How to Select a Waveplate

Transcription

1 How to Select a Waveplate A wave retarder is a component that resolves a light wave into two orthogonal polarization components and produces a phase shift between them. The resulting difference in phase shift upon transmission determines the effect on polarization. Ideally a retarder will not change the intensity of the incident light, it simply changes its polarization state. Most retarders are made from birefringent materials. Standard Waveplates: Linear birefringence Linear birefringence arises when the index of refraction of a material is different for two orthogonal linear polarization states, as in calcite, mica, or crystal quartz. This causes the two polarization components to propagate with different velocities through the retarder material. The amount of phase shift, or retardation, depends upon both the thickness of the material and the wavelength of the incident light. This is the operation mode of standard waveplates. Most waveplates are made from a birefringent uniaxial material, which is characterized by a unique axis of symmetry called the optic axis, and two indices of refraction. The index of refraction along the optic axis (for the light polarized along this axis) is called the extraordinary index, n e, and the index of refraction in the plane perpendicular to the optic axis is called the ordinary index, n o. If the material is positive uniaxial, i.e., n e > n o, then the optic axis is called the slow axis, as light travels more slowly along that direction. For negative uniaxial materials, n e < n o, and the optic axis is called the fast axis. Such waveplates are generally made from plane-parallel plates with the optic axis in the plane of the polished surfaces, so that the difference in birefringence is maximized. The resulting phase shift (φ), or retardation (R) at normal incidence is given by: Equation 1 Equation 2 A quarter waveplate (bottom) will produce circularly polarized light when the input polarization plane is aligned at 45 to the optic axis, whereas a half waveplate (top) will rotate the polarization. Note that the angle of rotation is 2θ, where θ is the angle between the incident polarization plane and the optic axis. Where t is the thickness of the waveplate, λ is the wavelength of light, and β(λ) is the birefringence n e (λ) n o (λ). Retardation is usually expressed in terms of the number (N) of waves. The majority of waveplates manufactured by CVI Laser Optics are based on linear birefringence of crystal quartz, a natural positive uniaxial material. The crystal is cut so that the optic axis is parallel to the front and back faces of the plate. Other crystalline materials such as mica are available on a custom basis.

2 Two common waveplates are the half waveplate and the quarter waveplate. A waveplate that imparts a retardation of λ/2 (known as a half waveplate) will rotate linearly polarized light through 90 if the input polarization is aligned at 45 to the optic axis. When elliptically polarized light is incident, the same half-wave plate will instead convert between right- and left-handed elliptical pola rizations. Half waveplates are often used in electro-optic modulators, continuously adjustable polarization rotators, variable laser beamsplitters and variable attenuators. For a half waveplate: Equation 3 Equation 4 A waveplate that imparts a retardation of λ/4 (known as a quarter waveplate) will convert linearly polarized light to circularly polarized light if the input polarization is aligned at 45 to the optical axis, or vice versa (otherwise the output is elliptical). This feature of quarter waveplates is utilized in optical isolators, electro-optic modulators, interferometers, ellipsometers, optical pumping and polar-metric imaging applications. It should be noted that the dispersion of the birefringence is very important in waveplate design; a quarter waveplate at a given wavelength is never exactly a half waveplate at half that wavelength. For a quarter waveplate: Equation 5 Equation 6 It is important to note that any integer number of waves of retardation will have no direct effect on the performance of the waveplate, i.e., they will not alter the state of polarization. Only fractional waves of retardation will alter the polarization state. However, because the integer part constitutes most of the overall retardation, it increases the sensitivity of the component s effective retardation to temperature and wavelength variation, as will be discussed later on. The order number of the waveplate is given by the integer m in the equations above. For m > 0, the waveplate is described as multiple-order. For m = 0, it is described as zero-order. Types of quartz waveplates All CVI Laser Optics catalog waveplates are manufactured from laser quality crystal quartz. Crystal quartz exhibits high laser damage threshold and excellent performance from the UV through near infrared wavelengths. Crystalline quartz also has a uniform structure so that accurate retardation can be obtained over the entire area of the plate at a given angular setting. It has however a relatively high birefringence: in the visible range, at 193 nm, and at 1.55 µm. As a result, very little thickness is needed to generate a true zeroorder waveplate. If made from a single plate, a zeroorder half waveplate for 800 nm would be about 45 µm thick, while a zero-order quarter waveplate for 532 nm would be about 14 µm thick. Such a thin part is difficult to manufacture, handle, clean and mount. True zeroorder can actually be made as single plates for near infrared applications (at 1550 nm a half waveplate is about 91µm thick) or using a thicker host substrate during manufacture and mounting, but this is an expensive option. The most common type of waveplate uses a single plate of crystal quartz in which the retardation is an integer number of waves (mλ), or orders, plus the desired fractional retardation (typically λ/2 or λ/4). This is known as a multiple-order waveplate. Multiple-order waveplates do not require a very thin piece of material. This makes them easier to manufacture, but the added thickness (resulting in order m) strongly increases their sensitivity to wavelength, temperature and angle of incidence. As such, they are suitable for use only at their design wavelength, and over a limited temperature range (typically +/-3 C). Our catalog QWPM multiple-order waveplates are manufactured with a thickness in the mm range. They offer excellent surface and transmitted wavefront quality when mounted, and high laser damage threshold. Precision polishing and tight parallelism tolerances ensure very accurate control of the retardation over the full aperture. They provide an economical and effective way to alter polarization when sensitivity to wavelength and temperature is not critical. They are well-suited for use with gas or solid-state lasers (due to the narrow bandwidth of those sources), preferably in a temperature-controlled environment. When greater thermal stability or improved useful bandwidth is required, a zero-order waveplate must be 2 IDEX Optics & Photonics Marketplace

