This paper describes an approach to develop and deploy low-cost plastic optical fiber sensors suitable for measuring low concentrations of pollutants in the atmosphere. The sensors are designed by depositing onto the exposed core of a plastic fiber thin films of sensitive compounds via either plasma sputtering or via plasma-enhanced chemical vapor deposition (PECVD). The interaction between the deposited layer and the gas alters the fiber's capability to transmit the light, so that the sensor can simply be realized with a few centimeters of fiber, an LED and a photodiode. Sensors arranged in this way exhibit several advantages in comparison to electrochemical and optical conventional sensors; in particular, they have an extremely low cost and can be easily designed to have an integral, i.e., cumulative, response. The paper describes the sensor design, the preparation procedure and two examples of sensor prototypes that exploit a cumulative response. One sensor is designed for monitoring indoor atmospheres for cultural heritage applications and the other for detecting the presence of particular gas species inside the RPC (resistive plate chamber) muon detector of the Compact Muon Solenoid (CMS) experiment at CERN in Geneva.