Two-wavelength holographic
recording in photopolymer using
four-energy-level system: experiments
and modeling
Chun-Hua Lin
Sheng-Lung Cho
Shiuan-Huei Lin
Sien Chi
Ken-Yuh Hsu
Two-wavelength holographic recording in
photopolymer using four-energy-level system:
experiments and modeling
Chun-Hua Lin,aSheng-Lung Cho,bShiuan-Huei Lin,c,*Sien Chi,a,band Ken-Yuh Hsua
aNational Chiao Tung University, Institute of Electro-Optical Engineering & Department of Photonics, Hsinchu 30010, Taiwan bYuan Ze University, Department of Electrical Engineering, Chungli 32001, Taiwan
cNational Chiao Tung University, Department of Electrophysics, Hsinchu 30010, Taiwan
Abstract. We investigate a two-wavelength method for recording a persistent hologram in a doped photopol-ymer. The recording method is based on two separated optical excitations of the four-energy-level system of the
doped element, one atλ ¼ 325 nm as the sensitizing wavelength and the other at λ ¼ 647 nm as the writing
wavelength, allowing for an experimental demonstration of nondestructive readout in phenanthrenequinone-doped poly(methyl methacrylate). Further, a four-energy-level rate equations model is proposed for describing the dynamics of hologram recording. The model successfully explains our experimental finding and further
pro-vides a general method to investigate such a two-wavelength holographic recording in photopolymer.© The Authors.
Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. [DOI:10.1117/1.OE.53.11.112303]
Keywords: two-wavelength holographic recording; holography; volume hologram; photopolymers; phenanthrenequinone-doped poly (methyl methacrylate).
Paper 131782SSP received Nov. 23, 2013; revised manuscript received Feb. 13, 2014; accepted for publication Feb. 17, 2014; published online Mar. 31, 2014.
1 Introduction
Photopolymers are promising write-once and read-many (WORM) holographic recording materials due to their advantageous properties of self-development, high
sensitiv-ity, and large modulation depth of the refractive index.1 A
number of holographic materials have been developed since
the first holographic photopolymer was reported in 1969.2
Currently, one can still observe intensive research activities that pursue material improvements and practical
applica-tions.3–6 Photopolymer’s self-developing property enables
it for many unique applications in real-time holography, such as holographic data storage, holographic filters,
holo-graphic interferometry, and holoholo-graphic optical elements.7–10
On the other hand, this characteristic leads to a reduction of diffraction efficiency as well as building up of scattering noise gratings, so that readout signal is degraded during hologram reconstruction. Thus, after the hologram is recorded, fixing process is necessary to turn off the remaining sensitivity and to prevent degradation of the hologram upon readout.
A simple approach to achieve nondestructive recon-struction is heating the recorded hologram so that all the remaining photoactive elements in the material are used up. It can also be achieved by flooding it with uniform
incoher-ent light after holographic recording.11,12 These postcuring
techniques are effective for eliminating material’s remaining
sensitivity. However, they also terminate material’s ability
for succeeding recordings before its dynamic range is utilized. And this ability is very important for many appli-cations, for example, in data storage, which often needs suc-ceeding recordings to write more information at the same location at later time.
The two-wavelength recording is one alternative to achieve nondestructive readout and maintain the remaining sensitivity at the same time. The idea is simple: the material is originally not sensitive to the writing light (usually at red or long wavelengths) so that holographic recording is not possible. When it is under simultaneous illumination of sensitizing (usually at UV or short wavelengths) and writing lights, the material is sensitive to writing light so that holo-graphic recording can be performed. During hologram re-construction, in the absence of sensitizing light, the material is again insensitive to the reading light so that nondestructive readout of the hologram is achieved. This scheme has been implemented with great success in doubly doped lithium
nio-bate crystals for reversible holographic recording.13,14Here,
the similar idea is extended to photopolymer for WORM applications.
Holographic recording based on two-wavelength photo-chemical (TWP) process in photopolymer was first demon-strated in carbazole dissolved poly(methyl methacrylate)
(PMMA) thin film of thickness 200 μm.15 Hologram with
1% diffraction efficiency was achieved by using sensitizing light at 333.6 nm and writing at 488 nm. Later, the hologram with 11% diffraction efficiency was recorded in
photopoly-mer thin film consisting of biacetyl-dissolved poly-
α-cya-noacrylate host.16A two-photon two-product processing has
been proposed to record a hologram with 10% diffraction efficiency in a photopolymer consisting of methylene blue,
diphenylisobenzofuranne, and a mixture of acrylamides.17
More recently, multilayer waveguide holographic memory card was reported in a photopolymer doped with two-color-photosensitive dye of bis(silyl)pentathiophene and radical photopolymerization initiator of
2,2-dimethoxy-2-phenylace-tophenone.18,19We recently reported 5% diffraction efficiency
from a TWP hologram recorded in a phenanthrenequinone-doped poly(methyl methacrylate) (PQ/PMMA) photopolymer *Address all correspondence to: Shiuan-Huei Lin, E-mail:[email protected]
sample of thickness 2 mm by using a UV sensitizing light at
325 nm and red writing light at 647 nm.20By adjusting the
intensity ratio of sensitizing and writing beams, diffraction
efficiency has been increased to >40%.21 This progress
strongly suggests that TWP holographic recording is promis-ing for practical applications of volume holograms. However, to our knowledge, there is still no theoretical modeling for TWP holographic recording in such photopolymers. Most experimental parameters are adjusted by experience. In order to find suitable light parameters for achieving high dif-fraction efficiency, it is necessary to carry out a systematic analysis on TWP recording and to investigate its physical implications.
