Download Part I : Theory of two

Photorefractive effect in LN:
Theoretical part
Weiwen Zou
May 16,2003
My view on the research
• 1. Microscopic changes: In different non-stoichiometric
crystals without or with different doping concentration
–
–
–
–
2
Defects (Intrinsic and extrinsic)
Impurity levels in the gap of crystal
Which location in lattice
…
• The gating ratio
• Absorption
change
• Sensitivity
• 2. Macroscopic performances (change):
• M#(M number)
• Dynamic range
• Dark decay
• Optical quality
• …..
Outline
• The concise introduction of photorefractive effect
– A common nonlinear optical effect
– The photorefractive effect
– Two wave mixing
– Holography
– Applications of photorefractive materials
• One-color holography Vs. two-color holography
– One-color holography
– Two-color holography
– Analogy
• LiNbO3 for the two-color holography
– Crystal growth and congruent melting
– Nonstoichiometry and stoichiometry
– LiNbO3 and its defects
3
– Charge transport models
Outline
• The performance change of the crystal due to doping
– Defect changes due to varying dopants
– Intrinsic defects
– Extrinsic defects
– Relative sequence
• Next plan
– Experiments of two-color holography (part II)
•
•
•
•
•
•
4
The two-color holography’s parameters
Determination methods and the corresponding precautions for them
Setup of the experiment
Doubly doped by Manganese(Mn) and Iron (Fe) (Nature,1998)
Doped by Indium (In)
Doped by Magnesium (Mg)
The concise introduction of
photorefractive effect
 A common nonlinear optical effect
 The photorefractive effect
• Two wave mixing
• Holography
• Applications of photorefractive materials
5
The concise introduction of photorefractive effect
A traditional nonlinear optical effect
Linear optics: the polarization in a medium is linear with the
illuminated optical field. In other word, the susceptibility is
independent with the optical field.
P  0  E
(1)
A traditional nonlinear optical effect: it can be described by
a nonlinear susceptibility which is dependent with the optical
field.
P
: The polarization of the medium
P  0  E  0  E  0  E 
(1)
(2 ) 2
(3) 3
E
0
: The optical field
: Absolute Electric constant
1
: The linear susceptibility of the
medium
 ( n)
: The different order nonlinear
susceptibility.
6
The concise introduction of photorefractive effect
The photorefractive effect
• Definition: The photorefractive effect is the change in refractive index of an
optical material that results from the optically induced distribution of carriers
in the material, such as electrons and holes etc.
• Characteristics: It is quite different from the other nonlinear optical effect
above. The reason is that, under a wide range of conditions, the change in
refractive index in steady state is independent of the intensity (or optical field)
of the light that induces the change.
• Mechanism: (See the figure of next page)
7
The concise introduction of photorefractive effect
Mechanism
Ferroelectric
Crystal
(+dopants)
Congruent
melting
X’tal(:dopa
nt)
Laser
illuminating
Space-charge
Electric field
ESC
Defects or
impurities
Dynamic
Equilibrium
State
Due to the
electrooptic
effect in
X’tal
The refractive index has
been changed by the E-O
principle. n->n’
8
This is the crystal’
certain nonlinear
performance named
as photorefractive
effect
Impurity or defect
is excited and
begins to diffuse or
drift
The concise introduction of photorefractive effect
The coherent beams interfere to
form the distribution of intensity
The carriers redistribute under
the light illumination
The space charge field is
formed by the redistribution of
the carriers induced by the
illuminating light
Due to the linear Electro-optical
effect in the material, the
refractive index variation
The phase relationship among the interfering
beams (1), the charge density (2)and the
space charge field (3):  3   2  2   1  2
9
The concise introduction of photorefractive effect
Two-wave mixing
(two-beam coupling)
Bragg
grating
Two beams are incident on the crystal.
Due to the photorefractive effect in the
crystal, a Bragg grating is formed.
Because the grating is formed by those
2 beams, each of them satisfies the
Bragg condition and is diffracted by the
grating.
LiNbO3
This is so-called two-wave mixing or
two-beam coupling.
Note: It exists by other nonlinear effects
such as Stimulated Brillioun Scatting
(BRS)...
10
The concise introduction of photorefractive effect
Holography(Writing)
Mirror
LiNbO3:Photosensitive
medium
Reference
beams
Object
beams
Hologram
Laser
beams
Lion: one object
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The concise introduction of photorefractive effect
Holography(Reading)
Diffracted
beams
Reference
beams
Hologram
Note: The reference beams
should satisfy the so-called
Bragg condition.
