Cole Van Vlack | Queen's University at Kingston (original) (raw)

Papers by Cole Van Vlack

Research in solid-state nanophotonics and quantum optics has been recently pushing the limits in ... more Research in solid-state nanophotonics and quantum optics has been recently pushing the limits in semiconductor microcavity design. High quality microcavities that confine light into small volumes are now able to drastically alter the local density of states (LDOS). Plasmonic systems can provide smaller effective confinements, however it is unclear if the benefits of confinement are good enough to balance material losses due to non-radiative
processes. This thesis presents a compendium of techniques for calculating photonic Green functions in various lossy, inhomogeneous magneto-dielectric systems. Subsequently we derive a rigorous theory of quantum light-matter interactions, valid in both weak and strong coupling limits, and show how the classical photonic Green function is developed to calculate Purcell factors, Lamb shifts, and the near and far field spectra from a single photon emitter. Using these techniques, this work investigates the classical and quantum optical properties of a variety of inhomogeneous structures, including their coupling to single photon emitters. This includes examining Purcell factors above negative index slabs and showing the convergence of many slow-light modes leads to a drastic increase in the LDOS along with large Lamb shifts. The optical trapping of metallic nanoparticles is examined
above a negative index slab and a silver half-space, showing the importance of interparticle coupling on the optical forces. Then the interaction between a quantum dot and a metallic nanoparticle is studied where far-field strong coupling effects are observed only when the metallic nanoparticle is considered beyond the dipole approximation. Finally, this work addresses the issue of the LDOS diverging in lossy materials, which necessitates a description of spontaneous emission beyond the dipole approximation; the “local field problem” in quantum optics is revisited and generalized to include local field corrections for use in any photonic medium. The strength of finite-difference time-domain techniques is demonstrated in a number of cases for the calculation of regularized Green functions in lossy inhomogeneous media. This thesis presents a comprehensive study of Green function approaches to model classical and quantum light-matter interactions in arbitrary nanophotonic structures, including quantum dots, semiconductor microcavities, negative index waveguides, metallic half-spaces and metallic nanoparticles.

The calculation of the local density of states (LDOS) in lossy materials has long been disputed d... more The calculation of the local density of states (LDOS) in lossy materials has long been disputed due to the divergence of the homogeneous Green function with equal space arguments. For arbitrary-shaped lossy structures, such as those of interest in nanoplasmonics, this problem is particularly challenging. A nondivergent LDOS obtained in numerical methods such as the finite-difference time-domain (FDTD) technique, at first sight appears to be wrong. Here we show that FDTD is not only an ideal choice for obtaining the regularized LDOS, but it can address the local-field problem for any lossy inhomogeneous material. We exemplify the case of a finite-size photon emitter (e.g., a single quantum dot) embedded within and outside a lossy metal nanoparticle and show excellent agreement with analytical results.

We investigate the quantum optical properties of a quantum-dot dipole emitter coupled to a finite... more We investigate the quantum optical properties of a quantum-dot dipole emitter coupled to a finite-size metal nanoparticle using a photon Green-function technique that rigorously quantizes the electromagnetic fields. We first obtain pronounced Purcell factors and photonic Lamb shifts for both a 7- and 20-nm-radius metal nanoparticle,without adopting a dipole approximation.We then consider a quantum-dot photon emitter positioned sufficiently near the metal nanoparticle so that the strong-coupling regime is possible. Accounting for nondipole interactions, quenching, and photon transport from the dot to the detector,we demonstrate that the strong-coupling regime should be observable in the far-field spontaneous emission spectrum, even at room temperature. The vacuum-induced emission spectra show that the usual vacuum Rabi doublet becomes a rich spectral triplet or quartet with two of the four peaks anticrossing, which survives in spite of significant nonradiative decays. We discuss the emitted light spectrum and the effects of quenching for two different dipole polarizations.

