photoisomerization-induced change of nonlinear absorption in azo-dye doped polymethylmethacrylate...

Optics Communications 236 (2004) 33–43

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Photoisomerization-induced change of nonlinear absorptionin azo-dye doped polymethylmethacrylate thin films

Sean Liu a,*, Jian Hung Lin a, Jin Horn Lin a, Victor M. Churikov a,Jiann T’suen Lin b, Tzer-Hsiang Huang c, Chia Chen Hsu d,*

a Department of Physics, National Chung Cheng University, Ming-Hsiung, Chia-Yi 621, Taiwanb Institute of Chemistry, Academia Sinica, Taipei 11529, Taiwan

c Department of Electronic Engineering, Wu Feng Institute of Technology, Ming-Hsiung, Chia-Yi 621, Taiwand Department of Physics and Graduate Institute of Opto-Mechatronics, National Chung Cheng University, Ming-Hsiung,

Chia-Yi 621, Taiwan

Received 6 November 2003; received in revised form 5 February 2004; accepted 5 March 2004

Abstract

Near-resonant optical pumping is used to encode an anisotropy of third-order susceptibility vð3Þ in azo-dye doped

polymethylmethacrylate thin films. The vð3Þ-anisotropy is probed with two nonlinear techniques: third harmonic gen-

eration (THG) and nonlinear transmission (NLT). Using the NLT technique, the photoisomerization-induced change

of the imaginary part of vð3Þ is probed. A dynamic microscopic model of the third-order nonlinearity behavior based on

angular hole burning and angular redistribution mechanisms of the photoisomerization effect is presented to describe

the observed optical nonlinear responses. Results from the model are generally consistent with optically pumped THG

and NLT experiments.

� 2004 Elsevier B.V. All rights reserved.

PACS: 42.65.Ky; 42.65.Sf; 42.70.Jk

Keywords: Polymer thin film; Trans–cis photoisomerization; Third harmonic generation; Nonlinear transmission

1. Introduction

Optical phenomena in azo-dye doped polymers

has recently become of special interest in view of

the application in photonics [1]. Additionally, azo

* Corresponding authors. Tel.: +886-527-20411x66305; fax:

+886-527-20587.

E-mail address: [email protected] (C.C. Hsu).

0030-4018/$ - see front matter � 2004 Elsevier B.V. All rights reserv

doi:10.1016/j.optcom.2004.03.013

dyes have potential application in the fabrication

of devices for optical switching [2], holographic

recording gratings [3,4], and integrated optics [5],

etc. The working principle of these devices, either

reversible or permanent, hinges on the polariza-tion-dependent refractive index and absorption

induced by the photoiosmerization of azo

dyes, which enables the encoding of different kinds

of macroscopic anisotropies with all-optical tech-

niques. Photo-induced birefringence and dichroism

ed.

mail to: [email protected]

Excited state

Trans

Cis

φ

σT

TC

CT

Fig. 1. The trans! cis isomerization and the cis! trans re-

laxation (wavy line) of azo-dye molecules. The trans-to-excited

state transition is optically induced.

34 S. Liu et al. / Optics Communications 236 (2004) 33–43

in photoisomerized-polymer thin films have been

widely studied during last two decades [1,6–9]. The

photo-assisted poling has been demonstrated by

Sekkat and Dumont [10]. The possibility of all-

optical encoding of quasi-permanent molecular

orientation and nonzero second-order susceptibil-ity has also been demonstrated by Fiorini et al. [11].

Along with the linear and quadratic optical prop-

erties, there has been growing interest in the third-

order nonlinear properties of azo-dye materials

[12,13]. Sekkat et al. demonstrated all-optical

control of the third-order susceptibility using elec-

tric field induced second-harmonic generation as a

probing technique [14].We have observed remarkable change of third

harmonic generation (THG) in the thin films of

polymethylmethacrylate (PMMA) doped with

disperse red 1 (DR1), under the blue-green (near

resonant) excitation as well as the near infrared

excitation [15–18]. The observed THG change was

too large to be explained solely by the linear ab-

sorption change arising from trans–cis isomeriza-tion [1,6–8], and was attributed to the change of the

third-order susceptibility vð3Þ. The THG then offers

the easiest way to probe photoinduced change in

vð3Þ, because of its high sensitivity and the simple

experimental setup. However, THG signal is pro-

portional to jvð3Þj2, and hence the observed THG

change is related to the changes of both real and

imaginary parts of vð3Þ. In this report, we show thatthe photoisomerization-induced change of the

