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# Equilateral Dispersive Prisms

• High Refractive Index
• Low Abbe Vd Number for Maximum Dispersion
• Material: F2, N-SF11, CaF2, or ZnSe

PS854

PS860

PS856

PS861

Application Idea

PS855 Prism on a KM200B
Platform Mount

Related Items

Top-Down Diagram of Dispersive Prism with Two Incident Rays

Our Dispersive Equilateral Prisms, which are fabricated from N-SF11, F2, 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.

General Specifications
Material F2a N-SF11a CaF2a ZnSea
Clear Aperture 70%
Surface Quality (Scratch-Dig) 40-20 60-40
Angular Tolerance ±5 arcmin ±3 arcmin ±10 arcmin
Number of Polished Faces 2b 3c
• Click Link for Detailed Specifications on the Substrate Glass
• One face and the bases are fine ground.
• The bases are fine ground.
Item # A=B=C=H
(mm)
Material Minimum Angle
of Deviation
Vdb Surface Flatness
@ 633 nm
PS850 10 ± 0.15 F2 47.9° @ 633 nm 36.37 λ/10
PS856 15 ± 0.1
PS858 20 ± 0.1
PS852 25 ± 0.1
PS854 50 ± 0.1
PS851 10 ± 0.15 N-SF11a 65.6° @ 633 nm 25.76 λ/10
PS857 15 ± 0.1
PS859 20 ± 0.1
PS853 25 ± 0.1
PS855 40 ± 0.1
PS862 10 +0.0/-0.3 CaF2 31.6° @ 633 nm 95.00 λ/2
PS863 25 +0.0/-0.3
PS860 10 +0.0/-0.3 ZnSe N/A N/A λ/2
PS861 25 +0.0/-0.3
• N-SF11 stains easily. Clean off fingerprints quickly.
• The Abbe number, Vd, is calculated by: Vd= (nd - 1) / (nF - nC), where nd, nF, and nC are the indices of refraction for the helium D-line (587.6 nm), the hydrogen F-line (486.1 nm), and the hydrogen C-line (656.3 nm). A lower Abbe number indicates more dispersion.

Material Wavelength Range Index of Refraction Abbe Number
F2 385 nm - 2 µm 1.617 @ 633 nm 36.37
N-SF11 420 nm - 2.3 µm 1.779 @ 633 nm 25.76
CaF2 180 nm - 8 µm 1.433 @ 633 nm 95.00
ZnSe 600 nm - 16 µm 2.403 @ 10.6 µm N/Aa
• ZnSe is opaque at some or all visible wavelengths, and thus the Abbe number is undefined.

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

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 Sellmeier equations. Each material is empirically assigned a set of coefficients, through which the index of refraction can be calculated at any wavelengtha.

Sellmeier Equation 1:

Materialb K1 L1 K2 L2 K3 L3 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-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 λmin and λmax.
• F2, N-SF11, CaF2, and ZnSe indices should be calculated using Sellmeier equation1.

### 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 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).

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)].

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.

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 - 60o = 2 - 60o

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 65.6o for N-SF11 and 47.9o 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-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 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
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.

## F2 Equilateral Dispersive Prisms (385 nm - 2 µm)

Click to Enlarge

Transmission data is for a 10 mm thick sample.

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.

Polarization Effects
For 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.

