All about polarization
Understanding and manipulating the polarization of light is crucial for many optical applications. Optical design frequently focuses on the wavelength and intensity of light, while neglecting its polarization. Polarization, however, is an important property of light that affects even those optical systems that do not explicitly measure it. The polarization of light affects the focus of laser beams, influences the cut-off wavelengths of filters, and can be important to prevent unwanted back reflections. It is essential for many metrology applications such as stress analysis in glass or plastic, pharmaceutical ingredient analysis, and biological microscopy. Different polarizations of light can also be absorbed to different degrees by materials, an essential property for LCD screens, 3D movies, and your glare-reducing sunglasses.
Understanding Polarization
Light is an electromagnetic wave, and the electric field of this wave oscillates perpendicularly to the direction of propagation. Light is called unpolarized if the direction of this electric field fluctuates randomly in time. Many common light sources such as sunlight, halogen lighting, LED spotlights, and incandescent bulbs produce unpolarized light. If the direction of the electric field of light is well defined, it is called polarized light. The most common source of polarized light is a laser.
Depending on how the electric field is oriented, we classify polarized light into three types of polarizations:
Linear polarization: The electric field of light is confined to a single plane along the direction of propagation. (Figure 1)
Circular polarization: The electric field of light consists of two linear components that are perpendicular to each other, equal in amplitude, but have a phase difference of π/2. The resulting electric field rotates in a circle around the direction of propagation and, depending on the rotation direction, is called left- or right-hand circularly polarized light. (Figures 2a & 2b)
Figure 1: The electric field of linearly polarized light is confined to a single plane along the direction of propagation.
Figure 2a
Figure 2b
Figures 2a & 2b: The electric field of circularly polarized light consists of two perpendicular, equal in amplitude, linear components that have a phase of difference of π/2. The resulting electric field describes a circle.
Elliptical polarization: The electric field of light describes an ellipse. This results from the combination of two linear components with differing amplitudes and/or a phase difference that is not π/2. This is the most general description of polarized light, and circular and linear polarized light can be viewed as special cases of elliptically polarized light. (Figures 3a & 3b)
Figure 3a
Figure 3b
Figures 3a & 3b: The electric field of elliptically polarized light consists of two perpendicular linear components with any amplitude and any phase difference. The resulting electric field describes an ellipse.
The two orthogonal linear polarization states that are most important for reflection and transmission are referred to as p- and s-polarization. P-polarized (from the German parallel) light has an electric field polarized parallel to the plane of incidence, while s-polarized (from the German senkrecht) light is perpendicular to this plane. (Figure 4)
Figure 4: P and S are linear polarizations defined by their relative orientation to the plane of incidence.
Manipulating Polarization
Polarizers
In order to select a specific polarization of light, polarizers are used. Polarizers can be broadly divided into reflective, dichroic, and birefringent polarizers.
Reflective polarizers transmit the desired polarization while reflecting the rest. Wire grid polarizers are a common example of this, consisting of many thin wires arranged parallel to each other. Light that is polarized along these wires is reflected, while light that is polarized perpendicular to these wires is transmitted. Other reflective polarizers use Brewster’s angle. Brewster’s angle is a specific angle of incidence under which only s-polarized light is reflected. The reflected beam is s-polarized and the transmitted beam becomes partially p-polarized.
Dichroic polarizers absorb a specific polarization of light, transmitting the rest; modern nanoparticle polarizers are dichroic polarizers.
Birefringent polarizers rely on the dependence of the refractive index on the polarization of light. Different polarizations will refract at different angles and this can be used to select certain polarizations of light.
Unpolarized light can be considered a rapidly varying random combination of p- and s-polarized light. An ideal linear polarizer will only transmit one of the two linear polarizations, reducing the initial unpolarized intensity I0 by half,
(Equation 1)
For linearly polarized light with intensity I0, the intensity transmitted through an ideal polarizer, I, can be described by Malus’ law,
(Equation 2)
where θ is the angle between the incident linear polarization and the polarization axis. We see that for parallel axes, 100% transmission is achieved, while for 90° axes, also known as crossed polarizers, there is 0% transmission. In real world applications the transmission never reaches exactly 0%, therefore, polarizers are characterized by an extinction ratio, which can be used to determine the actual transmission through two crossed polarizers.
