Fiber Bragg Grating: Reflected Wavelength & Why

A fiber Bragg grating (FBG) reflects a specific wavelength of light—called the Bragg wavelength—while transmitting all others. This wavelength is determined by the grating’s period and the effective refractive index of the fiber core, and it shifts in response to strain and temperature, which is why FBGs are used as sensors.

Formula

The Bragg wavelength is given by the simple relation:

λ_B = 2 · n_eff · Λ

• λ_B – the reflected wavelength (in nanometers, nm)
• n_eff – the effective refractive index of the fiber core (dimensionless, typically ~1.45 for silica)
• Λ – the grating period, i.e., the spacing between index variations (in nm)

This is the fundamental condition for constructive interference of light reflected from each index perturbation. Only the wavelength that satisfies this condition adds up in reflection; all other wavelengths cancel out and pass through.

Worked Example

Using the default values from the calculator:

1. Start with n_eff = 1.45 and Λ = 535 nm.
2. Multiply: 2 × 1.45 = 2.90.
3. Multiply by the period: 2.90 × 535 = 1551.5 nm.

The calculator returns 1551.5 nm, which is a typical telecom wavelength (C-band). If you change the period to 530 nm, the reflected wavelength becomes 1537 nm—showing how sensitive the Bragg wavelength is to the grating spacing.

How a Fiber Bragg Grating Works

An FBG is made by exposing the core of a single-mode optical fiber to a pattern of intense ultraviolet light, which permanently increases the refractive index in the exposed regions. The result is a periodic modulation of the core’s index—essentially a series of microscopic mirrors spaced by the grating period Λ.

When broadband light (containing many wavelengths) travels through the fiber, each index change reflects a tiny fraction of the light. For most wavelengths, these reflections are out of phase and cancel each other out. But at the Bragg wavelength, the reflections from each period are in phase and add constructively, producing a strong reflection peak. The rest of the spectrum continues through the fiber undisturbed.

This is analogous to how a diffraction grating works, but in a fiber and in reflection mode. The key difference is that the grating is written directly into the core, making it a compact, robust, and alignment-free component.

Why the Reflected Wavelength Shifts

The Bragg wavelength is not fixed—it changes when the fiber is stretched, compressed, or heated. Both strain and temperature alter the two terms in the equation:

• Strain: stretching the fiber increases the grating period Λ (geometric effect) and also changes n_eff slightly (photoelastic effect). The result is a linear shift of λ_B to longer wavelengths.
• Temperature: heating the fiber expands it (increasing Λ) and changes n_eff via the thermo-optic effect. Again, the reflected wavelength moves, typically by about 10 pm/°C at 1550 nm.

Typical sensitivity for a 1550 nm FBG is roughly 1.2 pm/με (microstrain) and 10 pm/°C. This dual sensitivity is both a blessing and a curse: it makes FBGs excellent sensors for either quantity, but if you measure strain, you must compensate for temperature, and vice versa.

How to Choose an FBG for Your Application

Selecting the right FBG involves several parameters beyond just the Bragg wavelength:

• Wavelength range: Choose a λ_B that fits your light source and detector. Common telecom wavelengths are 1310 nm and 1550 nm; shorter wavelengths (800–1060 nm) are used in some sensing applications.
• Bandwidth: The width of the reflection peak (typically 0.1–1 nm) determines how precisely you can measure wavelength shifts. Narrower is better for high-resolution sensing.
• Reflectivity: From a few percent to >99%. High reflectivity gives a stronger signal but can distort the spectrum; low reflectivity is used for multiplexing many FBGs on one fiber.
• Fiber type: Standard SMF-28 works for most cases, but photosensitive fibers (e.g., boron-germanium co-doped) allow stronger gratings with shorter exposure.
• Coating: Acrylate coatings are standard; polyimide coatings withstand higher temperatures (up to ~300°C) and are better for harsh environments.

For sensing, you also need to know the strain and temperature coefficients, which depend on the fiber and the grating design. Manufacturers usually provide these, or you can calibrate them yourself.

Common Problems and Misconceptions

One common misconception is that the FBG reflects a single, fixed wavelength. In reality, it reflects a narrow band of wavelengths—the peak is not infinitely sharp. The width depends on the grating length and index modulation depth.