Optics …, Jan 1, 2012

The theory of vortex electron beam electron energy loss spectroscopy (EELS), or vortex-EELS for s... more The theory of vortex electron beam electron energy loss spectroscopy (EELS), or vortex-EELS for short, is presented. This theory is applied, using Green function calculations within the finite-difference time-domain method, to calculate spatially resolved vortex-EELS maps of a metal split ring resonator (SRR). The vortex-EELS scattering cross section for the SRR structure is within an order of magnitude of conventional EELS typically for metal nanoparticles. This is promising in terms of feasibility for future measurements to map out the local magnetic response of metal nanostructures and to characterize their magnetic plasmon response in
applications, including metamaterials.

Optics Letters, Jan 1, 2012

We show explicitly how the commonly adopted prescription for calculating effective mode volumes i... more We show explicitly how the commonly adopted prescription for calculating effective mode volumes is wrong and leads to uncontrolled errors. Instead, we introduce a generalized mode volume that can be easily evaluated based on the mode calculation methods typically applied in the literature, and which allows one to compute the Purcell effect and other interesting optical phenomena in a rigorous and unambiguous way.

We present a study of light-induced forces between two coupled plasmonic nanoparticles above vari... more We present a study of light-induced forces between two coupled plasmonic nanoparticles above various slab geometries including a metallic half-space and a negative index material (NIM) slab waveguide. We investigate optical forces by nonperturbatively calculating the scattered electric field via a Green function technique which includes the particle interactions to all orders. For excitation frequencies near the surface plasmon polariton and slow-light waveguide modes of the metal and NIM, respectively, we find rich light-induced forces and significant dynamical back-action effects. Optical quenching is found to be important in both metal and NIM planar geometries, which reduces the spatial range of the achievable interparticle forces. However, reducing the loss in the NIM allows radiation to propagate through the slow-light modes more efficiently, thus causing the light-induced forces to be more pronounced between the two plasmonic particles. To highlight the underlying mechanisms by which the particles couple, we connect our Green function calculations to various familiar quantities in quantum optics.

Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides

We introduce the complex band structure and a medium-dependent (Green’s function) quantum-optics ... more We introduce the complex band structure and a medium-dependent (Green’s function) quantum-optics formalism to study the enhanced spontaneous emission factors and Lamb shifts from a quantum dot or atom near the surface of a slow-light metamaterial waveguide. Using a realistic loss factor of γ/2π=2 THz, Purcell factors of approximately 250 and 100 are found at optical frequencies for p-polarized and s-polarized dipoles, respectively, placed 28 nm (0.02λ0) above the slab surface. For smaller loss values, we demonstrate that the slow-light regime of odd metamaterial waveguide propagation modes can be observed and related to distinct resonances in the Purcell factors. Correspondingly, we predict unusually large and rich Lamb shifts of approximately −1 to −6 GHz for a dipole moment of 50 Debye. We also make a direct calculation of the far-field-emission spectra which contains direct measurable access to these enhanced Purcell factors and Lamb shifts.

Signatures of bound-state-assisted nonsequential double ionization

The time-dependent multiconfiguration Hartree method is optimized for intense laser dynamics and ... more The time-dependent multiconfiguration Hartree method is optimized for intense laser dynamics and applied to nonsequential double ionization in a two-electron diatomic model molecule with two dimensions per electron. The efficiency of our method brings these calculations from the realm of large scale computation facilities to single processor machines. The resulting two-electron spectrum exhibits pronounced signatures from which the ionic bound states involved in nonsequential double ionization are retrieved with the help of a semiclassical model. A mechanism for the ionization dynamics is suggested.

Correlated few-electron dynamics in intense laser fields

The time-dependent multi-configuration Hartree method is applied to nonsequential double ionizati... more The time-dependent multi-configuration Hartree method is applied to nonsequential double ionization and to high harmonic generation and molecular tomography in a two-electron diatomic model molecule with two-dimensions per electron. The efficiency of our method brings these calculations from the realm of large scale computation facilities to single processor machines. The resulting two-electron spectrum exhibits pronounced signatures from which the ionic bound states involved in nonsequential double ionization are retrieved with the help of a semi-classical model. A mechanism for the ionization dynamics is suggested. In HHG, all relevant multi-electron effects are identified and quantified and their implications on molecular tomography are discussed.

