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We study the coupling of light and the structural order parameter in thecharge density wave (CDW) state of the layered transition-metal dichalcogenide,Tantalum Disulfide ($1T-\mathrm{TaS_2}$). Using time-dependent densityfunctional theory calculations of the dielectric properties along thedistortions coordinates, we show that $1T-\mathrm{TaS_2}$ displays very largechange in its dielectric function along the amplitude (Higgs) mode due to thecoupling of the periodic lattice distortion with an in-plane metal-insulatortransition, leading to optomechanical coupling coefficients two orders ofmagnitude larger than the ones of diamond and ErFeO$_3$. In addition, we derivean effective model of the light-induced dynamics, which is in quantitativeagreement with experimental observations in $1T-\mathrm{TaS_2}$. We show thatlight-induced dynamics of the structural order parameter in $1T-\mathrm{TaS_2}$can be deterministically controlled to engineer large third-order non-linearoptical susceptibilities. Our findings suggest that CDW materials are promisingactive materials for non-linear optics.

Giant Optomechanical Coupling in the Charge Density Wave State of Tantalum Disulfide