Waveplates
While polarizers select certain polarizations of light, discarding the other polarizations, ideal waveplates modify existing polarizations without attenuating, deviating, or displacing the beam. They do this by retarding (or delaying) one component of polarization with respect to its orthogonal component. Correctly chosen waveplates can convert any polarization state into a new polarization state, and are most often used to rotate linear polarization, to convert linearly polarized light to circularly polarized light or vice versa.
Applications
Implementing polarization control can be useful in imaging applications. By placing a linear polarizer over the light source, the lens, or both, it is possible to eliminate glare and hot spots from reflective objects or bring out surface defects. (Figure 5)
Figure 5: Polarizers used in the right-hand image reduce glare.
Material stress can be quantified in transparent objects using the photoelastic effect. Stressed material becomes birefringent, and the stress and its related birefringence can be measured by using polarized light. (Figure 6)
Figure 6: Polarizers used on the right side of the image show stress on the lens of the glasses.
Polarization is also very important in the chemical, pharmaceutical, and food and beverage industries. Many important chemical compounds, such as active pharmaceutical ingredients or sugar, are “optically active” and rotate polarized light. The amount of rotation is determined by the nature and the concentration of the compound, allowing polarimetry to detect and quantify these compounds.
Polarizer Characteristics
Polarizers are defined by a few key parameters, some of which are specific to polarization optics. The most important characteristics are:
Extinction ratio: The ratio of transmission of the desired polarization to transmission of the undesired polarization. Also called contrast ratio, it is typically given normalized to the undesired polarization. The higher this value the purer the transmitted polarization; values can range from 100:1 for economical sheet polarizers to over 106:1 for high quality birefringent polarizers. The extinction ratio is a wavelength dependent property and you should be sure to verify the extinction ratio at your application’s wavelength. Removing glare does not require a high extinction ratio, analyzing low concentrations of pharmaceutical compounds on the other hand requires a very high extinction ratio.
(Equation 3)
Transmission: This value either refers to the transmission of light polarized linearly in the direction of polarization axis, or to the transmission of unpolarized light through the polarizer. Parallel transmission is the transmission of unpolarized light through two polarizers with their polarization axes aligned in parallel, while crossed transmission is the transmission of unpolarized light through two polarizers with their polarization axes crossed. For ideal polarizers transmission of linearly polarized light parallel to the polarization axis is 100%, parallel transmission is 50% and crossed transmission is 0%. This can be calculated with Malus’ law. (Equation 2)
Acceptance angle: The acceptance angle is the largest deviation from design incidence angle at which the polarizer will still perform within specifications. Most polarizers are designed to work at an incidence angle of 0° or 45°, or at Brewster’s angle. The acceptance angle is important for alignment but has particular importance when working with non-collimated beams. Wire grid and dichroic polarizers have the largest acceptance angles, up to a full acceptance angle of almost 90°.
Construction: Polarizers come in many forms and designs. Thin film polarizers are thin films similar to optical filters. Polarizing plate beamsplitters are thin, flat plates placed at an angle to the beam. Polarizing cube beamsplitters consist of two right angle prisms mounted together at the hypothenus. Birefringent polarizers consist of two crystalline prisms mounted together, where the angle of the prisms is determined by the specific polarizer design.
Clear aperture: The clear aperture is typically most restrictive for birefringent polarizers as the availability of optically pure crystals limits the size of these polarizers. Dichroic polarizers have the largest available clear apertures as their fabrication lends itself to larger sizes.
Optical path length: The length light must travel through the polarizer. Important for dispersion, damage thresholds and space constraints, optical path lengths can be significant in birefringent polarizers but are usually short in dichroic polarizers.
Damage threshold: The laser damage threshold is determined by the material used as well as the polarizer design, with birefringent polarizers typically having the highest damage threshold. Cement is often the most susceptible element to laser damage, which is why optically contacted beamsplitters or air spaced birefringent polarizers have higher damage thresholds.
Cost: Some polarizers require large, very pure crystals, which are expensive, while others are made of stretched plastic, which make them more economical.