In this paper, we present a theoretical modeling and experimental verification of the modeling for TWP holo-graphic recording in PQ/PMMA photopolymer. Based on the principle of TWP holographic recording adapted from
Ref.15, the key issues and parameters for theoretic modeling
are described in Sec. 2. In Sec. 3, PQ/PMMA fabrication,
TWP holographic recording, and nondestructive readout
are experimentally demonstrated. In Sec.4, theoretical
mod-eling of TWP holographic recording is introduced. Rate equations of population densities are listed and solved, and dynamics of TWP holograms is described. Computer simu-lations on TWP holograms are confirmed with optical experiments. The results reveal characteristics of TWP holo-grams and suggest methods for optimizing its performance.
Conclusions are made in Sec. 5.
2 Principle of Two-Wavelength Photochemical Holographic Recording
Investigations on the previous experimental results15–18,20,21
reveal that photosensitive molecules for the TWP holo-graphic recording share a common characteristic: they are α-diketone structure, which can be described by a four-energy-level absorption scheme with cascaded-excited metastable intermediate levels. An intermediate level of metastable state is essential for this scheme. This metastable level can be reached by absorption of only photons with higher energy and not photons of lower energy, resulting
in accumulation of excited molecules in this level.22There
they facilitate significant absorption of photons with lower energy and, thus, enable holographic recording.
Figure1depicts the schematic diagram for the above
four-level system. It consists of two singlet states, S0and Sn, plus
two triplet states, T1and Tn. Dye molecules are assumed to
be originally in the stable ground state S0. Under
two-wave-length illumination, the molecules will be pumped to their
final state at Tn, which is a chemically active or radical
state. Excitation S0→ Sn can be pumped by high-energy
photons at sensitizing wavelength but not by photons with
low energy at writing wavelength. The T1→ Tn transition
can be pumped by either UV or red photons.
The process of TWP holographic recording begins with simultaneous illuminations of sensitizing light and writing light. Dye molecules are first pumped by the uniform
sensi-tizing light to go from ground state S0to Sn. Then, they will
undergo a rapid decay (nanoseconds) into the triplet state T1
via intersystem crossing (ISC). There these excited mole-cules can be pumped by the writing light to reach radical
level via T1→ Tntransition. Finally, the excited radicals at
Tn react with other components to form the final
photo-chemical product, which bears index of refraction different from other parts of the photopolymer. Thus, a spatial modu-lation of refractive index or phase hologram that follows bright and dark interference fringes of writing light is cre-ated. During reading, without sensitizing illumination, the hologram can persist against uniform reading illumination at writing wavelength, and thus, nondestructive readout is achieved.
Ideally, if the T1→ Tntransition can be pumped by only
writing light, then spatial distribution of radicals and result-ing photoproduct will follow exactly that of the interference fringes of the object and reference beams; thus, high-effi-ciency holograms can be recorded. However, absorption
band of molecules at T1 state usually covers a broad
spec-trum. It often extends to sensitizing light such that part of the molecules will be pumped by the sensitizing light into higher
level of Tnstates. This part should be minimized because it
contains no optical information but uniform background, which will reduce spatial modulation of the index of refrac-tion and lead to a decrease in amplitude of hologram. Yet, the sensitizing light is necessary because without it the material is insensitive to writing light and holographic recording is not possible. Hence, how to adjust intensity ratio of sensitiz-ing to writsensitiz-ing lights is a key factor that determines the per-formance of TWP holograms. It shall be found by solving
rate equations in Sec.4that the optimum ratio is related to
the material’s level properties, such as absorption
cross-sections and quantum yields of sensitizing and writing lights. Before that, the fabrication of the photopolymer material in this study is described. The methods for determining the sensitizing and writing wavelengths are proposed and exper-imentally performed.
3 Experiments 3.1 Material
PQ/PMMA photopolymer is used in this study. The material
was fabricated by a two-step thermo-polymerization method.23
Thickness of the sample is 2 mm with PQ doping concentration of 0.7 wt.%. In such PQ/PMMA, the main mechanism for holo-graphic recording is the refractive index change induced by photochemical attachment between one PQ radical and one
residual MMA under light illumination.24The diffusions of
PQ and MMA molecules in polymer matrix can be ignored. 3.2 Wavelength Selection for Sensitizing and
Writing Light
Wavelengths of sensitizing and writing lights can be
determined by absorption spectroscopy. Figure 2(a) shows
a UV-VIS absorption spectrum of PQ/PMMA. In order to identify absorption characteristics of PQ molecules, the absorption spectroscopy of dilute solution PQ in MMA
(3 × 10−10mole∕l) is measured and showed in the same
figure. The red curve contains two characteristic absorption peaks below the blue wavelength (<450 nm). One peak is
centered at∼410 nm, corresponding to n → π transition,
and the other is centered at∼320 nm, corresponding to π →
π transition. Either one of the two peaks can be used for
the pumping of S0→ Sn singlet transition, which will be
followed up by ISC of Sn→ T1 to reach metastable level
T1. It has been reported that PQ molecules that reach at
T1 level via π → π transition have longer lifetime than
those via n → π transition.22,25,26 This will facilitate more
efficient accumulations of PQ molecules. Thus, the wave-length of sensitizing light is chosen to be 325 nm from an He-Cd laser.
