Showing papers by "Michael Mazilu published in 2019"

Nonlinear optical eigenmodes: perturbative approach

Abstract: In linear optics, the concept of a mode is well established. Often these modes correspond to a set of fields that are mutually orthogonal with intensity profiles that are invariant as they propagate through an optical medium. More generally, one can define a set of orthogonal modes with respect to an optical measure that is linear in intensity or quadratic/Hermitian in the fields using the method of Optical Eigenmodes (OEi). However, if the intensity of the light is large, the dipole response of an optical medium introduces nonlinear terms to Maxwell’s equations. In this nonlinear regime such terms influence the evolution of the fields and the principle of superposition is no longer valid and consequently, the method of Optical Eigenmodes breaks down. In this work, we define Optical Eigenmodes in the presence of these nonlinear source terms by introducing small perturbation fields onto a nonlinear background interaction and show how this background interaction influences the symmetries associated with the eigenmodes. In particular, by introducing orbital angular momentum (OAM) to the Hilbert space of the perturbation and background fields, we observe conservation laws and symmetries for which we derive associated operators.

Optical eigenmode description of single-photon light-matter interactions

Abstract: When light scatters from an object, it can impart some physical quantity such as momentum or angular momentum. This can act as a measurement on the photon, which collapses on to an eigenstate of the measurement operator. However the corresponding operator is not the same as that describing the total linear or angular momentum in free space. Optical eigenmodes provide a powerful method to describe this interaction by expanding the field as a linear combination of some basis modes and examining the eigenvalues and eigenvectors of the quadratic measure in question. We extend this to the quantum case by writing the quantum operator corresponding to a given measurement such as energy, momentum or angular momentum as a superposition of creation and annihilation operators for each eigenmode. Upon measurement we find that the possible states of a single photon are simply the classical eigenmodes of the measurement. As an application, we examine the force and torque on a general, possibly anisotropic, material. By looking at eigenvalues of the measurement operator we show that the amount of a given quantity transferred in an interaction with matter is not in general the expected amount which a photon carries in free space, even at the single photon level. In particular the difference in linear or angular momentum from before and after is in general not equal to ~k or ~ which are the eigenvalues of these quantities in free space.

Green-function Method for Nonlinear Interactions of Elastic Waves

Abstract: In the linear wave propagation regime, an analytical mesh-free Green-function decomposition has been shown as a viable alternative to FDTD and FEM. However, its expansion into nonlinear regimes has remained elusive due to the inherent linear properties of the Green-function approach. This work presents a novel frequency-domain Green function method to describe and model nonlinear wave interactions in isotropic hyperelastic media. As an example of the capabilities of the method, we detail the generation of sum frequency waves when initial quasi-monochromatic waves are emitted in a fluid by finite sources. The method is supported by both numerical and experimental results using immersion ultrasonic techniques.

Using optical eigenmodes for single photon description

Abstract: Photon states can be represented using many families of orthogonal fields, such as plane waves, Laguerre-Gaussian beams, Bessel beams, etc... Here, we show that optical eigenmodes offer a particular useful description of single photon quantum state in a light-matter interaction. In general, linear light-matter interaction is proportional to the intensity of the incident light field. These linear interactions can be described by a quadratic function of the incident fields. For example, the momentum imparted by a scattering beam onto an object is determined by integrating the flux of Maxwell’s stress tensor on a closed surface surrounding this scattering object. The quadratic and, more precisely, Hermitian nature of Maxwell’s stress tensor leads to a linear dependence onto the intensity of the field. However, due to the quadratic nature, we observe, at the same time, interference effects. Indeed, the momentum transfer resulting from the superposition of two beams is not the same as the sum of the momenta from each of the beams incident separately. This interference effect disappears when the two fields constituting the superposition are orthogonal with respect to the quadratic momentum measure. In general, this is the case when the fields are optical eigenmodes of the momentum measure [1-3]. The field orthogonality of the optical eigenmodes makes them a suitable representation of the fields associated with photon creation/annihilation operators. This representation allows for a simplification of the description of lightmatter interaction when considering quantum mechanical observable operators. For example, observing and measuring the momentum transfer of a photon to a scattering object collapses the quantum state of the photon onto one of the optical eigenmodes. Therefore, optical eigenmodes provide a natural framework to consider the interaction of quantum light states with macroscopic matter [4]. More generally, this property is applicable to all Hermitian quadratic measures of the field linked to quantum photon observables, such as energy, momentum and angular momentum.

Optical eigenmode description of partially coherent light fields

Abstract: Optical eigenmodes describe coherent solutions of Maxwells equations that are orthogonal to each other. These modes form a natural basis set of the electromagnetic Hilbert space that can be used to describe optical scattering interactions in a simple way. Many of the properties defined in quantum mechanics can formally be found in the optical eigenmodes framework. For example, the Hilbert spaces defined by two different scattering operators are separable only if the two operators commute with each other. Here, we expand the optical eigenmode framework to partially coherent light fields. In this case, we remark that the eigenmode decomposition of partially coherent fields leads to a formalism similar to the density matrix formalism used in quantum mechanics.

Eigenmode beam optimisation for optical micro-manipulation

Abstract: Optical micro-manipulation and trapping of micro-particles delivers a mechanical system in direct interaction with a beam of light. In this interaction, the optical properties such as polarisation, beam profile and wavelength of the trapping beam are important. Different beams are associated with different momentum transfer, trap stiffness and stabilisation properties, for example. One method to determine the best beam profile is through the use of the optical eigenmode approach. To use this method, we employ Mie scattering theory which enables the exact determination of the scattered field as a function of the incident field. More precisely, this approach allows us to calculate the Hermitian relationship between the incident field and the optical forces acting on the scattering objects. This Hermitian relationship defines also a set of orthogonal optical eigenmodes which deliver a natural basis to describe momentum transfer in light-matter interactions. This relationship defines also a set of orthogonal optical eigenmodes. Using these modes it is possible to define, for each numerical aperture, particle size or geometry, the optimal trapping beam.

Non-Classical Second-Order Nonlinear Elastic Wave Interactions

Abstract: We report a novel ultrasonic measurement technique based on non-classical nonlinear evanescent field interactions. We demonstrate significant enhancement in sensitivity of contactless measurements at interfaces, with the potential to detect material degradation, such as fatigue and ageing, which is currently not possible using linear ultrasonics.