Stability and accessibility of Turing rolls, soliton crystals, and single solitons in microresonators

dc.contributor.advisorMenyuk, Curtis R
dc.contributor.authorQi, Zhen
dc.contributor.departmentComputer Science and Electrical Engineering
dc.contributor.programEngineering, Electrical
dc.date.accessioned2023-04-05T14:16:53Z
dc.date.available2023-04-05T14:16:53Z
dc.date.issued2022-01-01
dc.description.abstractBroadband optical frequency combs generated in externally pumped, high-quality (Q) microresonators with the Kerr nonlinearity have important applications to metrology, high-resolution spectroscopy, and microwave photonics. In the time domain these frequency combs correspond to cnoidal waves, which are spatially and temporally stable periodic structures azimuthally propagating in the microresonator. Turing rolls, perfect solitons crystals, and single solitons in microresonators are all special cases of cnoidal waves. The types of cnoidal waves depend on experimental parameters, and each type has its own properties and applications. Determining the stability and accessibility of different types of cnoidal waves is the object of our dissertations research. In Chapter 1, we briefly introduce frequency combs and cnoidal waves. We mathematically represent the system using the Lugiato-Lefever equation (LLE) with two different normalizations. In Chapter 2, we analytically and numerically study the family of cnoidal wave solutions to the LLE normalized with respect to the frequency detuning. In the lossless case, we analytically obtain cnoidal wave solutions, and we then extend the solutions numerically to the case with loss. In Chapter 3, we investigate the stability and accessibility of cnoidal waves that correspond to Turing rolls or soliton crystals in microresonators. We apply highly-efficient dynamical methods to comprehensively explore the three-dimensional parameter space consisting of detuning, pump amplitude, and mode circumference to determine where stable solutions exist. In Chapter 4, we extend our previous study to consider thermal effects, which are present in real devices. Finally, in Chapter 5, we study the stability and accessibility of cnoidal waves in microresonators with avoided crossings. We find that deterministic generation of solitons is correlated with an enhanced region of stability for the single soliton. Varying both the offset and strength of an avoided crossing, we did not find simple rules that characterize when a single soliton can be deterministically accessed. However, we anticipate that our results are an important first step towards finding them.
dc.formatapplication:pdf
dc.genredissertations
dc.identifierdoi:10.13016/m2m53b-mg1h
dc.identifier.other12631
dc.identifier.urihttp://hdl.handle.net/11603/27312
dc.languageen
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Computer Science and Electrical Engineering Collection
dc.relation.ispartofUMBC Theses and Dissertations Collection
dc.relation.ispartofUMBC Graduate School Collection
dc.relation.ispartofUMBC Student Collection
dc.sourceOriginal File Name: Qi_umbc_0434D_12631.pdf
dc.subjectmicroresonators
dc.subjectnonlinear dynamics
dc.subjectnonlinear optics
dc.subjectsolitons
dc.titleStability and accessibility of Turing rolls, soliton crystals, and single solitons in microresonators
dc.typeText
dcterms.accessRightsAccess limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan through a local library, pending author/copyright holder's permission.
dcterms.accessRightsThis item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Qi_umbc_0434D_12631.pdf
Size:
11.61 MB
Format:
Adobe Portable Document Format

License bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Qi-Zhen_Lim.pdf
Size:
424.69 KB
Format:
Adobe Portable Document Format
Description: