Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću
Propagation of light in complex photonic lattices with saturable nonlinearity
Authors
Beličev, PetraContributors
Milanović, Vitomir B.Stepić, Milutin
Radovanović, Jelena V.
Hadžievski, Ljupčo
Radunović, Jovan
Doctoral thesis
Metadata
Show full item recordAbstract
U ovoj disertaciji teorijski i eksperimentalno su analizirani linearni i nelinearni efektikoji prate prostiranje vidljive laserske svetlosti kroz različite jednodimenzionalne (1D) fotonskerešetke napravljene od materijala sa zasićujućom (saturacionom) nelinearnošću, kao što je, naprimer, litijum niobat (LiNbO3). Zbog nelinearnog odziva kakvim se odlikuju ovakvi materijali,moguće je formiranje stabilnih prostornih lokalizovanih struktura na granicama između dveuniformne rešetke istih, odnosno različitih perioda, kao i unutar binarnih superrešetki, kako unelinearnom režimu, tako i u linearnom kada do lokalizacije dolazi u okolini defekta. Udoktorskoj tezi razvijeni su odgovarajući matematički modeli i primenjene različite numeričkemetode za dobijanje odgovarajućih rezultata, dok su neki od rezultata potvrđeni ieksperimentalno u nelinearnim 1D fotonskim rešetkama proizvedenim u LiNbO3. Korišćenimatematički modeli zasnovani su na sistemima spregnutih diferencno-diferencijalnih jednačina,ta...čnije 1D diskretnim nelinearnim Šredingerovim (Schrödinger) jednačinama sa nelinearnostimaKerovog (Kerr) i zasićujućeg tipa, dok je stabilnost dobijenih rešenja ispitivana primenommetoda linearne analize stabilnosti. Za rešavanje stacionarnih i dinamičkih jednačina izloženih utezi, korišćene su numeričke metode pod nazivom Gaus-Njutnova metoda (Gauss-Newton) iRunge-Kuta (Runge-Kutta) metoda, respektivno. Dobijeni numerički i eksperimentalni rezultatipokazuju da prisustvo defekta utiče na formiranje lokalizovanih modova kako u nelinearnom,tako i u linearnom režimu, tj. pri malim upadnim snagama nedovoljnim za ispoljavanjenelinearnog odziva sredine. Rezultati pokazuju da pored pojave linearnih lokalizovanih stanja, unelinearnom režimu dolazi do narušavanja simetrije lokalizovanih rešenja kada su ispunjeniodgovarajući uslovi. U slučaju prostiranja svetlosti kroz binarne superrešetke, rezultati ukazuju napostojanje novih tipova lokalizovanih rešenja, kao i otvaranje dodatnog procepa u zonskojstrukturi posmatrane rešetke. Pored ovoga, prikazani su i numerički rezultati dobijeni analizommeđusobnih interakcija solitonskih rešenja, kao i ispitivanjem osobina modova lokalizovanih napovršini rešetke.
In this dissertation the linear and nonlinear effects accompanying the propagationof visible laser light through a different one-dimensional (1D) photonic lattices made of materialwith a saturable nonlinearity, such as, for example, lithium niobate (LiNbO3) are bothinvestigated, theoretically and experimentally. Due to the nonlinear response of these materialsto the intensity of incident radiation, the light passing through the photonic lattice causes localchange in the refractive index, providing necessary conditions for the formation of stablelocalized spatial structures at the interfaces between two uniform lattices of the same or differentperiods, and also within the binary superlattices, in the nonlinear regime, as well as in the linearregime when the localization occurs in the vicinity of the defect. In this dissertation, appropriatemathematical models are developed and various numerical methods for obtaining the relevantresults are applied. Some of the results have been confirme...d experimentally in 1D nonlinearphotonic lattices fabricated in LiNbO3. Mathematical models are based on systems of coupleddifference- differential equations, namely the 1D discrete nonlinear Schrödinger equation withthe nonlinear term of Kerr and saturable type, while the stability of the obtained solutions wasinvestigated using the method of linear stability analysis. To solve stationary and dynamicequations presented in this dissertation, numerical methods such as the Gauss-Newton andRunge-Kutta methods are performed, respectively. The obtained numerical and experimentalresults show that the presence of the defect affects the formation of localized modes in thenonlinear, as well as in the linear regime, i.e. for intensities insufficient for the manifestation ofthe nonlinear response of the medium. Furthermore, the results indicate to the possibleappearance of the symmetry breaking of the mode profiles of certain nonlinear localizedsolutions when appropriate conditions are met. In the case of light propagation through binarysuperlattices, results show the emergence of new types of localized solutions and the opening ofan additional gap in the observed energy spectrum of the lattice. Additionally, numerical resultsobtained by analyzing the mutual interaction of soliton solutions, as well as examining theproperties of localized modes at the surface of the lattice, are presented as well.
