In the present work, we introduce a novel cochlear implant (CI) architecture, namely all-optical CI (AOCI), which directly converts acoustic to optical signals capable of stimulating the cochlear neurons. First, we describe the building-blocks (BBs) of the AOCI, and explain their functionalities as well as their interconnections. Next, we present a comprehensive system model that incorporates the technical characteristics and constraints of each BB, the transdermal-optical-channel particularities, i.e. optical path-loss and external-implanted device stochastic pointing-errors, and the cochlear neurons biological properties. Additionally, in order to prove the feasibility of the AOCI architecture, we conduct a link-budget analysis that outputs novel closed-form expressions for the instantaneous and average photon flux that is emitted on the cochlear neurons. Likewise, we define three new key-performance-indicators (KPIs), namely probability of hearing, probability of false-hearing, and probability of neural damage. The proposed theoretical framework is verified through respective simulations, which not only quantify the efficiency of the proposed architecture, but also reveal an equilibrium between the optical transmission power and the patient's safety, as well as the AOCI BBs specifications. Finally, it is highlighted that the AOCI approach is greener and safer than the conventional CIs.