Material Minimum Angle
of Deviation
Vdb Surface Flatness
@ 633 nm
Clear
Aperture
Surface
Quality
Angular
Tolerance
Number of
Polished Faces
Index of
Refraction Plot
F2a 47.9° @ 633 nm 36.37 λ/10 70% 40-20 Scratch-Dig ±5 arcmin 2c
• Click Link for Detailed Specifications on the Substrate Glass
• The Abbe number, Vd, is calculated by: Vd= (nd - 1) / (nF - nC), where nd, nF, and nC are the indices of refraction for the helium D-line (587.6 nm), the hydrogen F-line (486.1 nm), and the hydrogen C-line (656.3 nm). A lower Abbe number indicates more dispersion.
• One face and the bases are fine ground.
Based on your currency / country selection, your order will ship from Newton, New Jersey
+1 Qty Docs Part Number - Universal Price Available
 PS850 F2 Equilateral Dispersive Prism, 10 mm
$93.61  Today  PS856 F2 Equilateral Dispersive Prism, 15 mm$100.91
 Today
 PS858 F2 Equilateral Dispersive Prism, 20 mm
$108.21  Today  PS852 F2 Equilateral Dispersive Prism, 25 mm$121.20
 Today
 PS854 F2 Equilateral Dispersive Prism, 50 mm
$244.56  Today ## N-SF11 Equilateral Dispersive Prisms (420 nm - 2.3 µm) Click to Enlarge Download an Excel File with Raw Transmission Data Transmission data is for a 10 mm thick sample. 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. Polarization Effects For 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. Material Minimum Angle of Deviation Vdb Surface Flatness @ 633 nm Clear Aperture Surface Quality Angular Tolerance Number of Polished Faces Index of Refraction Plot N-SF11a 65.5° @ 633 nm 24.76 λ/10 70% 40-20 Scratch-Dig ±5 arcmin 2c • N-SF11 stains easily. Clean off fingerprints quickly. Click the link for detailed specifications on the substrate glass. • The Abbe number, Vd, is calculated by: Vd= (nd - 1) / (nF - nC), where nd, nF, and nC are the indices of refraction for the helium D-line (587.6 nm), the hydrogen F-line (486.1 nm), and the hydrogen C-line (656.3 nm). A lower Abbe number indicates more dispersion. • One face and the bases are fine ground. Based on your currency / country selection, your order will ship from Newton, New Jersey +1 Qty Docs Part Number - Universal Price Available  PS851 N-SF11 Equilateral Dispersive Prism, 10 mm$85.49
 Today
 PS857 N-SF11 Equilateral Dispersive Prism, 15 mm
$85.49  Today  PS859 N-SF11 Equilateral Dispersive Prism, 20 mm$91.18
 Today
 PS853 N-SF11 Equilateral Dispersive Prism, 25 mm
$91.18  Today  PS855 N-SF11 Equilateral Dispersive Prism, 40 mm$222.91
 Today

## CaF2 Equilateral Dispersive Prisms (180 nm - 8 µm)

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.

Material Minimum Angle
of Deviation
Vdb Surface Flatness
@ 633 nm
Clear
Aperture
Surface
Quality
Angular
Tolerance
Number of
Polished Faces
Index of
Refraction Plot
CaF2a 31.6° @ 633 nm 95.00 λ/2 70% 40-20 Scratch-Dig ±3 arcmin 2c
• Click Link for Detailed Specifications on the Substrate Glass
• The Abbe number, Vd, is calculated by: Vd= (nd - 1) / (nF - nC), where nd, nF, and nC are the indices of refraction for the helium D-line (587.6 nm), the hydrogen F-line (486.1 nm), and the hydrogen C-line (656.3 nm). A lower Abbe number indicates more dispersion.
• One face and the bases are fine ground.
Based on your currency / country selection, your order will ship from Newton, New Jersey
+1 Qty Docs Part Number - Universal Price Available
 PS862 CaF2 Equilateral Dispersive Prism, Uncoated, 10 mm
$354.94  Today  PS863 CaF2 Equilateral Dispersive Prism, Uncoated, 25 mm$551.88
 5-8 Days

## ZnSe Equilateral Dispersive Prisms (600 nm - 16 µm)

Zinc Selenide is ideal for use in the 600 nm 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.

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.

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

Material Surface Flatness
@ 633 nm
Clear
Aperture
Surface Quality Angular Tolerance Number of Polished Faces Index of
Refraction Plot
ZnSea λ/2 70% 60-40 Scratch-Dig ±10 arcmin 3b
• Click Link for Detailed Specifications on the Substrate Glass
• The bases are fine ground.
Dangerous Goods
Pleaes note that the PS861 prism is classified as a dangerous good in some countries. Depending on the delivery location, this item may need to be shipped separately from the rest of your order (and possibly with a different carrier) at an additional charge. This prism is stocked within the USA and Germany. Please contact our sales department if there are questions or concerns when placing an order.
Based on your currency / country selection, your order will ship from Newton, New Jersey
+1 Qty Docs Part Number - Universal Price Available
 PS860 ZnSe Equilateral Dispersive Prism, Uncoated, 10 mm
$558.37  Today  PS861 ZnSe Equilateral Dispersive Prism, Uncoated, 25 mm$1,023.69
 Today