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Magnetophotorefractive Effect and Interference Filters in Lithium Niobate

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Magnetophotorefractive Effect and Interference Filters in Lithium Niobate Risø-R-880(EN) Magnetophotorefractive Effect and Interference Filters in Lithium Niobate Carsten Dam-Hansen o- -3dB A;WIM = °-06 S -5- a (O ° " -D "i O cP • • o D a " D <u -in- • • * • • • -15" -0,20 -0,10 0,00 0,10 0,20 0,30 Wavelength detuning [Å] Risø National Laboratory, Roskilde, Denmark March 1996 ?• 7 ri 13 Magnetophotorefractive Effect and Interference Filters in Lithium Niobate Carsten Dam-Hansen Risø National Laboratory, Roskilde, Denmark March 1996 Abstract This thesis deals with the fundamental photorefractive and photo- voltaic properties of iron-doped lithium niobate crystals. Experimental observations of a strong magnetic field effect on the energy cou- pling and grating formation in a vectorial interaction scheme are presented. To the author's knowledge these are the first reported results in the field. It is shown that an enhancement of the diffraction efficiency of 60 % is possible by applying even a moderate magnetic field of 0.23 T. A new theoretical model of the magnetophotorefractive effect in the vectorial interaction scheme is presented. It describes the space-charge field formation, two- wave mixing and grating formation under the influence of an externally applied magnetic field. Good agreement with the experimental results and the first mea- surement of nondiagonal components of the magnetophotovoltaic tensor are re- ported. A theoretical model for the temperature properties of photorefractive interfer- ence filters with subangstrom bandwidths are presented and compared favourably with experimental investigations. A novel method for determining the spectral re- sponse of these filters from a combined thermal and angular response measurement is described. Front page figure: Spectral response of photorefractive interference filter with a centre wavelength at 514.5 nm written in a 10 mm long LiNbO3".Fe crystal. This thesis is submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy at the Technical University of Denmark. ISBN 87-550-2165-4 ISSN 0106-2840 Grafisk Service • Risø • 1996 Contents List of Figures Tables and Symbols 4 Preface 8 Dansk resumé 9 1 Introduction 11 2 Lithium Niobate 13 2.1 Structural and physical properties 13 2.2 Photorefractive effect 14 2.2.1 Band transport model 16 2.2.2 Linear electro-optic effect 18 2.3 Bulk photovoltaic effect 19 2.3.1 Physical origin 20 2.3.2 Phenomenological theory 22 2.4 Magnetophotovoltaic effect 24 2.4.1 Physical origin 24 2.4.2 Phenomenological theory 25 3 Magnetophotorefractive Effect 28 3.1 Vectorial interaction 31 3.1.1 Configuration and photovoltaic current 32 3.1.2 The space-charge field 34 3.1.3 Two-wave mixing 42 3.1.4 Diffraction efficiency 46 3.2 Experimental investigations 50 3.2.1 Experimental method 50 3.2.2 Experimental results 53 3.3 Discussion and perspectives 58 4 Photorefractive Interference Filters 51 4.1 Filter recording and response 63 4.2 Temperature properties 66 4.3 Experimental investigation 68 4.3.1 Experimental method 68 4.3.2 Experimental results 70 4.4 Discussion and perspectives 15 5 Conclusion 18 References 80 Appendices 85 A Physical tensors 85 B Material parameters 89 Risø-R-880(EN) List of Figures 1 Paraelectric and ferroelectric phase of LiNbC-3. 14 2 Measured absorption spectrum of LiNbC>3:Fe samples. 15 3 Light induced charge transport in LiNbO3. 16 4 Model of photovoltaic current generation. 20 5 Distribution of conduction band electrons. 21 6 Electron trajectory in a magnetic field. 24 7 Magnetophotorefractive geometries 28 8 Setup for vectorial interaction 32 9 Influence of diffusion mechanism vs. grating period. 38 10 Influence of diffusion mechanism vs. angle of incidence. 39 11 Vector diagram for spatially oscillating photovoltaic current. 40 12 Angular dependence of photovoltaic contributions. 41 13 Calculation of the perturbed space-charge field. 42 14 Exponential gain factor vs. angle of incidence. 45 15 Angular dependence of diffraction efficiency. 48 16 Magnetic field dependence of diffraction efficiency. 4$ 17 Experimental setup for vectorial interaction scheme. 50 18 Measured change in extraordinary intensity. 53 19 Measured diffraction efficiency vs. recording th\;e. 54 20 Measured diffraction efficiency vs. recording time. 56 21 Measured initial curvature of diffraction efficiency. 51 22 Geometries for filter recording. 64 23 Probing the photorefractive interference filter. 64 24 Calculated filter reflectance vs. phase mismatch. 65 25 Reflection geometry setup for filter recording. 68 26 Measured angular response of filter at different temperatures. 10 27 Measured optimal angle and center wavelength deviation. 11 28 Theoretical and measured and temperature sensitivity. 12 29 Measured temperature response of filter. 73 30 Spectral filter response. 