Nonlinear photonic crystals for frequency conversion of infrared light

Name: Kang Chiang Huen Degree: M Sc Department: Physics Thesis title: Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light Abstract Nonlinear photonic crystals for frequency conversion of 1064 nm infrared light were fabricated using electron beam lithography and Czochralski growth of bulk crystals Electron beam irradiation on lithium niobate single crystals was performed with the optimal range of line charge density lying within 170 nC/cm and 250 nC/cm and area charge density within 450 µC/cm2 to 550 µC/cm2 Phase imaging of the nonlinear photonic crystals buried under a thin layer of polymer provides a novel way of imaging patterned ferroelectrics in humid environment Spontaneous parametric down conversion imaging shows the non-uniformity in periodicity of Czochralski grown Y:LN nonlinear photonic crystals Raman spectroscopy through a superlattice period show that the domain inverted region is largely anti-parallel to the uninverted ones which is in favor of the displacive mechanism for domain inversion in ferroelectrics Conversion efficiency studies for second harmonic generation of 1064 nm wavelength of light yield a percentage of about 1.6 % Keywords: nonlinear photonic crystals, electron beam lithography, electrostatic force microscopy, lithium niobate, spontaneous parametric down conversion, Raman spectroscopy NONLINEAR PHOTONIC CRYSTALS FOR FREQUENCY CONVERSION OF INFRARED LIGHT Kang Chiang Huen (B.Sc., B.Sc.(Hon)) A thesis submitted for the Degree of Master of Science Department of Physics National University of Singapore 2004 Acknowledgements Acknowledgements “For every beginning have an end and every end a new beginning.” The time has come for me to bid farewell to my Masters course with the submission of a dissertation and to transit to the next phase of life The fruition of this dissertation had been made possible through the help of many It has been a pleasurable time to be with the friendly colleagues and amicable advisors in the optics laboratory of the department of physics The discussions we had, the ideas we exchanged and the daily friendly “Hi” were perhaps wander in my mind for as long as I can remember On the top of my thank list, I would like to express my most heartfelt gratitude to my advisors, Associate Professor Shen Ze Xiang and Professor Tang Sing Hai for their relentless help, advices and patience when things doesn’t seem to be in place My salutations also go to my colleagues out there, especially Dr Sun Wanxin, Dr Ma Guohong, Mr He Jun, Dr Su Hong and Mr Liu Lei, to my friends who had given me moral support through the course of my work particularly Mr Soh Boon Seng, Ms Tok Kwee Lee and to my family, specifically to my elder brother, who had been everencouraging in my pursuit for a more profound and deeper understanding of science Last but not least, I would like to thank that special someone in my life that had taught me that there is something in this world that never conform to the natural law of change, my beloved wife, Angeline, for her constant, unfailing support towards every aspect of me and of my life National University of Singapore, Singapore, 2004 Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light C H Kang i Table of Contents Table of Contents Acknowledgements i Table of Contents ii Summary iv List of Publications vi Chapter Introduction Chapter Nonlinear Photonic Crystal Theory 2.1 An Introduction to Nonlinear Optics 2.2 Phase Matching 2.3 Multi-dimensional Architectures Chapter Fabrication of Nonlinear Photonic Crystals 3.1 Lithium Niobate 3.2 Electron Beam Lithography 3.3 One- and Two- dimensional nonlinear photonic crystals 3.4 Crystal growth of Yttrium-doped Lithium Niobate (Y:LN) Chapter Characterization of Nonlinear Photonic Crystals 4.1 Scanning Probe Microscopy 4.2 Spontaneous Parametric Down Conversion (SPDC) Imaging 4.3 Raman Spectroscopy Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 20 41 ii Table of Contents 4.4 Conversion Efficiency of the Nonlinear Photonic Crystals Chapter Conclusions 60 References 62 Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light iii Summary Summary In this dissertation, the theoretical framework of nonlinear photonic crystals, the fabrication of them through electron beam lithography and Czochralski growth and their characterization through scanning probe microscopy, Raman spectroscopy, spontaneous parametric down conversion imaging and the conversion efficiency