imaginary part of vð3Þ can be probed solely by an

optically pumped nonlinear transmission (NLT)

experiment. The aim of this paper is to investi-

gate the influence of the photoisomerization effect

on the absolute value and also the imaginary part

of the third-order nonlinear susceptibility in azo-

dye doped PMMA thin films by experimental andtheoretical approaches. This paper is organized as

follows. In Section 2, the photoisomerization effect

on the third-order susceptibility is briefly pre-

sented. Section 3 shows the experimental methods

for both THG andNLT experiments, and Section 4

gives the experimental results. A theoretical model

is presented for simulation in Section 5. Some

comparisons between experimental results andtheoretical simulation are discussed in Section 6

that is followed by a summary.

2. Photoisomerization effects in azo-dye molecules

Photochemical molecules, such as azo dyes,

have two geometric isomers, denoted by trans and

cis (see Fig. 1). Generally, in the absence of anoptical pump field, the azo-dye molecules embed-

ded in a thin film are mainly in the more stable

trans conformation, with isotropic distribution

throughout the film. After turning on the pump

field, the trans molecules having electric dipole

components along the pump field polarization will

be preferentially isomerized to the cis form that

possesses negligible second hyperpolarizability (c).This isomerization process results in an angular

hole burning (AHB) of vð3Þ in the pump field di-

rection, and hence an anisotropy in vð3Þ. FollowingAHB, the photo-induced cis molecules relax ther-

mally to the trans form with random orientation

(or without a preferred orientation) (For simplic-

ity, we do not consider the torque acting on the

trans molecules during relaxation since the pumpfield is not strong enough. We also neglect the

torque due to the probe field). Those relaxed trans

molecules that happen to orient themselves paral-

lel to the pump field are further photo-isomerized

and thus starts another trans! cis! trans isom-

erization cycle. As the isomerization cycling goes

on, the cis! trans thermalization leads to a de-

tectable angular redistribution (AR) of the trans

molecules. The AR process tends to accumulate

trans molecules in the direction perpendicular to

the pump field. This causes a vð3Þ anisotropy in

S. Liu et al. / Optics Communications 236 (2004) 33–43 35

addition to that due to AHB. In general, both

AHB and AR processes reduce the number density

of trans molecules oriented along the pump field,

and result in large decrease of vð3Þ in this direction.

In the direction perpendicular to the pump field,

the AR effect dominates over the AHB effect atlow pumping intensity [16], and hence more mol-

ecules are accumulated in this direction. Therefore,

a small increase of vð3Þ in this direction is expected.

At high pump intensity, the AHB effect is domi-

nant, and itself will cause a decrease in vð3Þ in this

direction [16]. However, the decrease of vð3Þ in this

direction, combined with the increasing effect due

to AR, is much smaller than the decrease in theparallel direction. Consequently, a photoinduced

vð3Þ anisotropy is expected.

PMTIF

S

L

L

DM

M

FP

HW Q-switchedNd:YAG

HWP

BBO

(a)

3. Experimental methods

The blend of azo-dye molecules with PMMA

dissolved in chloroform was first spin-coated on aglass substrate and, then, was evaporated in a dry

chamber at 65 �C for 12 h to form thin films of

about 5 lm thickness. Fig. 2 shows the molecular

structures and absorption spectra of the thin film

samples #1 and #2 used in THG and NLT ex-

periments, respectively. As shown in this figure,

the absorption peak and the long wavelength

cutoff wavelength are, respectively, 487 and 600nm for sample #1, and 433 and 600 nm for sample

#2. The optical density at 532 nm is 0.923 for

400 600 800 10000

1

2

3

N NNC2H4OH

C2H5

NO

O

N N NNH

H

O

O

#1

#2

Abs

orba

nce

(A.U

.)

Wavelength (nm)

Fig. 2. Absorption spectra and molecular structures of the azo-

dye doped PMMA thin film samples #1 and #2.

sample #1, and 0.482 for sample #2. Linear ab-

sorption is negligible for both samples at 1064 nm.