Selection Guide
Reflective Polarizers
Reflective polarizers transmit the desired polarization and reflect the rest. They either use a wire grid, Brewster’s angle or interference effects. Brewster’s angle is the angle at which, based on the Fresnel equations, only s-polarized light is reflected. Because the p-polarized light is not reflected while the s-polarized light is partially reflected, the transmitted light is enriched in p-polarization (Figure 7)
Figure 7: Reflective polarizers, available as cube beamsplitters, plate beamsplitters or thin films, reflect the unwanted polarization state.
(Table1)
Key: $ - Low, $$ - Moderate, $$$ - High
Dichroic Polarizers
Dichroic polarizers transmit the desired polarization and absorb the rest. This is achieved via anisotropy in the polarizer; common examples are oriented polymer molecules and stretched nanoparticles. This is a broad class of polarizers, going from low cost laminated plastic polarizers to precision high cost glass nanoparticle polarizers. Most dichroic polarizers have good extinction ratios relative to their cost. Their damage thresholds and environmental stability are often limited, although glass dichroic polarizers outperform plastic dichroic polarizers in this aspect. Dichroic polarizers are well suited for microscopy, imaging and display applications, and are often the only choice when very large apertures are necessary. (Figure 8) 
Figure 8: Reflective polarizers, available as cube beamsplitters, plate beamsplitters or thin films, reflect the unwanted polarization state.
(Table2)
Birefringent Polarizers
Birefringent polarizers transmit the desired polarization and deviate the rest. They rely on birefringent crystals, where the refractive index of light depends on its polarization. Unpolarized light at non-normal incidence will split into two separate beams upon entering the crystal, as the refraction for s- and p-polarized light will be different. Most designs consist of two joined birefringent prisms, where the angle they are joined at and the relative orientation of their optical axes determine the functionality of the polarizer. Because these polarizers require optically pure crystals they are expensive, but have high laser damage thresholds, excellent extinction ratios and broad wavelength ranges. (Figure 9)
Figure 9: Cystalline polarizers, such as the Glan-Taylor polarizer, transmit a desired polarization and deviate the rest, using birefringent properties of their crystalline materials.
(Table3)
Understanding and manipulating the polarization of light is crucial for many optical applications. Optical design frequently focuses on the wavelength and intensity of light, while neglecting its polarization. Polarization, however, is an important property of light that affects even those optical systems that do not explicitly measure it. The polarization of light affects the focus of laser beams, influences the cut-off wavelengths of filters, and can be important to prevent unwanted back reflections. It is essential for many metrology applications such as stress analysis in glass or plastic, pharmaceutical ingredient analysis, and biological microscopy. Different polarizations of light can also be absorbed to different degrees by materials, an essential property for LCD screens, 3D movies, and your glare-reducing sunglasses.
Understanding Polarization
Light is an electromagnetic wave, and the electric field of this wave oscillates perpendicularly to the direction of propagation. Light is called unpolarized if the direction of this electric field fluctuates randomly in time. Many common light sources such as sunlight, halogen lighting, LED spotlights, and incandescent bulbs produce unpolarized light. If the direction of the electric field of light is well defined, it is called polarized light. The most common source of polarized light is a laser.
Depending on how the electric field is oriented, we classify polarized light into three types of polarizations:
Linear polarization: The electric field of light is confined to a single plane along the direction of propagation. (Figure 1)
Circular polarization: The electric field of light consists of two linear components that are perpendicular to each other, equal in amplitude, but have a phase difference of π/2. The resulting electric field rotates in a circle around the direction of propagation and, depending on the rotation direction, is called left- or right-hand circularly polarized light. (Figures 2a & 2b)
Figure 1: The electric field of linearly polarized light is confined to a single plane along the direction of propagation.
Figure 2a
Figure 2b
Figures 2a & 2b: The electric field of circularly polarized light consists of two perpendicular, equal in amplitude, linear components that have a phase of difference of π/2. The resulting electric field describes a circle.
Elliptical polarization: The electric field of light describes an ellipse. This results from the combination of two linear components with differing amplitudes and/or a phase difference that is not π/2. This is the most general description of polarized light, and circular and linear polarized light can be viewed as special cases of elliptically polarized light. (Figures 3a & 3b)
Figure 3a
Figure 3b
Figures 3a & 3b: The electric field of elliptically polarized light consists of two perpendicular linear components with any amplitude and any phase difference. The resulting electric field describes an ellipse.