were presented We have successfully obtained one- and two-dimensional nonlinear photonic crystals by electron beam irradiation on lithium niobate single crystals which results in the reversal of its ferroelectric domains through the whole thickness of the crystal of 500 µm Domain reversals become more prominent as charge density increases The optimal range of line charge density lies within 170 nC/cm and 250 nC/cm and area charge density within 450 µC/cm2 to 550 µC/cm2 It was found that these charge densities correspond to the coercive field of lithium niobate Continuous electron beam scanning on the upper surface of the crystal yields hexagonal segments on the bottom surface that elongate in the direction of irradiation and merge as charge density increases Atomic force micrographs revealed an approximate width of the hexagonal segments regardless of the pattern on the upper, irradiated surface as a result of the spreading of electrons on initial impingement Hence, this place a limit on the domain inverted size by direct writing alone Furthermore, examinations of the domain-reversed gratings using electric force microscopy show a direct correspondence of the position of the hexagonal segments to those in the atomic force microscopy images Phase imaging of the nonlinear photonic crystal buried under a thin layer of polymer provides a novel way of imaging patterned ferroelectrics in humid environment Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light v Summary Spontaneous parametric down conversion imaging shows the non-uniformity in periodicity of Czochralski grown Y:LN nonlinear photonic crystals From this imaging, we can pin-point which region of the crystal is more effective in frequency down conversion of 1064 nm to a particular wavelength of mid-IR light Raman spectroscopy through a superlattice period shows that the domain inverted region is largely anti-parallel to the uninverted ones which is in favor of the displacive mechanism for domain inversion in ferroelectrics Conversion efficiency studies for second harmonic generation of 1064 nm wavelength of light yield a percentage of about 1.6 % Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light v List of Publications List of Publications Papers Two-dimensional structures of ferroelectric domain inversion in LiNbO3 by direct electron beam lithography J He, S H Tang, Y Q Qin, P Dong, H Z Zhang, C H Kang, W X Sun, Z X Shen, JOURNAL OF APPLIED PHYSICS, 93 (12): 9943-9946 2003 Fabrication of two-dimensional nonlinear photonic crystals by electron beam lithography C H Kang, Z X Shen, S H Tang, MAT RES SOC SYMP PROC., 797, W5.10 2004 Nondestructive Electrostatic Phase Imaging of Ferroelectrics by Scanning Probe Microscopy Lift mode through a polymeric layer C H Kang, Z X Shen, S H Tang (To be submitted) Spontaneous parametric down conversion imaging as an evaluation tool for Domain Uniformity C H Kang, S H Tang, Z X Shen, V V Tishkova, G Kh Kitaeva (To be submitted) Posters Fabrication of two-dimensional nonlinear photonic crystals by electron beam lithography 2003 Materials Research Society Fall Meeting, Boston, USA, 2003 Fabrication and electrostatic phase imaging of two-dimensional nonlinear photonic crystals of lithium niobate International Conference on Materials for Advanced Technologies, Singapore, Singapore, 2003 Phase Imaging of Ferroelectric Materials, MRS-S National Conference, Singapore, Singapore, 2004 Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light vi Chapter Introduction Chapter Introduction At the roots of all science lies our unquenchable curiosity about our universe and ourselves A deep understanding of the structure and the dynamics, and hence the properties of matter, undoubtedly bestow us the ability to manipulate their characteristics and consequently, the birth of a revolutionary technology The mechanical properties of materials have been greatly exploited since the dawn of civilizations and in the last century, our understanding of electromagnetism allowed us to manipulate the electrical properties extensively The last decade has seen the emergence of a third wave with a similar goal as the above two, control over certain property of materials; this time on our dominance over the optical properties As the human race demands greater miniaturization of devices and faster flow of information, alternatives to electrons as the information carrier and semiconductors had to Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light Chapter