Advanced Vitreous State – The Physical Properties of Glass Active Optical Properties of Glass Lecture 21: Nonlinear Optics in Glass-Applications Denise Krol Department of Applied Science University of California, Davis Davis, CA 95616 dmkrol@ucdavis.edu dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 1 1
Nonlinear optical susceptibilities General formalism: P ( t ) = � (1) E ( t ) + � (2) E ( t ) 2 + � (3) E ( t ) 3 + ... = P (1) ( t ) + P (2) ( t ) + P (3) ( t ) + ... E and P can be written as sum of frequency components: � i � j t � i � j t � � E = E ( � j ) e P = P ( � j ) e j j output frequency ( ) = P (1) ( � ) � o E ( � ) = N e 2 1 � (1) � 2 � � 2 � i �� input frequencies, � o m � 0 pos or neg 2 � � j 2 ) � i � j � D ( � j ) = ( � 0 P (2) ( � p ) Nae 3 � 2 ( � p = � m + � n ) = E ( � m ) E ( � n ) = m 2 � D � p ( ) D � n ( ) D � m ( ) Value of χ (n) Nbe 4 depends on � (3) ( � q = � m + � n + � p ) = m 3 � D ( � q ) D ( � m ) D ( � n ) D ( � p ) frequencies dmkrol@ucdavis.edu 2 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Nonlinear optics in glass 2nd-order nonlinearities In normal glasses χ (2) =0 3nd-order nonlinearities All materials, including glasses, have a χ (3) In glass there are only three independent χ (3) tensor elements χ (3) processes involve the interaction of 3 input waves to generate a polarization (4th wave) at a mixing frequency with 3 different input frequencies there are many possible output frequencies � (3) (3 � = � + � + � ) � � (3) ( � = � + � � � ) Strength of generated signal depends on propagation length -optical fibers! Phase matching: Δ k=k 4 -k 3 -k 2 -k 1 =0 dmkrol@ucdavis.edu 3 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Units in nonlinear optics r r r r ( t ) = � (1) � ( t ) + � (2) � ( t ) 2 + � (3) � ( t ) 3 + ��� P E E E Gaussian system of units linear nonlinear r r r r ( t ) = � 0 � (1) � ( t ) + � (2) � ( t ) 2 + � (3) � ( t ) 3 + ��� [ ] P E E E MKS system ε 0 = permittivity of free space = 8.85 x 10 -12 F/m MKS system Gaussian system Electric Field, E V/m statvolt/cm Polarization, P C/m 2 statvolt/cm Intensity, I 1/ 2 I = nc � � 2 I = 2 n � 0 2 � E 2 E � � µ 0 � � Intensity, I W/m 2 erg/cm 2 -sec χ (2) cm/statvolt, esu m/V χ (2) (MKS) = 4.189 x 10 -4 χ (2) (Gaussian) χ (3) m 2 /V 2 (cm/statvolt) 2 , esu χ (3) (MKS) = 1.40 x 10 -8 χ (3) (Gaussian) dmkrol@ucdavis.edu 4 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
χ (2) can be induced in glass by thermal poling Second order optical nonlinearity ( χ (2) ) = 0 in glasses because glasses are isotropic To induce a χ (2) in glasses Thermal poling technique T (°C) V (kV) Thermal poling experiment 3 280 DC ~ 1 mm silica + Heat 25 t (min.) SHG process ω ω The induced χ (2) can be examined via 2 ω second harmonic generation (SHG) dmkrol@ucdavis.edu 5 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Thermal poling-proposed mechanism E DC + + - + - + - + - + HV,T Z + + + + + Z // - - - - - - - - - - - χ (2) ∝ χ (3) E DC - - - - - - - - - - - - - - - - - - - - - - RT // Z dmkrol@ucdavis.edu 6 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
χ (3) phenomena and applications in glass Effect Applications Nonlinear index Optical switching n =n 0 +n 2 I Supercontinuum generation n 2 ~ χ (3) ( ω = ω + ω−ω ) Stimulated Raman scattering Raman amplifiers and lasers Nonlinear photoinduced changes Fs laser structuring dmkrol@ucdavis.edu 7 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Nonlinear optical switch Nonlinear Material Output Signal 1 2 Switching Pulse Waveguide Interferometer Without switching pulse: waves in leg 1 and 2 interfere destructively, no output With switching puse: due to the nonlinear interaction, the switching pulse causes a phase shift in the part of the signal pulse propagating in leg 2. As a result waves in 1 and 2 interfere constructively, output From P.Thielen, PhD Dissertation, UC Davis, 2004 dmkrol@ucdavis.edu 