High-resolution spectrographs for very large telescopes lead to new challenges in grating technology to achieve optimum matching of the slit width to the seeing disc. This has led elsewhere to the development of long echelles of high blaze angle produced by mosaicking technology. An alternative approach, pursued in this paper and adopted for the Gemini High-Resolution Optical Spectrograph, is to immerse a monolithic echelle in a medium of refractive index greater than unity. This paper explores the consequences of this. It will be followed by Paper II, which will report on a major technology development programme in progress.