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Principles of Retarders Polarizers PRINCIPLES OF RETARDERS etarders are used in applications where control or Ranalysis of polarization states is required. Our retarder products include innovative polymer and liquid crystal materials. Crystalline materials such as quartz and Retarders magnesium fluoride are also available upon request. Please call for a custom quote. A retarder (or waveplate) is an optical device that resolves a light wave into two orthogonal linear polarization components and produces a phase shift between them. The resulting light wave is generally of a different polarization form. Ideally, retarders do not polarize, nor do they induce an intensity change in the Crystals Liquid light beam, they simply change its polarization form. state. The transmitted light leaves the retarder elliptically All standard catalog Meadowlark Optics’ retarders are polarized. made from birefringent, uniaxial materials having two Retardance (in waves) is given by: different refractive indices – the extraordinary index ne = ␤tր␭ and the ordinary index no. Light traveling through a retarder has a velocity v where: dependent upon its polarization direction given by ␤ = birefringence (ne - no) Spatial Light ␭ Modulators v = c/n = wavelength of incident light (in nanometers) t = thickness of birefringent element where c is the speed of light in a vacuum and n is the (in nanometers) refractive index parallel to that polarization direction. Retardance can also be expressed in units of length, the By definition, ne > no for a positive uniaxial material. distance that one polarization component is delayed For a positive uniaxial material, the extraordinary axis relative to the other. Retardance is then represented by: is referred to as the slow axis, while the ordinary axis is ␦Ј ␦␭ ␤ referred to as the fast axis. Light polarized parallel to the = = t fast axis travels at a higher velocity than light parallel to where ␦Ј is the retardance (in nanometers). Polarimeters the orthogonal slow axis. The above equations illustrate that retardance is strongly In figure 3-1, a plane polarized light wave incident on a dependent upon both incident wavelength and retarder birefringent material is vectorially decomposed into two thickness. orthogonal components vibrating along the fast and slow All retarders suffer small retardance oscillations as a axes. Plane polarized light is oriented at 45° relative to function of wavelength when a coherent light source is the fast axis of the retarder. The orthogonal polarization used. This etalon effect can be substantial, depending upon components travel through the material with different the physical characteristics of the retarder. Please see velocities (due to birefringence) and are phase shifted references 1, 5, and 6 listed on page 3 for more information. Mounts relative to each other producing a modified polarization fast 45˚ fast axis axis Input Output polarization polarization Custom Phase shift through retarder Fig. 3-1 The effect of a retarder of arbitrary phase on a plane-polarized input beam Tel (303) 833-4333 • Fax (303) 833-4335 • website: www.meadowlark.com Page 20 PRINCIPLES OF RETARDERS Polarizers Retarder Types Mica, a natural mineral, is cleaved to precise thicknesses Birefringence is common in materials with anisotropic offering true zero-order retarders. However, cleaving is molecular order such as crystals (both solid and liquid) difficult over large apertures and does not offer the and oriented polymers. Crystalline retarders are often necessary tolerance or spatial uniformity required for most made of mica, calcite, or most commonly, quartz. applications. Also, the long term supply of optical quality mica is uncertain. Retarders can be multiple-order (having several waves of Retarders retardance), compound zero-order, or true zero-order. Polymer materials offer a lower birefringence than quartz True zero-order retarders are often preferred for the most and can therefore be made into true zero-order retarders demanding applications requiring retardance stability of reasonable thickness. They are much less sensitive to with wavelength, temperature, and angle of incidence. incidence angle than either multiple- or compound zero- A true zero-order retarder is thin and must have a low order quartz retarders. Birefringence of the polymer we birefringence to be manufactured easily. use is nearly constant with wavelength, an advantage in applications where the source wavelength may shift. A review of several retarder types is presented below. Meadowlark Optics protects the polymer material using Liquid Quartz has a birefringence of ~0.0092 in the visible Crystals a proprietary lamination process between optically flat region. From the equations shown on the previous page, windows. This assembly provides the transmitted