The two orthogonal linear polarization states that are most important for reflection and transmission are referred to as p- and s-polarization. P-polarized (from the German parallel) light has an electric field polarized parallel to the plane of incidence, while s-polarized (from the German senkrecht) light is perpendicular to this plane. (Figure 4)
Figure 4: P and S are linear polarizations defined by their relative orientation to the plane of incidence.
Manipulating Polarization
Polarizers
In order to select a specific polarization of light, polarizers are used. Polarizers can be broadly divided into reflective, dichroic, and birefringent polarizers.
Reflective polarizers transmit the desired polarization while reflecting the rest. Wire grid polarizers are a common example of this, consisting of many thin wires arranged parallel to each other. Light that is polarized along these wires is reflected, while light that is polarized perpendicular to these wires is transmitted. Other reflective polarizers use Brewster’s angle. Brewster’s angle is a specific angle of incidence under which only s-polarized light is reflected. The reflected beam is s-polarized and the transmitted beam becomes partially p-polarized.
Dichroic polarizers absorb a specific polarization of light, transmitting the rest; modern nanoparticle polarizers are dichroic polarizers.
Birefringent polarizers rely on the dependence of the refractive index on the polarization of light. Different polarizations will refract at different angles and this can be used to select certain polarizations of light.
Unpolarized light can be considered a rapidly varying random combination of p- and s-polarized light. An ideal linear polarizer will only transmit one of the two linear polarizations, reducing the initial unpolarized intensity I0 by half,
(Equation 1)
For linearly polarized light with intensity I0, the intensity transmitted through an ideal polarizer, I, can be described by Malus’ law,
(Equation 2)
where θ is the angle between the incident linear polarization and the polarization axis. We see that for parallel axes, 100% transmission is achieved, while for 90° axes, also known as crossed polarizers, there is 0% transmission. In real world applications the transmission never reaches exactly 0%, therefore, polarizers are characterized by an extinction ratio, which can be used to determine the actual transmission through two crossed polarizers.
Waveplates
While polarizers select certain polarizations of light, discarding the other polarizations, ideal waveplates modify existing polarizations without attenuating, deviating, or displacing the beam. They do this by retarding (or delaying) one component of polarization with respect to its orthogonal component. Correctly chosen waveplates can convert any polarization state into a new polarization state, and are most often used to rotate linear polarization, to convert linearly polarized light to circularly polarized light or vice versa.
Applications
Implementing polarization control can be useful in imaging applications. By placing a linear polarizer over the light source, the lens, or both, it is possible to eliminate glare and hot spots from reflective objects or bring out surface defects. (Figure 5)
Figure 5: Polarizers used in the right-hand image reduce glare.
Material stress can be quantified in transparent objects using the photoelastic effect. Stressed material becomes birefringent, and the stress and its related birefringence can be measured by using polarized light. (Figure 6)
Figure 6: Polarizers used on the right side of the image show stress on the lens of the glasses.
Polarization is also very important in the chemical, pharmaceutical, and food and beverage industries. Many important chemical compounds, such as active pharmaceutical ingredients or sugar, are “optically active” and rotate polarized light. The amount of rotation is determined by the nature and the concentration of the compound, allowing polarimetry to detect and quantify these compounds.
Polarizer Characteristics
Polarizers are defined by a few key parameters, some of which are specific to polarization optics. The most important characteristics are:
Extinction ratio: The ratio of transmission of the desired polarization to transmission of the undesired polarization. Also called contrast ratio, it is typically given normalized to the undesired polarization. The higher this value the purer the transmitted polarization; values can range from 100:1 for economical sheet polarizers to over 106:1 for high quality birefringent polarizers. The extinction ratio is a wavelength dependent property and you should be sure to verify the extinction ratio at your application’s wavelength. Removing glare does not require a high extinction ratio, analyzing low concentrations of pharmaceutical compounds on the other hand requires a very high extinction ratio.