As shown in Fig. 2(a), the PQ/PMMA samples before
exposure and after saturated exposure are almost transparent for wavelengths longer than 550 nm. For nondestructive readout, the material should not be sensitive to reading light without illumination of sensitizing light. Hence, wavelengths >550 nm could be used for hologram reconstruction. However, in order to write holograms with TWP recording, the material should be sensitive to writing light under simultaneous illumination or preex-posure of sensitizing light. Under these requirements, wavelength for writing light can be found by UV-induced absorption spectroscopy.
Figure 2(b) shows spectroscopy curves of 325-nm
induced absorption change of PQ/PMMA. The absorption change spectroscopy was performed when the sample was preilluminated for 12 min by a uniform 325-nm He-Cd
laser at intensity of 1 W∕cm2. It is found that there is a
sig-nificant UV-induced absorbance change in the wide range from 550 to 700 nm. In addition, as illustrated by the
blue curve in Fig. 2(a), the photoproduct PQ-MMA has
almost no absorption at this range. Thus, the measured
results indicate that the excited PQ molecules at T1level
pro-vide the absorption change so that this range of wavelength is suitable for writing light. For convenience, a red beam with wavelength of 647 nm from a Krypton laser is chosen for writing and readout.
3.3 TWP Holographic Recording and Nondestructive Reading
The schematic diagrams for TWP holographic recording and
nondestructive reading experiments are shown in Fig.3(a).
A uniform beam of intensity 0.33 W∕cm2 from a 325-nm
He-Cd laser is used as the sensitizing light, and two
s-polar-ized beams (each of 0.22 W∕cm2) splitting from a 647-nm
Krypton laser are used as the writing lights. The writing lights are incident symmetrically on the sample with an intersection angle of 28 deg (2θ) in the air. By controlling the opening and closing of shutters S1, S2, and S3, TWP holographic record-ing and readrecord-ing were performed in PQ/PMMA.
First, the holographic recording without sensitizing light (by closing shutter S3 and opening S1 and S2) is performed. During recording, one of the writing beams was blocked (by closing S2) from time to time and the diffracted intensity from the other beam was measured by detector D1. Temporal evolution of the diffraction efficiency is shown as
300 400 500 600 700 0 1 2 3 4 600 620 640 660 680 700 -0.01 0.00 0.01 0.02 0.03 0.04 A b so rb an c e Wavelength (nm) π π* PQ in MMA PQ/PMMA Exposed PQ/PMMA Abso rbance Wavelength (nm) n π* x100 (a) 450 500 550 600 650 700 -0.01 0.00 0.01 0.02 0.03 0.04
UV-induced absorbance change
Wavelength (nm)
Un-exposed PQ/PMMA UV pre-exposure 12 min
(b)
Fig. 2 (a) UV-VIS spectra of phenanthrenequinone-doped poly (methyl methacrylate) (PQ/PMMA) and dilute solution of PQ/MMA (3 × 10−10mole∕L). (b) UV-induced absorption spectroscopy of PQ/ PMMA.
the curve IUV¼ 0 in Fig.3(b), where diffraction efficiency is defined as the ratio between the diffracted and the incident intensities. It is seen that maximum diffraction efficiency is
much below 10−3%; thus, holographic recording at only red
wavelength is almost negligible compared with that with UV sensitization shown in the following.
Then, TWP holographic recording with sensitizing light (by opening S3) is performed. The result is shown as the
curve IUV¼ 0.74I0 in Fig. 3(b), where I0 represents the
sum of total intensity of the writing beams. It is seen that, with simultaneous illumination of UV light, diffraction effi-ciency is >10%, which is an improvement over four orders of magnitude than that without UV light. Thus, the signifi-cance of material sensitization induced by sensitizing light is fully demonstrated.
After holographic recording, the Bragg selectivity curve of the hologram was measured by rotating the sample
mounted on a rotational stage. Figure4(a)shows a typical
curve for a hologram with ∼40% diffraction efficiency. It
can be seen clearly that the selectivity curve of the hologram
fits well with the Kogelnik’s formula27without considering
the absorption at 647 nm. This result indicates that a uniform 2-mm-thick hologram has been recorded by TWP method in our PQ/PMMA. In addition, in order to test the persistence property of the TWP hologram, a holographic reconstruction experiment is demonstrated. A TWP hologram with 5% diffraction efficiency was reconstructed with a red light (shutters S2 and S3 closed and S1 open) and the diffraction
efficiency was measured by using detector D1. Figure4(b)
shows the result. It is seen that diffraction efficiency remains almost unchanged after 24 h of continuous reading, although the sample is not saturated. This clearly demon-strates the capability of nondestructive property of the TWP hologram.
4 Four-Energy-Level Model of TWP Holographic Recording
4.1 Rate Equations and Solutions
Referring to the four-energy-level model for TWP
holo-graphic recording that was depicted in Fig.1, rate equations
for the population density of PQ molecules at each level can be written as dN0 dt ¼ −qUV0σUVρUVN0þ N2 τ20 þN1 τ10 ; (1) dN1 dt ¼ qUV0σUVρUVN0− N1 τ12 −N1 τ10 ; (2) dN2 dt ¼−qUV2σUVρUVN2−qRσRρRN2þ N3 τ32 þNB τB2 þN1 τ12 −N2 τ20 ; (3) dN3 dt ¼ qRσRρRN2− N3 τ32 − k3pN3M; (4) dNB dt ¼ qUV2σUVρUVN2− NB τB2 − kBPNBM; (5) Sample BS Mirror Kryp ton l a ser Kry p to n las er 2θθ He He--CdCdlaserlaser S3 S2 S1 D1 D2 (a) 0 200 400 600 800 1000 0 5 10 15 20 IUV= 0.74 I0 IUV= 0
Writing time (min.)
