Combined frequency and mode filter

A system comprising:

• an optical input and an optical filter, wherein the optical filter comprises:
• a first lens, having an optical axis, configured to focus beams propagating parallel to the optical axis at a focal point;
• a first optical element having a first semi-reflective surface that is curved and has a first radius of curvature around a first center of curvature on the optical axis;
• a second optical element having a second semi-reflective surface, wherein:
• the first radius of curvature is between 1 and 10,000 times a distance between the first semi-reflective surface and the focal point along the optical axis,
• the first semi-reflective surface and the second semi-reflective surface are arranged to form a resonator, and
• the first lens, the first semi-reflective surface, and the second semi-reflective surface are arranged along the optical axis such that light is transmittable along an optical path through the first lens and the resonator;
• and
• one or more expansion elements located outside the optical path and arranged such that expansion of the one or more expansion elements causes relative movement of the first semi-reflective surface and the second semi-reflective surface;
• wherein the optical input is configured to produce a beam containing at least one component of a target wavelength λ and direct the beam to the first lens along the optical axis, and
• wherein the first radius of curvature is equal to Z+Zr2/Z, where Z is a distance between the first semi-reflective surface and the focal point, and Zr is a Raleigh distance of the beam at the focal point,
• the Raleigh distance being π times a beam width at the focal point W squared, divided by a target wavelength of the optical filter (Zr=πW2/λ).

An optical filter comprising:

• a first lens, having an optical axis, configured to focus beams propagating parallel to the optical axis at a focal point;
• a first optical element having a first semi-reflective surface that is curved and has a first radius of curvature around a first center of curvature on the optical axis;
• a second optical element having a second semi-reflective surface, wherein:
• the first radius of curvature is twice a distance between the first semi-reflective surface and the focal point along the optical axis,
• the first semi-reflective surface and the second semi-reflective surface are arranged to form a resonator, and
• the first lens, the first semi-reflective surface, and the second semi-reflective surface are arranged along the optical axis such that light is transmittable along an optical path through the first lens and the resonator;
• and
• one or more expansion elements located outside the optical path and arranged such that expansion of the one or more expansion elements causes relative movement of the first semi-reflective surface and the second semi-reflective surface.