In the THG experimental layout shown in

Fig. 3(a), we used, as the source of both pump and

probe beams, a Q-switched 1064 nm Nd:YAG la-

ser (Continuum Surelite I) with 7 ns pulse width at10 Hz repetition rate. The 1064 nm fundamental

laser was frequency-doubled by a b-barium borate

(BBO) crystal to generate the 532 nm pump beam

indicated by dotted lines. The pump intensity and

polarization were controlled by a set of half-wave

plate and polarizer. The pump field was kept in the

s-polarization in all measurements. The 1064 nm

probe laser, unconverted to 532 nm by the BBOcrystal, was transmitted through the dichroic

mirror (DM), and was focused into the sample #1.

A half-wave plate was used to rotate the probe

polarization to bring out the co-polarized (k) or

the cross-polarized (?) configuration with respect

to the pump polarization. The notation that we use

in simulation in Section 5 below is such that the

probe field is always along the axis 3 of the labo-ratory frame of reference and the pump field can

PD

IFS

L

L

FL P

HW

PD

BSQ-switched

Diode-pumped

Nd:YAG

Nd:YAG

PHW

(b)

Fig. 3. Experimental setups for (a) THG with sample #1, and

(b) NLT with sample #2. Dotted lines indicate the propagation

of the pump beam; the solid lines, that of the probe beam. DM

stands for dichroic mirror; M, 532 nm reflection mirror; F,

color filter; HW, half-wave plate; P, polarizer; L, lens; S, thin

film sample; IF, interference filter; PMT, photomultiplier tube;

BS, beam splitter; and PD, photodiode.

0 1000 2000 30000.30

0.35

0.40

0.45

0 1000 2000 30000.20

0.30

0.40

(⊥)

pump offpump on

cross-polarized

TH

G in

tens

ity (

A.U

.)

pump offpump on

co-polarized (//)

Time (sec.)

(a)

(b)

Fig. 4. Time evolutions of photoinduced THG signal obtained

from the azo-dye doped PMMA thin film sample #1. The pump

and probe peak intensities are, respectively, 3.3 MW/cm2 and

7.3 GW/cm2. The cross-polarized (?) and co-polarized (k)configurations refer to the direction of the probe field relative to

that of the pump field. The THG signal from PMT is integrated

by a boxcar integrator and averaged over 10 shots by computer

software. The horizontal dashed line represents the original


be either in axis 3 (k configuration) or axis 1 (?configuration). A photomultiplier tube (PMT) and

an interference-filter passing only 355 nm were

used to detect the third harmonic signal.

The NLT experimental details shown in

Fig. 3(b) were similar to those of the THG ex-periment. The major differences were that the

pump laser was replaced by a frequency-doubled,

diode-pumped Nd:YAG laser (532 nm, cw), and

that the sample was #2. The 1064 nm Continuum

Surelite I laser was still used as the probe laser.

The probe laser was beamed through a pair of

lenses lined up along the optical z-axis. The thin

film sample was placed in between the lenses suchthat the transmitted probe beam was totally in-

tercepted by the photodetector (PD). The intensity

of the probe beam normally incident on the thin

film sample was measured by another photode-

tector. The angle between pump and probe beams

was about 34�. The NLT Tnl was determined by the

ratio of the transmitted intensity to the incident

intensity.Although the probe peak intensity (7.3 GW/

cm2) used in the THG experiment is many orders

of magnitude greater than that of the pump (3.3

MW/cm2), the pumping effect of the probe beam is

negligible because the probe wavelength (1064 nm)

is very much short of resonance. Moreover, multi-

photon excitation by the probe at this intensity is

negligible. The nonlinear absorption effect in theNLT experiment mainly arises solely from the azo

dye, as we had ascertained that the PMMA thin

film possessed no nonlinear absorption effect.

isotropic level of THG. The first and second vertical dotted

lines indicate the time at which the pumping beam was switched

on and off, respectively.
4. Experimental results
Fig. 4 shows the time evolutions of the THGsignal of the optically pumped sample #1 in both

co-polarized (k) and cross-polarized (?) configu-

rations. Note that the probe peak intensity used to

generate the THG signal is 7.3 GW/cm2 while the

pump peak intensity is set at 3.3 MW/cm2. The

changes of THG shown in the figure are mainly

due to the change of third-order susceptibility vð3Þ.In the first few seconds after we switch on thepump beam in the co-polarized (k) configuration,the THG signal exhibits a fast decay because of the

fast trans-number-density decrease as a result of

AHB. The THG signal then slowly decays in about20 min, due to the slow reorientation of trans

molecules in AR. A steady state is not reached

experimentally before switching off the pump.

