We report the existence of two new topologically ordered glass phases of smectics in strained aerogel. In contrast to the case of unstrained aerogel, we find compelling theoretical arguments that a smectic in uniaxially stretched aerogel exhibits, for homeotropic nematic-aerogel alignment, a `smectic Bragg glass' in the universality class of the `XY Bragg glass'. On the other hand, a uniaxial compression, with homeotropic alignment, leads to an entirely novel type of anisotropic smectic elastic glass phase that we call the `m = 1 Bragg glass'. This latter phase exhibits anomalous elasticity, characterized by exponents that we calculate to high precision. We present a phase diagram for the system in the aerogel density-strain parameter space, which should be accessible experimentally. We also make numerous other scaling predictions for experimentally observable quantities.



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