D iffra ction efficienc y (%) x4000 (b)
Fig. 3 Experimental results. (a) Optical setup. (b) Comparison of diffraction efficiency between with and without sensitizing light.
-0.10 -0.05 0.00 0.05 0.10 0 5 10 15 20 25 30 35 40 Experimental data Theoretical N o rm alized diffract ed power
Detuning angle (Deg.)
(a) 0 4 8 12 16 20 24 0 1 2 3 4 5 6 Diff ract ion efficie n cy (%) Reading Time (hr.) (b)
Fig. 4 Experimental result. (a) Bragg selectivity curve of a two-wave-length photochemical (TWP) hologram with diffraction efficiency of 40%. (b) Nondestructive readout of the TWP hologram.
where N0, N1, N2, N3, and NBare population densities
(mol-ecules·cm−3) of each level, respectively. M is the
concentra-tion of residual monomer, MMA.ρUVandρRare photon flux
(photons · s−1· cm−2) of UV sensitizing light and red
writ-ing light, with definitionρ ≡ I∕ðhνÞ, where h is the Planck
constant, I is the intensity, and ν is the frequency of light.
σUV and σR are molar absorption cross-sections (cm2) of
UV and red lights, respectively. qUV0 is the quantum yield
(molecules per photon) of UV light for the transition
S0 → Sn. Similarly, qR and qUV2 represent quantum yields
of red and UV lights, respectively, for the transition
T1→ Tn.τij(i, j ¼ 0, 1, 2, 3, B) represents lifetime
corre-sponding to the transition of upper level i and lower level j.
k3P and kBP are the attachment rate constants between the
free PQ radicals and MMA at level Tnto form
photoprod-ucts. The rate equation of growth of photoproduct density NP
can be written as
dNP
dt ¼ k3PN3M þ kBPNBM: (6)
The photoproduct bears index of refraction different from other parts of the photopolymer so that the phase hologram can be recorded as the uniform sensitizing light and the spatially modulated writing light are given. Based on the photochemical mechanisms in PQ/PMMA, the following approximations are made. It is assumed that initially all
PQ molecules are at the ground level S0, so at t ¼ 0, N0¼
NA and N1 ¼ N2¼ N3¼ NB¼ NP¼ 0, where NA is the
doping concentration of PQ molecules. During holographic writing process, the diffusion of PQ molecules is so small that they are distributed among the energy levels purely according to the local intensities of UV and red lights, so
NA¼ N0þ N1þ N2þ N3þ NBþ NP. Finally, if the
writ-ing time is long enough, all PQ molecules will be pumped to
become radicals at levels Tnand attach with MMA to form
final photoproduct; thus at t → ∞, NP¼ NA.
Further, since lifetime of PQ at each level is long (>100 s) compared with that of the ISC time (approximately nanosec-onds), hence, under sufficient pumping by the sensitizing and writing lights, all the level-relaxation terms in rate
equa-tions can be neglected except the term ofτ12 for the ISC
relaxation.28,29For simplicity and without loss of generality,
absorption cross-sections for both wavelengths are assumed as unity. This will not affect physical results because actually its effect is absorbed in the quantum yield of each level at that wavelength.
Under these simplifications, population densities of PQ molecules at each level and photoproduct can be solved and written as
N0ðtÞ ¼ NAexpð−qUV0ρUVtÞ; (7)
N1ðtÞ¼
qUV0ρUVτ12
1−qUV0ρUVτ12
NA½expð−qUV0ρUVtÞ−expð−t∕τ12Þ;
(8)
N2ðtÞ ¼
qUV0ρUVNAexp½−ðqUV2ρUVþ qRρRÞt
ð−qUV0ρUVþ qUV2ρUVþ qRρRÞð−1 þ qUV2ρUVτ12þ qRρRτ12Þ
þ qUV0ρUV ð1 − qUV0ρUVτ12Þ NA expð−qUV0ρUVtÞ ð−qUV0ρUVþ qUV2ρUVþ qRρRÞ − qUV0ρUVτ12 ð1 − qUV0ρUVτ12Þ NA expð−t∕τ12Þ ð−1 þ qUV2ρUVτ12þ qRρRτ12Þ ; (9) N3ðtÞ ¼ NAqRρRqUV0ρUVexpð−Mk3PtÞ ð1 − τ12Mk3PÞðqUV0ρUV− Mk3PÞðqUV2ρUVþ qRρR− Mk3PÞ
−qRρRqUV0ρUVNAðqUV2ρUVþ qRρR− Mk3PÞ−1exp½−ðqUV2ρUVþ qRρRÞt
ð−qUV0ρUVþ qUV2ρUVþ qRρRÞð−1 þ qUV2ρUVτ12þ qRρRτ12Þ
− qUV0ρUV ðqUV0ρUV− Mk3PÞ 1 ð1 − qUV0ρUVτ12Þ qRρRNAexpð−qUV0ρUVtÞ ð−qUV0ρUVþ qUV2ρUVþ qRρRÞ þ qUV0ρUVτ12 ð1 − qUV0ρUVτ12Þ qRρRNAð1∕τ12− Mk3PÞ−1expð−t∕τ12Þ ð−1 þ qUV2ρUVτ12þ qRρRτ12Þ ; (10) NBðtÞ ¼
NAqUV2ρUVqUV0ρUV expð−MkBPtÞ
ð1 − τ12MkBPÞðqUV0ρUV− MkBPÞðqUV2ρUVþ qRρR− MkBPÞ
−qUV2ρUVqUV0ρUVNAðqUV2ρUVþ qRρR− MkBPÞ−1exp½−ðqUV2ρUVþ qRρRÞt
ð−qUV0ρUVþ qUV2ρUVþ qRρRÞð−1 þ qUV2ρUVτ12þ qRρRτ12Þ
− qUV0ρUV
ðqUV0ρUV− MkBPÞ
1
1 − qUV0ρUVτ12
qUV2ρUVNA expð−qUV0ρUVtÞ
