Lorentz Dielectric Function Calculator

Model complex permittivity from resonance data in just seconds. Compare loss, index, reflectance, and dispersion. Download clear results for reports, labs, or design work.

Calculator Inputs

Use the selected unit below.
Same unit is used for resonance and damping.
Background permittivity away from resonance.
Controls display precision only.

Lorentz Oscillators

Example Data Table

Use these sample values to test the calculator.

Input Example Value Meaning
Analysis frequency 500 THz Frequency where ε is evaluated.
ε∞ 2.25 Background electronic contribution.
Oscillator 1 S = 1.00, ω₀ = 600, γ = 15 Main resonance contribution.
Oscillator 2 S = 0.15, ω₀ = 900, γ = 30 Secondary absorption band.
Frequency unit THz Used by all frequency fields.

Formula Used

The calculator uses the multi-oscillator Lorentz dielectric model:

ε(ω) = ε∞ + Σ [ Sⱼω₀ⱼ² / (ω₀ⱼ² - ω² - iγⱼω) ]

Here, ε∞ is high frequency permittivity. Sⱼ is oscillator strength. ω₀ⱼ is resonance angular frequency. γⱼ is damping. ω is the selected analysis angular frequency.

The complex refractive index is found from N = n + ik = √ε. Normal incidence reflectance is calculated with R = |(N - 1) / (N + 1)|². Absorption uses α = 4πk / λ.

How to Use This Calculator

  1. Enter the analysis frequency where the material response is needed.
  2. Select a unit for all frequency, resonance, and damping values.
  3. Enter the high frequency permittivity value.
  4. Add one or more Lorentz oscillators.
  5. Use strength for resonance weight, and damping for linewidth.
  6. Click the calculate button to view complex results above the form.
  7. Download the result table as CSV or PDF for reports.

Understanding the Lorentz Dielectric Model

What the Model Describes

The Lorentz dielectric model describes how a material responds to an oscillating electric field. It treats bound charges as damped oscillators. Each oscillator has a natural resonance. When light approaches that resonance, the material response changes strongly. This change affects permittivity, refraction, reflection, and absorption.

Why Complex Permittivity Matters

Complex permittivity has two useful parts. The real part controls stored electric energy. It also shapes the refractive index. The imaginary part describes loss. It rises when damping or absorption becomes important. A small imaginary part usually means a clearer material. A large value means stronger energy dissipation.

Using Oscillator Parameters

Oscillator strength controls the size of each spectral feature. Resonance frequency controls where that feature appears. Damping controls the width and smoothness of the peak. Low damping gives a sharp response. High damping gives a broad response. Multiple oscillators can represent several absorption bands. This is useful for glasses, crystals, polymers, coatings, and semiconductors.

Interpreting the Results

The calculator returns ε′ and ε″ directly. It also estimates the refractive index and extinction coefficient. These values help compare optical behavior at one selected frequency. Reflectance shows how much light reflects at a flat air interface. Absorption coefficient estimates how quickly light fades inside the material. Skin depth gives the related penetration length. These outputs are helpful for optical design. They also support classroom analysis and lab reports.

Practical Notes

Keep all oscillator values in the same selected unit. Use measured values when available. Use small trial changes to study sensitivity. Near resonance, results may change quickly. Very low damping can create extreme peaks. Always compare model output with experimental data. The model is powerful, but it is still an approximation. It works best when the chosen oscillators match real material behavior.

FAQs

What is the Lorentz dielectric function?

It is a complex material response model. It describes how bound charges react to an alternating electric field near resonance frequencies.

What does ε∞ mean?

It is the high frequency background permittivity. It represents response that is not included in the listed Lorentz oscillators.

What is oscillator strength?

Oscillator strength controls how strongly a resonance contributes to permittivity. Larger values produce stronger dispersion and absorption near resonance.

What is damping in this model?

Damping controls the linewidth of the resonance. Higher damping spreads the response over a wider frequency range and increases loss.

Can I use more than one oscillator?

Yes. This calculator supports three oscillators. Multiple oscillators help represent materials with several absorption or resonance bands.

Why is the result complex?

The real part describes stored electric response. The imaginary part describes energy loss, absorption, and damping effects in the material.

What unit should I choose?

Choose the unit used by your data. The calculator applies the same unit to frequency, resonance, and damping fields.

What does reflectance show?

Reflectance estimates the light fraction reflected at normal incidence from air into the modeled material surface.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.