3 used. However, as already discussed, a true zero-order quartz waveplate is too thin for easy fabrication and handling. A more robust zero-order waveplate design utilizes two multiple-order waveplates with the desired retardation difference, aligned with their optic axes crossed. The two component parts are precision polished and mated so that the difference in thickness yields the exact fractional retardation (typically λ/2 or λ/4). As the slow axis of one plate is aligned with the fast axis of the other, the large retardation value (mλ) cancels, leaving only the required fractional retardation. Thus they operate like a true zero-order waveplate regarding the variation of retardation with wavelength, allowing use over a larger wavelength band. Another benefit of this compound design is that temperature effects of the two component plates tend to cancel out, yielding good thermal stability. Field of view is somewhat reduced relative to a multipleorder waveplate, however, due to the increased thickness. Our QWPO zero-order waveplates are manufactured from two multiple order plates in a compound design. The thickness of each plate is about 0.65 mm (total thickness approximately 1.3 mm). They offer excellent surface and transmitted wavefront quality, with high retardation accuracy and superior laser damage threshold. They are particularly suited for use with diode lasers, with tunable or broadband sources like femtosecond lasers, or in applications where the operating temperature is not well controlled. CVI Laser Optics offers two choices for assembling our zero-order compound quartz waveplates, including optical contacting and air-spaced mounting, with ring mount optional for optically contacted waveplates. In either case, the two components must be precisely aligned to perform properly. Optically contacted compound waveplates offer a compact design with several advantages over a cemented construction. They have higher UV transmittance and laser damage resistance, while beam deviation and transmitted wavefront quality are best preserved. Air-spaced waveplates are preferred for highest power applications or for harsh environments, particularly when working with extreme temperature ranges, strong mechanical load, or for vacuum operation. In particular, we recommend our QWPO-AS air-spaced zero-order waveplates for wavelengths below 248 nm and repetition rates higher than 1 khz since high power UV light can separate optically contacted waveplates. The RT Polarization Rotators air-spaced design ensures low beam deviation and best transmitted wavefront quality as compared to cemented waveplates, while avoiding the durability limitation of the optically contacted interface. Air-spaced compound waveplates are, however, slightly more expensive due to their more complicated assembly and the AR coatings required to minimize reflection losses on all 4 optical surfaces. Some applications call for dual-wavelength waveplates, such as separation of Nd:YAG fundamental and harmonic wavelengths at high power. Our QWPD dual-wavelength waveplates achieve this by retarding one wavelength by λ (essentially leaving it unchanged), while retarding the second wavelength by λ/2 to rotate its linear polarization by 90. Once orthogonally polarized, the two beams can be separated using a polarizing beamsplitter cube. These waveplates use a multiple-order design in which the necessary retardation conditions are met for both wavelengths. This results in a relatively high order waveplate, making them suitable for use only over narrow bandwidth, angular apperture and operating temperature range. Dependence on wavelength, temperature and angle of incidence The change of retardation with wavelength is given, in waves, by: Equation 7 where N=β λ t/λ (Equation 8) is the retardation in waves at the design wavelength (λ). The wavelength dependency is directly proportional to the total retardation of the IDEX Optics & Photonics Marketplace 3