ð−qUV0ρUVþ qUV2ρUVþ qRρRÞ þ qUV0ρUVτ12 1 − qUV0ρUVτ12 qUV2ρUVNAð1∕τ12− MkBPÞ−1expð−t∕τ12Þ ð−1 þ qUV2ρUVτ12þ qRρRτ12Þ ; (11)
NPðtÞ ¼ NA−
NAqRρRqUV0ρUV expð−Mk3PtÞ
ð1 − τ12Mk3PÞðqUV0ρUV− Mk3PÞðqUV2ρUVþ qRρR− Mk3PÞ
− NAqUV2ρUVqUV0ρUVexpð−MkBPtÞ
ð1 − τ12MkBPÞðqUV0ρUV− MkBPÞðqUV2ρUVþ qRρR− MkBPÞ þ Mk3PqRρR ðqUV2ρUVþ qRρR− Mk3PÞ þ MkBPqUV2ρUV ðqUV2ρUVþ qRρR− MkBPÞ
× qUV0ρUVNA exp½−ðqUV2ρUVþ qRρRÞt
ðqUV2ρUVþ qRρRÞð−qUV0ρUVþ qUV2ρUVþ qRρRÞð−1 þ qUV2ρUVτ12þ qRρRτ12Þ
þ qRρRMk3P ðqUV0ρUV− Mk3PÞ þ qUV2ρUVMkBP ðqUV0ρUV− MkBPÞ ×ð1 − q 1 UV0ρUVτ12Þ NAexpð−qUV0ρUVtÞ ð−qUV0ρUVþ qUV2ρUVþ qRρRÞ þ − qRρRMk3P ð1∕τ12− Mk3PÞ − qUV2ρUVMkBP ð1∕τ12− MkBPÞ × qUV0ρUVτ12τ12NAexpð−t∕τ12Þ ð1 − qUV0ρUVτ12Þð−1 þ qUV2ρUVτ12þ qRρRτ12Þ : (12)
NpðtÞ represents temporal evolution of the concentration
of photoproduct that governs the dynamics of TWP holo-graphic recording. Before proceeding to investigation on dynamics of holographic recording, several observations can be made. First, above solutions show that, with
ρUV¼ 0, N0¼ NA and N1¼ N2¼ N3¼ NB¼ Np¼ 0
for all time, no matter what the value of ρR is, i.e., when
there is no UV light, all PQ molecules will stay at ground level and the material is not sensitive to red light. This con-firms the requirement that sensitizing light is necessary for enabling the TWP holographic recording.
Further,τ12is so quick that the terms involved with
expo-nential term of τ12 in Eqs. (9) to (12) can be neglected
compared with other terms of the solution. Under these
sim-plifications, it can be seen that Np(thus, TWP holographic
recording) is mainly conducted by the quantum yields of the
material, i.e., qUV0, qUV2, and qR as well as photon flux of
sensitizing and writing lights,ρUV andρR. In the next
sec-tion, the methods for finding these material parameters of PQ/PMMA through light-induced absorption experiments are described. Then, dynamics of TWP holograms can be investigated by adjusting intensity ratio of sensitizing and writing lights.
4.2 Light-Induced Experiment for Determining Level Parameters
According to the four-energy-level modeling, sensitizing
light is absorbed by PQ molecules both at levels S0 and
T1, and writing light is absorbed only by PQ molecules at
level T1. Molecules that absorb photons will be pumped
to higher energy levels S1 and Tn, respectively. Following
this consideration, light intensity absorption constantαUVðtÞ
can be derived as
αUVðtÞ ∝ qUV0N0ðtÞ þ qUV2N2ðtÞ þ α0: (13)
In the above equation, αUVðtÞ represents light intensity
absorption coefficient of UV light, and α0 accounts for
the material intrinsic absorption coefficient that does not con-tribute to population change, such as PMMA polymer matrix
absorption. Defining absorbance as DUVðtÞ ¼ αUVðtÞd,
where d represents material thickness, and substituting
N0ðtÞ and N2ðtÞ from Eqs. (7) and (9) into Eq. (13), the
absorbance can be written as
DUVðtÞ ≈ qUV0NAd
1 þð1 − q qUV2ρUV
UV0ρUVτ12Þð−qUV0ρUVþ qUV2ρUVþ qRρRÞ
expð−qUV0ρUVtÞ
þ qUV2NAd
qUV0ρUV exp½−ðqUV2ρUVþ qRρRÞt
ð−qUV0ρUVþ qUV2ρUVþ qRρRÞð−1 þ qUV2ρUVτ12þ qRρRτ12Þ
þ D0
≡ A1expð−t∕τ1Þ þ A2 expð−t∕τ2Þ þ D0; (14)
where coefficients A1and A2are related to quantum yields qUV0, qUV2, and qR, and photon fluxρUVandρR. Also,τ1 andτ2are time constants of the light-induced absorbance, which can be written as
1 τ1 ¼ qUV0ρUV; 1 τ2 ¼ qUV2ρUVþ qRρR: (15)
These time constants can be obtained by light-induced absorbance experiments; then, by curve fitting, the quantum
yields can be found. The setup described in Fig. 3(a) was
used for the absorbance measurements. Two measurements were performed. In the first one, there was no red light
illumination (shutters S1 and S2 closed and S3 open). The PQ/PMMA was illuminated with UV of intensity
0.583 W∕cm2, and the transmitted power was monitored
every 4 s by UV detector D2 located behind the sample. Experimental result is shown by the curve of small black
circles in Fig.5. By curve fitting with solid line, it was found
thatτ1¼ 625 7.2 s and τ2¼ 12435 15.6 s. By setting
ρR¼ 0 and ρUV¼ 9.53 × 1017 s−1cm−2 in Eq. (15),
quan-tum yields of UV light at levels S0and T1were obtained to
be qUV0¼ 1.68×10−21and qUV2¼ 8.44×10−23, respectively.
