URSI AP-RASC 2019, New Delhi, India, 09 - 15 March 2019 Manifesting the Effects of Thermal Nonlinearity in Optical Trapping for Rayleigh Regime Tushar Gaur (1) , Soumendra Nath Bandyopadhyay (2) , and Debabrata Goswami* (1,2) (1) Centre for Laser and Photonics, Indian Institute of Technology, Kanpur-2018016 (2) Department of Chemistry, Indian Institute of Technology, Kanpur-2018016 Abstract Since long the thermal effects have not been much explored in the optical trapping theory, in this paper, we are establishing the effects of optically induced thermal nonlinearity in the medium of optical trapping in the Rayleigh regime for both continuous wave and a pulsed laser. For a single beam, optical tweezers with high numerical aperture (N.A.) objectives are used as a routine. In such a tight focusing scenario, both optical nonlinearity and thermal effects may prevail in the cases of continuous wave (C.W.) and pulsed laser-mediated optical trapping events. In this paper we will introduce the effects sequentially, starting from optical nonlinearity and methods to implement this effect and subsequently introduce the thermal nonlinearity in the medium. The effects are significantly different when compared between CW and pulsed optical tweezers and will be discussed in detail in this paper. 1. Introduction Nobel prize for the year 2018 made the discovery of Optical Tweezer (OT) by Arthur Ashkin more prominent and brought his important discovery worldwide accolade. At the same time, the shared Nobel prize for ultra-fast lasers made it obvious for groups like ours who are using ultra-fast lasers in optical trapping to take the conjugation of two discoveries to the next level. Theoretical development for OT had been started years ago to simulate real experimental scenario. On this regard optical (Kerr) nonlinearity and its effect on OT have been discussed by some scientists. Discovery of optical non-nonlinearity has not only revitalized the study of light-matter interaction but also has provided a new basis for many exciting applications such as nonlinear optical modulation, Optical switching, optical delays, etc. But since so long, the effects of thermal nonlinearity were being subdued in optical tweezers theory. The inclusion of nonlinear optics in the study of forces on optically trapped particle before this work introduced the effects of electronic nonlinearity (Kerr Effect) [1,2], but this electronic nonlinearity is not the only nonlinear effect present in a medium, and thermal nonlinearity also plays a major role [3]. We show here that thermal effects in the medium play a prominent role in both CW and pulsed laser-mediated optical traps for Rayleigh range particles. In our numerical method, we have used a pulsed laser with a central wavelength of 780nm, a repetition rate of 76 MHz with a pulse width of 160 fs. The CW laser source is also set at 780nm, and the average power for both cases are kept the same for thorough comparison for the 60nm particle. 2. Measuring Thermal Nonlinearity Interaction of high-intensity light with the material through which it propagates results in changing the properties of the material which in turn results in the generation of higher order harmonics. For the case of nonlinear interaction, induced polarization in the material is given as: ()= [ 1 ()+ 2 2 ()+ 3 3 () …. Here is the higher order nonlinear susceptibility of the material with n representing the order of nonlinearity. E(t) is the incident electric field which in our case is the electric field for a Gaussian TEM00 beam. Here second order nonlinearity is zero for the materials showing inverse symmetry however third order nonlinearity is present irrespective of material showing inverse symmetry or not. Contribution of third order nonlinearity is given by: 3 ()= 3 3 () Now total refractive index in the presence of optically induced nonlinearity can be given as: = + 2 here, is the constant linear refractive index of the material and 2 is the strength of refractive index contributed by the nonlinearity in the material. Where 2 is given by: 2 = . 0395 2 3 () The more detailed theory about optical nonlinearity can be found in reference [4]. Due to this intensity-dependent refractive index of the material, the material under the illumination of light now acts as the self-focusing and self- defocusing lens. When n2 is positive, the material starts to show self-focusing and for negative n2 material starts showing self-defocusing. Although we are not considering