Equilateral Dispersive Prisms

Figure 1.1  Top-Down Diagram of Dispersive Prism with Two Incident Rays

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.

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.

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.

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Click Here to Download Index of Refraction Data

N-SF11, F2, and N-F2
Both 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 V_d, N-SF11 and F2 provide maximum dispersive power.

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.

Calcium Fluoride
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.

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 wavelength^a.

Sellmeier Equation:

Materialb	B1	C1	B2	C2	B3	C3	λmina (µm)	λmaxa (µm)	Plot
F2	1.345	9.977 x 10-3	2.091 x 10-1	4.705 x 10-2	9.374 x 10-1	1.119 x 102	0.32	2.5
N-F2	1.398	9.959 x 10-3	1.592 x 10-1	5.469 x 10-2	1.269	1.192 x 102	0.35	2.5
N-SF11	1.737	1.319 x 10-2	3.137 x 10-1	6.231 x 10-2	1.899	1.552 x 102	0.37	2.5
CaF2	5.676 x 10-1	2.526 x 10-3	4.711 x 10-1	1.008 x 10-2	3.848	1.201 x 103	0.23	9.7
ZnSe	4.298	3.689 x 10-2	6.278 x 10-1	1.435 x 10-1	2.896	2.208 x 103	0.55	18.0

• The Sellmeier equation is only accurate within the wavelength range specified by λ_min and λ_max.
• F2, N-F2, N-SF11, CaF₂, and ZnSe indices should be calculated using the Sellmeier equation.

Click Here to Download Index of Refraction Data

Figure 5.1  Light Propagation Path Through an Equilateral Prism

Angle of Minimum Deviation Through a Prism

If one were to use ray tracing techniques to determine the light propagation path due to the presence of the equilateral prism shown in Figure 5.1, 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 in Figure 5.1), 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).

To illustrate the relationship between the incident, exit, and deviation angles in the triangle in Figure 5.1, consider the equilateral triangle shown in Figure 5.2, which is identical to the one shown to in Figure 5.1 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 = 180°, and thus, B = 180° - (A + C) = 180° - [( - θ₁) + (β - θ₂)]. Finally, B + γ = 180°, so γ = 180° - B = [( - θ₁) + (β - θ₂)].

Now, consider the triangle outlined in green in Figure 5.2. Here, (90 - θ₁) + (90 - θ₂) + 60° = 180°. Thus, θ₁ + θ₂ = 60°. Substituting this relationship into the end result derived in the previous paragraph, yields γ = + β - (θ₁ + θ₂) = + β - 60°.

Figure 5.2  Light propagation path through an equilateral prism illustrating the relationship between the incident, exit, and deviation angles. 

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

γ = + β - 60° = 2 - 60°

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:  

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 65.6° for N-SF11 and 47.9° for F2.

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.

Selection Guide for Prisms

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.

Beam Steering Prisms

Prism	Material	Deviation	Invert	Reverse or Rotate	Illustration	Applications
Right Angle Prisms	N-BK7, UV Fused Silica, Calcium Fluoride, or Zinc Selenide	90°	90°	No		90° reflector used in optical systems such as telescopes and periscopes.
		180°	180°	No		180° reflector, independent of entrance beam angle. Acts as a non-reversing mirror and can be used in binocular configurations.
TIR Retroreflectors (Unmounted and Mounted) and Specular Retroreflectors (Unmounted and Mounted)	N-BK7	180°	180°	No		180° reflector, independent of entrance beam angle. Beam alignment and beam delivery. Substitute for mirror in applications where orientation is difficult to control.
Unmounted Penta Prisms and Mounted Penta Prisms	N-BK7	90°	No	No		90° reflector, without inversion or reversal of the beam profile. Can be used for alignment and optical tooling.
Roof Prisms	N-BK7	90°	90°	180o Rotation		90° reflector, inverted and rotated (deflected left to right and top to bottom). Can be used for alignment and optical tooling.
Unmounted Dove Prisms and Mounted Dove Prisms	N-BK7	No	180°	2x Prism Rotation		Dove prisms may invert, reverse, or rotate an image based on which face the light is incident on. Prism in a beam rotator orientation.
		180°	180°	No		Prism acts as a non-reversing mirror. Same properties as a retroreflector or right angle (180° orientation) prism in an optical setup.
Wedge Prisms	N-BK7	Models Available from 2° to 10°	No	No		Beam steering applications. By rotating one wedged prism, light can be steered to trace the circle defined by 2 times the specified deviation angle.
			No	No		Variable beam steering applications. When both wedges are rotated, the beam can be moved anywhere within the circle defined by 4 times the specified deviation angle.
Coupling Prisms	Rutile (TiO2) or GGG	Variablea	No	No		High index of refraction substrate used to couple light into films. Rutile used for nfilm > 1.8 GGG used for nfilm < 1.8

• Depends on Angle of Incidence and Index of Refraction

Dispersive Prisms

Prism	Material	Deviation	Invert	Reverse or Rotate	Illustration	Applications
Equilateral Prisms	F2, N-F2, N-SF11, Calcium Fluoride, or Zinc Selenide	Variablea	No	No		Dispersion prisms are a substitute for diffraction gratings. Use to separate white light into visible spectrum.
Dispersion Compensating Prism Pairs	Fused Silica, Calcium Fluoride, SF10, or N-SF14	Variable Vertical Offset	No	No		Compensate for pulse broadening effects in ultrafast laser systems. Can be used as an optical filter, for wavelength tuning, or dispersion compensation.
Pellin Broca Prisms	N-BK7, UV Fused Silica, or Calcium Fluoride	90°	90°	No		Ideal for wavelength separation of a beam of light, output at 90°. Used to separate harmonics of a laser or compensate for group velocity dispersion.