Then, UV absorbance was measured when the sample was simultaneously illuminated with UV and strong red lights (shutters S3 and S1 open and S2 closed). UV intensity
was 0.583 W∕cm2and red intensity was IR¼ 8.32 W∕cm2
(ρR¼ 2.71 × 1019 s−1cm−2). In this situation, red photons
were competing with UV photons for molecules at T1
level; thus, the UV absorbance would be reduced. Experimental result confirmed this prediction, as shown
by the curve of small blue squares in Fig.5. By curve fitting
with dashed lines, it was found that τ1 ¼ 623 6.8 s and
τ2¼ 5155 26.5 s. By using values of qUV0¼ 1.68 ×
10−21 and qUV2¼ 8.44 × 10−23, the value of qR¼ 4.19 ×
10−24 is obtained. These parameters will be used for the
following investigations on TWP holographic recordings.
4.3 Dynamics of TWP Holograms
During TWP holographic recording, intensity of the sensitiz-ing light is uniform, and intensity of the writsensitiz-ing light is a spatial variation of interference between object and refer-ence waves, which is written as
IRðxÞ ¼ I0 1 þ m1 cos 2π Λx ; (16)
where I0 is the sum of intensity of the object and reference
beams;Λ and m1are the period and the modulation depth of
the interference pattern, respectively. After substituting light
intensities IUV and IRðxÞ as well as level parameters qUV0
and qUV2, and qR, which were found in Sec. 4.2, into
Eq. (12), temporal evolution of the spatial distribution of
photoproduct PQ-MMA, NPðx; tÞ, can be calculated
numeri-cally. Since the main mechanism for holographic recording in the PQ/PMMA is the refractive index change induced by photochemical attachment between one PQ radical and one residual MMA, hence, the photo-induced refractive
index change, or the phase hologram, Δnðx; tÞ, which is
proportional to density of photoproduct, can be found as
Npðx; tÞ and, thus, can be written as
Δnðx; tÞ ∝ Npðx; tÞ: (17)
As an example, assuming I0 ¼ 0.44 W∕cm2 and
IUV¼ 0.131 W∕cm2, the temporal evolution of the
holo-gram profile, Δnðx; tÞ at t ¼ 20, 400, 800, and 3000 min,
respectively, are calculated and plotted in Fig. 6(a). It is
seen that the hologram profile deviates from purely sinusoi-dal function. By using Fourier analysis, temporal evolution
of the first harmonic term of the hologram amplitude, n1ðtÞ,
can be written as n1ðtÞ ∝ 1 Λ Z Λ∕2 −Λ∕2Δnðx; tÞ cos 2πΛx dx: (18)
Then, as mentioned in experimental results, the temporal
evolution of diffraction efficiency η can be calculated by
using Kogelnik’s formula:27
ηðtÞ ¼ sin2 n1ðtÞπd λ cos θin ; (19)
where d is the thickness of the material, λ is the wavelength
of the writing beam in material, andθinis the incident angle
of the probing beam in material. With given light intensities, temporal evolution of the diffraction efficiency can be
calcu-lated, as plotted in Fig.6(b). Note that only relative values
of the hologram amplitude and diffraction efficiency can
be obtained here because Eq. (17) is in proportional
relationship.
(a)
(b)
Fig. 6 The simulation results on TWP holographic recording. (a) Optical fringes and normalized grating profiles Δnðx; tÞ. (b) Diffraction efficiency (qUV0¼ 1.68 × 10−21, qUV2¼ 1.06 × 10−23,
qR¼ 4.19 × 10−24, NA¼ 1.93 × 1018cm−3, d ¼ 2 mm, θ ¼ 14 deg, Λ ¼ 1.34 μm, IUV¼ 0.131 W∕cm2, I0¼ 0.44 W∕cm2, M ¼ 1, k2¼ 3.96 × 10−5, k 3p¼ kbp¼ 1.95 × 10−5). 0 500 1000 1500 2000 2500 0.4 0.6 0.8 1.0 1.2 1.4 IR =0 IR =8.32 W/cm 2
Fitting curve for IR=0 Fitting curve for IR=8.32 W/cm2
32 5-nm a b os rbance UV illumination time(sec.)
Fig. 5 UV-induced absorbance at 325 nm. Symbols: experiments. Solid lines: curve fitting.
