Figure 6 shows the effect of two polarizing filters on originally unpolarized light. The first filter polarizes the light along its axis. When the axes of the first and second filters are aligned (parallel), then all of the polarized light passed by the first filter is also passed by the second. If the second polarizing filter is rotated, only the component of the light parallel to the second filter’s axis is passed. When the axes are perpendicular, no light is passed by the second.

Analog design solutions can reach theoretical efficiency above 90% but require more sophisticated production techniques.

To produce analog diffractives we utilize our laserwriting technique to produce a continuously-varying surface that produces the desired spot distribution.

If a polarizing filter reduces the intensity of polarized light to 50.0 %  of its original value, by how much are the electric and magnetic fields reduced?

4: Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

Photographs of the sky can be darkened by polarizing filters, a trick used by many photographers to make clouds brighter by contrast. Scattering from other particles, such as smoke or dust, can also polarize light. Detecting polarization in scattered EM waves can be a useful analytical tool in determining the scattering source.

If the wavefront deviation from the ideal is consistent and repeatable, a corrector plate can be introduced to correct the wavefront by inducing the appropriate phase delay at various points of the aperture to produce the desired wavefront.

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Polaroid sunglasses are familiar to most of us. They have a special ability to cut the glare of light reflected from water or glass as shown in the figure below.  Polaroids have this ability because of a wave characteristic of light called polarization. What is polarization? How is it produced? What are some of its uses? The answers to these questions are related to the wave character of light.

VIAVI Solutions laserwriting technology enables the production of corrector plates with high accuracy even if it requires correction of high-frequency wavefront distortion.

Figure 8 illustrates what happens when unpolarized light is reflected from a surface. Vertically polarized light is preferentially refracted at the surface, so that the reflected light is left more horizontally polarized. The reasons for this phenomenon are beyond the scope of this text, but a convenient mnemonic for remembering this is to imagine the polarization direction to be like an arrow. Vertical polarization would be like an arrow perpendicular to the surface and would be more likely to stick and not be reflected. Horizontal polarization is like an arrow bouncing on its side and would be more likely to be reflected. Sunglasses with vertical axes would then block more reflected light than unpolarized light from other sources.

A common use of a diffractive element is the splitting of a laser beam into an array of spots. In this case, a generally collimated beam incident on the element is separated into an array, either 1D or 2D.

Diffractive elements can also be used as diffusers to provide controlled illumination for certain specialized applications such as lithographic illumination systems.

Diffractive lenses are very thin elements with total depth height equal to λ/(n – 1), where λ is the operating wavelength and n is the index of refraction. A diffractive lens is composed of a series of zones that become finer towards the edge of the lens.

12: Light reflected at 55.6o from a window is completely polarized. What is the window’s index of refraction and the likely substance of which it is made?

6: Show that if you have three polarizing filters, with the second at an angle of 45o to the first and the third at an angle of 90.0o to the first, the intensity of light passed by the first will be reduced to 25.0% of its value. (This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light.)

The typical problem is to calculate the diffractive element surface structure, given the desired intensity distribution in the image plane.

Only the component of the EM wave parallel to the axis of a filter is passed. Let us call the angle between the direction of polarization and the axis of a filter θ. If the electric field has an amplitude E, then the transmitted part of the wave has an amplitude Ecosθ (see Figure 7). Since the intensity of a wave is proportional to its amplitude squared, the intensity I of the transmitted wave is related to the incident wave by

Circular polarizationexample

Diffractive elements typically operate under collimated, coherent illumination in the geometry shown below, with an optional focusing lens.

All we need to solve these problems are the indices of refraction. Air has n1 = 1.00, water has n2 = 1.333, and crown glass has  n’2  = 1.520. The equation   can be directly applied to find θb in each case.

Polarisationmeaning in Physics

5: When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to 1/ λ4. Does this mean there is more scattering for small λ than large λ? How does this relate to the fact that the sky is blue?  Hint:  red light has a wavelength of about 650 nm while blue light has a wavelength of about 400 nm.

3: If you have completely polarized light of intensity 150 W/m2 what will its intensity be after passing through a polarizing filter with its axis at an 89.0o angle to the light’s polarization direction?

In some applications a certain wavefront is required at some point of the optical system but, for whatever reason, the actual wavefront does not show the desired form.

Polarizing filters have a polarization axis that acts as a slit. This slit passes electromagnetic waves (often visible light) that have an electric field parallel to the axis. This is accomplished with long molecules aligned perpendicular to the axis as shown in Figure 9.