Keywords:
Nelinearni optički talasovodi / Nonlinear optical waveguides / Optički solitoni / Lokalizovani modovi / Nelinearnadinamika solitona / Optički prekidači / Optički uređaji / Optical solitons / Localized modes / Nonlineardynamics of solitons / Optical switches / Optical devicesSource:
Универзитет у Београду, 2012Publisher:
- Универзитет у Београду, Електротехнички факултет
Funding / projects:
- Photonics of micro and nano structured materials (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-45010)
URI
http://eteze.bg.ac.rs/application/showtheses?thesesId=215https://fedorabg.bg.ac.rs/fedora/get/o:5471/bdef:Content/download
http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=43479055
http://nardus.mpn.gov.rs/123456789/2237
https://vinar.vin.bg.ac.rs/handle/123456789/7244
Collections
Institution/Community
VinčaTY - THES AU - Beličev, Petra PY - 2012 UR - http://eteze.bg.ac.rs/application/showtheses?thesesId=215 UR - https://fedorabg.bg.ac.rs/fedora/get/o:5471/bdef:Content/download UR - http://vbs.rs/scripts/cobiss?command=DISPLAY&base=70036&RID=43479055 UR - http://nardus.mpn.gov.rs/123456789/2237 UR - https://vinar.vin.bg.ac.rs/handle/123456789/7244 AB - U ovoj disertaciji teorijski i eksperimentalno su analizirani linearni i nelinearni efektikoji prate prostiranje vidljive laserske svetlosti kroz različite jednodimenzionalne (1D) fotonskerešetke napravljene od materijala sa zasićujućom (saturacionom) nelinearnošću, kao što je, naprimer, litijum niobat (LiNbO3). Zbog nelinearnog odziva kakvim se odlikuju ovakvi materijali,moguće je formiranje stabilnih prostornih lokalizovanih struktura na granicama između dveuniformne rešetke istih, odnosno različitih perioda, kao i unutar binarnih superrešetki, kako unelinearnom režimu, tako i u linearnom kada do lokalizacije dolazi u okolini defekta. Udoktorskoj tezi razvijeni su odgovarajući matematički modeli i primenjene različite numeričkemetode za dobijanje odgovarajućih rezultata, dok su neki od rezultata potvrđeni ieksperimentalno u nelinearnim 1D fotonskim rešetkama proizvedenim u LiNbO3. Korišćenimatematički modeli zasnovani su na sistemima spregnutih diferencno-diferencijalnih jednačina,tačnije 1D diskretnim nelinearnim Šredingerovim (Schrödinger) jednačinama sa nelinearnostimaKerovog (Kerr) i zasićujućeg tipa, dok je stabilnost dobijenih rešenja ispitivana primenommetoda linearne analize stabilnosti. Za rešavanje stacionarnih i dinamičkih jednačina izloženih utezi, korišćene su numeričke metode pod nazivom Gaus-Njutnova metoda (Gauss-Newton) iRunge-Kuta (Runge-Kutta) metoda, respektivno. Dobijeni numerički i eksperimentalni rezultatipokazuju da prisustvo defekta utiče na formiranje lokalizovanih modova kako u nelinearnom,tako i u linearnom režimu, tj. pri malim upadnim snagama nedovoljnim za ispoljavanjenelinearnog odziva sredine. Rezultati pokazuju da pored pojave linearnih lokalizovanih stanja, unelinearnom režimu dolazi do narušavanja simetrije lokalizovanih rešenja kada su ispunjeniodgovarajući uslovi. U slučaju prostiranja svetlosti kroz binarne superrešetke, rezultati ukazuju napostojanje novih tipova lokalizovanih rešenja, kao i otvaranje dodatnog procepa u zonskojstrukturi posmatrane rešetke. Pored ovoga, prikazani su i numerički rezultati dobijeni analizommeđusobnih interakcija solitonskih rešenja, kao i ispitivanjem osobina modova lokalizovanih napovršini rešetke. AB - In this dissertation the linear and nonlinear effects accompanying the propagationof visible laser light through a different one-dimensional (1D) photonic lattices made of materialwith a saturable nonlinearity, such as, for example, lithium niobate (LiNbO3) are bothinvestigated, theoretically and experimentally. Due to the nonlinear response of these materialsto the intensity of incident radiation, the light passing through the photonic lattice causes localchange in the