4.4 Investigations on the TWP Holographic Recording
Following the same procedures described in Sec. 4.3, the
temporal evolutions of TWP holographic recordings are calculated by using the intensity ratio between UV and
red beams at IUV∕I0¼ 0.74, where I0 is fixed at
0.44 W∕cm2. The result is shown as solid blue line in
Fig. 7. In order to examine these calculations, TWP
holo-graphic recording experiments are carried out with the same beam conditions. The results are shown as black
open circles in Fig. 7. It is seen that the general trends of
the theoretical and experimental curves appear to match well. Thus, the experiments and calculations are repeated by using different intensity ratios. The maximum diffraction efficiencies corresponding to the given intensity ratio and the time to reach this point for all cases are summarized in
Table1. It is noted that simulation only gives relative values.
By setting the maximum diffraction efficiency for the case
IUV∕I0¼ 0.74 to be equal to that of the experimental
value (14.6%), the simulation results of diffraction efficiency for other cases are obtained.
As illustrated in Table1, the smaller intensity ratio gives
higher diffraction efficiency, and it takes longer time to reach the maximum. The following paragraph shows that the four-energy-level model can explain these characteristics.
First, the characteristic that weaker sensitizing light takes longer time to reach diffraction maximum is understandable.
Since the writing intensity I0is fixed, hence, smaller
inten-sity ratio means weaker sensitizing beam inteninten-sity, which in turn implies slower pumping rate to excite PQ molecules from the ground state to the metastable level. Thus, it will
need longer time to supply sufficient PQ molecules at
level T1, which will result in longer time to write a hologram.
The behavior of smaller intensity ratio of IUV∕I0
produc-ing higher diffraction efficiency can also be understood by the four-energy-level modeling. For a fixed writing intensity
I0, smaller intensity ratio means weaker background of UV
intensity; thus, the contrast of optical interference can be higher in this case. Further, it in turn implies less UV photons to compete with red photons for PQ molecules at energy
level T1. Thus, the population density of PQ radicals
pro-duced by red light, N3ðx; tÞ, can be enhanced compared
with that produced by UV, NBðx; tÞ. As a result, the spatial
modulation of the holograms produced by these radicals can be higher in this case; therefore, it gives higher diffraction efficiency.
The question is, can the diffraction efficiency keep grow-ing when the intensity ratio keeps reducgrow-ing to indefi-nitely small?
In order to investigate this problem, we followed the same procedures to calculate the maximal diffraction efficiency as
a function of IUV∕I0. Further, in order to avoid the problem
of oscillations in diffraction efficiency that is embedded in
sine function of Eq. (19), the maximal value of hologram
amplitude in Eq. (18),ðn1Þmax, is examined, which
corre-sponds to the maximal value of the spatial modulation of
the radical population density. Figure8(a)shows the results
for the cases I0 ¼ 0.44, 25.2, and 52 W∕cm2, respectively.
It is seen that the three curves almost overlap with each other, meaning that the hologram amplitude depends only on
0 500 1000 1500 0 5 10 15 20 D iffrac tion e fficienc y (%)
Writing time (min)
Fig. 7 The experimental result (black circles) and numerical calcula-tions (solid line) for temporal evolution of TWP holographic recording (I0¼ 0.44 W∕cm2).
Table 1 Maximum diffraction efficiency and writing time to reach maximum under different intensity ratios.
ηmax
Writing time to reach ηmax(min)
Ratio (IUV∕I0) Experiments (%) Simulation (%) Experiments Simulation
0.3 53.0 55.8 1026 1307 0.74 14.6 14.6 737 737 1.18 2.34 1.76 334 541 10-3 10-2 10-1 100 0 1 2 3 4 5
(a)
I 0 = 0.44 W/cm 2 I 0 = 25.2 W/cm 2 I 0 = 52 W/cm 2 IUV/I0 (n1 )ma x x10-4 (a) 10-3 10-2 10-1 100 100 101 102 103 104 105(b)
I0= 0.44 W/cm2 I0= 25.2 W/cm2 I0= 52 W/cm 2 IUV/I0Writing time (mi
n.)
(b)
Fig. 8 Numerical calculations. (a) Maximum hologram amplitude as a function of intensity ratio. (b) Hologram recording time to reach maximum versus the intensity ratio (qUV0¼ 1.68 × 10−21, qUV2¼
8.44 × 10−23, q
the intensity ratio and not the beam intensity. This result can be understood by recalling that amplitude of the hologram depends only on the difference of the photoproduct densities between the bright and dark regions. Therefore, a fixed intensity ratio will produce the same value of the spatial modulation of the refractive index, no matter how the beam intensities are changed.
It is also seen in Fig.8(a)that smaller intensity ratio
pro-duces larger hologram amplitude, as expected. However,
when the ratio is reduced too much, such as ∼ < 5 × 10−2
in Fig. 8(a), the hologram amplitude starts to decrease.
According to the four-level model, the hologram is written by the attachment of PQ radicals and MMA. The sum of
pop-ulation density NBðx; tÞ þ N3ðx; tÞ, which are excited from
PQ at level T1by UV and red photons, respectively, plays an
important role in determining the concentration of the
photo-product NPðx; tÞ. PQ molecules at level T1 are in turn
pumped from the ground level S0 by UV photons. If the
UV intensity is reduced too much such that the pumping
speed from S0→ T1 cannot support that for T1→ Tn,
then the spatial distribution of the photoproducts becomes different from that of the bright and dark fringes of the inter-ference pattern. Then the refractive index distribution is dis-torted from the sinusoidal function and the coefficient of the fundamental grating is decreased. Therefore, the hologram amplitude is decreased if the intensity ratio is reduced too much.
