Added LO-TO form of PoleResidue model

[caseyflex]

Simple functions to generate PoleResidue model from LO-TO form.

[tylerflex]

looks fine to me, just a couple comments.

[tomflexcompute]

Thanks @caseyflex for the implementation. I tested it on MoO3 with the literature result and it worked out greatly. Not super important but since the LOTO form of the permittivity is usually considered as a specific form of the Lorentz model, does it make sense to have it as td.Lorentz.from_loto instead of from the PoleResidue?

[caseyflex]

Thanks @caseyflex for the implementation. I tested it on MoO3 with the literature result and it worked out greatly. Not super important but since the LOTO form of the permittivity is usually considered as a specific form of the Lorentz model, does it make sense to have it as td.Lorentz.from_loto instead of from the PoleResidue?

Thanks for validating it against the literature result. Actually, from the paper "Infrared dielectric anisotropy and phonon modes of sapphire", it is my understanding that the Lorentz model is not quite as general as the LO-TO or pole-residue model. The paper states that within the Lorentz / HOA approach, the gamma_LO can be derived from the other parameters, while here we could treat them as independent. It could be nice to provide a utility within Lorentz class that will derive these automatically, but I'm not sure if this is a priority since you were already able to use this as-is.

[tomflexcompute]

Thanks @caseyflex for the implementation. I tested it on MoO3 with the literature result and it worked out greatly. Not super important but since the LOTO form of the permittivity is usually considered as a specific form of the Lorentz model, does it make sense to have it as td.Lorentz.from_loto instead of from the PoleResidue?

Thanks for validating it against the literature result. Actually, from the paper "Infrared dielectric anisotropy and phonon modes of sapphire", it is my understanding that the Lorentz model is not quite as general as the LO-TO or pole-residue model. The paper states that within the Lorentz / HOA approach, the gamma_LO can be derived from the other parameters, while here we could treat them as independent. It could be nice to provide a utility within Lorentz class that will derive these automatically, but I'm not sure if this is a priority since you were already able to use this as-is.

Yes indeed the formulation you used is more general. Typically gamma_LO and gamma_TO are the same and then it's equivalent to the usual Lorentz model I think. This additional flexibility we offer is better.