Understanding Diffraction Gratings: Optimal Blazing Angle and Wavelength

[Niles]

Hi

In lab classes today I worked with diffraction gratings, but there is one thing I can't quite seem to understand. If we deal with ruled diffraction gratings, then they are blazed at angle such that the first order is reflected back at the same angle as the incident angle with a specific wavelength, i.e. from the diffraction equation one gets

$$\lambda = \frac{2}{n}\sin \alpha$$

Here n is the grooves/mm. When I look at a grating at a manufacturer of optical components, I see that some grating is optimized for (actual numbers!) 400nm and is blazed at 13.0155556 degrees. This gives me the wavelength 375.4nm when there are 1200 grooves/mm.

Why can't they blaze the grating at an angle such that λ gives 400nm exactly? (By the way, this is not homework of any kind!)Niles.

 

[Andy Resnick]

The Richardson Grating Lab has a free handbook all about diffraction gratings, and is well worth the time to read.

The blaze angle is the angle between the facet normal and the grating normal, and maximum grating efficiency is achieved when the blaze angle is set such that the specular reflection angle is equal to the diffraction angle- the diffracted energy is concentrated into one diffraction order, and the gratings appear to 'light up' (or 'blaze') when viewed at that angle.

Selecting a blaze angle is not simply geometry: because the rulings are straight lines, polarization effects must also be considered. There are rough classes of blaze angles (Loewen et. al., Appl. Opt. 16 2711-2721 (1977)), and 13 degrees corresponds to a 'medium blaze angle'. For these, S-polarized light diffracts with a very high efficiency, but P-polarized does not. In addition, there is a strong anomaly (very low efficiency) at l/d = 2/3 (the ratio of wavelength to groove spacing).

Also to be considered is what diffraction order will be used- low blaze angles generally use the first order, while high blaze angles use second order or higher. Another consideration is if the grating is a transmission or reflection grating: reflection gratings, being metal, have a finite conductivity and this also affects the diffraction efficiency at visible wavelengths.

That's for ruled gratings: replicated gratings and holographic gratings do not have the same diffraction efficiency due to the gross change in groove shape.

The bottom line is the blaze angle is controlled to optimize the diffraction efficiency, not 'the' wavelength.

 

[Niles]

Thanks! I'll check out the handbook + the reference.

So this means that when I turn a blazed grating away from the Littrow mounting, I am basically changing the peak value of its diffraction efficiency curve. According to the handbook, it will always become smaller than the Littrow mounting blaze wavelength (http://gratings.newport.com/library/technotes/technote11.asp). But that explanation contradicts the geometric-optics interpretation of a grating as seen in the handbook, e.g.: http://gratings.newport.com/library/technotes/technote1.asp (figure 2) in the sense that I can go to both longer/shorter wavelengths by turning the grating.

What is wrong here?

 

[Andy Resnick]

I don't understand your question...

 

[Niles]

A reflection grating diffracts light such that a longer wavelength has a larger diffraction angle as seen e.g. here (figure 1): http://www.kosi.com/Holographic_Gratings/vph_ht_overview.php. This principle we can use to e.g. tune a laser, as seen here (figure 2): http://gratings.newport.com/library/technotes/technote1.asp. So depending on which direction I turn the grating, I can reflect shorter/longer wavelengths.

Now I look specifically at a blazed grating. From the explanation in the Richardson handbook, when I have a blazed grating in the Littrow mounting (incoming beam and outgoing beam in same direction), the corresponding wavelength λ_{B, Littrow} is the maximum of the efficiency-curve. They derive that (http://gratings.newport.com/library/technotes/technote11.asp, equation (6)) when I turn the grating away from the Littrow mounting, then the blazing wavelength changes such that λ_B = λ_{B, Littrow}cos(α-θ_blaze). Here α is the angle of the incoming beam wrt. the grating surface normal. So in other words, when I turn a blazed grating away from the normal, the peak of the efficiency curve is moved to shorter wavelengths (i.e. it reflects shorter wavelengths more effieciently).

These two explanations are not identical. This is my question from before.

Best (and merry Christmas!),
Niles.