Transparent Boundary Conditions 1D Klein Gordon

The wave equation is an example of an equation for which there are simple transparent boundary conditions. We can factorize the wave operator
$$partial_t^2 -partial_x^2 = (partial_t – partial_x)(partial_t + partial_x),.$$
The physical interpretation of this operator is that each factor is responsible for propagation right and left respectively. Then, to implement transparent boundary conditions on the right boundary, we can simply demand that nothing propagates left:
$$(partial_t + partial_x)psi|_{x = L} = 0,,$$
where the domain extends in $x$ from $-L$ to $L$.

Now, enter the Klein Gordon operator.
$$partial_t^2 -partial_x^2 + 1,.$$
Apparently no such factorization exists… But certainly there is a way to implement transparent boundary conditions?