refractive index, providing necessary conditions for the formation of stablelocalized spatial structures at the interfaces between two uniform lattices of the same or differentperiods, and also within the binary superlattices, in the nonlinear regime, as well as in the linearregime when the localization occurs in the vicinity of the defect. In this dissertation, appropriatemathematical models are developed and various numerical methods for obtaining the relevantresults are applied. Some of the results have been confirmed experimentally in 1D nonlinearphotonic lattices fabricated in LiNbO3. Mathematical models are based on systems of coupleddifference- differential equations, namely the 1D discrete nonlinear Schrödinger equation withthe nonlinear term of Kerr and saturable type, while the stability of the obtained solutions wasinvestigated using the method of linear stability analysis. To solve stationary and dynamicequations presented in this dissertation, numerical methods such as the Gauss-Newton andRunge-Kutta methods are performed, respectively. The obtained numerical and experimentalresults show that the presence of the defect affects the formation of localized modes in thenonlinear, as well as in the linear regime, i.e. for intensities insufficient for the manifestation ofthe nonlinear response of the medium. Furthermore, the results indicate to the possibleappearance of the symmetry breaking of the mode profiles of certain nonlinear localizedsolutions when appropriate conditions are met. In the case of light propagation through binarysuperlattices, results show the emergence of new types of localized solutions and the opening ofan additional gap in the observed energy spectrum of the lattice. Additionally, numerical resultsobtained by analyzing the mutual interaction of soliton solutions, as well as examining theproperties of localized modes at the surface of the lattice, are presented as well. PB - Универзитет у Београду, Електротехнички факултет T2 - Универзитет у Београду T1 - Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću T1 - Propagation of light in complex photonic lattices with saturable nonlinearity UR - https://hdl.handle.net/21.15107/rcub_nardus_2237 ER -
@phdthesis{ author = "Beličev, Petra", year = "2012", abstract = "U ovoj disertaciji teorijski i eksperimentalno su analizirani linearni i nelinearni efektikoji prate prostiranje vidljive laserske svetlosti kroz različite jednodimenzionalne (1D) fotonskerešetke napravljene od materijala sa zasićujućom (saturacionom) nelinearnošću, kao što je, naprimer, litijum niobat (LiNbO3). Zbog nelinearnog odziva kakvim se odlikuju ovakvi materijali,moguće je formiranje stabilnih prostornih lokalizovanih struktura na granicama između dveuniformne rešetke istih, odnosno različitih perioda, kao i unutar binarnih superrešetki, kako unelinearnom režimu, tako i u linearnom kada do lokalizacije dolazi u okolini defekta. Udoktorskoj tezi razvijeni su odgovarajući matematički modeli i primenjene različite numeričkemetode za dobijanje odgovarajućih rezultata, dok su neki od rezultata potvrđeni ieksperimentalno u nelinearnim 1D fotonskim rešetkama proizvedenim u LiNbO3. Korišćenimatematički modeli zasnovani su na sistemima spregnutih diferencno-diferencijalnih jednačina,tačnije 1D diskretnim nelinearnim Šredingerovim (Schrödinger) jednačinama sa nelinearnostimaKerovog (Kerr) i zasićujućeg tipa, dok je stabilnost dobijenih rešenja ispitivana primenommetoda linearne analize stabilnosti. Za rešavanje stacionarnih i dinamičkih jednačina izloženih utezi, korišćene su numeričke metode pod nazivom Gaus-Njutnova metoda (Gauss-Newton) iRunge-Kuta (Runge-Kutta) metoda, respektivno. Dobijeni numerički i eksperimentalni rezultatipokazuju da prisustvo defekta utiče na formiranje lokalizovanih modova kako u nelinearnom,tako i u linearnom režimu, tj. pri malim upadnim