12
One-color holography Vs. two-color
holography
• One-color holography
• Two-color holography
• Analogy
13
One-color Vs. two-color
One-color Holography(physics)
14
Note: All of these figures ©IBM
One-color Vs. two-color
Characters of one-color holography
• Advantage
– Easy to erase
– Mechanical stability
– Recording reversibility
• Disadvantage
– The reversibility makes the holograms volatile, so that they can be
easily erased during the process of reading the recorded
information.
• The reason : the reading process is that the hologram is due to the
space-charge field which is induced by the space-charge redistribution
stimulated by the interference between the object and reference beam
both of which has the same wavelength. So if one reading beam is
incident on the crystal, electrons trapped to form the space charge will
be excited uniformly to erase the hologram.
15
One-color Vs. two-color
The ways to solve the
disadvantage
• Thermal fixing
• Electrical fixing
• Two-wavelength fixing (2-color holography or “photogated” recording)
16
One-color Vs. two-color
Thermal fixing
• Mechanism(copy the space-charge pattern
into a pattern of immobile ions):
A copy of the stored index gratings is made by thermally activating
proton diffusion, which creates an optically stable complementary
proton grating to store the hologram.
• Disadvantages
– Long time for fixing
– Not easy for erosion.
17
One-color Vs. two-color
Electrical fixing
• Mechanism(copy space-charge pattern into
felloelectric domains)
• Disadvantage
– Not easy for erosion.
18
One-color Vs. two-color
Two-color holography
19
Ref. :Adibi et al.,J.Opt.Soc.Am.B, 18,
584-601 (1997)
One-color Vs. two-color
Two-color holography
Conduction band (C.B.)
Conduction band (C.B.)
Writing
Photon
Gate photon
Deep level
Shape
level
Shape
level
Deep level
Writing
Photon
Valence band (V.B.)
Carrier: Electron
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Valence band (V.B.)
Carrier: Hole
Gate photon
One-color Vs. two-color
Two-color holography
A shorter light (gating) excites the
carriers from the deep level, which
tend to be trapped at the shape level.
Then the small polaron formed is
sensitive to infrared light but is
metastable at room temperature.(long
dark decay.)
If coherent inhomogeneous beams (writing)
incident, they write the holograms as the
spatial distribution of filled shallow
centers(PR effect). Due to be unstable(dark
decay), the electrons at shallow centers will
be transferred to that at deep centers, so the
hologram is recorded in the deep level too.
21
Conduction
band e
eGate photon
K+
e-
X
e-
K e
Shallow level
e-
Deep level
Writing
Photon
e-
e-e+X
Valence band
While readout photon (with the same
wavelength of writing and satisfying the Bragg
condition) is not enough to excite electrons
from the deep level to the Conduction band.
Therefore, there holograms by this means are
stable and nonvolatile.
One-color Vs. two-color
Vs.
22
Note: All of these figures ©IBM
LiNbO3 for the two-color holography
• Crystal growth and congruent melting
• Non-stoichiometry vs. stoichiometry
• LiNbO3 intrinsic defects
• Charge transport models
23
LiNbO3 for the two-color holography
Crystal growth
• Congruent melting
• Reduction treatment: heat treatment in an
oxygen-poor atmosphere
• Doped with other transient (damageresistant) elements
24
Rough sketch of lithium nibote
25
Copyright:
crystaltechnology
LiNbO3 for the two-color holography
LiNbO3 and its structure
Lithium
Oxygen
Niobium
1. Li+ and Nb5+ have nearly
identical ionic radii.
2. The environments of
them are similar. Both ions
are surrouded by distorted
octahedra of six O2- ions.
26
3. Nb5+ - O2- is stronger than Li+ - O2-
Results: Lithium Niobate has a
tendency to non-stoichiometry with
Li/Nb<1 (usually 48.6:51.4).
Stoichiometry
Vs.
Non-stoichiometry
Usually, congruently melted LiNbO3 crystal is always a
non-stoichiometric one, which means
[Li  ]

5  48.6mol%  50%
[Li ]  [Nb ]
The formulation for it can be rewritten as
Li1x Nb1 x / 5O3 or [Li1 x Nbx / 5 y ][Nb1 y ]O3
However, other ways can form the stoichiometric crystal. For
example, before melting the concentration of Lithium can be
much more than that of Niobium.
