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In 1961, Peter Alden Franken, Alan Hill, C. Wilbur Peters and Gabriel Weinreich focused a pulsed ruby laser through a red optical filter into quartz. The filter suppressed xenon-flash background. A quartz-prism spectrograph used red-insensitive Eastman Type 103 plates. A single shot recorded a feature near $347.2\mathrm{nm}$ from $694.3\mathrm{nm}$ input. Removing the quartz or substituting glass removed the feature; changing polarization of waves and orientation followed their predicted pattern. These controls supported second-harmonic generation; photographic density gave an estimated yield.^[ref]

A spectrograph turns output frequency into a recording position. Its spectral separation makes a faint new component distinguishable from bright input light. The reported rounded wavelengths do not constitute an independent precision measurement of the ratio two. Nor do these observations demonstrate perfect phase matching or complete conversion. The experiment and Nicolaas Bloembergen's later theoretical account are distinct contributions to nonlinear optics.

Nicolaas Bloembergen helped develop the theory of nonlinear optics and its use in spectroscopy. When the electric polarization is not simply proportional to the applied electric field, different frequencies can mix and new optical components can appear. His Nobel lecture connects the intense fields supplied by lasers with these nonlinear responses and the spectroscopic information they reveal. This makes the laser both a source of light and a tool for deliberately changing the response of the material being measured.^[ref]

A physicist.^[ref]

Nicolaas Bloembergen and Arthur Leonard Schawlow received one quarter each for developing laser spectroscopy. Kai Manne Börje Siegbahn received one half for developing high-resolution electron spectroscopy.^[ref]

Nonlinear optics studies the response of matter to light when the induced electric polarization is not proportional to the driving electric field. An intense laser can make these additional terms observable. The striking consequence is that a material can emit light at a frequency absent from the incident beam: second-harmonic generation doubles it. This extends a s usable optical spectrum without requiring a second lasing transition.

Franken and colleagues frequency-doubling experiment established an optical harmonic in 1961. Nicolaas S theoretical work developed the description of interacting light waves in nonlinear matter. His 1981 lecture connects a nonlinear constitutive relation with Maxwell's equations and explains compensation of optical dispersion by birefringence.^[ref]

For an exponentially correlated local field, a single-frequency illustrative relaxation rate is $T_1^{-1}=C{\tau }_c/(1+{\omega }_0^2{\tau }_c^2)$. Its derivative with respect to ${\tau }_c$ changes sign at ${\omega }_0{\tau }_c=1$. Slow motion gives $T_1\propto {\tau }_c$, and fast motion gives $T_1\propto 1/{\tau }_c$; an Arrhenius plot consequently has a minimum of $T_1$ between opposite-slope limits.

For identical spin-one-half nuclei with homonuclear dipolar relaxation, include both transition frequencies:Writing $x={\omega }_0{\tau }_c$, the maximum of the rate satisfiesLet $\ell$ be jump length, ${\tau }_j$ the total waiting time, ${\tau }_c=c{\tau }_j$, and $f_D$ the diffusion jump correlation factor. In three dimensions $D=f_D{\ell }^2/(6{\tau }_j)=f_{D}c{\ell }^2/(6{\tau }_c)$. Combining this with $D=D_0\exp [-E_D/(k_{B}T)]$ givesThe numerical constant is one for the single-frequency illustration and 0.616 for the homonuclear dipolar model. Assumptions are a single activated process, exponential field correlations, a temperature-independent prefactor and coupling amplitude, and an established relation between local correlation and translational motion. Defect creation can enter the measured activation energy; it cannot automatically be identified with a bare migration barrier. The fluctuation-spectrum approach originates in the relaxation theory of Nicolaas Bloembergen, Edward Mills Purcell and Robert Pound.^[ref]