PHYSICAL REVIEW E 85, 041702 (2012) Light emission from dye-doped cholesteric liquid crystals at oblique angles: Simulation and experiment L. Penninck, * J. Beeckman, P. De Visschere, and K. Neyts ELIS (Electronics and Information Systems Department), Ghent University, St. Pietersnieuwstraat 41, Ghent, Belgium and Center for Nano- and Bio-photonics, Ghent University, St. Pietersnieuwstraat 41, Ghent, Belgium (Received 22 December 2011; published 9 April 2012) Dye-doped cholesteric liquid crystals with a helical pitch of the order of a wavelength have a strong effect on the fluorescence properties of dye molecules. This is a promising system for realizing tunable lasers at low cost. We apply a plane wave model to simulate the spontaneous emission from a layer of cholesteric liquid crystal. We simulate the spectral and angle dependence and the polarization of the emitted light as a function of the order parameter of the dye in the liquid crystal. Measurements of the angle dependent emission spectra and polarization are in good agreement with the simulations. DOI: 10.1103/PhysRevE.85.041702 PACS number(s): 42.70.Df, 42.79.Kr, 78.20.Bh, 78.15.+e I. INTRODUCTION The self-ordering and easy tunability of liquid crystals have already led to an impressive number of applications. Recently, the use of liquid crystals has been suggested in many types of devices such as tunable filters [1], tunable optical chips [2], nonlinear optical devices, etc. In this article we focus on light emission from liquid crystal devices. In past years liquid crystal lasers have been developed with interesting properties that are difficult to achieve in other laser systems, most notably tunability and low fabrication cost [3]. Cholesteric liquid crystals (CLC), in which the director describes a helix with submicrometer pitch, are a class of materials with very interesting optical properties. The periodic structure of the CLC leads to a photonic band gap (PBG). Excited dye molecules inside the CLC no longer emit photons into the PBG region. When a sufficient number of dye molecules is excited, laser emission is observed at the edge of the band gap. Such lasers can be tuned by electrical [4], mechanical [5], or thermal [6] means. A more complete overview can be found in review papers [7,8]. The performance of light emitting liquid crystal devices may be significantly improved by using more advanced optical structures. In order to develop new optical architectures a fundamental understanding of the emission process and accurate numerical design tools are necessary. The propagation of light waves in an infinite CLC has been extensively studied over the past decades. Analytical solutions for propagation along the helical axis were found by de Vries [9] and Kats [10]. For propagation under oblique angles several approximate solution methods were proposed [11] in the 1980s. About 10 years later an analytical solution was found [12]. Numerical studies [13] of finite structures were made with Berreman’s 4 × 4 method [14]. The case of light propagation through a CLC is thus well understood. The problem of light emission from a CLC is more involved since the interaction between the emitting dipole and the electromagnetic modes and the finite dimensions of the structure have to be accounted for. The effects of the CLC on the fluorescence spectrum and polarization were first studied * lieven.penninck@elis.ugent.be by Pollmann et al. [15] for wavelengths much shorter than the PBG (known as the Mauguin regime). Recent studies [16] have focused on emission wavelengths near the PBG (Bragg regime). An analytical model for the spontaneous emission from a CLC in the normal direction has been proposed by Schmidtke and Stille [17] based on the electric field profile of the eigenmodes of the CLC. This analytical approach is limited to basic structures and directions for which the eigenmodes are known. For more complex structures and/or emission directions for which the eigenmodes are not known, “brute force” numerical methods such as FDTD (finite-difference time domain) [18] can be used. However, such methods consume a lot of computer time and memory. In this work we simulate the spontaneous emission from a one-dimensional (1D) CLC stack based on a decomposition of the field in plane polarized waves [19]. The advantage of this method is that complex stacks can be modeled with very limited computational effort. We have used this method to investigate the angle and polarization dependence of the emitted spectrum and the influence of the orientation of the emitting dye. The simulation results are compared to the measured spectrum for different polarizations and emission angles. The materials and experimental methods are detailed in Sec. II. A simplified analytical model and the detailed numerical formulas are explained in Secs. III A and III B, respectively. In Sec. IV the experimental, theoretical, and numerical results are compared and discussed. II. EXPERIMENTAL PROCEDURE For the experiments we use a mixture of the nematic liquid crystal E7 (Merck) with a chiral dopant BDH1305 (Merck) and a laser dye DCM (Exciton). The three materials are mixed in a ratio of 94.03%/5.07%/0.9% by weight, respectively. To determine the molecular order parameter S dye of the dye a mixture containing no chiral dopant is made (0.98%/99.02% by weight of DCM/E7). The mixtures are heated above the clearing point and then returned to room temperature; the mixtures were stirred throughout this process. Premade single pixel cells (Instec) are filled with the mixtures by capillary action. The cells consist of two parallel 041702-1 1539-3755/2012/85(4)/041702(7) ©2012 American Physical Society