Chapter 47 Theoretical Calculation of Joint Spectral Intensity of Type-I BBO Crystal for SPDC Swati Gangwar, Shibu Saha, Parag Sharma, V. K. Jaiswal, and Ranjana Mehrotra Abstract Spontaneous Parametric Down-Conversion (SPDC) is a second order non- linear quantum optical phenomenon which finds application in quantum communica- tion network and quantum cryptography. One of the important characteristic param- eters of SPDC is Joint Spectral Intensity (JSI). In this paper, effect of crystal length on the Joint Spectral Intensity is studied for type-I phase- matching in BBO crystal. The strength of the JSI peak signifies the conservation of energy and momentum in a SPDC process which leads to generation of correlated photon pairs in a particular wavelength. The JSI is observed to decrease with crystal length for BBO crystal in the present study. 47.1 Introduction Spontaneous Parametric Down Conversion (SPDC) is a nonlinear instantaneous optical processes that converts one photon of higher energy into a pair of photons (signal and idler) of lower energy, in which the fundamental quantities like energy and momentum are conserved [1]. SPDC is purely a quantum optical process based on second order nonlinearity. The nonlinear susceptibility of the medium and the phase mismatch parameter are used to determine the efficiency of the nonlinear optical processes. When the phase matching condition k =0 has satisfied than realizing optimal energy conversion efficiency [2]. The phase-matching processes in SPDC are of two types. The down converted photons have the same polarization in Type-I phase matching while the down converted photons have orthogonal polarization in the type-II phase matching [3]. S. Gangwar (B ) · S. Saha · P. Sharma · V. K. Jaiswal Academy of Scientific and Innovative Research (AcSIR), Kamla Nehru Nagar, Ghaziabad 201002, UP, India e-mail: swatigangwar96@gmail.com S. Gangwar · S. Saha · P. Sharma · V. K. Jaiswal · R. Mehrotra CSIR-National Physical Laboratory, Dr. K. S. Krishnan Marg, New Delhi 110012, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 K. Singh et al. (eds.), ICOL-2019, Springer Proceedings in Physics 258, https://doi.org/10.1007/978-981-15-9259-1_47 211