If I will place Silicon as the active medium to create a Silicon Laser. Why I cannot achieve Lasing ? secondly, why do we always consider Laser mirrors in an standing position along the optical axis why we cannot use the active medium confined in a spherical ball shape mirror where we could place our active medium ?
a) Sillicon is an indirect semiconductor, hence, photon emission (stimulated or spontaneous) is extremely difficult to achieve or inefficient respecively (photon emission needs an electron AND phonon, simultaneously which is very unlikely). I think there was a demonstration of a silicon laser, but only with a lot of tricks and very inefficient.
b) ball shaped cavity should also be possible (with active medium inside). This is an interesting idea, probably it is not easy to realize - but I see no objections why it should not be possible. There might be issues with polarization, when the gain medium has different gain for different polarization (as it is common in semiconductor lasers). Some gain media only provide gain for one polarization. This might affect the operation in a ball shaped cavity.
But note that conventional laser cavity mirrors may also be spherical. Then the focal points are in the center of the cavity. So the whole configuration is essentially cut-out from a ball-type cavity, so ball type cavities must work.
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