4 waveplate, making multiple-order waveplates much more sensitive to wavelength variations. For instance, a λ/2 multiple-order waveplate designed for 532 nm (23λ/2, N=11.5, order m=11) is 23x more sensitive to wavelength variation than a true or compound zero-order waveplate (N=0.5). A λ/4 multiple-order waveplate designed for 532 nm (45λ/4, N=11.25, order m=22) will be 45x more sensitive to wavelength variation than a true or compound zero-order waveplate (N=0.5). To estimate the usable wavelength range, one can assume that the retardation (in nm) is independent of the wavelength (i.e., neglect the dispersion of the birefringence), yielding: Equation 9 The usable wavelength range will also depend on the required accuracy of the retardation. For instance, for a QWPO designed at 800 nm, the retardation tolerance is within λ/100 for wavelength changes up to ± 15 nm (λ/2 waveplate, N=0.5) or ± 30 nm (λ/4 waveplate, N=0.25), compared to ± 1 nm for a QWPM multiple-order waveplate. It should be noted that, at shorter wavelengths, multiple order waveplates (of the same thickness) have higher order numbers. For instance, at 355 nm, a half waveplate with approximately 0.67 mm thickness has an order number m{18 (R{37λ/2 or N{18.5), compared with m{11 (R{23λ/2 or N{11.5) at 532 nm. This, together with the higher dispersion of the birefringence, narrows the useful spectral bandwidth. Temperature affects not only expansion and therefore plate thickness, but also its birefringence. The change in retardation (in waves) due to temperature can be estimated as follows: Equation 10 Where α is the coefficient of linear expansion perpendicular to the optic axis. As for the wavelength dependence, it is directly proportional to the total retardation of the waveplate, making multiple-order waveplates much more sensitive to temperature changes than the compound zero order waveplates. For instance, for a λ/2 QWPO waveplate designed at 532 nm, the retardation tolerance is within λ/200 for temperature changes up to ± 80 C, compared to less than ± 4 C for a QWPM multiple-order waveplate. Retardation of a crystal quartz waveplate depends on its birefringence and the pathlength, and because the optic axis is in the plane of the surface, angle of incidence therefore affects retardation. The optical paths along and across the optic axis vary separately with the angle of incidence and orientation of the incident light: light incident at an angle rotated about the optic (slow) axis is retarded more, and light incident in the other direction is retarded less, while light incident in a plane at 45 sees practically no change in optical path as compared to normal. For multiple order waveplates, the change in retardation (in waves) with angle of incidence can be estimated at small angle as follows: for a rotation about the optic (slow) axis, and Equation 11 Equation 12 for a rotation perpendicular to the optic axis, where i is the angle of incidence (or tilt) in radians. The degree of sensitivity is thus determined by both the thickness of the plate(s), and the square of the angle of incidence to each axis taken separately. Unlike the wavelength and thermal dependence discussed above, the effect of angle of incidence does not cancel between the two components plates for compound zero-order waveplates. They possess the same sensitivity to angle of incidence as multiple order waveplates of the same thickness; our catalog QWPO waveplates are therefore twice more tilt sensitive than their QWPM counterparts. This effect can be reduced by using thinner waveplates. When working with collimated light, sensitivity to angle of incidence can be used to fine tune the retardation or adapt the retarder for use at another wavelength close to the design wavelength. Rotating the waveplate about the optic (slow) axis will increase the retardation or shift the design wavelength to a longer wavelength. Rotating the waveplate about its fast axis, on the other hand, decreases the retardation or shifts the design wavelength to a shorter wavelength. It should be noted that the waveplate s optic axis is often aligned at 45 to the incoming linear polarization, in which case the angle tuning should be performed in a plane at IDEX Optics & Photonics Marketplace