• Depends on Angle of Incidence and Index of Refraction

Beam Manipulating Prisms

Prism	Material	Deviation	Invert	Reverse or Rotate	Illustration	Applications
Anamorphic Prism Pairs	N-KZFS8 or N-SF11	Variable Vertical Offset	No	No		Variable magnification along one axis. Collimating elliptical beams (e.g., laser diodes) Converts an elliptical beam into a circular beam by magnifying or contracting the input beam in one axis.
Axicons (UVFS, ZnSe)	UV Fused Silica or Zinc Selenide	Variablea	No	No		Creates a conical, non-diverging beam with a Bessel intensity profile from a collimated source.

• Depends on Prism Physical Angle

Polarization Altering Prisms

Prism	Material	Deviation	Invert	Reverse or Rotate	Illustration	Applications
Glan-Taylor, Glan-Laser, and α-BBO Glan-Laser Polarizers	Glan-Taylor: Calcite Glan-Laser: α-BBO or Calcite	p-pol. - 0° s-pol. - 112°a	No	No		Double prism configuration and birefringent calcite produce extremely pure linearly polarized light. Total Internal Reflection of s-pol. at the gap between the prism while p-pol. is transmitted.
Rutile Polarizers	Rutile (TiO2)	s-pol. - 0° p-pol. absorbed by housing	No	No		Double prism configuration and birefringent rutile (TiO2) produce extremely pure linearly polarized light. Total Internal Reflection of p-pol. at the gap between the prisms while s-pol. is transmitted.
Double Glan-Taylor Polarizers	Calcite	p-pol. - 0° s-pol. absorbed by housing	No	No		Triple prism configuration and birefringent calcite produce maximum polarized field over a large half angle. Total Internal Reflection of s-pol. at the gap between the prism while p-pol. is transmitted.
Glan Thompson Polarizers	Calcite	p-pol. - 0° s-pol. absorbed by housing	No	No		Double prism configuration and birefringent calcite produce a polarizer with the widest field of view while maintaining a high extinction ratio. Total Internal Reflection of s-pol. at the gap between the prism while p-pol. is transmitted.
Wollaston Prisms and Wollaston Polarizers	Quartz, Magnesium Fluoride, α-BBO, Calcite, Yttrium Orthovanadate	Symmetric p-pol. and s-pol. deviation angle	No	No		Double prism configuration and birefringent calcite produce the widest deviation angle of beam displacing polarizers. s-pol. and p-pol. deviate symmetrically from the prism. Wollaston prisms are used in spectrometers and polarization analyzers.
Rochon Prisms	Magnesium Fluoride or Yttrium Orthovanadate	Ordinary Ray: 0° Extraordinary Ray: deviation angle	No	No		Double prism configuration and birefringent MgF2 or YVO4 produce a small deviation angle with a high extinction ratio. Extraordinary ray deviates from the input beam's optical axis, while ordinary ray does not deviate.
Beam Displacing Prisms	Calcite	2.7 or 4.0 mm Beam Displacement	No	No		Single prism configuration and birefringent calcite separate an input beam into two orthogonally polarized output beams. 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.
Fresnel Rhomb Retarders	N-BK7	Linear to circular polarization Vertical Offset	No	No		λ/4 Fresnel Rhomb Retarder turns a linear input into circularly polarized output. Uniform λ/4 retardance over a wider wavelength range compared to birefringent wave plates.
		Rotates linearly polarized light 90°	No	No		λ/2 Fresnel Rhomb Retarder rotates linearly polarized light 90°. Uniform λ/2 retardance over a wider wavelength range compared to birefringent wave plates.

• S-polarized light is not pure and contains some P-polarized reflections.

Beamsplitter Prisms

Prism	Material	Deviation	Invert	Reverse or Rotate	Illustration	Applications
Beamsplitter Cubes	N-BK7	50:50 splitting ratio, 0° and 90° s- and p- pol. within 10% of each other	No	No		Double prism configuration and dielectric coating provide 50:50 beamsplitting nearly independent of polarization. Non-polarizing beamsplitter over the specified wavelength range.
Polarizing Beamsplitter Cubes	N-BK7, UV Fused Silica, or N-SF1	p-pol. - 0° s-pol. - 90°	No	No		Double prism configuration and dielectric coating transmit p-pol. light and reflect s-pol. light. For highest polarization use the transmitted beam.