Let us imagine that there exists a material that reflects infrared radiation, but is transparent for visible light. Could we take an incandescent bulb and add this material to the inner surface of the glass hull? Then most of the infrared radiation isn't lost, but reflected onto the wire again. So we would need much less energy to heat up the wire to a sufficient temperature. The result would be an efficient light bulb with a broad, gapless spectrum in the visible range.
Is this possible like that? Have I done a fundamental mistake? Or do the required materials not exist?