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17: (a) 2.07 x10-2 o C/s (b) Yes, the polarizing filters get hot because they absorb some of the lost energy from the sunlight.

Many crystals and solutions rotate the plane of polarization of light passing through them. Such substances are said to be optically active. Examples include sugar water, insulin, and collagen (see Figure 13). In addition to depending on the type of substance, the amount and direction of rotation depends on a number of factors. Among these is the concentration of the substance, the distance the light travels through it, and the wavelength of light. Optical activity is due to the asymmetric shape of molecules in the substance, such as being helical. Measurements of the rotation of polarized light passing through substances can thus be used to measure concentrations, a standard technique for sugars. It can also give information on the shapes of molecules, such as proteins, and factors that affect their shapes, such as temperature and pH.

Suppose you put on two pairs of Polaroid sunglasses with their axes at an angle of 15.0o. How much longer will it take the light to deposit a given amount of energy in your eye compared with a single pair of sunglasses? Assume the lenses are clear except for their polarizing characteristics.

14: If θb is Brewster’s angle for light reflected from the top of an interface between two substances, and θb‘  is Brewster’s angle for light reflected from below, prove that θb + θb‘ = 90o..

Find Polaroid sunglasses and rotate one while holding the other still and look at different surfaces and objects. Explain your observations. What is the difference in angle from when you see a maximum intensity to when you see a minimum intensity? Find a reflective glass surface and do the same. At what angle does the glass need to be oriented to give minimum glare?

Glass and plastic become optically active when stressed; the greater the stress, the greater the effect. Optical stress analysis on complicated shapes can be performed by making plastic models of them and observing them through crossed filters, as seen in Figure 14. It is apparent that the effect depends on wavelength as well as stress. The wavelength dependence is sometimes also used for artistic purposes.

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Another interesting phenomenon associated with polarized light is the ability of some crystals to split an unpolarized beam of light into two. Such crystals are said to be birefringent (see Figure 15). Each of the separated rays has a specific polarization. One behaves normally and is called the ordinary ray, whereas the other does not obey Snell’s law and is called the extraordinary ray. Birefringent crystals can be used to produce polarized beams from unpolarized light. Some birefringent materials preferentially absorb one of the polarizations. These materials are called dichroic and can produce polarization by this preferential absorption. This is fundamentally how polarizing filters and other polarizers work. The interested reader is invited to further pursue the numerous properties of materials related to polarization.

To examine this further, consider the transverse waves in the ropes shown in Figure 3. The oscillations in one rope are in a vertical plane and are said to be vertically polarized. Those in the other rope are in a horizontal plane and are horizontally polarized. If a vertical slit is placed on the first rope, the waves pass through. However, a vertical slit blocks the horizontally polarized waves. For EM waves, the direction of the electric field is analogous to the disturbances on the ropes.

Circular polarization

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7: When light is reflected at Brewster’s angle from a smooth surface, it is 100% polarized parallel to the surface. Part of the light will be refracted into the surface. Describe how you would do an experiment to determine the polarization of the refracted light. What direction would you expect the polarization to have and would you expect it to be 100 %?

What is polarization in Chemistry

A fairly large angle between the direction of polarization and the filter axis is needed to reduce the intensity to 10.0% of its original value. This seems reasonable based on experimenting with polarizing films. It is interesting that, at an angle of 45o, the intensity is reduced to 50% of its original value (as you will show in this section’s Problems & Exercises). Note that 71.6o is 18.4o from reducing the intensity to zero, and that at an angle of 18.4o the intensity is reduced to 90.0% of its original value (as you will also show in Problems & Exercises), giving evidence of symmetry.

Figure 10 illustrates how the component of the electric field parallel to the long molecules is absorbed. An electromagnetic wave is composed of oscillating electric and magnetic fields. The electric field is strong compared with the magnetic field and is more effective in exerting force on charges in the molecules. The most affected charged particles are the electrons in the molecules, since electron masses are small. If the electron is forced to oscillate, it can absorb energy from the EM wave. This reduces the fields in the wave and, hence, reduces its intensity. In long molecules, electrons can more easily oscillate parallel to the molecule than in the perpendicular direction. The electrons are bound to the molecule and are more restricted in their movement perpendicular to the molecule. Thus, the electrons can absorb EM waves that have a component of their electric field parallel to the molecule. The electrons are much less responsive to electric fields perpendicular to the molecule and will allow those fields to pass. Thus the axis of the polarizing filter is perpendicular to the length of the molecule.

3: No light passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original two, some light can pass. Why is this? Under what circumstances does most of the light pass?

