uses that model for a single sphere. It estimates the far-field electric amplitude at a chosen angle. The tool can support optical work on dust, mist, litter aerosols, pigments, and small test beads. It appears in Cat Calculators because pet spaces often involve fine airborne particles, but the math is general.

Why Mie Theory Matters

Rayleigh formulas work only when particles are much smaller than the wavelength. Many real particles are not that small. Mie theory handles small, comparable, and larger spheres with one consistent series. It uses the particle radius, wavelength, medium index, and complex particle index. The imaginary part represents absorption. A higher value can reduce scattering and increase heat loss.

What The Result Means

The calculator reports perpendicular and parallel scattered electric field components. It also gives an unpolarized field estimate. Values are far-field amplitudes in volts per meter. They depend strongly on angle, radius, wavelength, and detector distance. The phase term is not shown as a plotted wave, but the amplitude factor includes distance spreading.

Advanced Inputs

The order limit controls how many Mie terms are summed. Automatic mode chooses a practical estimate from the size parameter. More terms may improve large-particle accuracy. Very high orders can increase runtime. The particle count and coherence factor estimate an ensemble field. Random particles add mainly by root-sum power. Fully coherent particles add as a field.

Using Results Carefully

This tool assumes smooth homogeneous spheres. Real cat litter dust, dander, droplets, and fibers are irregular. Their orientation, shape, and roughness can change measurements. Treat outputs as modeling estimates, not direct safety limits. Use controlled experiments for final decisions. Check units before every run. Keep wavelength and radius in nanometers. Use meters for detector distance. Compare several angles for a better scattering picture.

Practical Limits

Numerical results can become sensitive when absorption is extreme or the size parameter is very large. For stable checks, start with automatic terms. Then raise the order slowly and compare outputs. If values stop changing, the series is likely stable. Document every input, because small unit changes can shift the electric field strongly during detailed optical review later.

FAQs

What does this calculator estimate?

It estimates far-field scattered electric field amplitudes from a spherical particle using Mie theory. It also reports scattering, extinction, absorption efficiencies, and cross sections.

Why is this in Cat Calculators?

It can model optical scattering from fine particles found in pet spaces, such as litter dust or mist analogs. The calculation itself is general physics.

What is the size parameter?

The size parameter compares particle radius with wavelength inside the medium. It controls how many Mie terms are needed and how complex the scattering pattern becomes.

What does the absorption index mean?

It is the imaginary part of the particle refractive index. Larger values represent stronger absorption. This can change scattering amplitude and absorption efficiency.

Should I use automatic series terms?

Yes. Start with automatic terms. Then raise the term count if the particle is large or if you want to check convergence more carefully.

What is the analyzer angle?

It mixes the perpendicular and parallel amplitude functions into one reported field. Use it when a detector or polarizer has a chosen orientation.

Is this a safety calculator?

No. It is an optical modeling calculator. It does not determine health risk, exposure limits, or veterinary safety for cats or people.

Why can results change sharply?

Mie scattering has resonances and angular structure. Small changes in radius, wavelength, index, or angle can produce large changes in calculated field amplitude.