After we turn off the pump beam, THG rapidly

recovers 80 percent of its original strength due to

the fast thermal cis-to-trans relaxation followed

by the slow trans molecule reorientation caused by

the angular diffusion. This reveals that THG in


co-polarized configuration has negative transient

modulation relative to the pumping beam; namely,

THG decreases (increases) in the existence (ab-

sence) of pumping beam. On the other hand, in the

cross-polarized (?) configuration, there is a small

THG increase after the pump is on, due to thecombined effect of AHB and AR. Further on, after

we switch off the pump beam, the THG exhibits an

abrupt increase related to the fast cis-to-trans

thermal relaxation in several seconds, and then

returns slowly, because of the trans angular diffu-

sion, to its original magnitude. Although the

abrupt increase caused by the cis-to-trans relaxa-

0 200 400 600 800

0.86

0.88

0.90

0 200 400 600 800

0.80

0.90

1.00

(⊥)

pump offpump on

(a) cross-polarized

(//)

pump offpump on

(b)co-polarized

Non

linea

rtr

ansm

issi

on,T

nl(A

.U.)

Time (sec.)

Fig. 5. Time evolutions of NLT through the azo-dye doped

PMMA thin film sample #2. The averaged pump intensity is 3.4

W/cm2, and the probe peak intensity is 10 GW/cm2. The cross-

polarized (?) and co-polarized (k) configurations refer to the

direction of the probe field relative to that of the pump field.

The incident and transmitted signals from photodetectors are

integrated by a boxcar integrator and averaged over 10 shots by

computer software. The horizontal dashed line represents the

original isotropic level. The first and second vertical dotted lines

indicate the time at which the pump beam was switched on and

off, respectively.

tion is barely above noise level, it is supported by

the simulation presented in next section.

Fig. 5 shows the time evolutions of the NLT Tnlof the sample #2 placed at the focal point in the

optically pumped NLT experiment shown in

Fig. 3(b). Note that the probe peak intensity (10GW/cm2) used in this experiment is much stronger

than the pump intensity (3.4 W/cm2, averaged). As

shown in Fig. 5(b), a considerable increase of Tnl;kcan be observed after we switch on the pump

beam. As we turn off the pump beam, the Tnl;kstarts to decrease to its original level. This mani-

fests that Tnl;k has positive transient modulation

relative to the pumping beam; i.e., Tnl;k increases(decreases) in the action (lack of action) of pump.

However, the Tnl;? in Fig. 5(a) remains nearly un-

changed. The non-negligible and slow increase of

Tnl;k agrees with our expectation since, in the

presence of pump, the trans-number-density in the

direction parallel to the pump field decreases

slowly due to AR, as illustrated in Fig. 5(b). The

decrease of trans-number-density induces the de-crease of nonlinear absorption bk, which in turn

results in the increase of Tnl;k. After pump removal,

the azo-dye molecules in the thin film sample re-

store to their original isotropic distribution by

thermal relaxation and molecular angular diffu-

sion. Consequently, Tnl;k returns to its original

level.

5. Theoretical simulation

The results of the simulation developed here

shall be used to compare with the THG and NLT

experimental results presented above. The theo-

retical simulation is based on a theoretical model

developed by Sekkat and co-workers [6,7,19].Their model can be used to describe photoinduced

changes in linear optical properties and in second-

order nonlinear optical properties. Our simulation

is an extension of their work to third-order non-

linear effects. For the discussion of the trans–cis

photoisomerization of azo-dyes, trans and cis

molecules are to be denoted with T and C, re-

spectively. We hope to arrive at formulas andsimulation, which give insight into the photoiso-

merization process. The pump laser we used is


linearly polarized. For simplicity, it is assumed

that the trans molecules are rod-like with only one

major polarizability component parallel to the

molecular axis. The angular distribution of trans

molecules, which have experienced optical excita-

tion by the pump and multiple photoisomerizationcycles, is a function of the angle h between the

molecular axis and the symmetry axis defined by

the direction of the pump field. Based on AHB and

AR models, the rate equations describing the Tnumber density NT ðXÞ and the C number density