14 List of Tables 1 Specification of LiNbC>3:Fe samples. 52 2 Sign of phase mismatch parameter. 68 3 Measured temperature sensitivities. 12 4 Characteristica of photorefractive interference filter. 14 5 Form of 4th-rank pseudo-tensor for 3m point group 81 6 Form of Sf^kl for 3m point group 88 7 Form of IS&.J for 3m point group. 88 8 Form of 5^fc for 3m point group. 89 9 Material parameters for LiNbC-3:Fe crystals. 89 List of Symbols 1 a, ao, ae intensity absorption coefficient [m" ] 0/ effective intensity absorption coefficient [m-1] Risø-R-880(EN) 1 aa, ac principal linear thermal expansion coefficients [K" ] B magnetic field [T] B modulus of magnetic field [T] P thermal excitation rate [s-1] Pijk bulk photovoltaic tensor [V"1] Ptjk>P?j linear and circular bulk photovoltaic tensor [V"1] c velocity of light [m/s] D diffusion constant's"1] 6ijk levi-cevita (symbol) tensor AT change in temperature [K] ATFWHM thermal bandwidth [K] AAFWHM spectral bandwidth [m] Afc phase or momentum mismatch [m-1] dn/dT thermo-optic coefficient [K-1] e numerical electronic charge [C] ED characteristic diffusion field [V/m] Eq characteristic saturation field [V/m] EM characteristic drift field [V/m] characteristic photovoltaic field [V/m] characteristic bulk photovoltaic field [V/m] characteristic magnetophotovoltaic field [V/m] ei • q effective photovoltaic magnetic coefficient [V"1] ec, e0 unit vector in the direction of polarization ei unit vector along grating wave vector and the space-charge field unit vector along perturbed bulk photovoltaic current unit vector along perturbed magnetophotovoltaic current E total electric field [V/m] E, Ee, Eo complex field amplitude [V/m] Eo, Ei unperturbed and perturbed space-charge field [V/m] e energy [J] es static permittivity tensor [F/m] £f!,£§3 transverse and longitudinal static permittivity [F/m] £0 vacuum permittivity [F/m] jrt recombination rate [m3s~1] -1 Fe collision frequency [s ] F exponential gain factor [m~J] 2 / , Ie, Io, Iu I2 intensity [W/m ] Io unperturbed (total) intensity [W/m2] I\ perturbed intensity [W/m2] j total current density [A/m2] jo, ji unperturbed and perturbed current density [A/m2] jpv photovoltaic current density [A/m2] JoVi Ji>V unperturbed and perturbed photovoltaic current density [A/m2] ks Boltzmann constant [JK"1] -1 k, ke, k0 wave vectors [m ] 1 k,kCtk0 modulus of wave vectors [m" ] K grating wave vector [m-1] K modulus of grating wave vector [m-1] K coupling coefficient [m-1] 2 Kpj, specific photoconductivity [mV~ ] L interaction length [m] A free space wavelength [m] Aw writing wavelength [m] Risø-R-880(EN) Ac center wavelength [m] Ag center wavelength at reference temperature [m] A grating period [m] m intensity ratio M intensity modulation coefficient m* effective mass of electron [g] fio vacuum permeability [Vs/(Am)j (i mobility of thermalised electrons [m2/(Vs)] /ZHp mobility of nonthermalised electrons [m2/(Vs)j n,no,ne average, ordinary and extraordinary refractive index nw refractive index at writing wavelength n, no, ni number density conduction band electrons [m~3] NA concentration of acceptors [m~3] ND concentration of donors [m~3] 3 N£, N£Q, N£t number density of ionized donors, [m~ ] 77 diffraction efficiency q photovoltaic magnetic coupling vector [V"1] r displacement vector [m] r& Larmor radius [m] r", r,-jfc electro-optic tensor [m/V] <Tp|, photoconductivity [fl^m"1] s photoexitation cross section^J"1] S temperature sensitivity of center wavelength [m/Kj Sijki magneto photovoltaic tensor [V~1T~1] Stjki'Suk linear and cirular magneto photovoltaic tensor [V~1T~1] t time [s] T absolute temperature [K] Tc Curie temperature [K] TQ absolute reference temperature [K] T,T' characteristic time for perturbed space-charge field [s] To characteristic time for unperturbed space-charge field [s] TJI relaxation time [s] Tjso momentum isotropisation time for nonthermalised electrons [s] r£ energy relaxation time [s] wo velocity of nonthermalised electrons [m/s] VT velocity of thermalised electrons [m/s] £ factor describing effect of diffusion and asymmetry parameter <p angle between the grating wave vector and the optical axis [rad] xp, 0, ©c, 0O internal angle of incidence [rad] •tp', Q', Q'el 0'o external angle of incidence [rad] <I> quantum efficiency -1 w0 generation rate [s ] wc cyclotron frequency [rad/s] u angular frequency [s"1] Abbreviations and indices BPV Bulk photovoltaic effect MPV Magnetophotovoltaic effect L Linear C Circular FWHM full width half maximum FOV field of view [rad] Risø-R-880(EN) o ordinary eigenwave e extraordinary eigenwave i,j,k,l,r,s,t,u tensor indices representing x,y and z or a,b and c 0 unperturbed p irameter or value at reference temperature 1 perturbed parameter a vector a unit vector <i tensor * denoting complex conjugation Risø-R-880(EN) Preface The present thesis describes the work carried out in the period from March 1993 to March 1996 at the Optics and Fluid Dynamics Department (OFD), at Risø National Laboratory in Denmark.
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