Generalized optical design of the multiple-row circular multi-pass cell with dense spot pattern.

We present a generalized method for designing a novel circular multi-pass cell (MPC) with multifold overall optical path length, or alternatively enlarged path-to-volume ratio in the same magnification compared to traditional version, by exploiting the vertical dimension of cavity mirrors. Multiple rows of reflection spots can be generated on arbitrary number of different horizontal planes within the cell that consists of two easy-fabricating circular spherical mirrors. Base on this method, one can arbitrarily determine the interval of reflection spots in both horizontal and vertical directions, so that almost seamless and regular distributed dense spot pattern, and consequently large path-to-volume ratio can be achieved. A series of q-preserving configurations of the multiple-row circular multi-pass cell are calculated and simulated, in which the q-parameters of probe Gaussian beams can be approximately unchanged after the whole transmission within the cells. The maximum optical path length among these simulation cases is 201.8 m within 427.2 mL volume. Furthermore, we demonstrate a practical optical setup with 21.9 m optical path length within 100.1 mL, which is the smallest volume case among the existing actual MPCs with similar overall optical path lengths.