NCðXÞ oriented in the infinitesimal solid angle dXaround the direction X ¼ fh;ug can be written,

respectively, as [6,7,19]:

d

dtNT ðXÞ ¼ �NT ðXÞ/TC PrðhÞ

þ 1

sC

ZRCT ðX0 ! XÞNCðX0ÞdX0

� NT ðXÞZ

DT ðX ! X0ÞdX0

þZ

DT ðX0 ! XÞNT ðX0ÞdX0 ð1Þ

and

d

dtNCðXÞ ¼ � 1

sCNCðXÞ

þ IZ

PTCðX0 ! XÞNT ðX0Þ cos2 h0 dX0

� NCðXÞZ

DCðX ! X0ÞdX0

þZ

DCðX0 ! XÞNCðX0ÞdX0; ð2Þ

where PrðhÞ ¼ rT IP cos2 h is the probability of op-

tical excitation of trans molecules. IP, the time-averaged incident pump intensity, is related to the

effective pumping intensity I by I ¼ IP/TCrT , rT

being the linear absorption cross-section of T and

/TC the quantum yield for the transition T ! C. InEqs. (1) and (2) sC is the cis lifetime. RCT ðX0 ! XÞand PTCðX0 ! XÞ, respectively, are the probabili-

ties for the molecule to rotate from X0 to X in the

C ! T relaxation and in the T ! C transition.DT ðX0 ! XÞ and DCðX0 ! XÞ are the probabilities

per unit time that the molecule rotates spontane-

ously from X0 to X (angular diffusion). If we re-

strict the problem to axial systems and rod-like

molecules (i.e. they depend only on the rotation

angle w between X0 and X, and not on the azi-

muthal angle u), then Eqs. (1) and (2) can be

simplified and expressed on the basis of Legendre

polynomials (Pl):

NT ¼ 1

4p

Xl

ð2lþ 1ÞTlPlðcos hÞ;

NC ¼ 1

4p

Xl

ð2lþ 1ÞClPlðcos hÞ;ð3Þ

RCT ¼ 1

4p

Xl

ð2lþ 1ÞRCT ;lPlðcoswÞ;

PTC ¼ 1

4p

Xl

ð2lþ 1ÞPTC;lPlðcoswÞ;ð4Þ

DT ¼ dT4p

Xl

ð2lþ 1ÞDT ;lPlðcoswÞ;

DC ¼ dC4p

Xl

ð2lþ 1ÞDC;lPlðcoswÞ;ð5Þ

where dT and dC are constants related to trans and

cis molecular angular diffusion, respectively. Set-

ting RCT ;0 ¼ PTC;0 ¼ DT ;0 ¼ DC;0 ¼ 1, one obtainstwo infinite sets of coupled equations:

dCl

dt¼ IPTC;l½Kl�Tl�2 þ Kl0Tl þ KlþTlþ2�

� Cl½c0 þ dCð1� DC;lÞ�; ð6ÞdTldt

¼ �I ½Kl�Tl�2 þ Kl0Tl þ KlþTlþ2�

þ c0RCT ;lCl � dT ð1� DT ;lÞTl; ð7Þ

where

c0 ¼ s�1C ;

Kl� ¼ lðl� 1Þð2l� 1Þ�1ð2lþ 1Þ�1;

Kl0 ¼ ð2l2 þ 2l� 1Þð2l� 1Þ�1ð2lþ 3Þ�1;

Klþ ¼ ðlþ 1Þðlþ 2Þð2lþ 1Þ�1ð2lþ 3Þ�1:

Now we want to relate the angular distribution

of trans molecules to macroscopic nonlinear opti-

cal properties. The general relationship betweenmacroscopic and microscopic third-order tensor

components can be written as [1,20]:


vð3ÞIJKLð�ðx1 þ x2 þ x3Þ;x1;x2;x3Þ¼ NfIðx1 þ x2 þ x3ÞfJ ðx1ÞfKðx2ÞfLðx3ÞcIJKL;

ð8Þ

where

cIJKL ¼P

i;j;k;l cijklð�ðx1 þ x2 þ x3Þ;x1;x2;x3ÞRcos hIi cos hJj cos hKk cos hLlNT ðXÞdXR

NT ðXÞdX; ð9Þ

and N is the number density of molecule. In the last

equation cos hIi, represents the direct cosines, i.e.,

the cosine of the angle between the ith axis of the

molecular frame of reference (xyz, labeled with

subscripts i, j, k, and l) and the Ith axis of the lab-

oratory frame of reference (123, labeled with sub-

scripts I , J , K, and L). The local field factors fJ ðxÞ,etc., are related to the appropriate laboratory axis Jand frequency x. Under the influence of an optical

pump, the molecular angular distribution NT ðXÞ inEq. (9) is considerably modified, resulting in the

modification of the susceptibility vð3ÞIJKL. Assuming

that the only active (nonzero) component of the

second hyperpolarizability of the molecule is

cð¼ czzzzÞ, we observe only vð3Þ3333ð�3x;x;x;xÞ andvð3Þ3333ð�x;x;�x;xÞ tensor components for THGand NLT experiments, respectively.

