Waveplates Intro Windows � � Technical Notes . 222 Selection Guide . 225 � Prisms Multiple Order. 226 θ � �� Zero Order Lenses Crystal Quartz . 228 Mica . 230 Mirrors Polymer. 231 Beamsplitters First Order . 232 Dual Wavelength . 233 Waveplates Achromatic Air-Spaced. 234 Polarizers Polymer . 236 Polarization Rotators . 237 Components Ultrafast Etalons Filters Interferometer Accessories ���� ��������������������� Mounts Appendix ������� ���������� Index �������������� Waveplates Intro Technical Notes Waveplates operate by imparting unequal The slow and fast axis phase shifts are � � Windows phase shifts to orthogonally polarized field given by: components of an incident wave. This φs ω ω π λ λ = ns ( ) t/c = 2 ns ( )t/ � causes the conversion of one polarization φf = nf (ω)ωt/c = 2πnf (λ)t/λ Prisms state into another. where ns and nf are, respectively, the θ � indices of refraction along the slow and There are two cases: �� fast axes, and t is the thickness of the Lenses With linear birefringence, the index of waveplate. refraction and hence phase shift differs for two orthogonally polarized linear To further analyze the effect of a waveplate, polarization states. This is the operation we throw away a phase factor lost in Mirrors Figure 1. Orientation of the slow and fast axes measuring intensity, and assign the entire mode of standard waveplates. of a waveplate with respect to an X-polarized phase delay to the slow axis: input field. With circular birefringence, the index of iφ refraction and hence phase shift differs E2 = s(s · E1)e + f(f · E1) For a half waveplate: Beamsplitters φ = φ - φ = 2π(n (λ) - n (λ))t/λ 2 for left and right circularly polarized s f s f φ = (2m + 1)π, T|| = cos 2θ, and = 2π∆n(λ)t/λ 2 components. This is the operation mode of T⊥ = sin 2θ. This transmission result is the polarization rotators. In the above, ∆n(λ) is the birefringence same as if an initial linearly polarized wave Waveplates θ n (λ) - n (λ). The dispersion of the were rotated through an angle 2 . Thus, a Standard Waveplates: s f birefringence is very important in half waveplate finds use as a polarization Linear Birefringence waveplate design; a quarter waveplate at rotator. Polarizers Suppose a waveplate made from a uniaxial a given wavelength is never exactly a half For a quarter waveplate: material has light propagating perpendicular waveplate at half that wavelength. φ = (2m + 1)π/2; ie. an odd multiple of to the optic axis. This makes the field π/2. To analyze this, we have to go back to Let E1 be initially polarized along X, and let Ultrafast component parallel to the optic axis an Components the waveplate slow axis make an angle θ the field equation. Assume that the slow extraordinary wave and the component with the X-axis. This orientation is shown and fast axis unit vectors s and f form a right perpendicular to the optic axis an ordinary in Figure 1. handed coordinate system such that s x f = Etalons wave. If the crystal is positive uniaxial, n e +z, the direction of propagation. To obtain > n , then the optic axis is called the slow o When the waveplate is placed between circularly polarized light, linearly polarized axis, which is the case for crystal quartz. parallel and perpendicular polarizers the light must be aligned midway between Filters For negative uniaxial crystals, n < n , the e o transmissions are given by: the slow and fast axes. There are four optic axis is called the fast axis. 2 2 2 possibilities listed in the table below. T|| ∝ |E2x| = 1 - sin 2θsin φ/2 The equation for the transmitted field E , in ∝ | |2 2 θ 2 φ 2 T⊥ E2y = sin 2 sin /2 Input Field Input Field terms of the incident field E1 is: Along Along Accessories Interferometer Phase Shift (s + f)/√2 (s - f)/√2 iφs iφf Note that θ is only a function of the E2 = s(s · E1)e + f(f · E1)e waveplate orientation, and φ is only φ = π/2 + 2mπ RCP LCP where s and f are unit vectors along the a function of the wavelength, the φ = 3π/2 + 2mπ LCP RCP Mounts slow and fast axes. This equation shows birefringence is a function of wavelength explicity how the waveplate acts on Sometimes, waveplates described by and the plate thickness. the field. Reading from left to right, the the second line above are called 3/4 waveplate takes the component of the For a full waveplate: waveplates. For multiple order waveplates, Appendix input field along its slow axis and appends φ = 2mπ, T|| = 1, and T⊥ = 0, regardless of CVI permits the use of either of the the slow axis phase shift to it. It does a waveplate orientation. above classes of waveplates to satisfy the Index similar operation to the fast component. requirements of a quarter waveplate. 