G. P. Djotyan

Finite element analysis applied to cornea reshaping

A 2-D finite element model of the cornea is developed to simulate corneal reshaping and the resulting deformation induced by refractive surgery. In the numerical simulations, linear and nonlinear elastic models are applied when stiffness inhomogeneities varying with depth are considered. Multiple simulations are created that employ different geometric configurations for the removal of the corneal tissue. Side-by-side comparisons of the different constitutive laws are also performed. To facilitate the comparison, the material property constants are identified from the same experimental data, which are obtained from mechanical tests on corneal strips and membrane inflation experiments. We then validate the resulting models by comparing computed refractive power changes with clinical results. Tissue deformations created by simulated corneal tissue removal using finite elements are consistent with clinically observed postsurgical results. The model developed provides a much more predictable refractive outcome when the stiffness inhomogeneities of the cornea and nonlinearities of the deformations are included in the simulations. Finite element analysis is a useful tool for modeling surgical effects on the cornea and developing a better understanding of the biomechanics of the cornea. The creation of patient-specific simulations would allow surgical outcomes to be predicted based on individualized finite element models.

Population transfer in three-level Λ atoms with Doppler-broadened transition lines by a single frequency-chirped short laser pulse

We examine interaction of a single frequency-chirped laser pulse with three-level atoms that have a Λ configuration of levels. We show that it is possible to produce complete fast and robust population transfer of all atoms of the ensemble with Doppler-broadened transition lines from one ground state into the other ground state with negligibly small temporary population of the excited state by controlling the intensity of the laser pulse and the direction and speed of the frequency chirp.

Finite-Element Modeling of Posterior Lamellar Keratoplasty: Construction of Theoretical Nomograms for Induced Refractive Errors

Purpose: To estimate the theoretical corneal refractive error induced by mechanical weakening effects from posterior lamellar keratoplasty (PLKP) in the human cornea. Methods: The refractive effects of PLKP are simulated by finite-element modeling (FEM) as a mathematical function of the thickness of the excised posterior lamellar corneal button, with a nonlinear formulation of stress-strain relation for the corneal material. A theoretical nomogram was developed to correlate the refractive changes to button thickness. Results: The predicted refractive change after PLKP is less than 1 dpt for a 170-µm thickness posterior corneal button over a broad range of Young’s modulus.Thicker buttons result in greater surgically induced refractive errors. Conclusions: According to FEM analysis, the excision of a posterior lamellar button of less than 170 µm thickness produces a minimal predicted refractive change (<1 dpt) in the cornea after PLKP.

Biomechanical Model of Corneal Transplantation

PURPOSE Refractive consequences of corneal transplants are analyzed using corneal biomechanical models assuming homogeneous and inhomogeneous stiffness distributions across the cornea. Additionally, refractive effects of grafts combined with volume removal procedures are also evaluated to develop methods to reduce postoperative refractive management of patients. METHODS Refinements of a two-dimensional finite element model are applied to simulate the biomechanical and refractive effects of different corneal transplant procedures: anterior lamellar keratoplasty, posterior lamellar keratoplasty, and penetrating keratoplasty. The models are based on a nonlinearly elastic, isotropic formulation. Predictions are compared with published clinical data. RESULTS The model simulating the penetrating keratoplasty procedure predicts more change in the postoperative corneal curvature than models simulating anterior lamellar keratoplasty or posterior lamellar keratoplasty procedures. When a lenticle-shaped tissue with a central thickness of 50 microns and a diameter of 4 mm is removed from the anterior corneal surface along with the anterior lamellar keratoplasty or posterior lamellar keratoplasty, the models predict a refractive correction of -8.6 and -8.9 diopters, respectively. CONCLUSIONS Simulations indicate that a posterior lamellar keratoplasty procedure is preferable for obtaining a better corneal curvature profile, eliminating the need for specific secondary treatments.