5 For uncollimated light, however, the sensitivity to angle of incidence will reduce the performance of the waveplate. Angular effects are best minimized by keeping the angle of incidence and divergence of a beam to within 30 minutes. Waveplates are typically designed for use at normal incidence, but custom waveplates can be manufactured for best performance at a specific angle of incidence. Polarization Rotators: Circular birefringence A second type of birefringence known as circular birefringence arises when the index of refraction of a material is different for left-handed and right-handed circularly polarized light. This occurs when light travels parallel to the optic axis of crystal quartz, causing a phase shift between the two polarization components. The effect induced is a progressive rotation of the plane of polarization with path length. This is how polarization rotators work, and allows them to be used simply at normal incidence; no angular adjustment is required. Circular birefringence occurs in optically active materials, such as crystal quartz, when the plate is cut with the optic axis normal to its polished surfaces. When linearly polarized light is incident at 90 to the surface, i.e., parallel to the optic axis, the difference in velocity between the left-handed and right-handed circular polarizations has the effect of causing the resultant plane of polarization to rotate about the optic axis. The amount of rotation is directly proportional to the path length. The result of the superposition of the counter-rotating circular polarizations is always to produce linear polarization, without any intermediate elliptical polarization state. This is the distinction between optical activity (circular birefringence) and the more commonly known linear birefringence. A useful practical feature of rotators is that, unlike half waveplates, the rotation of polarization is independent of orientation. That is to say, when an input beam of light is propagating parallel to its optic axis, the rotation effect induced is independent of the angle at which the light is linearly polarized. Another difference with half waveplates is that their effect is reversed upon a second transmission in the opposite direction. For example, if the light is retro-reflected back through the polarization rotator, it will be returned to its original polarization state. Thus the polarization rotation effect can be made cumulative only upon repeated passes in the same direction, as in ring lasers. Polarization Rotators Our RT polarization rotators are made from a single laser quality crystal quartz plate cut with the optic axis normal to the polished surfaces. They use optical activity to rotate the plane of polarization of linearly polarized light by a fixed angle at a specific wavelength, maintaining the linear polarization state throughout propagation. The rotation angle at a particular wavelength is determined by the product of the specific optical rotatory power ( / mm) and thickness of the quartz plate. Quartz rotatory power is strongly dependent on the wavelength, varying nearly as the inverse of the square of the wavelength. A crystalline quartz rotator is therefore normally used at its specific design wavelength, and useful only over a narrow wavelength band. Quartz rotatory power is about 27 /mm at 532 nm, 6.4 /mm at 1064 nm and 3 /mm at 1550 nm. Due to the small rotatory power at longer wavelengths, quartz rotators are mostly used for wavelengths shorter than 1550 nm, as the required thickness may be significant, causing difficulties due to accumulation of material defects. Although higher in cost than a λ/2 waveplate, the rotation angle is independent on the initial orientation; only normal alignment to the incident beam is required. They can therefore perform more efficiently, delivering consistent rotation of polarization, especially when the direction of the input linear polarization is not stable. Furthermore, they can easily be provided at custom rotation angles, sizes, and wavelengths. Polarization rotators are only slightly temperature dependent. Making the final decision Bandwidth, degree of retardation, alignment convenience and operating temperature range will often determine the type of waveplate to be used, but additional factors may influence your final decision, such as LIDT, cost, and space constraints. All of our quartz waveplates are offered in an optional ring mount, or unmounted. Since high power UV light can separate optically contacted waveplates, we recommend use of QWPO-AS air-spaced zero-order waveplates for wavelengths shorter than 248 nm and repetition rates higher than 1 KHz. If you are planning to use a zero-order waveplate over a broad bandwidth, you may also want to consider the retardation tolerance at that bandwidth for the specific waveplate. For example, a QWPO waveplate with 16 nm of bandwidth for λ/200 λ/500 retardation tolerance can be used over a IDEX Optics & Photonics Marketplace 5

6 broader bandwidth of 80 nm, but with a lower retardation tolerance of λ/50. CVI Laser Optics manufactures semi-custom and custom retarders with different dimensions, shapes, design wavelengths and user-specified retardation. We can also manufacture low-order quartz waveplates for applications where a large field of view or higher stability with wavelength and temperature variation is required. Whatever your needs may be, our technical staff is ready to help you find the right off-the-shelf, semi-custom, or fully customized component to suit your application. Selection Guide: Product Code Description Effect of polarization Bandwidth Retardation Tolerance Additional Features QWPM Multiple-order waveplate, crystal quartz λ/2 or λ/4 retardation < nm (for λ/100) λ/200 - λ/500 Best for specific wavelengths & temperatures Less sensitive to angle of incidence than QWPO Available either unmounted or ring-mounted QWPD Dual-wavelength waveplate, crystal quartz Retards one wavelength λ/2, leaves other unchanged < 1 532/1064 nm λ/100 at both wavelengths Best for specific wavelenghs & temperatures Available either unmounted or ring-mounted QWPO Zero-order compound waveplate, crystal quartz λ/2 or λ/4 retardation nm (for λ/100) λ/200 - λ/500 Increased useful bandwidth Good thermal stability Optically contacted (unmounted or ring-mounted) and air-spaced versions available RT 90 Polarization rotator, crystal quartz Rotates linear polarization by 90 Single λ, but rotation varies smoothly with wavelength ±0.5 rotation tolerance No angular adjustment required; simply used at normal incidence Only slightly temperature dependent Narrow useful bandwidth 6 IDEX Optics & Photonics Marketplace