In Eq. (3) only terms with even l are needed to

express the vð3Þ of a system with center of sym-

metry; those with odd l are zero on symmetry

reason [20], and hence dropped henceforth. We

consider only the special cases of the pump field

parallel (k) or perpendicular (?) to the 3-axis. The

vð3Þ3333 tensor components containing only threeparameters, T0, T2, and T4, are given by [1,20]:

vð3Þ3333;k ¼ f 4c1

5T0

�þ 4

7T2 þ

8

35T4

�ð10Þ

and

vð3Þ3333;? ¼ f 4c1

5T0

�� 2

7T2 þ

3

35T4

�: ð11Þ

Substitution of terms with l ¼ 0; 2; 4 into Eqs. (6)

and (7) gives the following six coupled rate equa-

tions:

dT0dt

¼ �I1

3T0

�þ 2

3T2

�þ c0C0; ð12Þ

dT2dt

¼�I2

15T0

�þ 11

21T2þ

12

35T4

�þ c0RCT ;2C2� c2T2;

ð13Þ

dT4dt

¼ �I4

21T2

�þ 39

77T4 þ

10

33T6

�

þ c0RCT ;4C4 � c4T4; ð14Þ

dC0

dt¼ I

1

3T0

�þ 2

3T2

�� c0C0; ð15Þ

dC2

dt¼ IPTC;2

2

15T0

�þ 11

21T2 þ

12

35T4

�� ðc0 þ j2ÞC2

ð16Þand

dC4

dt¼ IPTC;4

4

21T2

�þ 39

77T4 þ

10

33T6

�� ðc0 þ j4ÞC4;

ð17Þwhere c2 � dT ð1� DT ;2Þ; c4 � dT ð1� DT ;4Þ; j2 �dCð1� DC;2Þ; j4 � dCð1� DC;4Þ. It is reasonable toassume that Cl and Tl decrease as l increases; wetruncate the expansions at l ¼ 4. Assuming thatthe initial conditions are T0ð0Þ ¼ N , T2ð0Þ ¼T4ð0Þ ¼ C0ð0Þ ¼ C2ð0Þ ¼ C4ð0Þ ¼ 0, and that the

rotation probabilities are isotropic, i.e., RCT ;2 ¼RCT ;4 ¼ PTC;2 ¼ PTC;4 ¼ 0, we solve the rate equa-

tions (12)–(17) to give the three time-dependent

functions T0ðtÞ, T2ðtÞ, and T4ðtÞ. By substituting

these functions into Eqs. (10) and (11), we obtain

the time-dependent vð3Þ3333;k and vð3Þ3333;?.NLT is a technique for measuring nonlinear

absorption coefficient (b). bg may be related to the

imaginary part of the third-order susceptibility,

Im[vð3Þ3333;g], and is given by [21–23]:

bg ¼3x

2e0c2n20Im½vð3Þ3333;g�; ð18Þ

where g ¼ k and ? are, respectively, for co-po-

larized and cross-polarized pump–probe configu-

rations. x is the probe frequency, e0 is the

permittivity of free space, c is the speed of light,


and n0 is the linear refractive index. For a tem-

porally Gaussian pulse with an incident Gaussian

spatial profile, it can be shown [21–23] that the on-

axis NLT Tnl;gðzÞ as a function of sample position zrelative to the lens focal point is given by

Tnl;gðzÞ ¼X1m¼0

ð�qgðzÞÞm

ðmþ 1Þ3=2; ð19Þ

where

qgðzÞ ¼I1Leffbg

1þ ðz2=z20Þ: ð20Þ

In this equation, I1 is the probe intensity, z0 is theRayleigh range given by z0 ¼ pw2

0=k, w0 being the

radius of the beam waist at the lens focus (z ¼ 0). kis the probe wavelength. The effective sample

length Leff takes into account the linear absorption

a:

Leff ¼ð1� e�aLÞ

a: ð21Þ

Considering the special case of NLT at the lens

focus (z ¼ 0) and substituting the time-dependent

functions of vð3Þ3333;k and vð3Þ3333;? obtained in Eqs. (10)

and (11) into Eqs. (18)–(21), we obtain time-de-

pendent functions for Tnl;k and Tnl;?.Because it is hard to obtain analytical solutions

to the six coupled equations (12)–(17), we resort to

a numerical solution with the setting: c0 ¼ 0:05,c2 ¼ 0:005, c4 ¼ 0:0005, j2 ¼ 0, j4 ¼ 0. The results

are presented in Fig. 6, where time evolutions of

vð3Þ3333;k, vð3Þ3333;?, Tnl;k and Tnl;? for different effective

pump intensities I (in arbitrary units) are shown.

