Advanced Vitreous State The Physical Properties of Glass

Transcription

1 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 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 1

2 Nonlinear optical susceptibilities General formalism: P(t) = " (1) E(t) + " (2) E(t) 2 + " (3) E(t) = P (1) (t) + P (2) (t) + P (3) (t) +... E and P can be written as sum of frequency components: E = E(" j )e #i" j t $ P = P(" j )e #i" j $ t j " (1) # $ o E(#) = Ne2 1 $ o m # 2 0 %# 2 % i#& ( ) = P(1) (#) j output frequency input frequencies, pos or neg P (2) (# " 2 (# p = # m + # n ) = p ) E(# m )E(# n ) = Nae 3 m 2 $ D (# p )D(# n )D # m Nbe 4 " (3) (# q = # m +# n +# p ) = m 3 $ D(# q )D(# m )D(# n )D(# p ) D(" j ) = (" 0 2 #" j 2 ) # i" j $ ( ) Value of χ (n) depends on frequencies dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 2

3 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: Δk=k 4 -k 3 -k 2 -k 1 =0 dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 3

4 Units in nonlinear optics Gaussian system of units r P (t) = " (1) # E r (t)+ " (2) # E r (t) 2 + " (3) # E r (t) 3 +### MKS system r P (t) = " 0 linear nonlinear [ ] # (1) $ E r (t) + # (2) $ E r (t) 2 + # (3) $ E r (t) 3 + $ $ $ ε 0 = permittivity of free space = 8.85 x F/m MKS system Gaussian system Electric Field, E V/m statvolt/cm Polarization, P C/m 2 statvolt/cm Intensity, I I = 2n " 1/ 2 # & 0 % ( E 2 $ ' µ 0 I = nc 2" E 2 Intensity, I W/m 2 erg/cm 2 -sec χ (2) m/v cm/statvolt, esu χ (2) (MKS) = 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 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 4

5 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 Thermal poling experiment T ( C) V (kv) 3 DC + Heat silica ~ 1 mm t (min.) SHG process ω ω 2ω The induced χ (2) can be examined via second harmonic generation (SHG) dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 5

6 Thermal poling-proposed mechanism E DC + HV,T Z // Z χ (2) χ (3) E DC RT // Z dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 6

7 χ (3) phenomena and applications in glass Effect Nonlinear index n =n 0 +n 2 I n 2 ~ χ (3) (ω=ω+ω ω) Applications Optical switching Supercontinuum generation Stimulated Raman scattering Raman amplifiers and lasers Nonlinear photoinduced changes Fs laser structuring dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 7

8 Nonlinear optical switch Signal Switching Pulse Nonlinear Material 1 2 Output 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 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 8

9 Material dependence of n 2 Classical anharmonic electron oscillator, far from resonance: " (3) (# = # +# $# ) % e 4 m 3 # 0 6 d 5 ω 0 Bond polarizability model by M. Lines: ω Long wavelength limit: E s is Sellmeier gap Frequency dependence n 2 (0) = 3.4(n ) 3 (n 2 0 "1)d 2 n 2 2 #10 "20 0 E S + % n 2 (" ) = n 2 (0)# 1$ h" ( - ' *,- & E S ) 2. 0 / 0 $3.5 dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 9

10 Material dependence of nonlinear index n 2 (10-16 cm 2 /W) T. Monro et al, Annu. Rev. Mater. Res :467 dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 10

11 self phase modulation pulse of light instantaneous frequency "(t) = # 0 $ # 0n 2 L c di(t) dt distance through fiber generation of new frequency components dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 11

12 Supercontinuum generation in microstructured fibers propagation of pulsed (100fs) Ti-sapphire laser light( 800 nm) results in supercontinuum generation : nm core cladding guidance properties determined by size and pattern of holes unusual dispersion high nonlinearity From Philip Russell et al. Source: dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 12

13 Raman gain Stokes Raman scattering At high laser intensities: stimulated Stokes Raman scattering fiber ω L ω S ω v vibrational energy P NL (" S,z) = 6# R (" S ) A L 2 A S e ik S z " R (# S ) = N 6m & $% ) ( + ' $q * 2 0 1, # 2 v - (# L -# S ) 2 + 2i.(# L -# S ) dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 13

14 χ (3) phenomena and applications in glass Effect Nonlinear index Stimulated Raman scattering Applications Optical switching Supercontinuum generation Raman amplifiers and lasers Nonlinear photoinduced changes Fs laser structuring Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 14

15 Interaction of glass with sub-bandgap, focused, fs laser pulses cw laser at 800 nm silica glass at low to moderate intensities sub-bandgap light is transmitted photon energy ultrashort (100fs) pulses and tight focusing (µm-size spot) Light-matter Interaction is localized in time at high and intensities space -> multiphoton 3-D absorption control of occurs modification deposition of laser energy into glass permanent modification

16 Femtosecond laser modification in glass energy abs ~100 fs 1) Multiphoton absorption 2) Avalanche photoionization 3) Plasma formation energy dissipation ~ 1µs? 4) Proposed mechanism: -Shockwave propagation (microexplosion) -Fast heating and cooling 5) Modified spot How does the material change on an atomic scale? Schaffer et al, MRS Bull 31, 620 (2006) dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 16

17 Femtosecond laser pulses can modify various glass properties Properties: Refractive index Absorption Composition (phase separation) Valence state (Sm3+ -> Sm2+) Crystal nucleation (Ag and Au colloids in glass) Applications: photonic devices lab-on-chip data storage optical switching 130 fs 800 nm bulk glass waveguide ~ 1 µj of energy Davis et. al, Opt. Lett., 21, 1729 (1996) dmkrol@ucdavis.edu Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 17

18 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 Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 18