Definitive Guide to Diffraction Grating

What is a Diffraction Grating?

A diffraction grating is a passive optical component that redirects light incident upon the surface at an angle that is unique for every wavelength in a given order. This redirection (or diffraction) is a result of the phase change of the electromagnetic wave as it encounters the regular, fixed structure of the grating surface. Every wavelength undergoes a different phase shift, and as a result, diffracts at a different angle, resulting in a dispersion of broadband light.

2 Basic Types of Diffraction Gratings

Ruled, Blazed Diffraction Gratings

The master gratings are produced by forming the surface of a soft metallic coating with a diamond form tool. The resulting groove profile has a well defined and controllable groove profile that directs energy efficiently into the desired wavelength range.

Ruled blazed gratings are very efficient, and are generally the best choice for applications requiring high signal strength. Because of the mechanical nature of the mastering process however, there can be random and periodic spacing errors that could detract from the purity of the diffracted spectra.

Theoretical Profile of a Ruled Blazed Grating

blog-diffraction-grating-theoretical-profile

The calculated theoretical groove depth is given as:

h = d(cosθ)(sinθ), where:

h = Theoretical groove depth
d = Distance between grooves
θ = Blaze angle

When a master ruled grating is generated, the diamond tool does not actually remove material and cut a theoretically shaped groove. Rather, the coating is burnished by the tool. As a result, there is some displacement and deformation of the material on the short facet into the previously ruled groove every time a new groove is formed. The resulting profile will show some peak round-off, and not achieve theoretical depth. Actual groove depth is typically 90% of theoretical.

Holographic Diffraction Gratings

Holographic master gratings are produced by exposing a thin layer of photoresist to 2 intersecting coherent, monochromatic beams. The resulting interference pattern differentially exposes the photoresist. After development, the sinusoidal variation in light intensity during exposure is transformed into a physical structure of the same profile. The addition of a reflective overcoat completes the process.

Holographic master gratings generally exhibit better stray light properties than ruled master gratings. Blazing is not as easy with holographic gratings however, and with certain notable exceptions, they will not be as efficient as ruled, blazed gratings.

Most holographic grating masters are generated initially with a symmetric groove profile. It is important to note that a symmetric profile holographic diffraction grating will only have symmetry in efficiency on either side of zero order when the light is incident at 0 degrees (normal incidence). This explains why some symmetric holographic gratings can achieve greater than 50% absolute efficiency in a given order, although most do not. Special techniques can be employed to give some holographic gratings an asymmetric profile, and hence, blaze properties. These gratings combine the beneficial low stray light properties of holographic grating with the high efficiency of ruled gratings.

Blaze Angle

The grooves of a ruled grating have a saw tooth profile with one side longer than the other. The angle made by a groove’s longer side and the plane of the grating is the “blaze angle.” The blaze angle for a blazed grating is generally the biggest factor in determining where the efficiency curve peaks under a certain set of conditions.

The blaze angle has absolutely no bearing on the diffraction angle at any wavelength.

The Grating Equation

The equation that dictates the diffraction properties of a grating is given by:

nλ = d(sin i + sin i’)

n = the order of diffraction
λ = wavelength of light
d = distance between adjacent grooves
i = angle of incidence with respect to grating normal
i’ = angle of diffraction with respect to grating normal

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NOTE

  • There is no unique solution for λ, for a given set of angles. Every allowable integer value of n will provide a different wavelength.
  • The longest wavelength that a grating can diffract (the diffraction limit) is equal to 2 times the spacing. The highest angle of incidence (i) achievable is 90 degrees (sin 90 = 1). The highest angle of diffraction achievable is 90 degrees. The lowest order of diffraction is 1. Plugging these values into the grating equation yields λ = 2d. which is the diffraction wavelength limit for any grating.
  • A special case occurs when the angle of incidence i is equal to the angle of diffraction i’. This is called the Littrow condition. Under this condition (in 1st order), the grating equation reduces to λ = 2d(sin i). This is the equation used to calculate the 1st order blaze angle for a desired blaze wavelength and groove spacing.

Grating Efficiency

Absolute grating efficiency is defined as the percentage of monochromatic light diffracted in a given order compared to all of the monochromatic light incident on the grating.

Relative grating efficiency is defined as the percentage of monochromatic diffracted light in a given order compared to the reflectance of the monochromatic incident light from a mirror coated with the same material.

Because no material is 100% reflective, absolute efficiency measurements will always yield a lower numerical efficiency value than a relative efficiency measurement on the same grating. Grating efficiency for a given wavelength and groove spacing is strictly a function of the groove shape and the reflectance of the coating. The optimum groove shape is then a function of the angle of incidence and order of use.

