Application Note 3 Polarization and Polarization Control

Transcription

1 Application Note 3 Polarization and Polarization Control 515 Heller Ave. San Jose, CA USA phone: (408) fa: (408) contact@newfocus.com

2 Polarization and Polarization Control Precise control of polarization behavior is necessar to obtaiptimal performance from our optical components and sstems. Characteristics such as reflectivit, insertion loss, and beam splitter ratios will be different for different polarizations. Such dependencies need to be carefull accounted for in aptical design. Polarization is also important because it can be used to transmit signals and make sensitive measurements. Even though the light intensit ma be constant, valuable information can be conveed in the polarization state of aptical beam. Deciphering its polarization will tell ou how the beam has been modified b af numerous material interactions (magnetic, chemical, mechanical, etc.). Sensors and measurement equipment can be designed to operate on such polarization changes. The goal of this application note is to eplain how wave plates and compensators work to convert light of one polarization state to another. The first step towards understanding polarization is to think of light as alectromagnetic wave, composed of alectric E-field and a magnetic H-field that travel together at the same velocit and in the same direction, k. E and H are vector quantities, meaning the can be represented b arrows that have both a magnitude (length) and a directiof orientation. Mawell s wave equations tell us that E and H are connected; the are alwas 90 out of phase and mutuall perpendicular to each other and to k. Once we know E we caasil determine H. Thus, we usuall deal onl with E and define a wave s polarization as the orientatiof its E-field. Tpes of Polarization There are basicall three polarization states: linear, circular, and elliptical. These terms describe the path traced out b the tip of the electric-field vector as it propagates in space. The output light from a laser is tpicall highl polarized, that is, it consists almost entirel of one linear polarization. On the other hand, unpolarized light, such as light from a light bulb, an LED, or the sun, is a random superpositiof all possible polarization states. 1 wavelength= Fig. 1: A linearl polarized wave. λ A snapshot in time of a linearl polarized wave is shown in Fig. 1. Notice that the spacing at which the E-field repeats itself is one wavelength, λ. Although the E-field alternates direction (sign), it stas confined to a single plane. If ou could see the wave at a fied point in z as it went b, ou would observe the arrow tip oscillating up and down along a line. The angle θ of this line with respect to some reference set of aes completel specifies this linear polarization state. Furthermore, we can decompose this wave into two linear wave components in the ais directions: E= E cos( ωt k z)+ E cos ( ωt k z), where ω=πc/ λ, is the angular frequenc of the wave, and k is its propagation constant, and c is the speed of light. The two cosine terms represent a traveling monochromatic wave. E and E are orthogonal components of E. Their magnitudes are given b E E = E cos θ, = E sin θ. For a linearl polarized wave, E and E are in phase with each other. k θ z Application Note 3, Rev H Copright 001, New Focus, Inc. All rights reserved.

3 Γ=0 0<Γ<π/ Γ=π/ π/<γ<π Time Fig. a: A circularl polarized wave. K Γ=π π<γ<3π/ Γ=3π/ 3π/<Γ<π Fig. 3: Various elliptical waves for different phase delas Γ. Fig. b: Using thumb and fingers to determine handedness. Fig. a sketches the evolutiof a circularl polarized wave in time. You can see that the E-field vector tip forms a heli or corkscrew shape. If ou stood at a fied location, sa z=0, ou would observe the E vector rotating in time, like the second hand on a watch. A circularl polarized wave can be either lefthanded or right-handed, depending on the clockwise or counterclockwise nature of the rotation. B convention, the wave in Fig. a is right-handed. Aas method for remembering the convention involves using our thumb and fingers. For a right-handed circular wave, wheu use our right hand and point our right thumb in the directiof propagation k, the fingers will curl in the same direction as the E-field rotation. (See Fig. b.) A left-handed circular wave will match with our left hand. One wa to create a circular wave is to combine two equal, orthogonal, linear waves that are 90 apart in phase. One linear wave reaches a maimum when the other goes to zero. You can see this in Fig. a where dashed and solid lines are used represent the two orthogonall polarized waves, and in the following epression: E E cos ωt E sin ωt. For a circular wave, the two linear components must be = ( )+ ( ) z Right-handed circular of the same magnitude, E = E. If E and E are not equal in magnitude, the result is allipticall polarized wave. Elliptical waves have the same propert of handedness used for circular waves. However, irder to completel characterize an elliptical wave, not onl do ou need to measure the ratio of major ais to minor ais (ellipticit), but ou also need to relate the beam aes to some frame of reference, such as a lab feature, device mount, or package marking. Elliptical polarization is the most general case of polarization. For instance, ou can think of a circle as being a special ellipse with equal major and minor aes. In general, allipticall polarized wave will be of the form: E= E cos( ωt)+ E cos( ωt + Γ). Γ is a phase dela difference between the two linear wave components. Several representative elliptical waves for a range of Γ values are shown in Fig. 3. Notice that the major and minor aes are not necessaril in the and directions. Also notice that the ellipse degenerates into a linear wave when Γ= -π, -π, 0, π, π (0 and 180 degrees). The polarization is circular when Γ= -3π/, -π/, π/, 3π / (90 degrees) and E = E. 3

