Advanced Vitreous State – The Physical Properties of...

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Advanced Vitreous State – The Physical Properties of Glass

Active Optical Properties of GlassLecture 21: Nonlinear Optics in Glass-Applications

Denise KrolDepartment of Applied ScienceUniversity of California, DavisDavis, CA [email protected]

[email protected] Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 1


Nonlinear optical susceptibilities

!

" (1) #( ) =P(1)(#)

$oE(#)

=Ne

2

$om

1

#0

2%# 2 % i#&

General formalism:

!

= P(1)(t) + P

(2)(t) + P

(3)(t) + ...

!

P(t) = " (1)E(t) + " (2)E(t)2 + " (3)E(t)3 + ...

E and P can be written as sum of frequency components:

!

E = E(" j )e#i" j t

j

$

!

P = P(" j )e#i" j t

j

$

!

" 2(# p =#m +#n ) =P(2)(# p )

E(#m )E(#n )=

Nae3

m2 $D # p( )D #n( )D #m( )

!

" (3)(#q =#m +#n +#p ) =Nbe

4

m3 $D(#q )D(#m )D(#n )D(#p )

output frequency

input frequencies, pos or neg

!

D(" j ) = ("0

2 #" j

2) # i" j$

Value of χ(n)

depends onfrequencies


Nonlinear optics in glass2nd-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

Strength of generated signal depends on propagation length-optical fibers!

Phase matching: Δk=k4-k3-k2-k1=0!

" (3)(3# =# +# +#) $ " (3)(# =# +# %#)


Units in nonlinear optics

linear nonlinear

!

r P ( t) = " (1) #

r E (t)+ " (2) #

r E ( t)

2+ " (3) #

r E (t)

3+ # # #Gaussian system of units

!

r P (t) = "

0# (1) $

r E (t) + # (2) $

r E (t)

2 + # (3) $r E (t)

3 + $ $ $[ ]MKS system

ε0 = permittivity of free space = 8.85 x 10-12 F/m

MKS system Gaussian system

Electric Field, E V/m statvolt/cmPolarization, P C/m2 statvolt/cmIntensity, I

Intensity, I W/m2 erg/cm2-sec

χ(2) m/V cm/statvolt, esu χ(2) (MKS) = 4.189 x 10-4 χ(2) (Gaussian)

χ(3) m2/V2 (cm/statvolt)2, esu χ(3) (MKS) = 1.40 x 10-8 χ(3) (Gaussian)

!

I =nc

2"E

2

!

I = 2n"0

µ0

#

$ %

&

' (

1/ 2

E2


χ(2) can be induced in glass by thermal poling

The induced χ(2) can be examined viasecond harmonic generation (SHG)

ω ω

2ω

SHG process

Second order optical nonlinearity (χ(2)) = 0 in glassesbecause glasses are isotropic

To induce a χ(2) in glasses Thermal poling technique

silica DC + Heat

~ 1 mm

Thermal poling experiment

t (min.)

T (°C)

280

25

V (kV)

3


Thermal poling-proposed mechanism

χ(2) ∝ χ(3) EDC

+ - + - + - + - +

+ + + + +HV,T

+

RT

- - - - - - - - - - -- - - - - - - - - - -- - - - - - - - - - -

Z

Z

EDC

//

// Z


Effect

Nonlinear index

Stimulated Raman scattering

Nonlinear photoinduced changes

n =n0+n2In2 ~ χ(3)(ω=ω+ω−ω)

χ(3) phenomena and applications in glass

Applications

Optical switchingSupercontinuum generation

Raman amplifiers and lasers

Fs laser structuring


Nonlinear optical switch

Signal

Switching

Pulse

Output

Nonlinear Material

Waveguide Interferometer

1

2

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


Material dependence of n2

ω0

Classical anharmonic electron oscillator, far from resonance:

!

" (3)(# =# +# $# ) %e4

m3#0

6d5

ω

!

n2(" ) = n2(0) # 1$h"

ES

%

& '

(

) *

2+

,

- -

.

/

0 0

$3.5

!

n2(0) =

3.4(n0

2+ 2)

3(n

0

2"1)d

2

n0

2ES

2#10

"20

Bond polarizability model by M. Lines:

Frequency dependence

Long wavelength limit:

Es is Sellmeier gap


Material dependence of nonlinear index

n2(10-16cm2/W)

T. Monro et al, Annu. Rev. Mater. Res. 2006. 36:467


distance through fiber

self phase modulationpulse of light

!

"(t) =#0$#0n2L

c

dI(t)

dtinstantaneous frequency

generation ofnew frequencycomponents


Supercontinuum generation inmicrostructured fibers

From Philip Russell et al. Source:www.bath.ac.uk/physics/groups/opto/rse/holeyfibres.html

core

cladding

guidance properties determinedby size and pattern of holesunusual dispersionhigh nonlinearity

propagation of pulsed (100fs) Ti-sapphirelaser light( 800 nm) results insupercontinuum generation : 400-1600 nm


Raman gain

!

PNL("

S,z) = 6#

R("

S) A

L

2ASeikS z

!

"R(#S ) =N

6m

$%

$q

&

' (

)

* + 0

2

,1

#v

2 - (#L -#S )2+ 2i.(#L -#S )

ωLωv

ωS

Stokes Raman scattering

vibrationalenergy

At high laser intensities:stimulated Stokes Raman scattering

fiber


χ(3) phenomena and applications in glass

Effect

Nonlinear index

Stimulated Raman scattering

Nonlinear photoinduced changes

Applications

Optical switchingSupercontinuum generation

Raman amplifiers and lasers

Fs laser structuring

Interaction of glass with sub-bandgap, focused, fs laser pulses

cw laser at 800 nmsilica glass

ultrashort (100fs) pulsesand tight focusing (µm-size spot)

permanent modification

deposition of laser energyinto glass

at low to moderate intensitiessub-bandgap light istransmitted

photon energy

at high intensities multiphotonabsorption occurs

Light-matter Interaction is localizedin time and space ->3-D control of modification

[email protected] Advanced Vitreous State - The Properties of Glass: Active Optical Properties of Glass 16Schaffer et al, MRS Bull 31, 620 (2006)

How does the material change on an atomic scale?

4) Proposed mechanism: -Shockwave propagation

(microexplosion) -Fast heating and cooling

3) Plasma formation

1) Multiphoton absorption2) Avalanche photoionization

5) Modified spot

Femtosecond laser modification in glass

?

energy abs~100 fs

energy

dissipation~ 1µs


Davis et. al, Opt. Lett., 21, 1729 (1996)

130 fs

~ 1 µJ of energy

800 nm bulk glass

waveguide

Properties:

Refractive indexAbsorptionComposition (phase separation)Valence state (Sm3+ -> Sm2+)Crystal nucleation (Ag and Au colloids in glass)

Femtosecond laser pulses can modify various glass properties

Applications:

photonic devices

lab-on-chipdata storageoptical switching


Some references

NLO Books:N. Bloembergen, Nonlinear OpticsR.W. Boyd, Nonlinear Optics

NLO in Glass ReviewsE. 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

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