Introduction be sought Further miniaturization in integrated electronic devices poses a problem of increased resistance and high levels of power dissipation The potential candidate to resolving these problems is making photons as the information carrier and the semiconductors of light are photonic crystals Photons as information carriers supersede electrons in that they can travel at much greater speeds, carry more information and have weaker interactions with the material in which they propagate The reason of the availability of a diverse range of electronic properties is due to the interaction of electrons with the periodic potential of the lattice structure of the materials It is this interaction that determines whether a material is classified as a metal, a semiconductor, or an insulator and by changing the structures we can tailor-make the conducting characteristics of, in principle, any materials This is the main propulsion for the search of the optical analogue of electronic materials Yablonovitch1 and John2 conceived the proposal of an optical analogue of semiconductors independently in 1987 that marks the birth of the field of photonic crystals While John attempts to draw an analogy between light localization and electronic localization as a pure academic interest, Yablonovitch is interested in making telecommunications lasers more efficient through the inhibition of spontaneous emission of light These are, nevertheless two facets of one central theme: confining the flow of electromagnetic waves So what are photonic crystals? Photonic crystals are microstructured superlattice metamaterials in which the dielectric constant is periodically modulated on a length scale comparable to the desired wavelength of light, with the existence of a photonic band gap A photonic crystal is categorized according to its dielectric periodicity in one, two or three Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light Chapter Characterization of Nonlinear Photonic Crystals within the crystal which, in fact, is most important for the frequency conversion process Therefore, it is necessary for us to develop a technique of examining our crystals to know which region of the crystal can more efficiently convert the pump laser to other wavelengths It is with this motivation that brought us to think of utilizing spontaneous parametric down conversion as the nonlinear response from the bulk of the crystal as a statistical average of all good and bad contributions to the efficiency of the frequency conversion process Spontaneous parametric down conversion (SPDC) is the scattering or decay of pump photons of frequency ω0 as a result of quantum field fluctuations in a medium with non-zero second order nonlinear susceptibility χ(2) and was first predicted in 1966 by Klyshko39 The nonlinear process is exemplified in FIG 4.9 below idler wave cw pump laser propagating along x signal wave FIG 4.9 Spontaneous parametric down conversion 4.2.1 Experimental A Y:LN crystal was placed on a two-dimensional motorized stage in an optical configuration for obtaining the SPDC spectrum The incident pump power and wavelength was W and 488 nm respectively The laser spot size was 50 µm A spectrum was taken at 100 µm intervals in a raster scan and eventually the entire crystal was mapped The accumulation time for each spectrum was 60 s The intensity of a particular peak, which Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 50 Chapter Characterization of Nonlinear Photonic Crystals correspond to a specific frequency conversion process, was noted for each spectrum and a three-dimensional map of intensity along x and y directions, with respect to the optical axis, was obtained FIG 4.10 shows the optical set-up for the mapping Optical axis Spectrometer Filter Beam splitter Pump Laser Lens Sample Tilting Stage Nonlinear response Motorized Stage Mirror FIG 4.10 Optical set-up for 2-dimensional SPDC mapping 4.2.2 Results and discussions A typical spectrum that was obtained is illustrated below in FIG 4.11 This spectrum shows peaks corresponding to different periods which implies non-uniformity in the grown crystal This is a major drawback of as-grown nonlinear superlattices The periods are calculated as in Chapter We can then select a wavelength peak which correspond to a period of interest and note the intensity on all the spectra so as to generate a map of intensity distribution with respect to the spatial position of the crystal as shown in FIG Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 