Continuous-wave mid-infrared radiation near 3.5 micrometers is generated by difference-frequency mixing of the output of a compact 1.1-1.5 micrometer dual-wavelength fiber amplifier in periodically poled LiNbO3. The diode side-pumped amplifier is constructed with double-cladding Yb-doped fiber followed by single-mode Er/Yb codoped fiber. Output powers of as much as 11 microW at 3.4 micrometers are obtained, and spectroscopic detection of CH4 and H2CO is demonstrated.