27
LiNbO3 for the two-color holography
Intrinsic defects on the congruent
melting crystals (without or with
reduction treatment)
Nb5
Li
Intrinsic
anti-site
defects
Postgrowth
reduction
treatment: A loss
of oxygens and
the diffusion of
the excess Li and
Nb5+ ions.
That Li/Nb is less than unity makes
some Nb ions locate at the Li sites
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Bipolaron
4
4
Li
Nb
Nb Nb
-
NbLi4
-
4
NbNb
LiNbO3 for the two-color holography
Charge transport models
Reason: Where the free charge carriers come from and where
they are trapped is crucial for the holography.
Function:
It determines macroscopic properties like absorption,
absorption changes, conductivity and holographic sensitivity.
Models:
One-center model without and with electron-hole competition;
two-center model;
the three-valence models.
Notes: Independent on the sign of the dominant charge carrier
(either electrons or holes) ; dependent on not only the host
29
material,
but also light intensity
Ref:
Appl.
Phys.
B,273Ref.
:K.K.Buse,
Buse, Appl.
Phys.
B, 64,
64,1997
291
(1997)
LiNbO3 for the two-color holography
One-center model
Electrons are excited by light or by thermal
processes from filled traps C- into the CB
Free electrons recombine from CB with
empty traps C0
In fact, one-color holography
is based on this model.
Arrows indicate excitation and recombination of
electrons at C-/C0. C can be any defects ions in
crystal, such as Fe3+, Nb Li 5+ and so
30
Ref:
Appl.
Phys.
B,273Ref.
:K.K.Buse,
Buse, Appl.
Phys.
B, 64,
64,1997
291
(1997)
LiNbO3 for the two-color holography
Models with electron-hole competition
Orlowski and Kratzig demonstrated by beam-couping experiments that simultaneously
electrons and holes can be involved in the charge transport.
Their relative contributions to the conductivity depend on the light wavelength and
on the oxidizaton-reduction state of the crystal.
This is the straight forward extension of the
one-center model.
Thermal and light-induced excitantions of
valence band electrons into C0
Recombination of electrons from C- with
valence band holes
31
Ref:
and
Kratzig
Solid
Ref.
:K.Orlowski
Buse, Appl.
Phys.
B, 64,,273state
commun. 14,1978
291
(1997)
LiNbO3 for the two-color holography
Two-center model
•
•
•
•
32
In 1983, it was formulated for explanation of grating erasures with two distinct
time constants(Thermal generation rates not considered)
In 1986,based on transient photocurrent measurements, shallow centers => the
charge transport
In 1988, light-induced absorption changes was explained by this model by
considering a large thermal generation rate of charge carriers at shallow
centers.
In 1989, this model is applied into the photoconductivity.
Ref:
Appl.
Phys.
B,273Ref.
:K.K.Buse,
Buse, Appl.
Phys.
B, 64,
64,1997
291
(1997)
LiNbO3 for the two-color holography
Two-center model
Conduction
band e
eK+
e-
X
e-
e-
K e
Shallow level
e-
Deep level
e-e+X
Valence band
Without considering the thermal generation rates
X and K are different photorefractive centers, respectively.
33
Ref. :K. Buse, Appl. Phys. B, 64, 273291 (1997)
LiNbO3 for the two-color holography
Two-center model
Conduction
band e
eGate photon
K+
e-
X
e-
K e
Shallow level
e-
Deep level
Writing
Photon
e-
e-e+X
Valence band
In fact, two-color holography
is based on this model.
34
LiNbO3 for the two-color holography
Three-valence model
At low light intensities, only C0 and C- are
present. (the same as one-center model)
For sufficiently high light intensities, the
electron concentration in CB becomes large
enough that an appreciable number of
electrons recombines with C- and generates
C2-. Then C- act as additional traps for C2-
The difference between three-valence model and twocenter model:
1. In two-center model, filled deep and shallow traps
are coupled only via the density of electrons in CB.
2. In three-valence, there is also an additional coupling
due to the relationship of the centers, which is the
same element.
35
There is only one center C which can occur in three
different valence states, denoted by 0, -1, 2-.
Ref:
Appl.
Phys.
B,273Ref.
:K.K.Buse,
Buse, Appl.
Phys.