51 Chapter Characterization of Nonlinear Photonic Crystals 4.12 The map thus obtained gives us a guide as to which regions are more efficient for a particular frequency conversion process thereby optimizing the conversion efficiency 29.82 29.35 28.04 27.69 28.78 28.41 30.31 30.74 31.72 FIG 4.11 A typical spectrum for one of the regions of the Y:LN superlattice (the labeling of the peaks correspond to the theoretical period in µm) Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 52 Chapter Characterization of Nonlinear Photonic Crystals FIG 4.12 Map of SPDC signal of 608 nm which corresponds to a period of 29.3 µm (red: higher intensity, blue lowest) 4.3 Raman Spectroscopy Domains form in numerous materials such as ferromagnetics, antiferromagnetics, ferroelectrics, antiferroelectrics and so on Within each of the domains, there exist polarizations of the same direction (ferroelectrics) or magnetizations of the same orientation (ferromagnetics) Direction of polarization or magnetization could be altered by the application of an electric field or a magnetic field respectively Two domain reversal mechanisms are predominant: displacive or rotational as shown in FIG 4.13 The displacive mechanism relies on the movement of dipoles parallel to the applied field whereas the latter relies on the gradual rotation of dipoles to the direction of the field By probing into the domain walls, the transition region from one direction of electric polarization to the other or the boundaries between two adjacent domains, we can learn about the route domain reversal of electric polarizations in lithium niobate underwent Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 53 Chapter Characterization of Nonlinear Photonic Crystals Since different orientations of electric polarizations will result in changes in the appearance of Raman peaks, Raman spectroscopy could be used to scan over domain walls Raman spectra of an unprocessed lithium niobate, that is, with a single domain, undergoing rotations corresponding to different orientations of electric polarization served as a reference for comparison of the Raman spectra obtained from the nonlinear photonic crystals Wall thickness (a) (b) FIG 4.13 Magnetic or electric polar vector (a) rotates in the wall thickness or (b) shrinks in the wall thickness 4.3.1 Experimental A virgin crystal of lithium Niobate placed on a goniometer was rotated from ° to 180° orthogonal with respect to the optical axis and their Raman spectra were obtained The one-dimensional nonlinear photonic crystal was also characterized using backscattering Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 54 Chapter Characterization of Nonlinear Photonic Crystals Raman spectroscopy in scanning steps of 12nm in a line of 7µm The geometry of scan is as illustrated below in FIG 4.14 7µm FIG 4.14 Scanning geometry for Raman Spectroscopy 4.3.2 Results and discussions Raman spectra obtained from virgin crystals as shown in FIG 4.15 showed changes in peak position and intensity This is particularly evident from the Raman spectrum of the crystal at right angle with strong peaks entirely different from the rest of the spectra We can observe that the general trend is that the intensity of the peaks decreases from 0° to 90° and increases from 90° to 180° as a result of the symmetry of the rotation and that the anti-parallel polarizations yield the essentially the same Raman spectrum Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 55 Chapter Characterization of Nonlinear Photonic Crystals Domain rotation on +c face (50× objective lens) 180 ° 90 ° 0° FIG 4.15 Raman spectra of rotated polarization of a virgin crystal Raman spectra of the one-dimensional nonlinear photonic crystal as shown in FIG 4.16 show no global structural changes as they yield identical spectra It could be due to the extremely small contribution from the domain wall to the total contribution of the rest of the region under a laser spot size of about µm As a result, its effects are masked when the region of non-inverted domains to inverted ones traversing the domain wall of very small thickness are scanned On the other hand, it may also suggest that domain rotation is not likely to be the Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 56 Chapter Characterization of Nonlinear Photonic Crystals FIG 4.16 Raman spectra of one-dimensional nonlinear photonic crystal candidate for the mechanism of domain reversals in lithium niobate by comparing the above