4 Birefringent Crstals Since the goal of this application note is to eplain how wave plates and compensators work to convert light from one polarization state to another, we must first review the properties of uniaial crstals. When light travels through a transparent material such as a crstal, it interacts with the atoms in the lattice. Consequentl, the speed of light inside the crstal is slower than that in a vacuum or air, tpicall b a factor between 1 and 3. The speed v varies inversel with the crstal s refractive inde n. That is, v=c/n. The larger the refractive inde, the more the light is retarded. The amount of phase retardation (or dela) Γ that a monochromatic wave acquires from traveling through the crstal is related to its speed (refractive inde), wavelength, and the path length L inside the crstal. z z L Γ=π L/ λ k Γ=π L/λ p Γ= nl ( Γin radians ). λ k The simplest class of crstals are those with cubic smmetr. In a cubic crstal, all 3 crstallographic directions or aes are equivalent. n =n =n z, and the crstal is opticall isotropic. Regardless of how the light is polarized with respect to the crstal, it will eperience the same refractive inde and phase dela. Therefore, an polarized light, aside from accumulating a constant phase dela, remains unchanged after traveling through a defect-free, isotropic crstal. (This is also true for amorphous substances like glass.) However, there eists another, more interesting, class of crstals that ehibit asmmetric (or anisotropic) optical properties. The are known as birefringent crstals. One birefringent tpe is uniaial, meaning that one crstal ais is different from the other two: n z n =n. Common uniaial crstals of optical qualit are quartz, calcite and MgF. The single crstal ais that is unique is often called the etraordinar ais (or sometimes, the optic ais), and its associated refractive inde is labeled, while the other two aes are ordinar aes with inde. Fig. 4: Rotating a uniaial crstal changes the phase dela (retardation) for a linearl polarized wave. For a concrete eample, refer to Fig. 4. Input light that is linearl polarized along the crstal s ais acts as ardinar wave and will eperience refractive inde. Rotating the crstal so that the light is linearl polarized along the crstal s z ais causes the light to act as atraordinar wave which sees a refractive inde. In these two cases, the phase delas, or optical path length, will be different even though the light travels the same phsical path length. A confusing point in the terminolog of uniaial crstals is the labels: fast ais and slow ais. Whichever ais has the smallest refractive inde is the fast ais. If <, as is the case with quartz, then the etraordinar ais is fast and the ordinar aes are slow. Conversel, if >, as with calcite and MgF, then the etraordinar ais is slow, and the ordinar aes are fast. B definition, quartz is said to be a positive uniaial crstal, whereas calcite is a negative uniaial crstal. 4

