= Solution
For bulk electric-dipole <second-harmonic generation>, the <crystal> must lack inversion <symmetry> and have a nonzero relevant component of its second-order <nonlinear optical susceptibility>. It should transmit both pump and harmonic, tolerate the required intensity, and allow <phase matching> by suitable <birefringence> or another phase-compensation mechanism. A large nonlinear coefficient, low optical loss and good optical quality are desirable. Noncentrosymmetry permits a response but does not guarantee one in every chosen geometry.
In the undepleted <plane wave> limit, contributions from successive layers give a harmonic amplitude proportional to $\int_0^L e^{i\Delta k z}dz$, where $\Delta k=k_{2\omega}-2k_\omega$. Hence
$$
I_{2\omega}\propto d_{\rm eff}^2 I_\omega^2L^2\operatorname{sinc}^2(\Delta kL/2).
$$
Tune orientation, <temperature> and pump <polarization> to maximize the nonlinear coupling and cancel <phase mismatch>. For continuous operation, an impedance-matched enhancement <optical resonator>, or intracavity doubling, raises the circulating intensity. Focus the <Gaussian beam> to balance intensity against <diffraction> and <spatial walk-off>; arbitrarily tight focusing shortens the useful overlap. Antireflection surfaces, stable resonance locking and efficient heat removal reduce avoidable loss and drift.
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