In this simulation the pump beam is switched on attime t ¼ 0, and off (I ¼ 0) at t ¼ 350 s; the values

of T0, T2, T4, C0, C2, and C4 at t ¼ 350 s are used as

the initial conditions for t > 350 s.

At the lowest effective pump intensity I ¼ 0:005shown in Fig. 6(a), vð3Þ3333;k decreases as time in-

creases from t ¼ 0, and does not reach a steady

value. In the case of medium effective pump in-

tensity, as shown in Fig. 6(b), a fast decay (AHB)followed by a slow decay (AR) of vð3Þ3333;k is ob-

served. For the highest effective pump intensity

I ¼ 0:5, shown in Fig. 6(c), vð3Þ3333;k reaches a steady

value (AHB) immediately after the pump is swit-

ched on, while the slow decay (AR) is not obvious

in this case.

Time evolution of vð3Þ3333;? differs greatly from

that of vð3Þ3333;k, as elaborated in the following. From

Eqs. (8) and (9), we know that contributions

to vð3Þ3333 comes mainly from the projection of the

second hyperpolarizability c of the trans molecules

along the probe field (cis molecules have negligiblec). Thus, each of the trans molecules oriented

closely to the probe field can effectively contribute

to the vð3Þ3333. The crux of matter is that how does

the perpendicular pumping bring about the trans

molecules oriented close and parallel to the probe

field. Though pumping is mainly associated with

the first and second terms on the right-hand side of

the coupled equations (1) and (2), respectively, itis the former term that specifies the temporal be-

havior of the trans-number density NT ðXÞ. This

leads to a slight depletion of the trans molecules

oriented closely to the pump field at low effective

pump intensity and an insignificant depletion in

directions close to the direction normal to the

pump field (i.e., an insignificant decrease in vð3Þ3333;?).

On the other hand, the AR effect, which persistswhen the pump intensity is low yet finite, tends to

accumulate trans molecules in the direction per-

pendicular to the pump field. The overall outcome

for low effective pump intensity is that the AR

dominates over AHB in directions close to the

normal of the pump field, and that the value of

vð3Þ3333;? increases with time, see Fig. 6(a) and (b).

When the effective pump intensity is very high as inthe case of Fig. 6(c), most trans molecules oriented

in directions close to the normal of the pump field

will be photoisomerized because of their nonvan-

ishing projections along the pump field. This leads

to a prominent depletion of trans molecules in not

just the parallel but also the perpendicular direc-

tion with respect to the pump field. Therefore, the

AHB effect dominates over the AR effect, andvð3Þ3333;? decreases with time at high effective pump

intensity as shown in Fig. 6(c).

Like vð3Þ3333;k, the strength of vð3Þ3333;? returns to its

original level in about 300 s after the pump is

switched off, no matter what the effective pump

intensities are. At lowest effective pump intensity in

Fig. 6(a), both vð3Þ3333;k and vð3Þ3333;? do not exhibit any

fast recovery component except for a slow one. Athighest effective pump intensity Fig. 6(c), the

abrupt increase of both vð3Þ3333;k and vð3Þ3333;?, after the

Fig. 6. Simulated time evolutions of vð3Þ3333 (frames (a), (b), and (c)), and of NLT Tnl (frames (d), (e), and (f)) for three effective pump

intensities: I ¼ 0:005, I ¼ 0:05, and I ¼ 0:5. The pump is switched on at t ¼ 0, and is switched off (I ¼ 0) at t ¼ 350 s. The co-polarized

pump/probe configuration is denoted with k and solid lines; the cross-polarized configuration is denoted with ? and dashed lines. All

curves are calculated by using c0 ¼ 0:05, c2 ¼ 0:005, c4 ¼ 0:0005, j2 ¼ 0, and j4 ¼ 0.


pump is switched off, is related to fast cis-to-transthermal relaxation, whereas the following slow re-

covery is related to angular diffusion. The abrupt

increase caused by the fast cis-to-trans relaxation is

still noticeable at the intermediate pump intensity,

as shown in Fig. 6(b). As is evident in Fig. 6, the

simulation results of Tnl are just up-side-down

mirror images of the corresponding simulation re-

sults of vð3Þ3333.

