In this lab students will explore polarization effects. They will verify the Law of Malus and determine Brewster's angle for a microscope slide. They will also explore the properties of birefringent materials and construct an optical isolator.
Linearly polarized light is produced if the direction of E and the direction of propagation define a plane. The electric vector traces out a straight line. For example, E = Ei = E0xexp(i(kz-wt))i.
The electric field vector E can always be resolved into two perpendicular components. If the light is linearly polarized, then the two components oscillate in phase. Ex = E0xexp(i(kz-wt)), Ey = E0yexp(i(kz-wt)). If it is elliptically polarized, the two components have a constant phase difference, and the tip of the electric field vector traces out an ellipse in the plane perpendicular to the direction of propagation. Ex = E0xexp(i(kz-wt)), Ey = E0yexp(i(kz-wt+f)).
Circularly polarized light is a special case of elliptically polarized light in which E0x = E0y and the two components have a 90° phase difference and the electric field vector traces out a circle in the plane perpendicular to the direction of propagation. When viewed looking towards the source, a right circularly polarized beam has a field vector that describes a clockwise circle (f = -p/2), while left circularly polarized light has a field vector that describes a counter-clockwise circle (f = p/2).
Let Ex = E0xexp(i(kz-wt)), Ey = E0yexp(i(kz-wt+f)).
 | Linearly polarized light: f = np, n = 0, 1, 2, ... |
| Circularly polarized light: E0x = E0y, f = np/2, n = 1, 3, 5, ... |
| Elliptically polarized light: f = arbitrary, but constant. |
| Unpolarized light: f, Ey, Ex are randomly varying on a timescale that is much shorter than that needed for observation. |
Polarization Mechanisms
Dichroism: Certain naturally occurring crystalline materials have transmittance properties which depend on the polarization state of light. The most common method of producing polarized light is to use polaroid material, made from chains of organic molecules, which are anisotropic in shape. Light transmitted is linearly polarized perpendicular to the direction of the chains. If linearly polarized light passes through polaroid material, then the transmitted intensity is given by It = I0cos2q, (Law of Malus), where q is the angle between E and transmission direction.
Reflection: When unpolarized light is incident on a boundary between two dielectric surfaces, for example on an air-glass boundary, then the reflected and transmitted components are partially plane polarized. The reflected wave is 100% linearly polarized when the incident angle is equal to the Brewster angle qB. We then have tanqB = n2/n1.
Birefringence (double refraction): Certain crystalline substances have a refractive index which depends upon the state of incident polarization. Unpolarized light entering a birefringent crystal not along the optic axis of the crystal is split into beams which are refracted by different amounts.
| Linearly birefringent, uniaxial crystalline materials are characterized by having a unique axis of symmetry, called the optic axis, which imposes constraints upon the propagation of light beams within the crystal. Two modes are permitted, either as an ordinary beam polarized in a plane normal to the optic axis, or as an extraordinary beam polarized in a plane containing the optic axis. Each of the beams has an associated refractive index. The two beams have different velocities and different angles of refraction in the crystal. The direction of the lesser index is called the fast axis because light polarized in that direction has the higher speed. Suitably cut and oriented prisms of birefringent materials can act as polarizers and polarizing beam splitters. |
| A thin plate of birefringent crystal cut parallel to the optic axis is known as a wave plate. Assume linearly polarized light is entering the wave plate normally. The components of E parallel and perpendicular to optic axis emerge with a phase difference d between them given by d = (2p/l)Dn. |
| A quarter-wave plate d = p/2 can be used to convert linearly polarized light to circularly polarized light. The incident linearly polarized light must be oriented at 45o to the wave plate's axes. |
| A half-wave plate d = p can be used to rotate the plane of linearly polarized light. The angle of rotation is 2q, where q is the angle between the angle of polarization and the wave plate's fast axis. |
| If a plane polarized beam propagates down the optic axis of a material exhibiting circular birefringence it is resolved into two collinear circularly polarized beams, each propagating with a slightly different velocity. When these two components emerge from the material, they recombine into a plane polarized beam whose plane of polarization is rotated from that of the incident beam. This effect of producing a progressive rotation of the plane of polarization with path length is called optical activity, and is used to produce optical rotators. |
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Laser Assembly |
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Beam Steering Assemblies |
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Lens Chuck Assemblies |
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Rotation Stage Assembly |
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Target Assemblies |
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Beam Splitter |
| Linear Polarizers |
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Quarter Wave Plate |
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Laser Power Meter |
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Project in Optics Workbook |
Part I:
Follow the instructions on pages 75 - 78 (Polarization of Light) of the Projects in Optics Workbook. Complete Steps 1 - 6. Fill in the table below and plot your results.
| q(deg) | 0 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 | 160 | 170 | 180 |
| It/Io |
Complete steps 7 - 12. Measure Brewster's angle and use this measured value to find the index of refraction of the microscope slide. Is this value reasonable?
Part II:
Follow the instructions on pages 79 - 81 of the Projects in Optics Workbook. Complete Steps 1 - 10. Verify that the quarter-wave plate produces circularly polarized light.
Complete steps 11 - 13. Verify that you have produced an optical isolator in step 11. Verify that the half-wave plate rotates the input polarization by 90o.
Open Microsoft Word and prepare a report using the template shown below.
| In a few words, describe the experiment. (What?) |
| In a few words, state the objective of the experiment. (Why?) |
| Comment on the procedure. Did you encounter difficulties or surprises? (How?) |
| Present your results and comment on your results. |
Print out your Word document, and hand it to your instructor, or save your Word document (your name_lab10.doc) and attach it to an e-mail message to your lab instructor.