# The Blaze Arrow

Many diffraction gratings are marked with an arrow to aid in their placement in optical systems. This Technical Note explains the meaning behind the arrow.

### Blazed Gratings

A diffraction grating whose surface-relief groove profile is asymmetric (see Figures 1a and 1b) will exhibit efficiency characteristics that depend on the orientation of the grating in the optical system, and such gratings are therefore called blazed gratings. When a blazed grating is oriented such that its efficiency in use is high, it is said to be used "on blaze". The proper orientation of a blazed grating is indicated by its blaze arrow (Figure 1c).

Figure 1. Grating profiles: (a) symmetric triangular and sinusoidal, (b) asymmetric triangular; (c) shows the blaze arrow corresponding to (b).

### Orientation of the Blaze Arrow

There are two primary definitions of the direction of the blaze arrow.

1. The blaze arrow points from the grating normal to the bisector between the incident and diffracted beams.
2. The blaze arrow points from the peak of the (asymmetric) groove to the trough of the groove.

The first definition is shown in Figure 2, where a grating is used to diffract light from point A to point B. For the light diffracted to point B to be blazed, the blaze angle must point as shown. If the blaze arrow points in the other direction, light will still be diffracted to B but with lower efficiency (intensity).

Figure 2. The blaze arrow points from the grating normal to the bisector between the incident and diffracted beams. (a) Light from A is incident on a grating at an angle α to the grating normal GN, and is diffracted by the grating toward point B and an angle β to GN. The grating normal GN is the line perpendicular to the grating surface. The line FN is the bisector of the angle between the incident and diffracted directions. In this example, α < 0 and β > 0 since they lie on opposite sides of GN. (b) The bisector is called FN since it is the facet normal for the blaze condition.

The second definition can be understood quite simply by flipping an asymmetric triangular groove profile upside down (i.e., about the horizontal) to form a series of "arrowheads" (Figure 3). These arrowheads point in the same direction as the blaze arrow.

Figure 3. Inverting the groove profile forms arrowheads that indicate the direction of the blaze arrow.

Both of these definitions derive from the same observation, namely that an asymmetric triangular-groove grating is used at the blaze condition when the incident and diffracted beams are oriented such that they satisfy the mirror reflection condition at the primary facet. Looking at Figures 2a and 2b, it is apparent that the angle that the incident angle makes with the facet normal FN is equal and opposite to the angle made by the diffracted light and FN.

### Determination of the Blaze Angle

Since the blaze condition is the configuration in which the incident and diffracted beams are equal (when measured from the facet normal) yet lie on opposite sides of the facet normal, the blaze angle is simply the angle between the facet normal and the grating normal (Figure 4).

Figure 4. The blaze angle θ and its relationship to the grating normal GN and facet normal FN.

For a given diffraction order m, wavelength λ to be blazed, and incidence and diffraction angles α and β (measured from the grating normal – see Figure 2a), the grating equation is

mλ = d(sinα + sinβ)

and the blaze angle θ is given by

θ = (α + β) / 2

where in each equation α and β are signed angles (that is, one is negative if they lie on opposite sides of the grating normal). Equations (1) and (2) can also be used to determine the blaze condition (i.e., the values of α and β) for a particular wavelength λ if the blaze angle θ of the grating is known.