Bragg Wavelength Shift Calculator

For a fiber Bragg grating, the Bragg wavelength responds to strain and temperature. A widely used linear model is:

• λ₀ is the initial Bragg wavelength.
• ε is the axial strain (dimensionless).
• pe is the effective photoelastic coefficient.
• α is the thermal expansion coefficient (1/°C).
• ξ is the thermo-optic term (1/°C).
• ΔT is the temperature change in °C.

1. Select a calculation mode (predict, solve strain, or solve temperature).
2. Enter the initial Bragg wavelength and choose its unit.
3. Provide strain and/or measured shift, depending on the mode.
4. Enter temperature change and coefficients for your fiber and packaging.
5. Click Calculate to show results above the form.
6. Use Download CSV or Download PDF for reporting.

These examples use common silica coefficients (pe = 0.22, α = 0.55×10⁻⁶/°C, ξ = 8.6×10⁻⁶/°C). Values are illustrative.

1. Bragg wavelength shift in fiber gratings

Fiber Bragg gratings (FBGs) reflect a narrow spectral line at the Bragg wavelength. When the fiber is strained or heated, the grating period and effective refractive index change. The reflected peak shifts accordingly, allowing precise conversion of spectral data into mechanical strain or temperature change.

2. Physical meaning of the linear model

This calculator applies the common linear relation Δλ/λ₀ = (1 − pe)·ε + (α + ξ)·ΔT. The first term captures the photoelastic response to axial strain. The second term captures thermal expansion and the thermo‑optic contribution. For many measurement ranges, this approximation is accurate and easy to calibrate.

3. Strain sensitivity with typical silica coefficients

Using the default values λ₀ = 1550 nm and pe = 0.22 gives (1 − pe) = 0.78. The strain sensitivity becomes λ₀(1 − pe) = 1209 nm per unit strain, which equals about 1.209 pm per microstrain. For 500 µε at ΔT = 0, the expected shift is roughly 605 pm.

4. Temperature sensitivity and thermal drift

The temperature term uses (α + ξ). With α = 0.55×10⁻⁶/°C and ξ = 8.6×10⁻⁶/°C, the sum is 9.15×10⁻⁶/°C. At λ₀ = 1550 nm, this corresponds to about 14.18 pm/°C. A 25 °C increase can produce a shift near 355 pm, even with zero strain.

5. Choosing pe, α, and ξ for your setup

Coefficient selection matters because packaging, coatings, and host materials can change the effective response. Silica fibers often use pe around 0.20–0.23, but bonded sensors may show different apparent strain transfer. Thermal expansion depends on the grating region and mounting. If you have calibration data, enter your measured coefficients for best accuracy.

6. Using inverse modes for calibration

In addition to forward prediction, this tool can solve unknown strain from measured Δλ and known ΔT, or solve ΔT from measured Δλ and known strain. These inverse modes help during setup, when you validate sensitivity against a reference gauge or temperature probe. Keep units consistent and use signed values to represent direction and cooling.

7. Units, reporting, and reproducible results

Internally, the calculator converts wavelengths to nanometers for numerical stability, then presents results in your selected output units. The results table includes Δλ, λ₀, shifted wavelength, and the fractional shift. The CSV and PDF exports capture the same table, which is useful for lab notes, quality records, and sharing results with teammates.

8. Interpreting uncertainty and instrument resolution

Uncertainty depends on the interrogator resolution, peak fitting, and sensor mounting. With the default sensitivity near 1.209 pm/µε, a 1 pm peak uncertainty corresponds to about 0.83 µε. With about 14.18 pm/°C, a 1 pm uncertainty corresponds to roughly 0.07 °C. Repeat measurements and temperature compensation reduce drift in long tests.

1) What does a positive Δλ mean?

A positive shift means the reflected peak moved to a longer wavelength. This commonly happens with tensile strain or heating, depending on your coefficients. A negative shift indicates compression or cooling, assuming the same sign conventions.

2) Why does the calculator use both α and ξ?

α represents thermal expansion of the grating period, while ξ represents the refractive index change with temperature. Both effects move the Bragg wavelength, so the model uses (α + ξ) to combine them in a single thermal term.

3) Can I solve strain and temperature at the same time?

Not from one grating and one measured shift. You need additional information, such as a second grating with different thermal response, a reference temperature sensor, or an isolated strain gauge. Then you can separate the two contributions.

4) What if my sensor is bonded to metal or composite?

Bonding can change the effective strain transfer and thermal expansion seen by the grating. Use calibration data from your actual mounting method when possible. If not available, treat results as estimates and validate against a reference measurement.

5) Which units should I use for Δλ?

Picometers are common because many FBG shifts are in the tens to hundreds of pm. Nanometers are convenient for larger shifts or broader scanning instruments. The calculator converts units automatically, so choose whatever matches your instrument readout.

6) Why is pe close to 0.22 by default?

Many silica fibers use an effective photoelastic coefficient near 0.22 in simplified FBG sensing models. Your exact value can vary with fiber type and wavelength. If you have a measured coefficient, enter it to refine the strain response.

7) How do I reduce temperature cross-sensitivity?

Use temperature compensation. Common approaches include a second, strain-isolated reference grating, co-located temperature sensing, or packaging that reduces thermal transfer. In analysis, solve strain using measured ΔT, or solve ΔT using measured strain, as appropriate.