Raman spectra to that obtained under a series of rotation of the LN crystal corresponding to different orientation of polarization The Raman spectra obtained from scanning over domain walls not show any of the rotated spectra However, because of the identical spectra, we have directly proven that the inverted domains are indeed antiparallel to the non-inverted ones Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 57 Chapter Characterization of Nonlinear Photonic Crystals 4.4 Conversion Efficiency of the Nonlinear Photonic Crystals The principle involved in this part of characterization is extremely straight forward A high power pump laser with a wavelength of 1064 nm irradiates the nonlinear photonic crystal whereby 532 nm light is generated as a result of second harmonic generation The amount of light thus generated is then normalized to the input thereby obtaining the conversion efficiency of the nonlinear photonic crystals 4.4.1 Experimental 10 ns pulses of an Nd:YAG laser of 1064 nm with 280 µJ energy per pulse was used to irradiate the two-dimensional square lattice nonlinear photonic crystal on a axes, temperature controllable stage Through a series of lenses and filters, the output of 532 nm was detected by a sensitive photodetector placed behind a 1064 nm filter The optical scheme is exemplified below in FIG 4.17 Nd:YAG 1064nm M M M M F1 Half-wave plate L Crystal on 5-axes stage F2 D FIG 4.17 Optical Scheme for Conversion efficiency measurements Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 58 Chapter Characterization of Nonlinear Photonic Crystals 4.4.2 Results and discussions It was found that the normalized conversion efficiency is about 1.6 % under optimized directions, angles and temperature This could be attributed to the fact that the inverted domains (the individual repeating pattern) by electron beam lithography are irregular which would greatly affect the intended periodicity of our superlattices Since the periodicity of the superlattice bears an intimate relationship with the wavelength of generated light, it is not surprising that irregular repeating patterns result in low conversion efficiency Moreover, based on our understanding of domain propagation through the crystal the inverted domains are conical in shape Hence, the laser beam experiences varying periodicities along its propagation which result in adverse contribution to the conversion of 1064 nm infrared light to 532 nm green light On comparison of domain inversion by electro-poling, whereby a pulse of voltage is applied to optically lithographed electrodes, which results in regular non-segmented inverted domains (for the one-dimensional case) or hexagonal inverted domains (for the two-dimensional case), we can observe that the critical difference lies in a concerted domain inversion when the pulse of voltage is applied Nevertheless, the intrinsic nature of the direct writing process does not allow concerted domain inversion as electrons are not deposited all at once Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 59 Chapter Conclusions Chapter Conclusions In conclusions, we have successfully obtained one- and two-dimensional nonlinear photonic crystals by electron beam irradiation on lithium niobate single crystals which results in the reversal of its ferroelectric domains through the whole thickness of the crystal Domain reversals become more prominent as charge density increases The optimal range of line charge density lies within 170 nC/cm and 250 nC/cm and area charge density within 450 µC/cm2 to 550 µC/cm2 It was found that these charge densities correspond to the coercive field of lithium niobate Continuous electron beam scanning on the upper surface of the crystal yields hexagonal segments on the bottom surface that elongate in the direction of irradiation and merge as charge density increases Atomic force micrographs revealed an approximate width of the hexagonal segments regardless of the pattern on the upper, irradiated surface as a result of the Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 60 Chapter Conclusions spreading of electrons on initial impingement Hence, this place a limit on the domain inverted size by direct writing alone Furthermore, examinations of the domain-reversed gratings using electric force microscopy show a direct correspondence of the position of the hexagonal segments to those in the atomic force microscopy images Phase imaging of the nonlinear photonic crystal buried under a thin layer of polymer