Reflective Coatings

Bare Aluminum (Al) – Offers good reflectance in UV, VIS and IR.

Protected Aluminum (Al) – Aluminum coat with a thin overcoat of magnesium flouride (MgF2) which prevents the formation of aluminum oxide which is absorbing in deep UV. It provides no benefit over bare aluminum for gratings used in VIS and IR.

Gold (Au) – Superior performance over aluminum in the NIR region. Below 600nm the reflectance of gold falls off significantly and is a poor choice. Above 1200nm, gold offers very little advantage for a single pass application.

diffraction-grating-aluminum-vs-gold-reflectance

Polarization Effects

Gratings exhibit polarization dependent behavior. This effect can range from mild to extreme.

The efficiency of a grating in polarized light is dependent on the orientation of the plane of polarization relative to the direction of the grooves. For maximum efficiency, the grating should be oriented such that plane of polarization is oriented perpendicular (s-polarization) to the length of the grooves.

Dispersion

Dispersion is the ability of a grating to angularly separate adjacent wavelengths of light. The higher the separation, the higher the dispersion.

Dispersion is strictly a function of the angle of diffraction.

As the angle of diffraction approaches 90 degrees, the angular dispersion increases. Decreasing the groove spacing, increasing the angle of incidence and operating in higher orders are all effective ways to increase dispersion. Any set of conditions allowable by the grating equation that increases the angle of diffraction will increase angular dispersion.

Diffraction Grating Selection Criteria

  1. Determine the groove spacing that fits the dispersion requirements for the application.
  2. Select the grating with the highest efficiency in the spectral region of interest.
    ** At this point, in 80% of the cases, you are done selecting your grating  **
  3. Temper the selection with any mitigating factors, such as (but not limited to) stray light performance, polarization effects, or energy distribution between orders, when multiple orders are being used.

Visual Appearance

Of all of the topics that can be discussed relating to a diffraction grating, visual appearance is probably the most subjective, misunderstood, and maligned property one can think of. The reasons are understandable. When someone looks at a grating and sees what appears to be a flaw, the natural impulse is to imply a negative affect on performance. This may or may not be the case in theory, but is hardly ever the case in practice. A grating’s visual appearance, unless obviously grossly damaged, should never be used to assess its functionality.

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The simple fact of the matter is that, except in extreme cases, the performance of a diffraction grating is primarily a function of the things that you cannot see with the naked eye. The grating efficiency is a function of the shape of the groove and the reflectance of the coating. You cannot evaluate this with the naked eye. The stray light performance is primarily a function of the micro, not macro, structure of the grating surface. You cannot see a rough groove structure, or nonspecular reflective surface with the naked eye, but it’s easy to see a small dig or light scratch.

Quality vs. Function Here is where subjectivity comes into play. Everyone will have a different definition of quality. Some will include appearance, some will include only function, and some will include a combination of function/appearance/consistency relative to cost. When a universal definition is adopted, there will be no more debate on this matter. Until then, the debate continues.

Digs – Digs are characterized as regular or irregular inclusions in or on the surface of the grating. They can be resident on the master grating, or introduced during the replication or coating process.

Scratches – Scratches are characterized in the conventional sense, deformation lines running in any direction other than the direction of the grating grooves.

Ruling Glitches – Ruling glitches appear to be scratches that are perfectly straight and perfectly parallel to the groove direction. They appear only on ruled gratings, and are an artifact of the ruling process. During the ruling operation of the master grating, a small bit of the aluminum coating on the master blank will occasionally seize onto the diamond stylus and deform a few grooves before clearing itself from the tool. The deformed grooves are parallel all others, and are ruled at the same pitch as all others. If the deformed grooves are extremely ragged, it can be argued that they could degrade stray light performance, but their most likely affect is to simply redefine the blaze properties for those few grooves. Ruling glitches are not considered to be functional defects unless extremely excessive in quantity.

Pinholes – Pinholes in a reflection grating serve only to reduce the total amount of light available for diffraction by the ratio of their area to the total area illuminated. This is insignificant. Any light passing through a pinhole in the coating is automatically rejected from the optical path of the system.

Blaze Arrow Orientation

diffraction-grating-blaze-arrow-marking

All of Optometrics’ gratings are marked on one edge with a blaze arrow. The figure below shows a typical arrow, and its relation to the blaze angle of the grating. For best efficiency, the arrow should be oriented such that the tip of the arrow points towards the source, inscribing the smallest angle possible, as shown.

For best efficiency, the arrow should be oriented so that the tip points back towards the source, inscribing the smallest angle possible, as shown below.

diffraction-grating-blaze-arrow-orientation

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