Optical Phase Shift on Reflection Calculator

Formula Used

The calculator uses Fresnel reflection coefficients for one smooth interface.

s polarization: r_s = (N₁ cos θ_i − N₂ cos θ_t) / (N₁ cos θ_i + N₂ cos θ_t)

p polarization: r_p = (N₂ cos θ_i − N₁ cos θ_t) / (N₂ cos θ_i + N₁ cos θ_t)

Snell relation: N₁ sin θ_i = N₂ sin θ_t

Phase shift: φ = atan2(Im(r), Re(r))

Reflectance: R = |r|²

The complex index is entered as N₂ = n₂ + i k₂.

How to Use This Calculator

1. Enter the incident medium refractive index.
2. Enter the reflecting medium refractive index.
3. Add extinction coefficient for absorbing materials.
4. Enter the incidence angle in degrees.
5. Enter wavelength for equivalent path conversion.
6. Select s, p, or unpolarized mode.
7. Press Calculate to view the result.
8. Use CSV or PDF download for records.

Example Data Table

Optical Phase Shift on Reflection Guide

What the calculator does

An optical wave can change phase when it reflects. The change depends on refractive index, extinction coefficient, angle, and polarization. This calculator estimates that phase using Fresnel reflection coefficients. It also reports reflectance, coefficient magnitude, transmitted angle status, and equivalent optical path.

Why phase matters

Phase is important in mirrors, thin films, interferometers, coatings, sensors, and laser cavities. A half wave shift can turn constructive interference into destructive interference. A small phase error can also move a fringe, reduce contrast, or detune a cavity.

Interface behavior

At normal incidence between clear materials, a reflection from a higher index medium gives a phase shift near 180 degrees. A reflection from a lower index medium gives a phase shift near zero degrees. Oblique incidence is richer. The s and p polarization coefficients can have different signs, magnitudes, and phases.

Absorbing materials

Metals and absorbing films use a complex refractive index. The extinction coefficient creates a complex reflection coefficient. The phase is then not limited to zero or 180 degrees. This is useful for coated mirrors, semiconductor surfaces, plasmonic layers, and polished metal samples.

Total internal reflection

When light travels from high index material toward lower index material, high angles can exceed the critical angle. The reflected intensity becomes almost total for a clear boundary. The reflected field still gains a polarization dependent phase. That phase is used in prisms, phase retarders, and fiber optics.

Practical use

Enter values from trusted optical data. Use the same wavelength as the material index source. Choose s or p polarization for angled beams. Use unpolarized mode for average reflectance only. Read phase with its sign and normalized value. Export results when documenting a design, lab measurement, or coating comparison.

Accuracy notes

The model assumes a flat, smooth, single interface. It does not include multilayer interference, surface roughness, scattering, magnetic media, or anisotropic crystals. For precision coatings, compare these results with a transfer matrix model. For a first estimate, the Fresnel phase gives a strong and reliable starting point.

For best workflow, test simple air glass cases first. Then add angle, absorption, and polarization changes. This makes unusual phase jumps easier to notice during careful optical checks.

FAQs

What is optical phase shift on reflection?

It is the phase change gained by a light wave when it reflects from an interface. It depends on material index, angle, absorption, and polarization.

Why is the phase often 180 degrees?

At normal incidence, reflection from a higher refractive index medium gives a negative electric field reflection coefficient. That negative sign represents a 180 degree phase shift.

Can phase shift be zero?

Yes. Reflection from a lower index medium at normal incidence gives a positive reflection coefficient. The phase shift is then near zero degrees.

Why do s and p results differ?

At oblique incidence, electric field orientation changes boundary behavior. The s and p Fresnel coefficients can have different magnitudes and phases.

What does k2 mean?

k2 is the extinction coefficient of the reflecting medium. It models absorption. Metals and lossy films often need this value.

What happens at total internal reflection?

Reflectance becomes very high for a clear boundary. The reflected wave still receives a phase shift, which differs for s and p polarization.

Is unpolarized phase a single number?

No. Unpolarized light is treated as mixed s and p components. The calculator gives average reflectance and still lists both phase values.

Can this model handle coatings?

It handles one interface only. Multilayer coatings need transfer matrix methods because internal reflections create additional phase and interference effects.