Prismatic dispersionexamples

Calcium FluorideCaF2 is commonly used for applications requiring high transmission in the infrared and ultraviolet spectral ranges. The material exhibits a low refractive index, varying from 1.35 to 1.51 within its usage range of 180 nm to 8.0 µm, as well as an extremely high laser damage threshold. Calcium fluoride is also fairly chemically inert and offers superior hardness compared to its barium fluoride, magnesium fluoride, and lithium fluoride cousins.

By applying Snell's Law to the interfaces of prism and using a little calculus, a general equation for the relationship between the index of refraction of the equilateral prism n and the angle of minimum deviation γ can be obtained:

Prismatic dispersionnotes

Double prism configuration and birefringent calcite produce a polarizer with the widest field of view while maintaining a high extinction ratio.

Prismdispersionformula

Note: Transmission data is for two 25 mm right-angle prisms contacted into a cube. Click here to download substrate transmission data.

s-pol. and p-pol. are displaced by 2.7 or 4.0 mm. Beam displacing prisms can be used as polarizing beamsplitters where 90o separation is not possible.

Polarization EffectsFor p-polarized light (blue line) incident on a dispersing prism at the angle of least deviation, the graph to the right shows that only a small percentage of the p-polarized light is reflected at the surface. Thus, for this polarization, the transmission through a prism fabricated from N-F2 will be excellent even though there is no AR coating on the surface.

Now, consider the triangle outlined in green in the figure below. Here, (90 - θ1) + (90 - θ2) + 60o = 180o. Thus, θ1 + θ2 = 60o. Substituting this relationship into the end result derived in the previous paragraph, yields γ = + β - (θ1 + θ2) = + β - 60o.

s-pol. and p-pol. deviate symmetrically from the prism. Wollaston prisms are used in spectrometers and polarization analyzers.

Dispersionof light through prism diagram

F2 is a flint glass that offers excellent performance in the visible and NIR spectral range. It offers a high refractive index and low Abbe number, making it excellent for use in an equilateral dispersive prism. Compared to N-SF11, it offers superior chemical resistance and slightly higher transmission.

N-F2 is a RoHS compliant material that has been engineered to have nearly identical optical properties as F2. At 633 nm, both N-F2 and F2 have an index of refraction of 1.617, and they have nearly identical Abbe numbers of 36.43 and 36.37, respectively.

Note: Transmission data is for two 25 mm right-angle prisms contacted into a cube. Click here to download substrate transmission data.

Our Dispersive Equilateral Prisms, which are fabricated from F2, N-F2, N-SF11, CaF2, or ZnSe are available in sizes ranging from 10 mm to 50 mm. These prisms create less stray light than diffraction gratings, thereby eliminating the higher order problems typically associated with gratings.

Polarization EffectsFor p-polarized light (blue line) incident on a dispersing prism at the angle of least deviation, the graph to the right shows that only a small percentage of the p-polarized light is reflected at the surface. Thus, for this polarization, the transmission through a prism fabricated from N-SF11, a RoHS-compliant version of SF11, will be excellent even though there is no AR coating on the surface.

N-SF11, F2, and N-F2Both N-SF11 and F2 offer excellent performance in the visible range. When compared to each other, F2, which is a flint glass, has superior chemical resistance and better transmission than N-SF11. For instance, at 420 nm the theoretical internal transmittance of a 10 mm thick piece of F2 is 0.995, whereas for the same thickness of N-SF11, the internal transmittance is 0.910. If the glass is increased to a thickness of 25 mm, these internal transmission values decrease to 0.987 and 0.790, respectively. With high indices of refraction and low Abbe Numbers Vd, N-SF11 and F2 provide maximum dispersive power.

When handling optics, one should always wear gloves. This is especially true when working with zinc selenide, as it is a hazardous material. For your safety, please follow all proper precautions, including wearing gloves when handling these prisms and thoroughly washing your hands afterward. Due to the low hardness of ZnSe, additional care should be taken to not damage these prisms. Click here to download a pdf of the MSDS for ZnSe.

Dispersive prisms are typically used at the minimum angle of deviation. This is the angle for which the wavelength of interest will travel parallel to the base of the prism, and the angle of incidence is equal to the angle of refraction when measured with respect to the normal of the prism face at the respective interface (see the Equilateral Tutorial tab for more information). At the minimum angle of deviation, a maximum clear aperture is achieved and reflective loss of p-polarized light is reduced since the angle of incidence is nearly Brewster's angle. For s-polarization, a custom antireflective coating can be used to minimize surface reflections.