Analog phase functions can also be used for higher efficiency and lower sensitivity to depth errors that minimizes zero order, if the scatter angles are small.

Polarization by reflection

VIAVI Solutions has developed rigorous design and modeling codes that optimize the diffractive element maximizing performance for the specific manufacturing method.

In flat screen LCD televisions, there is a large light at the back of the TV. The light travels to the front screen through millions of tiny units called pixels (picture elements). One of these is shown in Figure 12 (a) and (b). Each unit has three cells, with red, blue, or green filters, each controlled independently. When the voltage across a liquid crystal is switched off, the liquid crystal passes the light through the particular filter. One can vary the picture contrast by varying the strength of the voltage applied to the liquid crystal.

Diffractive lenses can be used to reduce the number of elements in conventional lens systems and eliminate the need for exotic materials in correcting chromatic aberrations.

Diffractive diffusers can be implemented with binary or analog phase functions with efficiencies of about 80% and 90-95%, respectively.

Examples of polarization in society

Long Wave, Inc. is the largest of three companies Miller owns. Miller's other companies include DocSoft, a XML software company, and South 20, a wood company.

2: The angle between the axes of two polarizing filters is 45.0 degrees. By how much does the second filter reduce the intensity of the light coming through the first?

What angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by 90.0 %?

where n1 is the medium in which the incident and reflected light travel and n2 is the index of refraction of the medium that forms the interface that reflects the light. This equation is known as Brewster’s law, and θb is known as Brewster’s angle, named after the 19th-century Scottish physicist who discovered them.

Light is one type of electromagnetic (EM) wave. As noted earlier, EM waves are transverse waves consisting of varying electric and magnetic fields that oscillate perpendicular to the direction of propagation (see Figure 2). There are specific directions for the oscillations of the electric and magnetic fields. Polarization is the attribute that a wave’s oscillations have a definite direction relative to the direction of propagation of the wave. (This is not the same type of polarization as that discussed for the separation of charges.) Waves having such a direction are said to be polarized. For an EM wave, we define the direction of polarization to be the direction parallel to the electric field. Thus we can think of the electric field arrows as showing the direction of polarization, as in Figure 2.

4: What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity 1.00 kW/m2 to reduce the intensity to 10.0W/m2?

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If you hold your Polaroid sunglasses in front of you and rotate them while looking at blue sky, you will see the sky get bright and dim. This is a clear indication that light scattered by air is partially polarized. Figure 11 helps illustrate how this happens. Since light is a transverse EM wave, it vibrates the electrons of air molecules perpendicular to the direction it is traveling. The electrons then radiate like small antennae. Since they are oscillating perpendicular to the direction of the light ray, they produce EM radiation that is polarized perpendicular to the direction of the ray. When viewing the light along a line perpendicular to the original ray, as in Figure 11, there can be no polarization in the scattered light parallel to the original ray, because that would require the original ray to be a longitudinal wave. Along other directions, a component of the other polarization can be projected along the line of sight, and the scattered light will only be partially polarized. Furthermore, multiple scattering can bring light to your eyes from other directions and can contain different polarizations.

1: What angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?

Polarization of light notes PDF

There is a range of optical effects used in sunglasses. Besides being Polaroid, other sunglasses have coloured pigments embedded in them, while others use non-reflective or even reflective coatings. A recent development is photochromic lenses, which darken in the sunlight and become clear indoors. Photochromic lenses are embedded with organic microcrystalline molecules that change their properties when exposed to UV in sunlight, but become clear in artificial lighting with no UV.

(a) On a day when the intensity of sunlight is 1.00 kW/m2, a circular lens 0.200 m in diameter focuses light onto water in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of 20.0o. Assuming the sunlight is unpolarized and the polarizers are 100% efficient, what is the initial rate of heating of the water in oC/s, assuming it is 80.0% absorbed? The aluminum beaker has a mass of 30.0 grams and contains 250 grams of water. (b) Do the polarizing filters get hot? Explain.

VIAVI Solutions has developed both design and analysis models to generate and evaluate solutions for diffractive elements in general and beam splitters in particular. We can also produce these element in either binary or analog format.

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However, for applications where one has a certain number, 2, 3, …, of discrete wavelengths it is possible to design a diffractive lens that shows 100% theoretical efficiency at each of those wavelengths. We call this particular design a “MOD” lens, which stands for “multi-order diffractive” lens.

Diffractive elements are thin phase elements that operate by means of interference and diffraction to produce arbitrary distributions of light or to aid in the design of optical systems.

