In common media, electromagnetic wave always possesses a fluctuant field variation, analogous to an undulant surface of sea. While electromagnetic wave in the media with zero index metamaterials (ZIMs), whose refractive indices are near zero, homogeneous or constant field distribution will emerge, resembling a tranquil surface of lake. Such impression almost could be found in all previous literatures related to ZIMs. However, in this letter, we theoretically and numerically find that, in a cavity structure with ZIMs, when higher order modes (e.g., dipole modes) are excited inside cavity, inhomogeneous field could take place in ZIMs. Such a finding challenges the common perception in ZIMs: It is generally considered that homogeneous or constant field is generated in ZIMs. In addition, the proposed cavity structure herein could be used to manipulate radiation of light, such as enhancing or suppressing radiation, controlling radiation pattern and achieving isotropic or directive radiation, thereby potential applications are expected. These effects are well confirmed by numerical simulations.