provides a novel way of imaging patterned ferroelectrics in humid environment as the images show phase contrast changes in accordance to magnitude and polarity changes of the tip which is in accordance to our intuitive understanding of bias tip and ferroelectric sample interaction Spontaneous parametric down conversion imaging shows the non-uniformity in periodicity of Czochralski grown Y:LN nonlinear photonic crystals From this imaging, we can pin-point which region of the crystal is more effective in frequency down conversion of 1064 nm to a particular wavelength of mid-IR light Raman spectroscopy through a superlattice period show that the domain inverted region is largely anti-parallel to the uninverted ones based on the comparison with the spectra obtained with a rotated single domain crystal of lithium niobate This is in favor of the displacive mechanism for domain inversion in ferroelectrics Conversion efficiency studies for second harmonic generation of 1064 nm wavelength of light yield a percentage of about 1.6 % The apparently low conversion is attributed to the intrinsic tapered domain propagation using the electron beam technique which affects the uniformity of periodicity which in turn affects the conversion efficiency as phase mismatch is no longer small Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 61 References References E Yablonovitch, Phys Rev Lett 58, 2059 (1987) S John, Phys Rev Lett 58, 2486 (1987) Y Fink, J N Winn, S Fan, C Chen, J Michel, J D Joannopoulos and E L Thomas, Science 282, 1679 (1998) S Lin, E Chow, V Hietala, P R Villeneuve, and J D Joannopoulos, Science 282, 274 (1998) S Y Lin, J G Fleming, and I El-Kady, Opt Lett 28, 1683 (2003) P V Parimi, W T Lu, P Vodo, and S Sridhar, Nature 426, 404 (2003) J A Armstrong, N Bloembergen, J Ducuing, and P S Pershan, Phys Rev 127, 1918 (1962) S Thaniyavarn, T Finddakly, D Boeher, and J Moen, Appl Phys Lett 46, 933 (1985) C J Van Der Poel, J D Bierlen, J B Brown, and S Colak, Appl Phys Lett 57, 2074 (1992) 10 G Rosenman, Kh Garb, A Skliar, M Oron, D Eger, and M Katz, Appl Phys Lett 73, 865 (1998) 11 J He, S H Tang, Y Q Qin, P Dong, H.Z Zhang, C H Kang, W X Sun, and Z X Shen, J Appl Phys 93, 9943 (2003) 12 V Berger, Phys Rev Lett 81, 4136 (1998) 13 N G R Broderick, G W Ross, H L Offerhaus, D J Richardson, and D C Hanna, Phys Rev Lett 84, 4345 (2000) Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 62 References 14 C Restoin, S Massy, C Darrud-Taupiac, and A Barthelemy, Opt Mater 22, 193 (2003) 15 M Fujimura, K Kintaka, T Suhara, and H Nishira, J Lightwave Tech 11, 1360 (1993) 16 Z Y Zhang, L C Wang, Y Y Zhu and N B Ming, Ferroelectrics 215, 113 (1998) 17 C Restoin, C Darraud-Taupiac, J L Decossas, J C Vareille, J Hauden and A Martinez, J Appl Phys 88, 6665 (2000) 18 H Bluhm, A Wadas, A Roshko, J A Aust and D Nam, Appl Phys Lett 71, 146 (1997) 19 D A Kleinman, Phys Rev 126, 1977 (1962) 20 J A Giordmaine, Phys Rev Lett., 8, 19, (1962) 21 P D Maker, R W Terhune, M Nissenoff and C M Savage, Phys Rev Lett., 8, 21 (1962) 22 D E Zelmon, D L Small and D Jundt, J Opt Soc Am B 14, 3319 (1997) 23 Y Ishigame, T Suhara and H Nishihara, Opt Lett 16, 375 (1991) 24 Y Q Qin, Y Y Zhu, S N Zhu and N B Ming, J Appl Phys., 84, 6911 (1998) 25 B Y Gu, Y Zhang and B Z Dong, J Appl Phys 87, 7629 (2000) 26 S Saltiel and Y S Kivshar, Opt Lett 25, 1204 (2000) 27 K K Wong (editor), Properties of Lithium Niobate, (2002) 28 B T Matthias and J P Remeika, Phys Rev., 76, 1886, (1949) 29 A M Prokhorov and Yu S Kuzminov, Physics and chemistry of crystalline lithium niobate (1990) Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 63 References 30 L E Myers, R C Eckardkt, M M Fejer, R L Byer, J Opt Soc Am B 12 2102 (1995) 31 CASINO program downloaded from http://www.montecarlomodeling.mcgill.ca/download/download.html 32 M Fujimura, T Suhara and H Nishihara, Elec Lett 28, 721 (1991) 33 C Restoin, C Darraud-Taupiac, J L Decossas, J C Vareille and J Hauden, Mat Sci Semicon Proc., 3, 405 (2000) 34 P G Ni, B Q Ma, X H Wang, B Y Cheng and D Z Zhang, Appl Phys Lett 82, 4230 (2003) 35 N F Evlanova, I I Naumova, T O Chaplina, S V Lavrishchev and S A Blokhin, Phys Solid State 42, 1727 (2000) 36 B Bhushan, Springer Handbook of Nanotechnology, (2003) 37 C H Lei, A Das, M Elliott and J E Macdonald, Nanotechnology 15, 627 (2004) 38 J Tamayo and R Garcia, Appl Phys Lett 73, 2926 (1998) 39 G Kh Kitaeva and A N Penin, J Expt Theo Phys 98, 272 (2004) Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 64 [...]