Diffraction Grating Calculator

lines/mm
deg (°)
Integer
Diffraction Angle (θm)
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Order does not exist (Evanescent).

How it works?

The Grating Equation

A diffraction grating splits light into its constituent wavelengths (colors). The angle at which each color leaves the grating is determined by constructive interference. This behavior is governed by the universal Grating Equation:

$$ m \lambda = d (\sin \theta_m - \sin \theta_i) $$

Where:

  • \(\theta_m\) : Diffracted Angle (Output).
  • \(\theta_i\) : Incident Angle (Input).
  • \(\lambda\) : Wavelength of light.
  • \(m\) : Diffraction Order (Integer: 0, ±1, ±2...).
  • \(d\) : Grating Period (Distance between grooves, \( d = 1 / \text{density} \)).

Why calculate Diffraction Angles?

Core Applications
  • Spectroscopy: Spreading light to analyze chemical composition.
  • Laser Tuning: Selecting a specific wavelength (Littrow configuration).
  • Pulse Compression: Chirped Pulse Amplification (CPA) for ultrafast lasers.
  • Telecommunications: Wavelength filtering in WDM systems.

Dispersion and Order

Unlike a prism, which relies on refraction, a diffraction grating relies on interference. This allows for much higher dispersion (separation of colors) and is more predictable.

The "Order" (m) is crucial. m=0 is just a reflection (like a mirror). m=1 is the first dispersed spectrum. Higher orders (m=2, 3) offer more dispersion but often overlap, which is why calculating the exact angles is vital to avoid "ghosts" in your data.

1. Spectrometers (Czerny-Turner)

The heart of almost every spectrometer is a reflective grating. By rotating the grating (changing θi), different wavelengths (λ) are directed onto the detector slit. This calculator mimics that rotation math.

2. Littrow & Littman Configs

External Cavity Diode Lasers (ECDL) use a grating to tune the laser color. In the "Littrow" configuration, the light is reflected directly back to the source (θi = θm). You can solve this by setting input/output angles to match in the formula.

3. Pulse Compression

Ultrafast femtosecond lasers use pairs of gratings to stretch and compress pulses. The angle of incidence dictates the "chirp" applied to the pulse. Precision here prevents the laser from damaging its own amplifier.

4. Beam Steering

Transmissive gratings are increasingly used in LIDAR and AR/VR headsets to steer beams non-mechanically. Calculating the diffraction angle allows engineers to map the Field of View (FOV) of the device.

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