We propose a method to suppress the chemical reactions between ultracold bosonic ground-state ^{23}Na^{87}Rb molecules based on optical shielding. By applying a laser with a frequency blue-detuned from the transition between the lowest rovibrational level of the electronic ground state X^{1}Σ^{+}(v_{X}=0,j_{X}=0), and the long-lived excited level b^{3}Π_{0}(v_{b}=0,j_{b}=1), the long-range dipole-dipole interaction between the colliding molecules can be engineered, leading to a dramatic suppression of reactive and photoinduced inelastic collisions, for both linear and circular laser polarizations. We demonstrate that the spontaneous emission from b^{3}Π_{0}(v_{b}=0,j_{b}=1) does not deteriorate the shielding process. This opens the possibility for a strong increase of the lifetime of cold molecule traps and for an efficient evaporative cooling. We also anticipate that the proposed mechanism is valid for alkali-metal diatomics with sufficiently large dipole-dipole interactions.

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