8 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Material dependence of n 2 Classical anharmonic electron oscillator, far from resonance: e 4 � (3) ( � = � + � � � ) � 6 d 5 m 3 � 0 ω 0 ω Bond polarizability model by M. Lines: 2 + 2) 3 ( n 0 2 � 1) d 2 n 2 (0) = 3.4( n 0 � 10 � 20 Long wavelength limit: 2 E S 2 n 0 E s is Sellmeier gap � 3.5 � � 2 � � n 2 ( � ) = n 2 (0) � 1 � h � � � Frequency dependence � � E S � � � � � � dmkrol@ucdavis.edu 9 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Material dependence of nonlinear index n 2 (10 -16 cm 2 /W ) T. Monro et al, Annu. Rev. Mater. Res. 2006. 36:467 dmkrol@ucdavis.edu 10 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
self phase modulation pulse of light � ( t ) = � 0 � � 0 n 2 L dI ( t ) instantaneous frequency c dt generation of new frequency distance components through fiber dmkrol@ucdavis.edu 11 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Supercontinuum generation in microstructured fibers propagation of pulsed (100fs) Ti-sapphire laser light( 800 nm) results in supercontinuum generation : 400-1600 nm core cladding guidance properties determined by size and pattern of holes unusual dispersion high nonlinearity From Philip Russell et al. Source:www.bath.ac.uk/physics/groups/opto/rse/holeyfibres.html dmkrol@ucdavis.edu 12 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Raman gain Stokes Raman scattering At high laser intensities: stimulated Stokes Raman scattering fiber ω S ω L vibrational ω v energy 2 A S e ik S z P NL ( � S , z ) = 6 � R ( � S ) A L 2 � � � R ( � S ) = N 1 � � � � � 2 � ( � L � � S ) 2 + 2 i � ( � L � � S ) 6 m � q � v � � 0 dmkrol@ucdavis.edu 13 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
χ (3) phenomena and applications in glass Effect Applications Nonlinear index Optical switching Supercontinuum generation Stimulated Raman scattering Raman amplifiers and lasers Nonlinear photoinduced changes Fs laser structuring dmkrol@ucdavis.edu 14 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Interaction of glass with sub-bandgap, focused, fs laser pulses silica glass at low to moderate intensities cw laser at 800 nm sub-bandgap light is transmitted photon energy Light-matter Interaction is localized in time and space -> at high intensities multiphoton ultrashort (100fs) pulses 3-D control of modification absorption occurs and tight focusing ( µ m-size spot) deposition of laser energy into glass permanent modification
Femtosecond laser modification in glass 1) Multiphoton absorption 2) Avalanche photoionization energy abs 3) Plasma formation ~100 fs ? 4) Proposed mechanism: -Shockwave propagation energy (microexplosion) -Fast heating and cooling dissipation ~ 1 µ s 5) Modified spot How does the material change on an atomic scale? Schaffer et al, MRS Bull 31, 620 (2006) dmkrol@ucdavis.edu 16 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Femtosecond laser pulses can modify various glass properties Properties: Applications: Refractive index photonic devices Absorption Composition (phase separation) lab-on-chip Valence state (Sm3+ -> Sm2+) data storage Crystal nucleation (Ag and Au colloids in glass) optical switching 130 fs bulk glass 800 nm waveguide ~ 1 µ J of energy Davis et. al , Opt. Lett., 21, 1729 (1996) dmkrol@ucdavis.edu 17 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
Some references NLO Books: N. Bloembergen, Nonlinear Optics R.W. Boyd, Nonlinear Optics NLO in Glass Reviews E. M. Vogel, M.J. Weber, D. M. Krol, “Nonlinear optical phenomena in glass”, Phys. Chem. Glasses 32, 231 (1991). K. Tanaka, “Optical nonlinearity in photonic glasses”, J. Materials Science: 16, 633 (2005) Fs laser structuring of glass “Ultrafast lasers in materials research”, Special issue, MRS Bulletin August 2006 dmkrol@ucdavis.edu 18 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass
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