Spatial dispersion of Grating

Spatial dispersion of a single grating
Calculator of spatial dispersion for single grating

Parameter calc.

Program info

Main formulas

References

1. Laser wavelength: nm
2. Grating incident angle: °
3. Grating groove density: lines/mm
4. Grating width: mm
5. Diffraction order:
6. Focusing lens focal length: mm

This program is used to calculate the spatial dispersion of a laser after passing through a single grating.
Function: calculate diffraction angle, angular resolving power, linear resolving power, spectral resolving power, and the resolved linewidth (FWHM) of a single grating.

1. Grating diffraction angle:

$$\theta = \sin^{-1}(\frac{m\lambda}{d}-\sin\gamma)$$

2. Angular resolving power of a grating:

$${D_{\theta}} =\frac{\delta\theta}{\delta\lambda}=\frac{m}{dcos\theta}$$

3. Linear resolving power of a grating:

$${D_{l}} =f{D_{\theta}}$$

4. Spectral resolving power of a grating:

$$A= \frac{ \lambda}{\delta\lambda}=mN=\frac{ L}{\lambda}(sin\gamma+sin\theta)$$

5. Resolved linewidth (FWHM):

$$\delta\lambda= \frac{\lambda}{A}$$

where γ is the incident angle, θ is the diffraction angle, m is the diffraction order, λ is the wavelength, d is the grating period, f is the focal length of the focusing lens, L is the grating width, and N=L/d is the number of grooves.

[01] Cai Lüzhong et al., Optics, pp. 230-231.

Spatial Dispersion of a Single Grating