Simple spectral technique to identify the ordinary and extraordinary axes of a liquid crystal retarder María del Mar Sánchez-López a , Asticio Vargas b,c , Aaron Cofré b , Ignacio Moreno d,n , Juan Campos e a Instituto de Bioingeniería, Universidad Miguel Hernández de Elche, 03202 Elche, Spain b Departamento de Ciencias Físicas, Universidad de La Frontera, Temuco, Chile c Center for Optics and Photonics, Universidad de Concepción, Casilla 4016, Concepción, Chile d Departamento de Ciencia de Materiales, Óptica y Tecnología Electrónica, Universidad Miguel Hernández de Elche, 03202 Elche, Spain e Departamento de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain article info Article history: Received 3 February 2015 Received in revised form 16 March 2015 Accepted 22 March 2015 Available online 24 March 2015 Keywords: Waveplates Birefringence Liquid Crystal Retarders abstract We present a very simple method to distinguish between ordinary and extraordinary axes in an optical retarder. The method is based on inserting the retarder in between two crossed linear polarizers, or- iented at 45° to the neutral axes. By tilting the retarder to obtain oblique-incidence illumination, a dif- ferent behavior is observed depending on the orientation of the ordinary/extraordinary axes relative to the tilt direction. Simply using white light illumination from a tungsten lamp and spectral analysis by means of a portable spectrometer, it is possible to differentiate between ordinary and extraordinary axes. Theoretical analysis is provided, as well as the experimental verification with a liquid crystal variable retarder (LCR). A significant difference of the LCR retardance variation is obtained for different or- ientation of the LC director relative to the tilt direction. & 2015 Elsevier B.V. All rights reserved. 1. Introduction Linear wave-plates (or linear retarders) are key elements in most optical systems requiring control of the state of polarization (SOP) [1]. They are made of anisotropic uniaxial material where the optical axis lies in the plate plane. Two parameters must be known for their proper use: the retardance ϕ they introduce be- tween ordinary and extraordinary waves for the operating wave- length () λ , and the orientation of the principal optical axis relative to the laboratory reference frame. Under the common assumption of a linear retarder (i.e., devoid of depolarization or diattenuation), the neutral axes can be found by simply inserting the retarder between crossed polarizers. Since retarders are usually mounted on in-plane rotatable mounts, their neutral axes are found by rotating the retarder and searching for the angles where a null transmission between the crossed polar- izers is retained. However, this simple method does not resolve the ambiguity among the ordinary and extraordinary neutral axis. In addition, different methods have been developed to measure the waveplates’ retardance [2]. Those based on heterodyne inter- ferometry provide very precise measurements [3,4], but they are limited to use monochromatic light with specific wavelength and require complex systems. Other techniques use spectral mea- surements. When the wave-plate is inserted between crossed polarizers, and the system is illuminated with a continuous broadband light source, the transmitted light exhibits an oscillat- ing spectrum due to the approximated λ À1 dependence of the spectral retardance ( ) ϕλ [5–8]. However, again, these methods do not distinguish between ordinary and extraordinary axes. Therefore, different techniques have been developed to dis- tinguish between fast and slow axes. They are usually based in precise phase measurements for orthogonal polarization compo- nents using the heterodyne interference technique [9–12]. In Ref. [12] an oblique incidence on the wave-plate was selected. Another technique requires a prism retarder as a reference, so the combi- nation of the test wave-plate with the prism reveals the relative orientation of their neutral axes [13]. The technique in Ref. [14] is based on measuring the intensity reflected on a metallic surface as a function of the angle of incidence when the incident light first traverses the wave-plate. The distinction between ordinary and extraordinary axes can be especially relevant in liquid crystal variable retarders (LCR), where the orientation of the optical axis changes with applied voltage. In ferroelectric LCRs, the optical axis switches between two stable positions within the wave-plate plane [15], while in nematic LCRs it tilts towards the direction of light propagation, Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/optcom Optics Communications http://dx.doi.org/10.1016/j.optcom.2015.03.052 0030-4018/& 2015 Elsevier B.V. All rights reserved. n Corresponding author. E-mail address: i.moreno@umh.es (I. Moreno). Optics Communications 349 (2015) 105–111