Maximizing the hyperpolarizability poorly determines the potential

Atherton, Timothy J.; Lesnefsky, Joseph; Wiggers, Greg; Petschek, Rolfe G.

doi:10.1364/josab.29.000513

Cited by 26 publications

(48 citation statements)

References 15 publications

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“…Monte Carlo simulations discovered the optimum energy spectrum for such molecules and provided a strong indicator of the origin of the gap [7]. Optimization of the effective potential energy an electron experiences across the main direction of a quasi-linear molecule showed that the hyperpolarizabilities may be increased by tuning a few parameters [8], by modulation of conjugation along a chain [9], or by donor-acceptor substitution and insertion of spacers [10]. However, there is no general rule about how to construct the ideal potential energy profile across a molecule to maximize the nonlinear optical response.…”

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confidence: 99%

Phase disruption as a new design paradigm for optimizing the nonlinear-optical response

2015

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The intrinsic optical nonlinearities of linear structures, including conjugated chain polymers and nanowires, are shown to be dramatically enhanced by the judicious placement of a charge diverting path sufficiently short to create a large phase disruption in the dominant eigenfunctions along the main path of probability current. Phase disruption is proposed as a new general principle for the design of molecules, nanowires and any quasi-1D quantum system with large intrinsic response and does not require charge donor-acceptors at the ends. © The design and realization of ultrafast nonlinear optical materials with large responses to optical frequency electric fields remains an active field of pure and applied research [1][2][3][4]. To date, no general design rules for obtaining large nonlinearities from any structure have been articulated, and the response of materials remains well below that allowed by quantum physics. In this letter, we propose a general principle that may explain why modern molecules fall short of their potential and use it to demonstrate simple structures with nonlinear responses approaching the physical limits.The off-resonance electronic nonlinear optical response of a molecule is completely determined by its energy spectrum and transition moments. Normalized to its maximum value, the sum over states expression for the intrinsic first hyperpolarizability along the x-axis may be written as [5] where the sum is over all states, x nℓ is the n, ℓ element of the position matrix withx = x − x 00 , E n0 = E n − E 0 is the difference in energy of eigenstates n and 0, N is the number of electrons and m their mass. We include as many as 100 energy eigenstates to calculate β, but systems with large β are always well approximated using only three states. For brevity, we focus on the first hyperpolarizability, though our results also hold for the second hyperpolarizability, γ xxxx . For the remainder of this letter, all hyperpolarizabilities are divided by their maximum values and represent intrinsic tensor properties. It is evident from Eqn.(1) that a system optimized for nonlinear optics will necessarily have eigenfunctions with a large degree of overlap as well as a large change of dipole moment between contributing levels. This is an essential trade-off to achieve a large response. It is generally recognized that the hyperpolarizabilities of most molecules fall at least 30 times short of the limits. [5,6]. Monte Carlo simulations discovered the optimum energy spectrum for such molecules and provided a strong indicator of the origin of the gap [7]. Optimization of the effective potential energy an electron experiences across the main direction of a quasi-linear molecule showed that the hyperpolarizabilities may be increased by tuning a few parameters [8], by modulation of conjugation along a chain [9], or by donor-acceptor substitution and insertion of spacers [10]. However, there is no general rule about how to construct the ideal potential energy profile across a molecule to maximize the nonlinea...

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confidence: 99%

Phase disruption as a new design paradigm for optimizing the nonlinear-optical response

2015

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“…The energy difference between the ground and first excited state, E 10 , sets a fundamental limit on the electric polarizability and first hyperpolarizability. These limits have been corroborated by experiment [12], potential optimization [13][14][15][16][17], and calculations on quantum graphs [18][19][20][21] though a recent Monte Carlo study utilizing filtered sampling suggests that these limits may be an overestimate by approximately 30% [22].…”

Section: Introductionmentioning

confidence: 84%

Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability

Crowell¹,

Kuzyk²

2018

J. Opt. Soc. Am. B

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We investigate the efficacy of boosting the nonlinear-optical response by using novel systems such as those in an excited state or with a degenerate ground state. By applying the Three Level Ansatz (TLA) and using the Thomas-Reiche-Kuhn (TRK) sum rules as constraints, we find the electric polarizability and first hyperpolarizability of excited state systems to be bounded, but larger than those derived for a system in the ground state. It is shown that a system with a degenerate ground state can have divergent polarizabilities and that such divergences are real and not relics of a pathology in the perturbation theory. Furthermore, we demonstrate that these divergences only occur on time scales short compared to the relaxation time of the population difference to an equilibrium value. Such systems provide a way to get ultra-large nonlinear optical response.We discuss examples of huge enhancements in molecules and double quantum dots using a double quantum well as a model. arXiv:1805.06977v2 [physics.optics]

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“…In fact, the g = −5 curve seems to rise to its maximum as the delta moves from the left edge, but then it drops to a lower value, rather than increasing and perhaps exceeding the 0.71 limit. This effect appears to be related to the universal result that all graphs whose β are calculated by starting with a Hamiltonian and a potential of any kind have β xxx ≤ 0.7089, the potential optimization limit 29,33 . The sum rules do not constrain β xxx from equaling unity, as has been shown in a Monte Carlo calculation that starts with the energies and transition moments (top-down), rather than with a Hamiltonian and its energies and states (bottom-up) 52 .…”

Section: The Compressed Delta Atommentioning

confidence: 98%

“…Recent examination of the origin of the limits has suggested that the true limits are indeed those from potential optimization and not those determined solely by the sum rules 32 . Corroborating results have also been provided 33 , but have shown that optimization poorly determines the potential.…”

Section: Introductionmentioning

confidence: 99%

Dressed Quantum Graphs With Optical Nonlinearities Approaching the Fundamental Limit

Lytel

Kuzyk

2013

J. Nonlinear Optic. Phys. Mat.

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We dress bare quantum graphs with finite delta function potentials and calculate optical nonlinearities that are found to match the fundamental limits set by potential optimization. We show that structures whose first hyperpolarizability is near the maximum are well described by only three states, the so-called three-level Ansatz, while structures with the largest second hyperpolarizability require four states. We analyze a very large set of configurations for graphs with quasi-quadratic energy spectra and show how they exhibit better response than bare graphs through exquisite optimization of the shape of the eigenfunctions enabled by the existence of the finite potentials. We also discover an exception to the universal scaling properties of the three-level model parameters and trace it to the observation that a greater number of levels are required to satisfy the sum rules even when the three-level Ansatz is satisfied and the first hyperpolarizability is at its maximum value, as specified by potential optimization. This exception in the universal scaling properties of nonlinear optical structures at the limit is traced to the discontinuity in the gradient of the eigenfunctions at the location of the delta potential. This is the first time that dressed quantum graphs have been devised and solved for their nonlinear response, and it is the first analytical model of a confined dynamic system with a simple potential energy that achieves the fundamental limits.

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Maximizing the hyperpolarizability poorly determines the potential

Cited by 26 publications

References 15 publications

Phase disruption as a new design paradigm for optimizing the nonlinear-optical response

Phase disruption as a new design paradigm for optimizing the nonlinear-optical response

Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability

Dressed Quantum Graphs With Optical Nonlinearities Approaching the Fundamental Limit

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