Gratings with grooves that have a sawtooth profile (blazed gratings) exhibit a high diffraction efficiency for certain orders and wavelengths.

In Fig. 5, light is directed at a reflective grating at angle *α* and light of wavelength λ is diffracted at angle *β*. Here, *α* and *β* are the angles made with the normal to the grating and counterclockwise direction is taken as positive. Grating equation (2)' can be updated as the following relationship:

Fig.5 Reflective Grating

When the relationship between the incident light and the *m*th-order diffracted light describes mirror reflection with respect to the facet surface of the grooves, most of the energy is concentrated into the mth-order diffracted light. The facet angle of the grooves at this point is called the **"blaze angle"** and, represented by *θ*_{B}, satisfies the following:

Fig. 6 Littrow Mounting

The corresponding wavelength is called the **"blaze wavelength"** and is represented by λ_{B}. Combining equations (8) and (9) gives the following:

It can be seen from this equation that the blaze wavelength varies with the blaze angle *θ*_{B} and the incident angle *α* (i.e., the usage method). In gerneral, the wavelength (λ_{B(Litt)}) where first-order diffracted light returns along the same path as the incident light is used to represent the blaze characteristics of gratings. In this case, *α* = *β* = *θ*_{B} then equation (8) gives the following:

This is called the **"Littrow mounting"**. In our catalogs, the blaze wavelengths given for plane gratings are the blaze wavelengths for this configuration. Equation (12) is Substituted equation (11) for equation (10) and applied *m* to both sides.

The relationship between the blaze wavelength λ_{B} for other configurations and the blaze wavelength λ_{B(Litt)}used in the catalog is given by the following:

It can be seen from this equation that, when not using the Littrow configuration, the blaze wavelength λ_{B} is shorter than λ_{B(Litt)}.

For incident angle *α*, the relationship between λ_{B(Litt)} and λ_{B} is given by the following:

For example, for a groove density *N* of 600 grooves/mm and an incident angle α of 60°, in order to obtain first-order light with a wavelength of 300 nm, substiture λ_{B} = 300 nm in equation (13) to obtain λ_{B(Litt)} = 484 nm. In this case, then, select a grating for which λ_{B(Litt)} = 500 nm from the catalog.

The blaze wavelengths given for concave gratings in catalog are the blaze wavelengths for the configuration **(mounting)** in the optical system used.

The arrows on the gratings indicate the blaze direction and the relationship between the groove profile and this direction is shown in Fig. 6.

- SHIMADZU DIFFRACTION GRATINGS
- 01. Introduction to Diffraction Gratings
- 02. What are Diffraction Gratings
- 03. The Grating Equations
- 04. Dispersion
- 05. Grating Resolution
- 06. Free Spectral Range
**07. Blaze Wavelength**- 08. Diffraction Efficiency & Relationship between Diffraction Efficiency and Polarization
- 09. Anomalies
- 10. Profile of Grating Grooves
- 11. Toroidal Diffraction Gratings
- 12. Replicas
- 13. Coatings
- 14. Transmission Gratings
- 15. Choice of a Grating
- 16. Handling of Gratings