The rapid progress on developing new and improved multifunctional materials, for optoelectronic and spin based phenomena/devices, have increased the importance of the fundamental understanding of their coherent states and nonlinear optical properties. This study is aimed at characterizing, modeling, and controlling the fundamental electronic, phononic, and spin properties of several classes of materials through nonequilibrium and nonlinear light-matter interactions, coupled with a novel design of the material phases, interfaces, and heterostructures. This research directly addresses the Grand Challenges identified in the Basic Energy Sciences Advisory Committee report "Directing Matter and Energy: Five Challenges for Science and the Imagination" (Hemminger, 2007) [1], in particular, the area: "Matter far beyond equilibrium" and addresses the questions, "How do remarkable properties of matter emerge from complex correlations of the atomic or electronic constituents and how can we control these properties?" and "How do we design and perfect atom- and energy-efficient synthesis of revolutionary new forms of matter with tailored properties?". The knowledge gained from these fundamental studies can provide new information for a broad community to provide concepts for the next generation of multifunctional materials and devices, and resulted in several publications and conference presentations. The materials studied in this dissertation included multiferroic BaTiO3-BiFeO3 [2], ferroelectric Pb0.52Zr0.48TiO3 (PZT), InAs/AlAsSb multi-quantum-well [3], lead halide perovskite [4], n-type InAsP films [5, 6], and nanolaminate plasmonic crystals [7]. Probing multiferroics, which are materials that can exhibit ferromagnetic, ferroelectric, and ferroelastic orders simultaneously in a single phase, was a main focus of this study. BiFeO3 (BFO) is the most widely investigated multiferroic due to its high Neel and Curie temperatures and has antiferromagnetic and ferroelectric properties [8]. An inherent drawback of BFO is its large leakage currents. In this project, (1 − x)BaTiO3-(x)BiFeO3, x = 0.725 (BTO-BFO) heterostructures were investigated [9], where the conductivity of the solid solution can be reduced by adding another perovskite material, BaTiO3 [2]. We aimed to study optically induced coherent states in our BTO-BFO structures. Time resolved pumpprobe spectroscopic measurements were performed at room temperature as well as at low temperature (100 K) up to 10 T. Coherent acoustic phonons were observed both in a film and nanorods, resulting in coherent phonon frequencies of 27 and 33 GHz, respectively [2]. Coherent phonon spectroscopy is a sensitive tool to characterize the interfaces and can be employed as an effective ultrasensitive quantum sensor [10]. Furthermore, in the nanorods arrays of BTO-BFO, an additional oscillation with frequency in the range of 8.1 GHz was observed. This frequency is close to a theoretically predicted magnon frequency which could indicate the coexistence of coherent phonons and magnons in the nanorods arrays [2]. In an analogy to photonics which relies on electromagnetic waves, magnonics utilizes spin waves to carry and process information, offering several advantages such as an operation frequency in the THz range. Recently, "a quantum tango" [11] was reported where coupled coherent magnon and phonons modes were formed on a surface patterned ferromagnet. Furthermore, BTO-BFO heterostructures were probed using transient birefringence and magneto-optical Kerr effect spectroscopy. The results demonstrated that the magnetic field dependence of coherent phonons, measured by these two techniques, exhibits more sensitivity to the external magnetic fields compared to the differential reflectivity technique [2]. Moreover, nonlinear optical properties of this structure were investigated via second harmonic generation spectroscopy, where wavelength and polarization dependence of this nonlinear observation will be discussed in this dissertation. As part of this study, another class of multiferroic materials, with strong ferroelectric and piezoelectric properties, Pb0.52Zr0.48TiO3 (PZT) was studied [12]. In this project, the nonlinear optical properties of PZT nanorod arrays were investigated. Clear signatures of second harmonic generations from 490-525 nm (2.38-2.53 eV) at room temperature, were observed. Furthermore, time resolved differential reflectivity measurements were performed to study dynamical properties in the range of 690-1000 nm where multiphoton processes were responsible for the photoexcitations. We compared this excitation scheme, which is sensitive mainly to the surface states, to when the photoexcited energy (∼ 3.1 eV) was close to the bandgap of the nanorods. Our results offer promises for employing these nanostructures in nonlinear photonic applications. Furthermore, the established techniques during my research provided new insights on optical properties of InAs/AlAsSb multi-quantum-well [3], lead halide perovskite [4], n-type InAsP films [5, 6], and nanolaminate plasmonic crystals [7], and the results will be briefly presented in this dissertation. / Doctor of Philosophy / My research activities have explored multifunctional materials and heterostructures with strongly enhanced coupled electric and magnetic orders and optical properties. In particular, pursuing novel heterostructure designs such as multiferroics can provide control over electric and magnetic ordering in mixed dimensionality. This, together with control at the level from lattice structure to electron spin states can give rise to improved or even qualitatively new and robust materials properties. For example, a better understanding of the phenomena associated with the spin degree of freedom of electrons allows for advancement in spintronic device applications such as storage, logic, and sensors, which are associated with quantum computers and quantum communications [13, 14, 15]. Overarching questions and goals of my activities included: What are the microscopic origins and mechanisms of nonlinear response in strongly coupled nanostructured materials and its relationship to electronic, spin, and lattice degrees of freedom? (2) What are the effects of dimensionality and quantum confinement on optical properties? (3) How do we control and manipulate the coherent states, such as coherent phonons and magnons using external and internal fields, material composition, and morphology to achieve maximal efficiency and tunability? Addressing many of the challenges in the fast-paced technological world requires continued developments of new materials with enhanced optical properties. The knowledge gained from my fundamental studies can provide new information for the next generation of multifunctional materials and devices with advanced optical properties and resulted in several publications and conference presentations.