... the conception of the idea of photonic crystals Indeed, they are the wonderland for photons; for within these lands photons displayed Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 3 Chapter 1 Introduction unprecedented, remarkable properties that would contribute immensely to optical science and technology When intense light propagates in photonic crystals, nonlinear behavior... the intra-atomic electric field, in the case of laser radiation, the response becomes nonlinear The physical origin of this nonlinearity could Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 8 Chapter 2 Nonlinear Photonic Crystal Theory be thought of as the anharmonic oscillation of the positive and negative charges of a dipole Since nonlinear response usually manifests itself... 3.1 shows the crystal structure of LN Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 21 Chapter 3 Fabrication of Nonlinear Photonic Crystals (a) (b) FIG 3.1 Crystal Structure of LiNbO3 (a) a succession of the distorted octahedrons along the polar c axis (b) an idealized arrangement of the atoms in a unit cell along the c axis The popularity of LN crystals led to a mature industry... Czochralski-growth of bulk superlattices and characterization of these superlattices by various microscopic and spectroscopic techniques, and subsequently ends with several concluding remarks Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 6 Chapter 2 Nonlinear Photonic Crystal Theory Chapter 2 Nonlinear Photonic Crystal Theory We begin our exploration into nonlinear photonic crystals. .. Quasi-phase matching (QPM) through a sequence of nonlinear segments of opposite polarization is one of the solutions to the cancellation problem as was mentioned earlier By changing the sense of the polarization vector, a Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 15 Chapter 2 Nonlinear Photonic Crystal Theory change of phase of π could be achieved resulting in a proper phase... m is the QPM order Intense light propagating along x FIG 2.1 A 1-dimensional first-order QPM nonlinear photonic crystal with each ferroelectric domain having a length equal to lc and period Λ = 2 lc Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 16 Chapter 2 Nonlinear Photonic Crystal Theory For a first-order up -conversion frequency doubling process of λ = 1064 nm, and based... calculation of the domain period must take into account this fact Measurements of refractive index for extraordinary waves were made by Zelmon et al22 and we obtain d1 = 29.1 µm Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 17 Chapter 2 Nonlinear Photonic Crystal Theory 2.3 Multi-dimensional Architectures The simplest kind of 1-dimensional nonlinear photonic crystal is a stack of alternative... phenomena of light propagation in media in which the response of the medium (i.e the polarization of the medium) is not directly proportional to the field strength of the electromagnetic wave used to describe the light It had its beginnings, customarily taken to be, with the first observation of the Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 7 Chapter 2 Nonlinear Photonic. .. can Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 22 Chapter 3 Fabrication of Nonlinear Photonic Crystals be formed by the conventional photolithographic process are ultimately diffraction limited by the wavelength of light; electron beams having very much shorter wavelengths are thus capable of producing extremely fine features This has important consequences in the field of. .. Conversion of Infrared Light 19 Chapter 3 Fabrication of Nonlinear Photonic Crystals Chapter 3 Fabrication of Nonlinear Photonic Crystals The stage is now set to experimentally realize some aforesaid structures It has been our interest in fabricating artifacts that give frequency conversion of infrared light as these processes provide routes towards the generation of coherent light where laser sources ... the range of the coercive field of lithium niobate of 20.6 kV/mm Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light 38 Chapter Fabrication of Nonlinear Photonic Crystals FIG... conception of the idea of photonic crystals Indeed, they are the wonderland for photons; for within these lands photons displayed Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light. .. case of laser radiation, the response becomes nonlinear The physical origin of this nonlinearity could Nonlinear Photonic Crystals for Frequency Conversion of Infrared Light Chapter Nonlinear Photonic