Symmetry breaking is a fundamental concept in physics and the consideration of it leads to the emergence of new material properties and behaviors. In the field of metamaterials, symmetry consideration is a route to generate new kinds of optical properties, such as bianisotropy, harmonic generation, topological phase transition. Specifically, exceptional points are non-Hermitian singularities where both eigenvalues of eigenmodes of a system response matrix coalesce, that can be generated when we lower the symmetry of the metamaterial to a combined parity-time (PT) symmetry without satisfying the individual symmetries. These exceptional points can be useful in sensing. Although PT symmetry prescribes a systematic recipe for implementing exceptional points, there are alternative methods to construct exceptional points by breaking mirror symmetry with bianisotropy. In this thesis, I use the tool of transformation optics to generate exceptional points by coordinate-transforming a known PTsymmetric system. The transformed systems are still equipped with exceptional points and phase transitions but will not possess the PT-symmetry in conventional sense anymore. Furthermore, we explore the existence of exceptional points in the airborne acoustic platform by coupling two resonances of the meta-atom without obeying any spatial-PT-symmetry. By determining the eigenmode (stability) of the meta-atom, the exceptional point is observed at a complex frequency in the lower half of the complex frequency plane.
In addition, time modulation provides another degree of freedom for symmetry breaking, such as the continuous time translational symmetry. Specifically, I have constructed airborne acoustic platform in which the modulation frequency of material parameters can be significantly greater than the signal frequency. It allows us to consider the concept of temporal effective medium, in analogy to effective medium in spatial domain. However, different from spatial modulation, we need to consider whether the system response can follow the change of modulation parameters. Therefore, I consider a general time-modulating dispersive medium with a Lorentzian resonance and find that the temporal effective medium formula becomes different when we time modulate different resonance parameters, such as resonating frequency, strength and linewidth. Using the acoustic platform's capability of modulating resonance parameters at a dozen times faster than the signal frequency, I experimentally verify these effective medium formulas by scattering experiments. As further applications of the time-modulation of material parameters. I further set the modulation frequency to match the frequency difference between two tailor-made resonance modes and demonstrate the phenomenon of unidirectional amplification in frequency conversion. I further show that when we time modulating a resonating system with an exceptional point, such an exceptional point can be modulated to other harmonic frequencies. As a whole, the findings in this thesis based on PT-symmetry breaking and time translational symmetry breaking could further be used for controlling constitutive parameters in both space and time. Additionally, the design of exceptional points based on coupling resonant modes and time modulation can be utilized for further applications, such as sensing.