Local coherence and the temporal development of second harmonic emission

Abstract

In a variety of mesoscopically disordered systems, high levels of optical excitation resulting from pulsed laser irradiation can establish optical coherence within separate particles or locally ordered domains, leading to second harmonic emission whose temporal signature characterizes the decay of the excited state population. Examples of such systems will include colloids, cell and membrane suspensions, and many plastics, glasses and other modern materials. With pulsed excitation of sufficient intensity to elicit the onset of saturation, second harmonic emission on the throughput of a subsequent probe beam exhibits a characteristic decay and recovery. Detailed calculations show that such features arise not only in systems whose optical response involves two discrete levels, but also in systems of considerably greater electronic complexity. Deconvolution of the temporal trace of the harmonic signal serves as an independent means of monitoring the decay of the excited state. The extent of recovery in the harmonic signal also serves to register the extent of local coherence, and hence in many systems the localization of structural order. Finally, the principles introduced in the theory are shown to be applicable to other types of system such as certain photochromic materials.

A sum rule for nonlinear optical susceptibilities

“…In previous work based on a two-level approximation it has been shown that such tensors rigorously satisfy what we have loosely termed a 'mirror' rule [1]. This simply affirms that the molecular tensor for an elastic optical process in a pumped system is the negative of its ground state value, i.e.…”

“…It has been known for some time that this approximation leads to an excited state polarisability that is the exact negative of the ground state polarisability, and the same proves true for the ground and excited state first hyperpolarisability. In the bulk, similar relationships hold for the linear and second order optical susceptibility tensors, and the consequential possibility of observing novel harmonic resurgence phenomena in suitable media has been noted [1]. Recently, it has also been shown that the susceptibility relationships retain validity even when resonance damping is entertained [2,3], provided the correct choice is made for the sign of the damping corrections, as exacted by the principles of time-reversal invariance.…”

Quantum delocalization in photon-pair generation

“…Hence, essentially due to local effects of constructive optical interference, it is possible for compacted nanoparticles of similar dimensions to exhibit enhanced nonlinear optical activity, compared to the bulk. An analogous manifestation of coherence came to light in connection with second-harmonic generation (the time reversal of SPDC) in nanomaterials [92][93][94][95]. Beyond this point, the trailing off to an asymptotic limit signifies that as the sample size grows beyond a couple of wavelengths, the scale of such advantages is quickly lost-because additional contributions presenting destructive interference come into play.…”

Perturbation theory and the two-level approximation: A corollary and critique

“…The result emerges in the form of a traceless operator in Hilbert space, symbolized by P r r h j r j i ¼ 0, where r denotes a matter state and the operator is here to be identified with the operator form of the polarizabilityâ ij , hyperpolarizabilityb ijk or higher-order response tensor. The result is exact and widely applicable; however with the two-level model it imposes a rarely observed corollary -that components of the excited state response tensors are precisely the negative of the corresponding ground state components [34].…”

“…From the earlier general expression, a result identified with the two-level approximation is readily determined by an algorithmic method [32][33][34]. This again involves the restriction of both intermediate states featured within Eq.…”