We report a fully guided-wave source of polarisation entangled photons based on a periodically poled lithium niobate waveguide mounted in a Sagnac interferometer. We demonstrate the sources quality by converting polarisation entanglement to postselection-free energy-time entanglement for which we obtain a near-optimal $S$-parameter of $2.75 pm 0.02$, i.e. a violation of the Bell inequality by more than 35 standard deviations. The exclusive use of guided-wave components makes our source compact and stable which is a prerequisite for increasingly complex quantum applications. Additionally, our source offers a great versatility in terms of photon pair emission spectrum and generated quantum state, making it suitable for a broad range of quantum applications such as cryptography and metrology. In this sense, we show how to use our source for chromatic dispersion measurements in optical fibres which opens new avenues in the field of quantum metrology.
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