{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/23730"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/23730","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"The Stochastic Dynamics of Optomechanical Sensors for Atomic Force Microscopy","abstract":"This work explores the stochastic dynamics and important diagnostics of a mechanical resonator (nanobeam) used in cavity optomechanical sensors for atomic force microscopy. Atomic force microscopy (AFM) is a tool to image surface topology down to the level of individual atoms. Conventional AFM has been an essential tool for micro and nanoscale studies in physics, chemistry, and biology. Cavity optomechanical sensors for AFM extend the utility of conventional AFM into a new regime of high sensitivity k is approximately 1 N/m and high frequency f0 is approximately 10 MHz. Cavity optomechanical sensors for AFM are unique because they use near field optics to transduce the position of a nanobeam. The nanobeam is not able to be transduced by more conventional AFM techniques, such as laser interferometry, because the nanobeam is smaller than the spot size of the laser. This work determines the noise spectrum G of a nanobeam in water and in air. Also important diagnostics of the nanobeam are determined in air and in water. These important diagnostics include the quality factor Q and natural frequency in fluid omega_f. It is found that the nanobeam is overdamped in water. However, the nanobeam is underdamped in air and has quality factor of Q is approximately 4. The noise spectrum is determined from deterministic numerical calculations and the Fluctuation-Dissipation Theorem. This is possible because the same molecular processes, Brownian motion, cause both the fluctuations of the nanobeam and the dissipation of the nanobeam.","abstract_html":"This work explores the stochastic dynamics and important diagnostics of a mechanical resonator (nanobeam) used in cavity optomechanical sensors for atomic force microscopy. Atomic force microscopy (AFM) is a tool to image surface topology down to the level of individual atoms. Conventional AFM has been an essential tool for micro and nanoscale studies in physics, chemistry, and biology. Cavity optomechanical sensors for AFM extend the utility of conventional AFM into a new regime of high sensitivity k is approximately 1 N/m and high frequency f0 is approximately 10 MHz. Cavity optomechanical sensors for AFM are unique because they use near field optics to transduce the position of a nanobeam. The nanobeam is not able to be transduced by more conventional AFM techniques, such as laser interferometry, because the nanobeam is smaller than the spot size of the laser. This work determines the noise spectrum G of a nanobeam in water and in air. Also important diagnostics of the nanobeam are determined in air and in water. These important diagnostics include the quality factor Q and natural frequency in fluid omega_f. It is found that the nanobeam is overdamped in water. However, the nanobeam is underdamped in air and has quality factor of Q is approximately 4. The noise spectrum is determined from deterministic numerical calculations and the Fluctuation-Dissipation Theorem. This is possible because the same molecular processes, Brownian motion, cause both the fluctuations of the nanobeam and the dissipation of the nanobeam.","abstract_has_math":false,"creators":["Epstein, Stephen David"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Science and Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Paul, Mark R."],"committee_members":["Ragab, Saad A.","Ross, Shane D."],"year":2013,"date_issued":"2013-08-28","date_published":"2013-08-28","updated_at":"2026-07-22T22:18:53Z","subjects":["optomechanics","atomic force microscopy","noise spectrum"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:1470"],"render_values":[{"text":"vt_gsexam:1470","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/23730","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Paul, Mark R."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Ragab, Saad A.","Ross, Shane D."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Science and Mechanics"]},{"key":"dc:creator","label":"Author","values":["Epstein, Stephen David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-08-29T08:00:17Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-08-29T08:00:17Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-08-28"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Mechanics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["optomechanics","atomic force microscopy","noise spectrum"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:1470"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/23730"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This work explores the stochastic dynamics and important diagnostics of a mechanical resonator (nanobeam) used in cavity optomechanical sensors for atomic force microscopy. Atomic force microscopy (AFM) is a tool to image surface topology down to the level of individual atoms. Conventional AFM has been an essential tool for micro and nanoscale studies in physics, chemistry, and biology. Cavity optomechanical sensors for AFM extend the utility of conventional AFM into a new regime of high sensitivity k is approximately 1 N/m and high frequency f0 is approximately 10 MHz. Cavity optomechanical sensors for AFM are unique because they use near field optics to transduce the position of a nanobeam. The nanobeam is not able to be transduced by more conventional AFM techniques, such as laser interferometry, because the nanobeam is smaller than the spot size of the laser. This work determines the noise spectrum G of a nanobeam in water and in air. Also important diagnostics of the nanobeam are determined in air and in water. These important diagnostics include the quality factor Q and natural frequency in fluid omega_f. It is found that the nanobeam is overdamped in water. However, the nanobeam is underdamped in air and has quality factor of Q is approximately 4. The noise spectrum is determined from deterministic numerical calculations and the Fluctuation-Dissipation Theorem. This is possible because the same molecular processes, Brownian motion, cause both the fluctuations of the nanobeam and the dissipation of the nanobeam."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["The Stochastic Dynamics of Optomechanical Sensors for Atomic Force Microscopy"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Paul, Mark R."],"dc:contributor.committeemember":["Ragab, Saad A.","Ross, Shane D."],"dc:contributor.department":["Engineering Science and Mechanics"],"dc:creator":["Epstein, Stephen David"],"dc:date.accessioned":["2013-08-29T08:00:17Z"],"dc:date.available":["2013-08-29T08:00:17Z"],"dc:date.issued":["2013-08-28"],"dc:description.abstract":["This work explores the stochastic dynamics and important diagnostics of a mechanical resonator (nanobeam) used in cavity optomechanical sensors for atomic force microscopy. Atomic force microscopy (AFM) is a tool to image surface topology down to the level of individual atoms. Conventional AFM has been an essential tool for micro and nanoscale studies in physics, chemistry, and biology. Cavity optomechanical sensors for AFM extend the utility of conventional AFM into a new regime of high sensitivity k is approximately 1 N/m and high frequency f0 is approximately 10 MHz. Cavity optomechanical sensors for AFM are unique because they use near field optics to transduce the position of a nanobeam. The nanobeam is not able to be transduced by more conventional AFM techniques, such as laser interferometry, because the nanobeam is smaller than the spot size of the laser. This work determines the noise spectrum G of a nanobeam in water and in air. Also important diagnostics of the nanobeam are determined in air and in water. These important diagnostics include the quality factor Q and natural frequency in fluid omega_f. It is found that the nanobeam is overdamped in water. However, the nanobeam is underdamped in air and has quality factor of Q is approximately 4. The noise spectrum is determined from deterministic numerical calculations and the Fluctuation-Dissipation Theorem. This is possible because the same molecular processes, Brownian motion, cause both the fluctuations of the nanobeam and the dissipation of the nanobeam."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:1470"],"dc:identifier.uri":["http://hdl.handle.net/10919/23730"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["optomechanics","atomic force microscopy","noise spectrum"],"dc:title":["The Stochastic Dynamics of Optomechanical Sensors for Atomic Force Microscopy"],"dc:type":["Thesis"],"thesis:degree_discipline":["Engineering Mechanics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:18:53Z"}