Polarization EffectsFor p-polarized light (blue line) incident on a dispersing prism at the angle of least deviation, the graph to the right shows that only a small percentage of the p-polarized light is reflected at the surface. Thus, for this polarization, the transmission through a prism fabricated from F2 will be excellent even though there is no AR coating on the surface.

Dispersionof light through prism experiment

N-F2 is a RoHS compliant material that has been engineered to have nearly identical optical properties as F2. Like F2, it is a flint glass that offers excellent performance in the visible and NIR spectral range. It offers a high refractive index and low Abbe number, making it excellent for use in an equilateral dispersive prism.

This equation can be used for prisms with n < 2.0; if the refractive index is higher, this geometry will cause total internal reflection at angle C above. ZnSe dispersive prisms, like the PS860 and PS861 prisms sold below, will have a beam exiting from the bottom face of the prism.

When both wedges are rotated, the beam can be moved anywhere within the circle defined by 4 times the specified deviation angle.

Zinc Selenide is ideal for use in the 600 nm to 16 µm range. It features low absorption (including in the red visible wavelength range) and high resistance to thermal shock. ZnSe is ideal for use in CO2 laser systems operating at 10.6 µm, including those with HeNe alignment lasers. Note that due to their high refractive index, these prisms can not be used in the traditional orienation described in the Equilateral Tutorial tab above.

Zine Selenide Zinc Selenide is ideal for use in the 600 nm to 16 µm wavelength range. It features low absorption (including in the red visible wavelength range) and high resistance to thermal shock. ZnSe is ideal for use in CO2 laser systems operating at 10.6 µm, including those with HeNe alignment lasers. Please note that, due to its low hardness, care should be taken when handling ZnSe optics.

The index of refraction of various materials can be calculated via the Sellmeier equation. Each material is empirically assigned a set of coefficients, through which the index of refraction can be calculated at any wavelengtha.

Dispersionof light through prism

Prismatic dispersionformula

Please refer to the Prism Guide tab above for assistance in selecting the appropriate prism for your application, or to view Thorlabs' extensive line of prisms, please click here.

At the design wavelength (633 nm), the indices of refraction for N-SF11 and F2 are 1.779 and 1.617, respectively. Solving for γ in the equation above yields 65.6o for N-SF11 and 47.9o for F2.

If one were to use ray tracing techniques to determine the light propagation path due to the presence of the equilateral prism shown to the right, you would find that for most incidence angles, the angle of deviation of the transmitted ray (denoted by γ in the figure to the right) is roughly the same, regardless of the angle of incidence  considered. However, although the angle of deviation is largely unchanged, there is a minimum value that is obtainable. This angle is known as the minimum angle of deviation; it occurs when the light ray passing through the prism is parallel to the prism's base (as shown to the right), and therefore, = β (i.e., the angle of the light ray entering the prism is identical to that of the light ray exiting the prism).

Thorlabs will accept all ZnSe prisms back for proper disposal. Please contact Tech Support to make arrangements for this service.

Single prism configuration and birefringent calcite separate an input beam into two orthogonally polarized output beams.

Thorlabs offers a wide variety of prisms, which can be used to reflect, invert, rotate, disperse, steer, and collimate light. For prisms and substrates not listed below, please contact Tech Support.

By rotating one wedged prism, light can be steered to trace the circle defined by 2 times the specified deviation angle.

Prismatic dispersionin physics

To illustrate the relationship between the incident, exit, and deviation angles in the triangle to the right, consider the equilateral triangle shown below, which is identical to the one shown to the right but has several more angles labeled. Using the geometric relationships that exist for vertical angles, it becomes apparent that A = - θ1 and C = β - θ2. Since the angles A, B, and C define a triangle, we know that A + B + C = 180o, and thus, B = 180o - (A + C) = 180o - [( - θ1) + (β - θ2)]. Finally, B + γ = 180o, so γ = 180o - B = [( - θ1) + (β - θ2)].

For the angle of minimum deviation, = β, so there is a simple relationship between the angle of incidence and the angle of minimum deviation:

N-SF11 is a flint glass that offers excellent performance in the visible and NIR spectral range. It offers a high refractive index and low Abbe number, making it excellent for use in an equilateral dispersive prism.

CaF2 is commonly used for applications requiring high transmission in the infrared and ultraviolet spectral ranges. The material exhibits a low refractive index, varying from 1.35 to 1.51 within its usage range of 180 nm to 8.0 µm, as well as an extremely high laser damage threshold. Calcium fluoride is also fairly chemically inert and offers superior hardness compared to its barium fluoride, magnesium fluoride, and lithium fluoride cousins.