5 Wave Plates and Applications Birefringent wave plates, or retardation plates, are etremel useful for applications where ou want to snthesize and analze light of different polarization states. For eample, using a quarter-wave plate, ou can convert an input beam from linear polarization to circular (or elliptical) polarization and vice versa. Using a half-wave plate, ou can continuousl adjust the polarization angle of a linearl-polarized beam. With just these two tpes of wave plates, ou can build aptical isolator, a variable attenuator, or a variableratio beam splitter. A wave plate is simpl a cut and polished slice of uniaial crstal, like that shown in Fig. 4. The plane of the slice contains the etraordinar (or optic) ais. An input beam that is normall incident on the wave plate will be resolved into ordinar and etraordinar ais Table 1: Common polarization conversions using wave plates. Input Slow θ Fast Output θ=0 is the fast ais θ=90 is the slow ais Input Output Quarter-wave Linear, θ=45 Right circular Linear, θ=-45 Left circular Right circular Linear, θ=-45 Left circular Linear, θ=45 Linear, an θ 45 Elliptical Half-wave Linear, angle θ Linear, angle - Left circular Right circular Right circular Left circular An wave plate Linear, θ=0 or 90 Unchanged θ components, each with a different refractive inde. The beam that emerges has a phase-dela difference or retardation between the aes of p Γ= ( ) ( Γ ) λ n n L e o in radians. If ou choose the wave plate thickness L so that the retardation corresponds to π/ radians (or 90 ), then it is called a quarter-wave plate. A phase shift of Γ=π/ will convert linearl polarized light to circular and vice versa as we saw in Fig 3. Half-wave plates have π radians (or 180 ) of retardation. As shown in Figure 3, a retardation of Γ=π will flip linearl polarized light. If the incoming beam is at an angle θ with respect to the fast ais, the light will be flipped b θ around the fast ais. This is especiall convenient since our laser or apparatus is often too large to rotate. Quarter wave and half wave are not measures of phsical thickness, rather the are in reference to a specific wavelength. Therefore, all fied-thickness wave plates should be properl labeled with the wavelength of light the were designed for (e.g., 1/4 wave at 63.8 nm). Furthermore, since the refractive indices of all materials are strongl wavelength dependent (dispersive), it is wrong to assume a wave plate that is quarter-wave for 1060-nm light, for eample, will be a half-wave plate for 530-nm light. In Table 1, we summarize the most common applications of wave plates. Irder to follow the prescriptions in Table 1, ou need to find the fast and slow aes of our wave plate and then rotate the wave plate so that the input or output polarization is at the correct angle. In practice, it is difficult to polish a wave plate for a retardatiof less thane wavelength. The crstal would be ver thin, fragile and imprecise. An alternative eists. Since waves repeat themselves ever π radians, an phase difference that is an integral multiple of π can be subtracted out. Therefore, most fied-thickness wave plates are reall multiple-order wave plates. Instead of just π/ retardation, a practical quarter-wave plate ields Nπ+π/ retardation, where N is the order of the wave plate. Multiple-order wave plates do not act eactl like zero-order wave plates, however. If ou change the wavelength of our laser or light source, 5

6 ou will find that the retardation will change much more rapidl for multiple-order wave plates than for zero-order plates. Also, multiple-order retardation is N+1 times more sensitive to angle-tilting about normal incidence. This means that a ver small amount of tilt can be used to fine tune a multiple-order wave plate. But, it also means that larger errors will occur if non-parallel light ras of converging or diverging beams are used. For more precise measurements, zeroorder wave plates are available. The are made b combining two wave plates that have retardations that differ b eactl the desired retardation. Zero-order wave plates are much less sensitive to angular, wavelength, and temperature deviations. Soleil Babinet and Berek s Compensators Fortunatel, there are techniques available for making true zero-order wave plates whose retardation can be continuousl adjustable. Such a variable wave plate is called a polarization compensator, and it can be used to achieve an retardation, including quarter- and half-wave, for a broad range of wavelengths. We will talk about two tpes of compensators: the Soleil Babinet compensator and the Berek s compensator. The principle behind the Soleil Babinet is eas to understand. It effectivel consists of two uniaial plates stacked together. The etraordinar aes of the two plates are perpendicular to each other so the roles of the ordinar and etraordinar aes are reversed as the light travels through one plate and then the other. A phase difference or retardation that is accumulated in the first plate ma be partiall or completel canceled out b the second plate. A variable compensator is made b replacing the first plate with two complementar wedges. In this manner, the total effective thickness of the first plate can be adjusted b sliding one wedge with respect to the other. (See Fig. 5.) When the first plate thickness is eactl equal to the second plate thickness, there is zero net retardation. Although its operation is easil understood, a Soleil Babinet compensator can be relativel epensive because it requires three pieces of carefull crafted and mounted uniaial crstal. Another drawback of the Soleil Babinet is that it ma be quite loss due to reflections from the si interfaces present in the design. 1b Light 1a Fig. 5: Soleil Babinet compensator. Retardation is adjusted b changing the effective thickness of plate 1. A second tpe of compensator, the Berek s compensator, is attractive because it consists of onl one plate of uniaial crstal, thereb cutting down the cost and optical loss while still maintaining the versatilit of the Soleil Babinet. The Berek s polarization compensator, pictured in Fig. 6, consists of a single plate cut with the etraordinar ais perpendicular to the plate. When light is at normal incidence to the plate, it propagates with a velocit independent of polarization. There is no retardation because the light onl eperiences a refractive inde. The light is ignorant of the etraordinar ais. But, when the plate is tilted toward or awa from the light beam, one of the aes in the plane of incidence becomes slightl etraordinar. The ais now has affective refractive inde given b the formula: 1 = cos θr n n + sin θr. n e o Light Even though the amount of retardation in the Berek s compensator depends on the degree of tilt, it has angular sensitivit equal to a Soleil Babinet compensator. 1b 1a e 6

