We have developed a novel multiscale computational scheme to describe coupled dynamics of light electromagnetic field with electrons and atoms in crystalline solids, where first-principles molecular dynamics based on time-dependent density functional theory is used to describe the microscopic dynamics. The method is applicable to wide phenomena in nonlinear and ultrafast optics. To show usefulness of the method, we apply it to a pump-probe measurement of coherent phonon in diamond where a Raman amplification takes place during the propagation of the probe pulse.Nonlinear optics in solids is the study of the interaction of intense laser light with bulk materials [1][2][3]. It is intrinsically a complex phenomena arising from a coupled nonlinear dynamics of light electromagnetic fields, electrons, and phonons. They are characterized by two different spatial scales, micro-meter for the wavelength of the light and less than nano-meter for the dynamics of electrons and atoms.In early development, nonlinear optics has developed mainly in perturbative regime and in frequency domain [4,5]. However, it has changed rapidly and drastically. Nowadays, measurements are carried out quite often in time domain using pump-probe technique as a typical method and the time resolution reaches a few tens of attosecond [6,7]. Extremely nonlinear phenomena has attracted interests such as high harmonic generation in solids [8,9], ultrafast control of electrons motion in dielectrics that aims for future signal processing using pulsed light [10][11][12], and ultrafast coherent optical phonon control [13][14][15][16][17][18][19][20][21][22] and photoinduced structural phase transition of materials [23][24][25][26].In this paper, we report a progress to develop firstprinciples computational method to describe nonlinear optical processes in solids that arise from coupled dynamics of light electromagnetic fields, electrons, and atoms in crystalline solids. In condensed matter physics and materials sciences, first-principles computational approaches represented by density functional theory have been widely used and recognized as an indispensable tool [27]. Development of first-principles approaches in optical sciences is, however, still in premature stage due to the complexity of the phenomena and the requirement of describing time-dependent dynamics.Our method utilize time-dependent density functional theory (TDDFT) for microscopic dynamics of electrons [28,29]. The TDDFT is an extension of the density functional theory so as to be applicable to electron dynamics in real time [30]. In microscopic scale, ultrafast dynamics of electrons have been successfully explored solving the time-dependent Kohn-Sham (TDKS) equation, the basic equation of TDDFT, in real time [31][32][33]. We have further developed a multiscale scheme coupling FIG. 1. Schematic illustration of the multiscale scheme for a light propagation through a material.the light electromagnetic fields and electrons in solids [34], and applied it to investigate extremely nonlinear optical...