We have begun development of a tool for investigating the bound state dynamics of single electron... more We have begun development of a tool for investigating the bound state dynamics of single electron systems in intense fields. This was done by
implementing the method of uniform complex scaling in a 1D test system in two different ways and have shown that the use of the ”c-norm” in non-Hermitian quantum mechanics can fail for time dependent simulations. We have developed the method of complex backscaling which transforms the wavefunction from the complex scaled space back into real space and have shown that it is more robust than the ”c-norm” and predicts the correct ionization when compared to simulations done in real space. We have also begun using the complex scaling method in a 2D N_2^+ model but it seems that the nature of the potential requires a more difficult type of scaling which causes problems within the calculations.

Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase

It has previously been reported that a peak at the spectral position of the second harmonic of an... more It has previously been reported that a peak at the spectral position of the second harmonic of an excitation laser can be generated in an inversion-symmetric medium in the regime of extreme nonlinear optics and that this peak may be exploited to measure the carrier-envelope phase of the excitation pulse. Here we revisit this phenomenon with regard to reverse engineering the carrier-envelope phase and demonstrate that the thin-film thickness and the incident field can have a drastic influence on pulse propagation, and so the reverse engineering would likely fail.

Carrier-Envelope-Offset Phase Control of Ultrafast Optical Rectification in Resonantly Excited Semiconductors

Ultrashort pulse light-matter interactions in a semiconductor are investigated within the regime ... more Ultrashort pulse light-matter interactions in a semiconductor are investigated within the regime of resonant optical rectification. Using pulse envelope areas of around 1.5–3.5π, a single-shot dependence on carrier-envelope-offset phase (CEP) is demonstrated for 5 fs pulse durations. A characteristic phase map is predicted for several different frequency regimes using parameters for thin-film GaAs. We subsequently suggest a possible technique to extract the CEP, in both sign and amplitude, using a solid state detector.

Research in solid-state nanophotonics and quantum optics has been recently pushing the limits in ... more Research in solid-state nanophotonics and quantum optics has been recently pushing the limits in semiconductor microcavity design. High quality microcavities that confine light into small volumes are now able to drastically alter the local density of states (LDOS). Plasmonic systems can provide smaller effective confinements, however it is unclear if the benefits of confinement are good enough to balance material losses due to non-radiative
processes. This thesis presents a compendium of techniques for calculating photonic Green functions in various lossy, inhomogeneous magneto-dielectric systems. Subsequently we derive a rigorous theory of quantum light-matter interactions, valid in both weak and strong coupling limits, and show how the classical photonic Green function is developed to calculate Purcell factors, Lamb shifts, and the near and far field spectra from a single photon emitter. Using these techniques, this work investigates the classical and quantum optical properties of a variety of inhomogeneous structures, including their coupling to single photon emitters. This includes examining Purcell factors above negative index slabs and showing the convergence of many slow-light modes leads to a drastic increase in the LDOS along with large Lamb shifts. The optical trapping of metallic nanoparticles is examined
above a negative index slab and a silver half-space, showing the importance of interparticle coupling on the optical forces. Then the interaction between a quantum dot and a metallic nanoparticle is studied where far-field strong coupling effects are observed only when the metallic nanoparticle is considered beyond the dipole approximation. Finally, this work addresses the issue of the LDOS diverging in lossy materials, which necessitates a description of spontaneous emission beyond the dipole approximation; the “local field problem” in quantum optics is revisited and generalized to include local field corrections for use in any photonic medium. The strength of finite-difference time-domain techniques is demonstrated in a number of cases for the calculation of regularized Green functions in lossy inhomogeneous media. This thesis presents a comprehensive study of Green function approaches to model classical and quantum light-matter interactions in arbitrary nanophotonic structures, including quantum dots, semiconductor microcavities, negative index waveguides, metallic half-spaces and metallic nanoparticles.