a true zero-order quartz quarter waveplate for 550 nm wavefront quality necessary for precision optical operation is only 15 ␮m thick. Such a thin, fragile applications. retarder presents handling difficulties in both fabrication and mounting. Fabrication of achromatic polymer retarders is accomplished by precisely orienting and layering several More commonly, multiple-order quartz retarders having a polymer sheets. This stack is then laminated between whole number of waves plus the desired fractional optical flats. Achromatic polymer retarders offer the retardance (typically quarter- or half-wave) are offered. versatility needed for broadband applications with Modulators Precision polishing of the quartz substrate provides Spatial Light demanding performance requirements. excellent surface and transmitted wavefront quality. However, multiple-order retarders can be extremely Liquid crystal retarders are electrically variable sensitive to incident angle, wavelength, and waveplates. Retardance is altered by applying a variable, temperature. As a rule of thumb, the retardance (in low voltage waveform. These retarders are made by waves) for a 1 mm thick quartz retarder varies by about placing a thin liquid crystal layer between parallel -0.3% per °C. Quartz retarders are sometimes preferred windows spaced a few microns apart. Different liquid for their durability and high transmission properties. crystal materials range in birefringence from 0.07 to 0.26, enabling fabrication of thin, true zero-order retarders in A compound zero-order quartz retarder improves Polarimeters the visible to near infrared region. performance by combining two multiple-order quartz waveplates with the desired retardance difference. The Fresnel Rhombs use total internal reflection to create fast axis of one plate is aligned with the slow axis of the a phase shift between two orthogonal polarization other, cancelling the large retardance values and leaving components. Fresnel rhombs make excellent achromatic only the desired fractional retardance difference retarders. A more complete description of reflection (typically quarter- or half-wave). Thermal stability of retarders can be found in the references listed on page 3. compound zero-order quartz retarders is improved as Other tunable birefringent retarders use electro-optic Mounts temperature effects of the two retarders cancel. crystals such as KD*P (potassium dideuterium phosphate). This material is used in Pockels cell Note that a compound zero-order quartz retarder retarders which can operate at megahertz frequencies but does not provide for improved field of view over a require very high voltage for retardance control. multiple-order retarder. Custom Page 21 Tel (303) 833-4333 • Fax (303) 833-4335 • e-mail: [email protected] Polarizers POLARIZATION CONTROL WITH POLYMERS 0.70 Quartz aturally-occurring crystalline materials (calcite, mica, and 0.60 tilt around Polymer Nquartz) have traditionally been the birefringent materials slow axis of choice for retarders. Today’s applications require performance 0.50 tilt around versatility beyond the limitations of those crystals. fast axis Retarders Retardance (waves) 0.40 Meadowlark Optics specializes in the use of birefringent polymers and liquid crystals for polarization control in precision 0 10 20 30 40 50 optical applications. These innovative materials offer a unique Incidence Angle (degrees) combination of high performance and cost-effectiveness. Fig. 3-3 Half-wave retarder performance with incidence angle Birefringent Polymers The temperature sensitivity of laminated polymer retarders Our polymer retarder assembly consists of birefringent polymer is about 0.04%/°C, allowing operation over moderate material laminated between two precision polished, optically temperature ranges without significantly degrading Crystals flat BK-7 windows. Antireflection coatings and index retardance accuracy. We can also thermally calibrate Liquid matching optical cement help to maximize transmission in the polymer retarders for specific operating temperatures. visible to near infrared region. This construction (shown in Large aperture quartz retarders are difficult to fabricate and figure 3-2) ensures excellent transmitted wavefront quality, become cost-prohibitive beyond two inches in diameter. while minimizing beam deviation and surface reflection losses. Meadowlark Optics’ polymer retarders with large apertures Input plane wave can be fabricated for a reasonable price. Please call for a ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ custom quote. Spatial Light Modulators 0.300 Polymer BK 7 Zero-Order retarder windows Polymer Index 0.275 matching Achromatic cement Polymer ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ ➛ 0.250 Output plane wave Retardance (waves) 0.225
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