Hence, an optimal value exists for the intensity ratio
IUV∕I0. The optimal condition can be estimated when the
two pumping speeds are equal to each other, i.e.,
qUV0ρUV¼ qUV2ρUVþ qRρR, which gives the intensity
ratio as IUV I0 ¼ qR qUV2 ðλred∕λUVÞ ðqUV0∕qUV2− 1Þ : (20)
Taking qUV0 ¼ 2.01 × 10−21, qUV2¼ 8.44 × 10−23, and
qR¼ 4.19 × 10−24, which were obtained from light-induced
experiments, the intensity ratio is 0.0052. This number is very close to the calculated value (0.0082 0.0001) of
theo-retical curve in Fig.8(a). Thus, Eq. (20) gives a useful
guide-line to choose the intensity ratio.
Note that the beam intensity actually affects the hologram
writing speed. Figure 8(b)plots the time to reach maximal
hologram amplitude as a function of the intensity ratio for
three cases of I0¼ 0.44, 25.2, and 52 W∕cm2, respectively.
The figure shows that stronger beam intensity takes shorter writing time to reach the maximal hologram amplitude, which was observed in the experiments.
It is also worthy to note that in Table1, the time to reach
maximum diffraction efficiency of the experimental results deviates a little bit from the numerical calculations. The dif-ference in temporal evolution can be attributed to the simpli-fications in the modeling. For example, the diffusion effect of free PQ molecules has been neglected. In holographic recording, the writing time is in the order of 1000 min. The diffusion length of PQ molecules in PMMA matrix at room temperature can be calculated to be in the order of
sub-micrometers,30–32which is a fraction of typical fringe spacing
of the interference fringe. Hence, the spatial modulation of the hologram will be affected. Thus, a more detailed inves-tigation to account for the spatial diffusion of molecules is necessary for improving the accuracy of the modeling.
5 Conclusions
We have presented a methodology for investigating TWP holographic recording in PQ/PMMA. Samples of thickness 2 mm have been fabricated. Absorption spectroscopy was used to determine the wavelengths for TWP holographic recording in this material. An He-Cd laser at 325 nm was chosen as the sensitizing light and a Krypton laser at 647 nm as the writing light. TWP holograms of 53% diffrac-tion efficiency and nondestructive readout of this hologram have been demonstrated.
The four-energy-level model for the system has been illustrated. Rate equations are listed and solutions for the amplitudes of the TWP holograms have been found. It is found that the key parameters that govern the characteristics
of the TWP holograms are quantum yields (qUV0, qUV2, and
qR) of the material and photon flux (ρUVandρR) of the
inci-dent lights. The quantum yields of PQ/PMMA material are found by the UV-induced absorbance experiments. Then, using these material parameters, the TWP holographic recording has been theoretically calculated and compared with the experimental results for different intensity ratios of the gating and writing lights. It is demonstrated that the intensity ratio between sensitizing and writing lights determines the maximal achievable diffraction efficiency of the hologram and that the beam intensity determines the writing speed of holographic recording.
Confirmation of the numerical calculations with experi-mental results demonstrates the validity of this model for TWP holographic recording in PQ/PMMA. This methodol-ogy for investigating the dynamics of TWP holographic recording can be extended to other photopolymers with sim-ilar photochemical schemes.
Acknowledgments
Financial support by National Science Council, Taiwan, under contracts #NSC 101-2221-E-009-112-MY3 and #NSC 101-2221-E-009-111-MY3 are gratefully acknowledged. References
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Chun-Hua Lin received his BS in electrophysics in 2001 from the National Chiao Tung University, an MS in electro-optical engineering in 2003, and a PhD in electro-optical engineering in 2013 from National Chiao Tung University in Taiwan, China. He is currently a postdoctoral fellow researcher at the Department of Photonics, National Chiao Tung University, Taiwan. His research interests are in photopolymer, holographic storage, and liquid crystal optics. Sheng-Lung Cho received his BS in control engineering in 1986 from National Chiao Tung University in Taiwan and his MS in industry engi-neering in 1992 from Tsing Hua University in Taiwan. He is currently a PhD student in electrical engineering at Yuan Ze University in Taiwan. His research interests are in optical fiber communication and holo-graphic optical elements.
Shiuan-Huei Lin received his BS in electrophysics in 1990, and his MS and PhD in electro-optical engineering in 1992 and 1996, respec-tively, all from National Chiao Tung University in Taiwan. He is cur-rently a professor in the Department of Electrophysics at the National Chiao Tung University. His research interests are in holographic stor-age, optical computing, optical devices, holographic materials, and holography for optical information processing.
Sien Chi received his BSEE degree from National Taiwan University, Taipei, Taiwan, and his MSEE degree from National Chiao-Tung University, Taiwan, in 1959 and 1961, respectively. He received his PhD degree in electrophysics from Polytechnic Institute, Brooklyn, New York, in 1971. From 1971 to 2004, he was a professor at National Chiao-Tung University. He is currently a chair professor at Yuan-Ze University, Taiwan. He is a fellow of the Optical Society of America. His research interests are optical-fiber communications, fast and slow light, passive optical networks, and microwave photonics. Ken-Yuh Hsu received his BS in electrophysics in 1973 and his MS in electronic engineering in 1975, both from National Chiao Tung University in Taiwan. He received his PhD in electrical engineering from the California Institute of Technology in 1989. He is currently a professor at the Department of Photonics & Institute of Electro-Optical Engineering at the National Chiao Tung University. His research interests are in the area of optical computing, optical neural networks, and holography for information storage and processing.