The calculation of the local density of states (LDOS) in lossy materials has long been disputed d... more The calculation of the local density of states (LDOS) in lossy materials has long been disputed due to the divergence of the homogeneous Green function with equal space arguments. For arbitrary-shaped lossy structures, such as those of interest in nanoplasmonics, this problem is particularly challenging. A nondivergent LDOS obtained in numerical methods such as the finite-difference time-domain (FDTD) technique, at first sight appears to be wrong. Here we show that FDTD is not only an ideal choice for obtaining the regularized LDOS, but it can address the local-field problem for any lossy inhomogeneous material. We exemplify the case of a finite-size photon emitter (e.g., a single quantum dot) embedded within and outside a lossy metal nanoparticle and show excellent agreement with analytical results.

We investigate the quantum optical properties of a quantum-dot dipole emitter coupled to a finite... more We investigate the quantum optical properties of a quantum-dot dipole emitter coupled to a finite-size metal nanoparticle using a photon Green-function technique that rigorously quantizes the electromagnetic fields. We first obtain pronounced Purcell factors and photonic Lamb shifts for both a 7- and 20-nm-radius metal nanoparticle,without adopting a dipole approximation.We then consider a quantum-dot photon emitter positioned sufficiently near the metal nanoparticle so that the strong-coupling regime is possible. Accounting for nondipole interactions, quenching, and photon transport from the dot to the detector,we demonstrate that the strong-coupling regime should be observable in the far-field spontaneous emission spectrum, even at room temperature. The vacuum-induced emission spectra show that the usual vacuum Rabi doublet becomes a rich spectral triplet or quartet with two of the four peaks anticrossing, which survives in spite of significant nonradiative decays. We discuss the emitted light spectrum and the effects of quenching for two different dipole polarizations.

Optics …, Jan 1, 2012

The theory of vortex electron beam electron energy loss spectroscopy (EELS), or vortex-EELS for s... more The theory of vortex electron beam electron energy loss spectroscopy (EELS), or vortex-EELS for short, is presented. This theory is applied, using Green function calculations within the finite-difference time-domain method, to calculate spatially resolved vortex-EELS maps of a metal split ring resonator (SRR). The vortex-EELS scattering cross section for the SRR structure is within an order of magnitude of conventional EELS typically for metal nanoparticles. This is promising in terms of feasibility for future measurements to map out the local magnetic response of metal nanostructures and to characterize their magnetic plasmon response in
applications, including metamaterials.

Optics Letters, Jan 1, 2012

We show explicitly how the commonly adopted prescription for calculating effective mode volumes i... more We show explicitly how the commonly adopted prescription for calculating effective mode volumes is wrong and leads to uncontrolled errors. Instead, we introduce a generalized mode volume that can be easily evaluated based on the mode calculation methods typically applied in the literature, and which allows one to compute the Purcell effect and other interesting optical phenomena in a rigorous and unambiguous way.

We present a study of light-induced forces between two coupled plasmonic nanoparticles above vari... more We present a study of light-induced forces between two coupled plasmonic nanoparticles above various slab geometries including a metallic half-space and a negative index material (NIM) slab waveguide. We investigate optical forces by nonperturbatively calculating the scattered electric field via a Green function technique which includes the particle interactions to all orders. For excitation frequencies near the surface plasmon polariton and slow-light waveguide modes of the metal and NIM, respectively, we find rich light-induced forces and significant dynamical back-action effects. Optical quenching is found to be important in both metal and NIM planar geometries, which reduces the spatial range of the achievable interparticle forces. However, reducing the loss in the NIM allows radiation to propagate through the slow-light modes more efficiently, thus causing the light-induced forces to be more pronounced between the two plasmonic particles. To highlight the underlying mechanisms by which the particles couple, we connect our Green function calculations to various familiar quantities in quantum optics.

Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides

We introduce the complex band structure and a medium-dependent (Green’s function) quantum-optics ... more We introduce the complex band structure and a medium-dependent (Green’s function) quantum-optics formalism to study the enhanced spontaneous emission factors and Lamb shifts from a quantum dot or atom near the surface of a slow-light metamaterial waveguide. Using a realistic loss factor of γ/2π=2 THz, Purcell factors of approximately 250 and 100 are found at optical frequencies for p-polarized and s-polarized dipoles, respectively, placed 28 nm (0.02λ0) above the slab surface. For smaller loss values, we demonstrate that the slow-light regime of odd metamaterial waveguide propagation modes can be observed and related to distinct resonances in the Purcell factors. Correspondingly, we predict unusually large and rich Lamb shifts of approximately −1 to −6 GHz for a dipole moment of 50 Debye. We also make a direct calculation of the far-field-emission spectra which contains direct measurable access to these enhanced Purcell factors and Lamb shifts.

Signatures of bound-state-assisted nonsequential double ionization

The time-dependent multiconfiguration Hartree method is optimized for intense laser dynamics and ... more The time-dependent multiconfiguration Hartree method is optimized for intense laser dynamics and applied to nonsequential double ionization in a two-electron diatomic model molecule with two dimensions per electron. The efficiency of our method brings these calculations from the realm of large scale computation facilities to single processor machines. The resulting two-electron spectrum exhibits pronounced signatures from which the ionic bound states involved in nonsequential double ionization are retrieved with the help of a semiclassical model. A mechanism for the ionization dynamics is suggested.

Correlated few-electron dynamics in intense laser fields

The time-dependent multi-configuration Hartree method is applied to nonsequential double ionizati... more The time-dependent multi-configuration Hartree method is applied to nonsequential double ionization and to high harmonic generation and molecular tomography in a two-electron diatomic model molecule with two-dimensions per electron. The efficiency of our method brings these calculations from the realm of large scale computation facilities to single processor machines. The resulting two-electron spectrum exhibits pronounced signatures from which the ionic bound states involved in nonsequential double ionization are retrieved with the help of a semi-classical model. A mechanism for the ionization dynamics is suggested. In HHG, all relevant multi-electron effects are identified and quantified and their implications on molecular tomography are discussed.

We have begun development of a tool for investigating the bound state dynamics of single electron... more We have begun development of a tool for investigating the bound state dynamics of single electron systems in intense fields. This was done by
implementing the method of uniform complex scaling in a 1D test system in two different ways and have shown that the use of the ”c-norm” in non-Hermitian quantum mechanics can fail for time dependent simulations. We have developed the method of complex backscaling which transforms the wavefunction from the complex scaled space back into real space and have shown that it is more robust than the ”c-norm” and predicts the correct ionization when compared to simulations done in real space. We have also begun using the complex scaling method in a 2D N_2^+ model but it seems that the nature of the potential requires a more difficult type of scaling which causes problems within the calculations.

Third-harmonic generation in disguise of second-harmonic generation revisited: role of thin-film thickness and carrier-envelope phase

It has previously been reported that a peak at the spectral position of the second harmonic of an... more It has previously been reported that a peak at the spectral position of the second harmonic of an excitation laser can be generated in an inversion-symmetric medium in the regime of extreme nonlinear optics and that this peak may be exploited to measure the carrier-envelope phase of the excitation pulse. Here we revisit this phenomenon with regard to reverse engineering the carrier-envelope phase and demonstrate that the thin-film thickness and the incident field can have a drastic influence on pulse propagation, and so the reverse engineering would likely fail.

Carrier-Envelope-Offset Phase Control of Ultrafast Optical Rectification in Resonantly Excited Semiconductors

Ultrashort pulse light-matter interactions in a semiconductor are investigated within the regime ... more Ultrashort pulse light-matter interactions in a semiconductor are investigated within the regime of resonant optical rectification. Using pulse envelope areas of around 1.5–3.5π, a single-shot dependence on carrier-envelope-offset phase (CEP) is demonstrated for 5 fs pulse durations. A characteristic phase map is predicted for several different frequency regimes using parameters for thin-film GaAs. We subsequently suggest a possible technique to extract the CEP, in both sign and amplitude, using a solid state detector.