* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Demonstration: quarter-wave plate and half-wave plate
Thomas Young (scientist) wikipedia , lookup
Dispersion staining wikipedia , lookup
Ultraviolet–visible spectroscopy wikipedia , lookup
Retroreflector wikipedia , lookup
Surface plasmon resonance microscopy wikipedia , lookup
Refractive index wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Anti-reflective coating wikipedia , lookup
Ellipsometry wikipedia , lookup
APPLIED COMPUTATIONAL OPTICS GROUP released on 23.03.2015 Demonstration: quarter-wave plate and half-wave plate Site Zhang* and Frank Wyrowski Abstract A waveplate, made out of optically anisotropic materials, is an optical device that manipulates the polarization of light propagating through it. For example, a quarter-wave plate converts linearly polarized light into circularly polarized light and vice versa; a half-wave plate changes the polarization direction of linearly polarized light. We demonstrate simulations of light propagation through the two types of waveplates in the software VirtualLabTM . * Correspondence: [email protected] Keywords: Quarter-wave plate, half-wave plate, polarization Introduction ∆φ = 2π∆nL , λ0 uniaxialcrystal y op tic al ax is x E e-wave Waveplates are usually made out of uniaxial crystals cut into the shape of a plate with properly chosen optical axis orientation and thickness. The optical axis of the crystal should be parallel to the plate surface, as in Fig. 1 we set the x-axis parallel to the optical axis. In such a way, two polarization directions can be defined for a normal incident plane wave: the ordinary wave polarized along x-axis with the refractive index no , and the extraordinary wave polarized along y-axis with the refractive index ne . They travel at different speeds inside the crystal and that leads to a phase difference between them when they leave the crystal. The phase difference ∆φ depends on the thickness of the crystal and it can be expressed as o- z wa ve (1) where ∆n = |ne − no | is the difference between ordinary and extraordinary refractive indices, L is the thickness of the crystal plate and λ0 is the vacuum wavelength of the light. By letting ∆φ = (2m + 1) π2 or ∆φ = (2m + 1)π in Eq. (1), a quarterwave plate or a half-wave plate is obtained respectively. If one chooses m = 0, a zero-order waveplate is obtained, which is very thin and the fabrication becomes difficult. For non-zero m, one gets a multipleorder waveplate with larger thickness, which brings convenience in the mounting but higher (undesired) sensitivity to wavelength and temperature [1]. L Figure 1: Sketch of a typical waveplate made out of uniaxial crystal. VirtualLabTM Demostrations Based on the techniques described in [2,3], fully vectorial simulations of light propagation through waveplates have been carried out in the 1 software VirtualLabTM . Quarter-wave plate We design a quarter-wave plate for the wavelength λ0 =633 nm, with quartz crystal with no = 1.543 and ne = 1.552 [4]. We choose, as an example, ∆φ = 8.5π in Eq. (1), and obtain a multiple-order quarter waveplate with m = 8. Then it is trivial to find the corresponding thickness L =299 µm. Using these parameters we set up a quarterwave plate and use a linearly polarized Gaussian wave 2 mm in front of it as the incidence. Fig. 2 shows the effect that a quarter-wave plate converts linear polarization into circular. Quarter-wave plate: • vacuum wavelength: λ0 =633 nm • refractive indices: no = 1.543 and ne = 1.552 • crystal thickness: L =299 µm • Gaussian wave waist radius: 100 µm • incident polarization: linear 45◦ Figure 2: Effect of a quarter-wave plate: the incident Gaussian wave (left) has a 45◦ linear polarization, while the transmitted wave (right) has a circular polarization. Half-wave plate Keeping all parameters the same as for the quarter-wave plate, but doubling the thickness i.e. letting L =598 µm, a half-wave plate is obtained, and its effect is shown in Fig. 3. Half-wave plate: • vacuum wavelength: λ0 =633 nm • refractive indices: no = 1.543 and ne = 1.552 • crystal thickness: L =598 µm • Gaussian wave waist radius: 100 µm • incident polarization: linear 45◦ Figure 3: Effect of a half-wave plate: the incident Gaussian wave (left) has a 45◦ linear polarization, while the transmitted wave (right) has a −45◦ linear polarization i.e. 90◦ rotation of the incident one. As expected, Fig. 3 sees a rotation of polarization by 90◦ . 2 Bibliography [1] Mounted multi-order wave plates. from http://www.thorlabs.de (online). [2] Site Zhang, Daniel Asoubar, and Frank Wyrowski. Rigorous modeling of laser light propagation through uniaxial and biaxial crystals. Proc. SPIE, 9346:93460N–93460N–13, 2015. [3] S. Zhang and F. Wyrowski. Introduction to field tracing in homogeneous anisotropic media. www.applied-computational-optics.org (online), March 2015. [4] Quartz crystal - refractive index. from http://www.crystran.co.uk (online).