B, 64,
64,1997
291
(1997)
LiNbO3 for the two-color holography
Applications
• Production of outstanding interference filters and wavelength
demultiplexers (Holographic gratings)
• Construction of volume holographic memories (Holographic gratings)
• Optical detection systems of ultrasonic waves (Non-steady-sate
photocurrents)
• Laser-beam clean-up (two-wave mixing)
• Efficient coupling of light from a multimode into a single-mode
fiber(Self-pumped phase conjugation)
• Optical computing
• Enhanced detection of phase modulations
• Femtosecond optical storage and processing
36
The performance change of the crystal
due to doping
• Defect Changes due to varying dopants
• Intrinsic defects
• Extrinsic defects
• Relative sequence
37
The performance change due to doping
Defect changes by the doping procedure
38
•
When a certain element is doped into the non-stoichiometric LN, the impurity
ion enters into the sites so that the concentration of the intrinsic defects
decrease, which is formed by the non-stoichiometric composition.

If the concentration of the impurity ions exceed the so-called optical-damage
threshold value, all the intrinsic defects are almost displaced by the impurities.

It results that the absorption band by the intrinsic defects is shifted owning to
the new-formed defects.
The performance change due to doping
The importance of defects
• Deferent configuration (or formulation) of
one crystal with different defects will have
different holographic performance
according to its mechanism.
39
The performance change due to doping
Intrinsic defects
• O- trapped holes (Cation vacancy)
• Nb4+ small polaron (An electron self-trapped at Nb orNb
• Bipolarons (Nb Nb :diamagnetic pairs of electrons trapped at
5+
Nb
4+
Nb
Li
4+
NbNb5+NbLi5+ complex)
• Oxygen Vacancies (VO)
40
Li
5+)
The performance change due to doping
Extrinsic defects
• Magnesium (Mg)
• Iron(Fe)
• Further extrinsic defects
41
The performance change due to doping
Cation vacancy:
O
trapped holes
• Form: by capturing a defect electron(hole) at one of the neighboring O2- ,
local charge compensation can be achieved under ionizing radiation
• Evidence:
– ESR(electron spin resonance) of congruent Lithium niobate by twophoton X- and by e--irradiation. It consists of several overlapping lines,
which cannot be disentangled, due to unresolved Li and Nb hyperfine
interaction.
– Optical absorption band: peak at 2.5ev (approximate 0.495um). It is
caused by the light induced transfer of the hole from its original trapping
site to an equivalent O2- ions around the defect (like a small polaron).
– The Dark decay dynamics of the absorption coeffeicent change. (Pro.
Tomita’ Group)
42
Ref.: O.F.Schirmer et. al.,J.Phys.
Chem.Solids, 52, 185-200 (1991)
The performance change due to doping
Cation vacancy:
O
trapped holes
• Temperature dependence of the X-ray-induced O- coloration:
– In the 50-200 K range, decaying at the same rate as the absorption due
to Nb4+, the ioniztion energy of which: 0.54ev
– In 100-200K, using isochronal annealing, optical absorption and ESR
decay simultaneously.
– In about 15K, X-irradiation in LN doped with 9% Mg, no trapped holes
are formed; with 6% Mg the concentration is rather low.
• In Mg-doped crystal, the electron trapping energy is much less than in
undoped crystals. => The Nb4+ electrons recombine with O- at rather
low temperature.
• The concentration of cation vacancies rises with decreasing [Li]/[Nb],
whereas self-trapping of holes cannot be excluded for high [Li]/[Nb].
43
Ref.: O.F.Schirmer et. al.,J.Phys.
Chem.Solids, 52, 185-200 (1991)
The performance change due to doping
Small polarons
• Evidence:
– A characteristic 10-line pattern by two-photon (2*2.46ev) and Xirradiation of congruent undoped LN, which is caused by hyperfine
interaction with the nucleus of 93Nb (the only stable isotope of Nb)
– In reduced undoped LN after illumination with light of wavelength <
600nm at T<80K, the same ESR was found.
• Before illumination, peak at approximate 2.5ev(500nm) due to bipolarons
• After illumination, 1.6ev (760nm) attributed to small polarons and the low
energy party of the band explained by small polaron absoption based on
• Form: an electron self-trapped at a
NbLi5+ ion to a free small polaron. (1.6
ev)
44
Ref.: O.F.Schirmer et. al.,J.Phys.
Chem.Solids, 52, 185-200 (1991)
The performance change due to doping
Bipolarons
(Electron pairs trapped at NbLi-NbNb)
• Form: Electron pairs trapped at NbLi-NbNb
• Evidence:
– In reduced undoped LN after illumination with light of wavelength <
600nm at T<80K, the same ESR was found.