6. Discussion

Experimental data presented in Figs. 4 and 5

are basically explainable with the simulations

shown in Fig. 6. The THG data shown in Fig. 4

agree generally with the temporal behavior of vð3Þ3333

shown in Fig. 6(b). Only a small discrepancy

is found in the co-polarized THG recovery pro-cess: the fast THG recovery (or increase) in the


experimental data has greater amplitude than that

in simulation. On the other hand, the slow THG

recovery component (related to angular diffusion)

in experimental data is slower than that in simu-

lation. Note that the small abrupt increase in the

THG recovery observed in the cross-polarizedconfiguration immediately following the switch-

ing off of the pump, as shown in Fig. 4(a), is

manifested in Fig. 6(b).

The NLT experimental data (Fig. 5) also agree

well with the simulation result in Fig. 6(d). Nev-

ertheless, the nearly unchanged Tnl;? of Fig. 5(a) is

beyond our expectation. It is possible that the

change is too small to be observed by the NLTmeasurements since Tnl is related to an off-resonant

Imvð3Þ3333ð�x;x;�x;xÞ tensor component, which is

much smaller than the near-resonant jvð3Þ3333

ð�3x;x;x;xÞj2 responsible for THG. Note that

in the NLT experimental data (also in the simu-

lation curve Fig. 6(d)), no fast growth or fast decay

of Tnl is observed. This is because that the pump

laser is rather weak and hence the AHB effect be-comes insignificant. It is evident in Fig. 6(d) that

the variation of Tnl;? with time is rather small, as

compared with Tnl;k. This is also observed in the

NLT experimental data shown in Fig. 5, where we

observed a nearly unchanged Tnl;? and a consid-

erable change of Tnl;k.This simulation is suitable for a qualitative

comparison with experimental results. It will beeasy to improve the agreement between experi-

ments and simulation, if exact values of molecular

constants, such as rT and /TC, are used in the

simulation. We cannot expect a precise curve fit-

ting to experimental data since it is difficult to

assign precise values to the lifetime sC of cis mol-

ecules, the precise diffusion constants DT and DC,

and the rotation probabilities RCT and PTC. Fur-thermore, this theoretical simulation is based on a

continuous-wave pump/probe configuration, while

we use a pulsed laser as a pumping source in THG

experiment. It takes a longer time to build up the

anisotropy of vð3Þ in THG experiment since the

trans molecules will partially recover to their iso-

tropic distribution in between laser pulses when

there is no radiation field acting on the thin film.Consequently, there is some difference for the

evolution time between THG experimental results

and simulation. In NLT experiment, we use a cw,

instead of a pulsed, laser as a pumping source and

hence the evolution time in NLT experimental

results is more similar to that in simulation. Al-

though we have not attempted to unravel precise

parameters from experimental data, the charac-teristic behaviors of the variations associated with

photoisomerization can easily be observed in this

simulation.

7. Summary

Thin films of azo-dye doped PMMA exhibitpolarization sensitive THG and NLT (due to

nonlinear absorption) at a near-resonant pumping

wavelength of 532 nm. Such photoinduced an-

isotropy is illustrated by AHB and AR mecha-

nisms of photoisomerization effect, and is probed

with the light of 1064 nm wavelength in both co-

polarized and cross-polarized configurations.

THG signal varies with time significantly in thedirection parallel to pump field while it changes

slightly in the perpendicular direction. The tem-

poral behavior of Tnl in the NLT measurement

generally obey trends similar to those of NT ðXÞ inthe THG experiment, except that the decreasing

NT ðXÞ corresponds to the increasing Tnl. After the

optical pump is removed, both THG and NLT

signals recover their original levels due to thermalrelaxation.

Acknowledgements

The authors greatly acknowledge the financial

supports from the National Science Council and

Academia Sinica of Taiwan. T.H. Huang ac-

knowledges the NSC support under the contract #

NSC90-2112-M-194-014.

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photoisomerization-induced change of nonlinear absorption in azo-dye doped polymethylmethacrylate...

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