222 Americas (505) 296-9541 | Europe +44 (0) 1624 647000 | Asia +82 (0) 32 673-6114 | Order now at www.cvilaser.com Waveplates Intro Technical Notes Windows Multiple Order Waveplates or broad bandwidth sources (example: CVI’s line of MWPS Series Mica Waveplates femtosecond lasers). A zero order are an inexpensive zero order waveplate For the full, half, and quarter waveplate waveplate can greatly improve the useful solution. They are useful in low power examples given in the preceeding section, Prisms bandwidth in a compact, high damage applications and in detection schemes. the order of the waveplate is given by the threshold device. integer m. For m > 0, the waveplate is Polymer Waveplates termed a multiple order waveplate. For As an example, consider the design of Polymer waveplates offer excellent angular Lenses m = 0, we have a zero order waveplate. a broadband half waveplate centered field-of-view since they are true zero-order at 800nm. Maximum tuning range is The birefringence of crystal quartz waveplates. Figure 4 compares the change obtained if the plate has a single π phase near 500nm is approximately 0.00925. in retardance as a function of incidence Mirrors shift at 800nm. If made from a single plate Consider a 0.5mm thick crystal quartz angle for polymer and quartz waveplates. of crystal quartz, the waveplate would be waveplate. A simple calculation shows A polymer waveplate changes by less than about 45µm thick, which is too thin for Beamsplitters that this is useful as a quarter waveplate 1% over a ±10° incidence angle. easy fabrication and handling. The solution for 500nm; in fact, it is a 37 λ/4 waveplate is to take two crystal quartz plates differing Retardance accuracy with wavelength at 500nm with m = 18. Multiple order in thickness by 45 µm and align them with change is often of key concern. For waveplates are inexpensive, high damage Waveplates the slow axis of one against the fast axis example, an off-the-shelf diode laser has threshold retarders. Further analysis shows of the other. The net phase shift of this a center wavelength tolerance of ±10nm. that this same 0.5mm plate is a 19 λ/2 zero order waveplate is π. The two plates Changes with temperature and drive half waveplate at 488.2nm and a 10λ full may be either air-spaced or optically conditions cause wavelength shifts which Polarizers waveplate at 466.5nm. The transmission contacted. The transmission of an 800nm may alter performance. These polymer of this plate between parallel polarizers zero order half waveplate between parallel waveplates maintain excellent waveplate is shown in Figure 2 as a function of performance even with minor shifts in the Components polarizers is shown in Figure 3 using a Ultrafast wavelength. The retardance of the plate 0-10% scale. Its extinction is better than source wavelength. at various key points is shown. Note 100:1 over a bandwidth of about 95nm how quickly the retardance changes with ���� centered at 800nm. ������ ������� wavelength. Because of this, multiple order Etalons ���� ����������� ��������� waveplates are generally useful only at their CVI produces multiple order and zero ������� design wavelength. order crystal quartz waveplates at any ���� ����������� wavelength between 193nm and 2100nm. ����������� ���� Zero Order Waveplates ��������� Filters Virtually all popular laser wavelengths are ���� As discussed above, multiple order kept in stock, and custom wavelength parts � �� �� �� �� �� ������������������������� Interferometer waveplates are not useful with tunable are available with short delivery time. Accessories Figure 4. Retardance vs. Incidence Angle for Quartz and Polymer waveplates. ��� �� �� λ � λ � λ The temperature sensitivity of laminated ���� ���� ������������� Mounts �� � polymer waveplates is about 0.15 nm/°C, �� � allowing operation over moderate λ λ λ λ λ �� �� �� �� �� �� �� �� �� �� �� ������������ � � temperature ranges without significantly Appendix ������������ � �� � degrading retardance accuracy. A λ λ �� λ� �� �� �� �� �� � comparison of different waveplate types � � ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� ���� and their dependence on wavelength is ��������������� ��������������� shown in figure 5 on the next page. Index Figure 2. Transmission of a 0.5 mm thick crystal Figure 3. Zero order crystal quartz half quartz waveplate between parallel polarizers. waveplate for 800nm. continued Americas (505) 296-9541 | Europe +44 (0) 1624 647000 | Asia +82 (0) 32 673-6114 | Order now at www.cvilaser.com 223 Waveplates Intro Technical Notes ����� ���������� Three wavelength ranges are available in Dual Wavelength Waveplates ���������� �������������� Windows ����� both quarter and half wave retardances. Dual wavelength waveplates are used in ������� Retardation tolerance is better than λ/100 ����� a number of applications. One common over the entire wavelength range. We application is separation of different ����������� Prisms ����� plot the intensity transmission and the wavelengths with a polarization beam ����� actual phase shift for each design versus ���� ���� ���� ���� ���� splitter by rotating the polarization of one wavelength on page 235. ���������������������λ�λ�� l wavelength by 90°, and leaving the other Lenses Figure 5. Wavelength performance of common For quarter waveplates, perfect retardance unchanged. This frequently occurs in quarter wave retarders.