This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.
The analysis of the model is conducted in two parts. First, by formally taking an average over the spatial variable, the system of partial differential equations is reduced to a system of ordinary differential equations describing the temporal behavior of the spatially-averaged dynamic quantities. Several qualitative properties of the solutions of this system are proved and stability of the solutions under various operating conditions is investigated. The rate equations are solved numerically and the effects on the solutions of changes in the physical parameters are discussed.
The second part of this study is concerned with the qualitative and numerical analysis of the spatial and temporal model of a Ti: Sapphire ring laser. Several qualitative properties of the solution are established. The system of partial differential equations is solved numerically by integration along the characteristic lines using an implicit integration scheme developed for this problem. The computed solutions are compared to those obtained by using a stable finite difference approximation. The results of the comparison demonstrate that the implicit integration scheme is viable as well as efficient for numerically solving the system of partial differential equations and can be considered a useful analytical tool for studying the dynamics of this type of laser system.
All computer codes are written in FORTRAN and currently run on a DEC VAX 11/750.
","abstract_html":"<p>This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.</p> <p>The analysis of the model is conducted in two parts. First, by formally taking an average over the spatial variable, the system of partial differential equations is reduced to a system of ordinary differential equations describing the temporal behavior of the spatially-averaged dynamic quantities. Several qualitative properties of the solutions of this system are proved and stability of the solutions under various operating conditions is investigated. The rate equations are solved numerically and the effects on the solutions of changes in the physical parameters are discussed.</p> <p>The second part of this study is concerned with the qualitative and numerical analysis of the spatial and temporal model of a Ti: Sapphire ring laser. Several qualitative properties of the solution are established. The system of partial differential equations is solved numerically by integration along the characteristic lines using an implicit integration scheme developed for this problem. The computed solutions are compared to those obtained by using a stable finite difference approximation. The results of the comparison demonstrate that the implicit integration scheme is viable as well as efficient for numerically solving the system of partial differential equations and can be considered a useful analytical tool for studying the dynamics of this type of laser system.</p> <p>All computer codes are written in FORTRAN and currently run on a DEC VAX 11/750.</p>","abstract_has_math":false,"creators":["Roberts, Lila Freeman"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["J. Swetits","A. M. Buoncristiani","Stan Weinstein","John Heinbockel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1988,"date_issued":"1988-01-01T08:00:00Z","date_published":"1988-01-01T08:00:00Z","updated_at":"2026-07-24T03:35:23Z","subjects":["Model","Solid-state","Laser system","Dynamics","Dynamic Systems","Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.odu.edu/mathstat_etds/105","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["J. Swetits","A. M. Buoncristiani","Stan Weinstein","John Heinbockel"]},{"key":"dc:creator","label":"Author","values":["Roberts, Lila Freeman"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-10-16T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Model","Solid-state","Laser system","Dynamics","Dynamic Systems","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.odu.edu/mathstat_etds/105"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.
The analysis of the model is conducted in two parts. First, by formally taking an average over the spatial variable, the system of partial differential equations is reduced to a system of ordinary differential equations describing the temporal behavior of the spatially-averaged dynamic quantities. Several qualitative properties of the solutions of this system are proved and stability of the solutions under various operating conditions is investigated. The rate equations are solved numerically and the effects on the solutions of changes in the physical parameters are discussed.
The second part of this study is concerned with the qualitative and numerical analysis of the spatial and temporal model of a Ti: Sapphire ring laser. Several qualitative properties of the solution are established. The system of partial differential equations is solved numerically by integration along the characteristic lines using an implicit integration scheme developed for this problem. The computed solutions are compared to those obtained by using a stable finite difference approximation. The results of the comparison demonstrate that the implicit integration scheme is viable as well as efficient for numerically solving the system of partial differential equations and can be considered a useful analytical tool for studying the dynamics of this type of laser system.
All computer codes are written in FORTRAN and currently run on a DEC VAX 11/750.
"]},{"key":"dc:title","label":"Title","values":["A Mathematical Model of the Dynamics of an Optically Pumped Four-Level Solid State Laser System"]}]}],"canonical_facts":{"dc:contributor":["J. Swetits","A. M. Buoncristiani","Stan Weinstein","John Heinbockel"],"dc:creator":["Roberts, Lila Freeman"],"dc:date.available":["2019-10-16T07:00:00Z"],"dc:description.abstract":["This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.
The analysis of the model is conducted in two parts. First, by formally taking an average over the spatial variable, the system of partial differential equations is reduced to a system of ordinary differential equations describing the temporal behavior of the spatially-averaged dynamic quantities. Several qualitative properties of the solutions of this system are proved and stability of the solutions under various operating conditions is investigated. The rate equations are solved numerically and the effects on the solutions of changes in the physical parameters are discussed.
The second part of this study is concerned with the qualitative and numerical analysis of the spatial and temporal model of a Ti: Sapphire ring laser. Several qualitative properties of the solution are established. The system of partial differential equations is solved numerically by integration along the characteristic lines using an implicit integration scheme developed for this problem. The computed solutions are compared to those obtained by using a stable finite difference approximation. The results of the comparison demonstrate that the implicit integration scheme is viable as well as efficient for numerically solving the system of partial differential equations and can be considered a useful analytical tool for studying the dynamics of this type of laser system.
All computer codes are written in FORTRAN and currently run on a DEC VAX 11/750.
"],"dc:identifier":["https://digitalcommons.odu.edu/mathstat_etds/105"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Model","Solid-state","Laser system","Dynamics","Dynamic Systems","Mathematics"],"dc:title":["A Mathematical Model of the Dynamics of an Optically Pumped Four-Level Solid State Laser System"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:23Z"}