7 Light Light θr Linear-to-Circular Polarization: (Fig. 8) A quarter-wave plate converts linear polarization to circular polarization. To verif that ou have circularl polarized light, reflect the transmitted light back through the quarter-wave plate. The reflected polarization should now be orthogonal to the incident polarization. A polarizing element that transmits the incident wave will therefore block the reflected beam. Fig. 6: Berek s compensator. The etraordinar ais is perpendicular to the plate. Tilt causes birefringence and phase retardation. ' Output Linear Polarization Input Circular Polarization Verifing Polarization States You cabtain and verif an polarization state using a polarizer and a wave plate such as the New Focus Model 5540 Berek s variable wave plate. Eamples Linear-to-Linear Polarization: (Fig. 7) A half-wave plate changes the orientatiof linearl polarized light b an angle of θ, where θ is the angle between the input polarization and the wave plate s fast ais. To verif that ou have the correct linear polarization direction, orient a polarizer so that it blocks the desired polarization. Linear Polarization Half-Wave Plate Linear Polarization Glan Thompson Polarizer Fig. 7: A half-wave plate produces a relative phase difference of π radians between the fast- and slow-ais waves. If the incoming light is polarized at an angle α with respect to the fast ais, the outgoing light will be rotated b α about the fast ais. Half-wave plates can also flip the handedness of circularl or ellipticall polarized light. Quarter-Wave Plate Fig. 8: A quarter-wave plate introduces a relative phase shift of π/ between the fast- and slow-ais waves. It converts linearl polarized light into ellipticall polarized light. For the special case where the incident light is oriented at 45 with respect to either principal ais, the resulting light is circularl polarized. Left-Hand Circular (LHC) vs. Right-Hand Circular (RHC): (Fig. 9, pg. 8) Determining handedness is difficult if ou don t know the orientatiof the fast and slow aes of our wave plate. With the New Focus Model 5540 Berek s polarization compensator, however, identifing the fast and slow aes is simple. The compensator works b tilting a uniaial piece of material, whose face is perpendicular to the optic ais. The slow ais is alwas in the plane of incidence, perpendicular to the tilt rotation ais. Once the orientatiof the fast and slow aes is known, left- and right-hand circular polarization can be determined b using a polarizer and the compensator as a quarter-wave plate. For LHC input, if the slow ais of the quarterwave plate is along, the output of the wave plate will be linear at -45 to and transmitted through the polarizer as shown pg. 8. RHC will be blocked. Rotating the wave plate or polarizer b 90 reverses this result. 7

8 Circular Polarization Linear Polarization Quarter-Wave Plate Glan Thompson Polarizer Fig. 9: For LHC, if the fast ais of the quarter wave plate is aligned so that the polarization component along is retarded b π/ with respect to, all the light will be transmitted through the polarizer. If is retarded b π/ with respect to, the polarizer will block the light. Summar For optimal performance iur eperiment, precise control of the polarizatiof our optical beam is necessar. Wave plates can be used to convert the polarization from one state to another. When choosing a wave plate, keep in mind that single-order wave plates are less sensitive to temperature and wavelength variations and beam divergence. References A good reference is: Hecht, E Optics, nd ed. Reading, MA: Addison-Wesle Publishing Co. More rigorous references are: Born, M.; Wolf, E Principles of Optics. Oford: Pergammon Press. Yariv, A.; Yeh, P Optical Waves in Crstals. New York: John Wile and Sons. 515 Heller Ave. San Jose, CA USA phone: (408) fa: (408) contact@newfocus.com