As a general rule, diffractive elements work best at a single wavelength. At any other wavelength the efficiency as well as image contrast are reduced.

Continuous elements reach efficiencies over 90% (neglecting surface losses) and enable the production of more general patterns.

This example illustrates a common issue with diffractive diffusers: zero order. This diffuser is being illuminated with a HeNe laser but its phase depth is not exactly correct for this source. As a result, the zero order is brighter than the other orders.

In a typical wavefront corrector application the input wavefront contains some distortion that needs to be eliminated to produce a uniform, flat wavefront.

By now you can probably guess that Polaroid sunglasses cut the glare in reflected light because that light is polarized. You can check this for yourself by holding Polaroid sunglasses in front of you and rotating them while looking at light reflected from water or glass. As you rotate the sunglasses, you will notice the light gets bright and dim, but not completely black. This implies the reflected light is partially polarized and cannot be completely blocked by a polarizing filter.

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Binary elements attain efficiencies near 80% (neglecting surface losses) and often represent cost-effective solutions if feature sizes are too small for analog fabrication and if the desired pattern has centrosymmetry.

Light reflected at these angles could be completely blocked by a good polarizing filter held with its axis vertical. Brewster’s angle for water and air are similar to those for glass and air, so that sunglasses are equally effective for light reflected from either water or glass under similar circumstances. Light not reflected is refracted into these media. So at an incident angle equal to Brewster’s angle, the refracted light will be slightly polarized vertically. It will not be completely polarized vertically, because only a small fraction of the incident light is reflected, and so a significant amount of horizontally polarized light is refracted.

Obviously, corrector plates need to be aligned with the incident wavefront and work best if the distortion in the wave front is repeatable and stationary.

When the intensity is reduced by 90.0% it is 10% or 0.100 times its original value. That is, I = 0.100 I0. Using this information, the equation I = I0 cos2θ can be used to solve for the needed angle.

5: At the end of Example 1, it was stated that the intensity of polarized light is reduced to 90.0% of its original value by passing through a polarizing filter with its axis at an angle of 18.4 degrees to the direction of polarization. Verify this statement.

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(a) At what angle will light traveling in air be completely polarized horizontally when reflected from water? (b) From glass?

Linear polarization

The binary solution is one of the most common and useful approaches to produce a beam splitter if the desired spot distribution is centrosymmetric.

where Io is the intensity of the polarized wave before passing through the filter. (The above equation is known as Malus’s law.)

The Sun and many other light sources produce waves that are randomly polarized (see Figure 4). Such light is said to be unpolarized because it is composed of many waves with all possible directions of polarization. Polaroid materials, invented by the founder of Polaroid Corporation, Edwin Land, act as a polarizing slit for light, allowing only polarization in one direction to pass through. Polarizing filters are composed of long molecules aligned in one direction. Thinking of the molecules as many slits, analogous to those for the oscillating ropes, we can understand why only light with a specific polarization can get through. The axis of a polarizing filter is the direction along which the filter passes the electric field of an EM wave (see Figure 5).

While you are undoubtedly aware of liquid crystal displays (LCDs) found in watches, calculators, computer screens, cellphones, flat screen televisions, and other myriad places, you may not be aware that they are based on polarization. Liquid crystals are so named because their molecules can be aligned even though they are in a liquid. Liquid crystals have the property that they can rotate the polarization of light passing through them by 90o. Furthermore, this property can be turned off by the application of a voltage, as illustrated in Figure 12. It is possible to manipulate this characteristic quickly and in small well-defined regions to create the contrast patterns we see in so many LCD devices.

The diffractive element that produces a beam splitter is basically a grating with some complicated shape that generates the desired distribution of spots.

If the pattern or spot array to be produced has centrosymmetry then it can be manufactured with a binary phase mask, otherwise it needs to be continuous.

Since the part of the light that is not reflected is refracted, the amount of polarization depends on the indices of refraction of the media involved. It can be shown that reflected light is completely polarized at a angle of reflection θb, given by

13: (a) Light reflected at 62.5o from a gemstone in a ring is completely polarized. Can the gem be a diamond? (b) At what angle would the light be completely polarized if the gem was in water?

The MOD lens* is a little deeper than the conventional diffractive lens by an integer factor p. At the same time the zone size increases.

The main advantage of diffractive diffusers compared to refractive ones, such as our Engineered Diffusers™, is the sharp intensity fall-off, which is as wide as the diffraction-limited spot corresponding to the incident beam size at the operating wavelength.