(Equation 3)
Transmission: This value either refers to the transmission of light polarized linearly in the direction of polarization axis, or to the transmission of unpolarized light through the polarizer. Parallel transmission is the transmission of unpolarized light through two polarizers with their polarization axes aligned in parallel, while crossed transmission is the transmission of unpolarized light through two polarizers with their polarization axes crossed. For ideal polarizers transmission of linearly polarized light parallel to the polarization axis is 100%, parallel transmission is 50% and crossed transmission is 0%. This can be calculated with Malus’ law. (Equation 2)
Acceptance angle: The acceptance angle is the largest deviation from design incidence angle at which the polarizer will still perform within specifications. Most polarizers are designed to work at an incidence angle of 0° or 45°, or at Brewster’s angle. The acceptance angle is important for alignment but has particular importance when working with non-collimated beams. Wire grid and dichroic polarizers have the largest acceptance angles, up to a full acceptance angle of almost 90°.
Construction: Polarizers come in many forms and designs. Thin film polarizers are thin films similar to optical filters. Polarizing plate beamsplitters are thin, flat plates placed at an angle to the beam. Polarizing cube beamsplitters consist of two right angle prisms mounted together at the hypothenus. Birefringent polarizers consist of two crystalline prisms mounted together, where the angle of the prisms is determined by the specific polarizer design.
Clear aperture: The clear aperture is typically most restrictive for birefringent polarizers as the availability of optically pure crystals limits the size of these polarizers. Dichroic polarizers have the largest available clear apertures as their fabrication lends itself to larger sizes.
Optical path length: The length light must travel through the polarizer. Important for dispersion, damage thresholds and space constraints, optical path lengths can be significant in birefringent polarizers but are usually short in dichroic polarizers.
Damage threshold: The laser damage threshold is determined by the material used as well as the polarizer design, with birefringent polarizers typically having the highest damage threshold. Cement is often the most susceptible element to laser damage, which is why optically contacted beamsplitters or air spaced birefringent polarizers have higher damage thresholds.
Cost: Some polarizers require large, very pure crystals, which are expensive, while others are made of stretched plastic, which make them more economical.
Selection Guide
Reflective Polarizers
Reflective polarizers transmit the desired polarization and reflect the rest. They either use a wire grid, Brewster’s angle or interference effects. Brewster’s angle is the angle at which, based on the Fresnel equations, only s-polarized light is reflected. Because the p-polarized light is not reflected while the s-polarized light is partially reflected, the transmitted light is enriched in p-polarization (Figure 7)
Figure 7: Reflective polarizers, available as cube beamsplitters, plate beamsplitters or thin films, reflect the unwanted polarization state.
(Table1)
Key: $ - Low, $$ - Moderate, $$$ - High
Dichroic Polarizers
Dichroic polarizers transmit the desired polarization and absorb the rest. This is achieved via anisotropy in the polarizer; common examples are oriented polymer molecules and stretched nanoparticles. This is a broad class of polarizers, going from low cost laminated plastic polarizers to precision high cost glass nanoparticle polarizers. Most dichroic polarizers have good extinction ratios relative to their cost. Their damage thresholds and environmental stability are often limited, although glass dichroic polarizers outperform plastic dichroic polarizers in this aspect. Dichroic polarizers are well suited for microscopy, imaging and display applications, and are often the only choice when very large apertures are necessary. (Figure 8)
Figure 8: Reflective polarizers, available as cube beamsplitters, plate beamsplitters or thin films, reflect the unwanted polarization state.
(Table2)
Birefringent Polarizers
Birefringent polarizers transmit the desired polarization and deviate the rest. They rely on birefringent crystals, where the refractive index of light depends on its polarization. Unpolarized light at non-normal incidence will split into two separate beams upon entering the crystal, as the refraction for s- and p-polarized light will be different. Most designs consist of two joined birefringent prisms, where the angle they are joined at and the relative orientation of their optical axes determine the functionality of the polarizer. Because these polarizers require optically pure crystals they are expensive, but have high laser damage thresholds, excellent extinction ratios and broad wavelength ranges. (Figure 9)
Figure 9: Cystalline polarizers, such as the Glan-Taylor polarizer, transmit a desired polarization and deviate the rest, using birefringent properties of their crystalline materials.
(Table3)