• Before illumination, peak at approximate 2.5ev(500nm) due to bipolarons
• After illumination, 1.6ev (760nm) attributed to small polarons
• The reduced crystal is diamagnetic and no ESR signal accompanying the
absorption band =>the absorption at 2.5ev not due to small polarons and oxygen
trapped holes
• Characteristics:
45
– Dissociation: By heating or light illumination, a transfer of one of the paired
electrons out of the cluster.
– The efficiency of coloration by reducing ~ the [Li]/[Nb] ratio: raising the
ration decreases the coloration. (because only in strongly non-stoichiometric
crystals is a sufficient number of sites for electrons trapped after O left the
crystal.)
Ref.: O.F.Schirmer et. al.,J.Phys.
Chem.Solids, 52, 185-200 (1991)
The performance change due to doping
Magnesium (Mg)
• General comment: its properties is strongly related to those of the intrinsic
defects
• Evidence:
– 4.6mol% MgO compared with a lower Mg concentration, the effect for reducing
the optical damage is much strongly.
– A distinct threshold at a critical Mg concentration: [Mg]c>4.5mol%.
– The effect due to the Mg concentration bigger than critical value (not deliberately
doped with Fe)
• The optical absorption in reduced crystals (due to intrinsic defects) decreases
• The intensity of X-ray-induced luminescence increases by several orders of magnitude
while other related properties, such as width and energy of the band, also change abruptly.
• The absorption edge shows a blueshift
• The X-ray-induced Nb4+ ESR intensity decreases to zero.
– Codoped with Fe and Mg, the photoconductivity increases and the photovoltaic
effect is not be effected
46
Ref.: O.F.Schirmer et. al.,J.Phys.
Chem.Solids, 52, 185-200 (1991)
The performance change due to doping
Magnesium (Mg)
• Similarity: The features for high [Li]/[Nb] are similar to those for low
[Li]/[Nb] but with high [Mg] doping.
– All of those experiment results for high [Li]/[Nb] are the same as those of high
doping.
– With [Mg] fixed and the ratio of [Li]/[Nb] varying, the threshold for the change of
properties is influenced by the ratio.
• Function: For Mg only indirectly influences the behavior of the specimens
investigated, the function of Mg doping is to replace the NbLi.
47
Ref.: O.F.Schirmer et. al.,J.Phys.
Chem.Solids, 52, 185-200 (1991)
The performance change due to doping
Iron (Fe)
• Fe2+ and Fe3+
–
–
–
–
Only both the charge states occur in the doped Fe crystal.
Converted into each other by reduction and oxidation treatments, respectively
In Both of them, Fe occupies the same type of lattice sites.
Optical absorption:
• Fe2+: 1.1ev (d-d transitions -->Donor state transitions) and 2.6 ev(Fe2+-Nb5+ intervalence
transfer), the latter of which is similar those of trapped hole and bipolaron absorption.
• Fe3+:
•
48
Function:
[ Fe2 ]
– The photoconductivity:  p  I  [ Fe3 ]
Ref.: O.F.Schirmer et. al.,J.Phys.
Chem.Solids, 52, 185-200 (1991)
The performance change due to doping
Relative sequence of defects I
CB
~2.5ev
~1.6ev
Small polarons/ Mg2+
Bipolarons/O- holes
VB
49
The performance change due to doping
Relative sequence II(impurity levels)
CB
Mn
2+
3+
Cu
1+
2+
Fe
2+
3+
Ti
3+
4+
VB
50
Ref.: O.F.Schirmer et. al.,J.Phys.
Chem.Solids, 52, 185-200 (1991)
The performance change due to doping
Interrelation between intrinsic and
extrinsic defects
Any possible manipulations with dopants induce change in the subsystem of
intrinsic defects and, by their common influence cause variations of the
properties of LN
Because of the high concentration of intrinsic defects, the conventional congruent
crystals are tolerant to impurities substituting for Li or Nb ions
There are different complexes, such as “impurity ion-intrinsic defect” or
“impurity-impurity” and so on, due to the variation and the concentration
of the dopants
The strong coupling of extrinsic and intrinsic defects is one of the most
important features of LN, which is indeed rather flexible and very sensitive
to changes in both defects.
51
Ref.: G.Malovichko et.al.Appl. Phys.
B, 68, 785-793 (1997)
Next plan
• Experiments of two-color holography
– The two-color holography’s parameters
– Determination methods and the corresponding precautions for them
– Setup of the experiment
– Doubly doped by Manganese(Mn) and Iron (Fe) (Nature,1998)
– Doped by Indium (In)
– Doped by Magnesium (Mg) (The main topic in our group)
52
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