A beam-expander optical system , comprising: a convex mirror having a first mirror substrate made of metal and having a convex substrate surface and a first reflective multilayer coating formed on the convex substrate surface ; a concave mirror having a second mirror substrate made of the metal and having a concave substrate surface and a second reflective multilayer coating formed on the concave substrate surface , with the convex and concave mirrors being arranged in an off-axis, afocal configuration having greater than unity magnification; characterized in that the first and second reflective multilayer coatings each includes alternating layers of HfO 2 and SiO 2 that define at least first and second sections (S1 and S2), wherein the first section (S1) is closest to the convex or concave substrate surface and is configured to optimally reflect a first wavelength of light and substantially transmit mid-wavelength IR light, wherein the second section (S2) resides atop the first section (S1) and is configured to optimally reflect a second wavelength of light that is shorter than the first wavelength of light and wherein the second section (S2) substantially transmits the mid-wavelength IR light; the first and second reflective multilayer coatings each include a third section (S3) atop the second section (S2) and configured to optimally reflect a third wavelength of light that is shorter than the second wavelength of light and substantially transmit the mid-wavelength IR light; the first wavelength of light is an infrared wavelength, the second wavelength of light is a visible wavelength and the third wavelength of light is an ultraviolet wavelength; and the beam-expander optical system has a high-efficiency transmittance T BE > 95% for the first and second wavelengths of light. a convex mirror having a first mirror substrate made of metal and having a convex substrate surface and a first reflective multilayer coating formed on the convex substrate surface ; a concave mirror having a second mirror substrate made of the metal and having a concave substrate surface and a second reflective multilayer coating formed on the concave substrate surface , with the convex and concave mirrors being arranged in an off-axis, afocal configuration having greater than unity magnification; characterized in that the first and second reflective multilayer coatings each includes alternating layers of HfO 2 and SiO 2 that define at least first and second sections (S1 and S2), wherein the first section (S1) is closest to the convex or concave substrate surface and is configured to optimally reflect a first wavelength of light and substantially transmit mid-wavelength IR light, wherein the second section (S2) resides atop the first section (S1) and is configured to optimally reflect a second wavelength of light that is shorter than the first wavelength of light and wherein the second section (S2) substantially transmits the mid-wavelength IR light; the first and second reflective multilayer coatings each include a third section (S3) atop the second section (S2) and configured to optimally reflect a third wavelength of light that is shorter than the second wavelength of light and substantially transmit the mid-wavelength IR light; the first wavelength of light is an infrared wavelength, the second wavelength of light is a visible wavelength and the third wavelength of light is an ultraviolet wavelength; and the beam-expander optical system has a high-efficiency transmittance T BE > 95% for the first and second wavelengths of light. <EOS>