Creation of a coherent superposition of quantum states by a single frequency-chirped short laser pulse

Traditional schemes for coherent population transfer or generation of coherent superposition states in multilevel atoms or molecules usually utilize two or more laser beams with radiation bandwidth smaller than the frequency interval between the working levels. We show the possibility of creation of the coherent superposition of three metastable states of a four-level atom with tripodlike level structure using a single short frequency-chirped laser pulse. The bandwidth of the pulse envelope (without chirp) must be comparable to or exceed the frequency distance between the two metastable levels. No appreciable excitation of the atom takes place during the creation of the coherent superposition state, thus diminishing significantly the effect of decoherence due to the spontaneous decay of the excited state. The proposed method of creation of superposition states is robust against variations in the laser pulse parameters. Since this method does not require maintaining steady resonance with the atomic transitions (owing to the frequency chirp of the laser pulse), it is effective both in homogeneously and inhomogeneously broadened media.

Coherent writing and reading of information using frequency-chirped short bichromatic laser pulses

We propose to use the sensitivity of the population transfer in three-level L-atoms to the relative phases and amplitudes of frequency-chirped short bichromatic laser pulses for coherent, fast and robust storage and processing of phase or intensity optical information. The information is being written into the excited state population which in a second step is transferred in a fast and robust way into a nondecaying storage level. It is shown that an arbitrary superposition of the ground states can be generated by controlling the relative phase between the laser pulses.

Theory of the adiabatic passage in two-level quantum systems with superpositional initial states

Abstract An analytic theory of the adiabatic passage (AP) regime of interaction of short frequency chirped laser pulses with a two-level quantum system (QS) being initially in the superpositional quantum state is presented. We show that the initial value of the non-diagonal elements of the density matrix can influence the dynamics of the population transfer during the action of the laser pulse, but do not influence essentially the final populations of the states of the QS obtained at the end of the interaction near the AP regime. A novel solution to the Bloch equations is obtained in the form of a converging power series generalizing the ordinary AP solution.

Manipulation of two-level quantum systems with narrow transition lines by short linearly polarized frequency-chirped laser pulses

We propose and investigate theoretically a novel scheme for transient slowing and cooling of two-level quantum systems with narrow transition linewidths by a sequence of counterpropagating, short, linearly polarized laser pulses with special frequency chirping. Both internal degrees of freedom and the motion of the center of mass of quantum systems are considered quantum mechanically. Interaction with a large number of laser pulses during the decay time permits a drastic decrease in the cooling time of such systems.

Pre-excitation studies for rubidium-plasma generation

The key element in the Proton-Driven-Plasma-Wake-Field-Accelerator (PWFA) project is the generation of highly uniform plasma from Rubidium vapor. A scientifically straightforward, yet highly challenging way to achieve full ionization is to use high power laser which can assure the barrier suppression ionization (BSI) along the 10 m long active region. The Wigner-team in Budapest is investigating an alternative way of uniform plasma generation. The proposed Resonance Enhanced Multi-Photon Ionization (REMPI) scheme can be probably realized by much less laser power. In the following we plan to investigate the resonant pre-excitations of the Rb atoms, both theoretically and experimentally. In the following our theoretical framework is presented together with the status report about the preparatory work of the planned experiment.

Visualization of superposition states and Raman processes with two-dimensional atomic deflection

Deflection of atoms in \Lambda-type configuration passing through two crossed standing light waves is proposed for probing and visualization of atomic superposition states. For this goal, we use both the large-dispersive and Raman-resonant regimes of atom-field interaction giving rise to a position-dependent phase shifts of fields and perform double simultaneous spatial measurements on an atom. In this way, it is demonstrated that the deflection spatial patterns of atoms in \Lambda-configuration passing through modes of standing waves are essentially modified if the atoms are initially prepared in a coherent superposition of its low levels states as well as when the superposition states are created during the process of deflection. The similar results take place for the joint momentum distribution of atoms. Further, considering both one-photon and two-photon excitation regimes of \Lambda-atoms we also illustrate that the two-dimensional patterns of defected atoms qualitatively reflects the efficiency of the Raman processes.