snagama nedovoljnim za ispoljavanjenelinearnog odziva sredine. Rezultati pokazuju da pored pojave linearnih lokalizovanih stanja, unelinearnom režimu dolazi do narušavanja simetrije lokalizovanih rešenja kada su ispunjeniodgovarajući uslovi. U slučaju prostiranja svetlosti kroz binarne superrešetke, rezultati ukazuju napostojanje novih tipova lokalizovanih rešenja, kao i otvaranje dodatnog procepa u zonskojstrukturi posmatrane rešetke. Pored ovoga, prikazani su i numerički rezultati dobijeni analizommeđusobnih interakcija solitonskih rešenja, kao i ispitivanjem osobina modova lokalizovanih napovršini rešetke., In this dissertation the linear and nonlinear effects accompanying the propagationof visible laser light through a different one-dimensional (1D) photonic lattices made of materialwith a saturable nonlinearity, such as, for example, lithium niobate (LiNbO3) are bothinvestigated, theoretically and experimentally. Due to the nonlinear response of these materialsto the intensity of incident radiation, the light passing through the photonic lattice causes localchange in the refractive index, providing necessary conditions for the formation of stablelocalized spatial structures at the interfaces between two uniform lattices of the same or differentperiods, and also within the binary superlattices, in the nonlinear regime, as well as in the linearregime when the localization occurs in the vicinity of the defect. In this dissertation, appropriatemathematical models are developed and various numerical methods for obtaining the relevantresults are applied. Some of the results have been confirmed experimentally in 1D nonlinearphotonic lattices fabricated in LiNbO3. Mathematical models are based on systems of coupleddifference- differential equations, namely the 1D discrete nonlinear Schrödinger equation withthe nonlinear term of Kerr and saturable type, while the stability of the obtained solutions wasinvestigated using the method of linear stability analysis. To solve stationary and dynamicequations presented in this dissertation, numerical methods such as the Gauss-Newton andRunge-Kutta methods are performed, respectively. The obtained numerical and experimentalresults show that the presence of the defect affects the formation of localized modes in thenonlinear, as well as in the linear regime, i.e. for intensities insufficient for the manifestation ofthe nonlinear response of the medium. Furthermore, the results indicate to the possibleappearance of the symmetry breaking of the mode profiles of certain nonlinear localizedsolutions when appropriate conditions are met. In the case of light propagation through binarysuperlattices, results show the emergence of new types of localized solutions and the opening ofan additional gap in the observed energy spectrum of the lattice. Additionally, numerical resultsobtained by analyzing the mutual interaction of soliton solutions, as well as examining theproperties of localized modes at the surface of the lattice, are presented as well.", publisher = "Универзитет у Београду, Електротехнички факултет", journal = "Универзитет у Београду", title = "Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću, Propagation of light in complex photonic lattices with saturable nonlinearity", url = "https://hdl.handle.net/21.15107/rcub_nardus_2237" }
Beličev, P.. (2012). Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću. in Универзитет у Београду Универзитет у Београду, Електротехнички факултет.. https://hdl.handle.net/21.15107/rcub_nardus_2237
Beličev P. Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću. in Универзитет у Београду. 2012;. https://hdl.handle.net/21.15107/rcub_nardus_2237 .
Beličev, Petra, "Prostiranje svetlosti u kompleksnim fotonskim rešetkama sa zasićujućom nelinearnošću" in Универзитет у Београду (2012), https://hdl.handle.net/21.15107/rcub_nardus_2237 .