Another issue is that the reflected wavelength is not perfectly stable over time. Gratings can “decay� if not properly annealed during manufacturing, causing a slow drift in λ_B. This is why high-quality FBGs are thermally stabilized.

A practical problem is cross-sensitivity: a wavelength shift could be due to strain, temperature, or both. To separate them, you need either a reference grating (isolated from strain) or a second grating with different sensitivities (e.g., in a different fiber).

Also, be aware that bending the fiber beyond its minimum radius can cause loss and distort the reflection spectrum. And if the fiber is coated with a material that absorbs moisture, the resulting swelling can shift the wavelength—this is sometimes used as a humidity sensor, but it can be an unwanted artifact.

FBG vs. Other Sensing Technologies

Compared to electrical strain gauges, FBGs have several advantages: they are immune to electromagnetic interference, can be multiplexed (many sensors on one fiber), are small and lightweight, and can operate in harsh environments (high temperature, corrosive, explosive). The main drawbacks are the cost of the interrogator (the device that reads the wavelength) and the fact that the fiber is fragile if not properly packaged.

Compared to other optical sensors like Fabry-Perot interferometers or Brillouin scattering systems, FBGs are point sensors (they measure at a specific location), whereas Brillouin systems measure along the entire fiber but with lower spatial resolution. FBGs offer a good balance of sensitivity, multiplexing capability, and cost.

Safety and Handling of FBG Fibers

Fiber Bragg gratings are made of glass, so they are brittle and can break if bent sharply or pulled hard. Always handle the fiber with care, avoid kinking, and use proper strain relief. When cleaving or splicing, wear safety glasses to protect against tiny glass shards. The UV light used to write gratings is hazardous to eyes and skin—never look directly at the beam. In operation, the light in the fiber is usually low-power, but if you are using a high-power laser, follow laser safety procedures, including avoiding direct eye exposure to the fiber end.

For temperature sensing, ensure the FBG is rated for the intended range. Standard acrylate coatings are only rated to about 85°C; polyimide goes to 300°C; specialty coatings can go higher. Exceeding the rating can damage the coating and cause the grating to fade.

Frequently Asked Questions

What is the typical reflected wavelength of an FBG?

Most commercial FBGs are written for the telecom C-band, around 1550 nm, or the O-band at 1310 nm. However, the wavelength can be anywhere from about 400 nm to 2000 nm, depending on the fiber and grating period. The calculator above lets you find the exact wavelength for any period and refractive index.

Can an FBG reflect multiple wavelengths?

Yes, if you write multiple gratings with different periods in the same fiber, each reflects its own Bragg wavelength. This is the basis of wavelength-division multiplexing in FBG sensor arrays—one fiber can carry dozens of sensors, each with a unique λ_B.

How accurate is the Bragg wavelength formula?

The formula λ_B = 2n_effΛ is exact for an ideal uniform grating. In practice, the effective index varies slightly along the grating, and the index modulation depth can cause a small shift, but the formula is accurate to better than 0.1% for most gratings.

Why does the reflected wavelength change with temperature?

Temperature affects both the physical length of the grating (thermal expansion) and the refractive index (thermo-optic effect). The index change dominates, contributing about 90% of the shift. The total temperature sensitivity is roughly 10 pm/°C at 1550 nm.

Can I use an FBG to measure strain without temperature interference?

Yes, by using a reference FBG that is isolated from strain but exposed to the same temperature. Subtract the reference wavelength shift from the sensing grating’s shift to get the strain-only component. Alternatively, use two FBGs with different sensitivities written in different fiber types.

What is the difference between a fiber Bragg grating and a long-period grating?

A fiber Bragg grating has a short period (sub-micron) and reflects light backward. A long-period grating has a period of hundreds of micrometers and couples light from the core into cladding modes, producing loss peaks in transmission rather than reflection. Long-period gratings are used for band-rejection filters and refractive index sensing.

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in n_eff | Effective refractive index | - | 1.45 | 1
in Λ | Grating period | nm | 535 | 1
out λ_B | Bragg wavelength | nm | 2 * n_eff * Λ | 2