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Why still there is no commercial Ti:Sapphire fiber laser? And basically I didn't find information about any fiber laser at transition metals? What is the main problem here?

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If by "transmission metals" you mean "transition metals", then there are transition metal doped fiber lasers, indeed I believe erbium doped fibers may have been the original gain medium for a fiber laser.

As for a Ti:Sapphire fiber laser, I'll stick with the most salient physics reason hindering the building of such a device: there will of course be commercial reasons that limit production of Ti:Sapphire laser.

Quite simply, it is very difficult to build a core-cladding structure into a single sapphire fiber crystal, and you almost certainly need such a structure to achieve single-moded working of the fiber. Given that one of the Ti:Sapphire's main reasons for being and claim to fame is that it can output extremely narrow (several femtosecond) pulses, single moded working of the fiber gain medium is absolutely essential to this goal, because the modes of fibers always differ starkly in their propagation constants (axial component of the wavevector) and therefore few moded fibers would be hopelessly dispersive.

Without a core-clad structure, the only way to make a crystal into a single moded structure is as a single mode photonic wire, i.e. a glass fiber with subwavelength diameter. With sapphire, I calculate such a structure would need to be a wire about $300{\rm nm}$ in diameter for one-modedness at $700{\rm nm}$ wavelength. Such a device is likely to be lossy (I understand the surface quality of synthetic sapphire fibers is not good) but, much more importantly, the power bearing capability of such a thin structure would be very limited. High power lasers call for a very weakly guiding fiber with large mode field diameter so that the light intensity is is low enough that the whole system won't vaporize itself.

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  • $\begingroup$ On the plus side, wouldn't Kerr self-focusing be less of a problem if you're already at the single-mode regime? Not that it would help much - by the time you get to useful power levels, a single sapphire strand would probably be long since evaporated. $\endgroup$ Jul 5, 2016 at 12:46
  • $\begingroup$ Note also that the "transmission" has been edited. $\endgroup$ Jul 5, 2016 at 13:39
  • $\begingroup$ Well, what if we create glass ceramics with Ti:Sa cristals? Or why we don't try to make the fiber with Cr3+ or Ti3+ ions? They still have good enough fluorescent properties? I didn't find information about fiber lasers without rare earth ions $\endgroup$ Jul 5, 2016 at 13:39

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