Two-wavelength holographic recording in photopolymer using

Two-wavelength holographicrecording in photopolymer usingfour-energy-level system: experimentsand modeling

Chun-Hua LinSheng-Lung ChoShiuan-Huei LinSien ChiKen-Yuh Hsu

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Two-wavelength holographic recording inphotopolymer using four-energy-level system:experiments and modeling

Chun-Hua Lin,a Sheng-Lung Cho,b Shiuan-Huei Lin,c,* Sien Chi,a,b and Ken-Yuh Hsua

aNational Chiao Tung University, Institute of Electro-Optical Engineering & Department of Photonics, Hsinchu 30010, TaiwanbYuan Ze University, Department of Electrical Engineering, Chungli 32001, TaiwancNational 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 thedoped element, one at λ ¼ 325 nm as the sensitizing wavelength and the other at λ ¼ 647 nm as the writingwavelength, 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 describingthe 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.©TheAuthors.Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires fullattribution 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 IntroductionPhotopolymers are promising write-once and read-many(WORM) holographic recording materials due to theiradvantageous properties of self-development, high sensitiv-ity, and large modulation depth of the refractive index.1 Anumber of holographic materials have been developed sincethe first holographic photopolymer was reported in 1969.2

Currently, one can still observe intensive research activitiesthat pursue material improvements and practical applica-tions.3–6 Photopolymer’s self-developing property enablesit for many unique applications in real-time holography,such as holographic data storage, holographic filters, holo-graphic interferometry, and holographic optical elements.7–10

On the other hand, this characteristic leads to a reduction ofdiffraction efficiency as well as building up of scattering noisegratings, so that readout signal is degraded during hologramreconstruction. Thus, after the hologram is recorded, fixingprocess is necessary to turn off the remaining sensitivity andto prevent degradation of the hologram upon readout.

A simple approach to achieve nondestructive recon-struction is heating the recorded hologram so that all theremaining 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 postcuringtechniques are effective for eliminating material’s remainingsensitivity. However, they also terminate material’s abilityfor succeeding recordings before its dynamic range isutilized. 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 samelocation at later time.

The two-wavelength recording is one alternative toachieve nondestructive readout and maintain the remainingsensitivity at the same time. The idea is simple: the materialis originally not sensitive to the writing light (usually at redor long wavelengths) so that holographic recording is notpossible. When it is under simultaneous illumination ofsensitizing (usually at UVor short wavelengths) and writinglights, 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 materialis again insensitive to the reading light so that nondestructivereadout of the hologram is achieved. This scheme has beenimplemented with great success in doubly doped lithium nio-bate crystals for reversible holographic recording.13,14 Here,the similar idea is extended to photopolymer for WORMapplications.

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 with1% diffraction efficiency was achieved by using sensitizinglight at 333.6 nm and writing at 488 nm. Later, the hologramwith 11% diffraction efficiency was recorded in photopoly-mer thin film consisting of biacetyl-dissolved poly-α-cya-noacrylate host.16 A two-photon two-product processing hasbeen proposed to record a hologram with 10% diffractionefficiency in a photopolymer consisting of methylene blue,diphenylisobenzofuranne, and a mixture of acrylamides.17

More recently, multilayer waveguide holographic memorycard was reported in a photopolymer doped with two-color-photosensitive dye of bis(silyl)pentathiophene and radicalphotopolymerization initiator of 2,2-dimethoxy-2-phenylace-tophenone.18,19 We recently reported 5% diffraction efficiencyfrom 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]

Optical Engineering 112303-1 November 2014 • Vol. 53(11)

Optical Engineering 53(11), 112303 (November 2014)


http://dx.doi.org/10.1117/1.OE.53.11.112303

http://dx.doi.org/10.1117/1.OE.53.11.112303

http://dx.doi.org/10.1117/1.OE.53.11.112303

http://dx.doi.org/10.1117/1.OE.53.11.112303

http://dx.doi.org/10.1117/1.OE.53.11.112303

http://dx.doi.org/10.1117/1.OE.53.11.112303

sample of thickness 2 mm by using a UV sensitizing light at325 nm and red writing light at 647 nm.20 By adjusting theintensity ratio of sensitizing and writing beams, diffractionefficiency has been increased to >40%.21 This progressstrongly suggests that TWP holographic recording is promis-ing for practical applications of volume holograms. However,to our knowledge, there is still no theoretical modeling forTWP holographic recording in such photopolymers. Mostexperimental parameters are adjusted by experience. Inorder to find suitable light parameters for achieving high dif-fraction efficiency, it is necessary to carry out a systematicanalysis on TWP recording and to investigate its physicalimplications.

In this paper, we present a theoretical modeling andexperimental verification of the modeling for TWP holo-graphic recording in PQ/PMMA photopolymer. Based onthe principle of TWP holographic recording adapted fromRef. 15, the key issues and parameters for theoretic modelingare described in Sec. 2. In Sec. 3, PQ/PMMA fabrication,TWP holographic recording, and nondestructive readoutare experimentally demonstrated. In Sec. 4, theoretical mod-eling of TWP holographic recording is introduced. Rateequations of population densities are listed and solved, anddynamics of TWP holograms is described. Computer simu-lations on TWP holograms are confirmed with opticalexperiments. 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 PhotochemicalHolographic 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 areα-diketone structure, which can be described by a four-energy-level absorption scheme with cascaded-excitedmetastable intermediate levels. An intermediate level ofmetastable state is essential for this scheme. This metastablelevel can be reached by absorption of only photons withhigher energy and not photons of lower energy, resultingin accumulation of excited molecules in this level.22 Therethey facilitate significant absorption of photons with lowerenergy and, thus, enable holographic recording.

Figure 1 depicts the schematic diagram for the above four-level system. It consists of two singlet states, S0 and Sn, plustwo triplet states, T1 and Tn. Dye molecules are assumed tobe originally in the stable ground state S0. Under two-wave-length illumination, the molecules will be pumped to theirfinal state at Tn, which is a chemically active or radicalstate. Excitation S0 → Sn can be pumped by high-energyphotons at sensitizing wavelength but not by photons withlow energy at writing wavelength. The T1 → Tn transitioncan be pumped by either UV or red photons.

The process of TWP holographic recording begins withsimultaneous illuminations of sensitizing light and writinglight. Dye molecules are first pumped by the uniform sensi-tizing light to go from ground state S0 to Sn. Then, they willundergo 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 radicallevel via T1 → Tn transition. Finally, the excited radicals atTn react with other components to form the final photo-chemical product, which bears index of refraction differentfrom other parts of the photopolymer. Thus, a spatial modu-lation of refractive index or phase hologram that followsbright and dark interference fringes of writing light is cre-ated. During reading, without sensitizing illumination, thehologram can persist against uniform reading illuminationat writing wavelength, and thus, nondestructive readout isachieved.

Ideally, if the T1 → Tn transition can be pumped by onlywriting light, then spatial distribution of radicals and result-ing photoproduct will follow exactly that of the interferencefringes of the object and reference beams; thus, high-effi-ciency holograms can be recorded. However, absorptionband of molecules at T1 state usually covers a broad spec-trum. It often extends to sensitizing light such that part of themolecules will be pumped by the sensitizing light into higherlevel of Tn states. This part should be minimized because itcontains 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, thesensitizing light is necessary because without it the materialis insensitive to writing light and holographic recording isnot possible. Hence, how to adjust intensity ratio of sensitiz-ing to writing lights is a key factor that determines the per-formance of TWP holograms. It shall be found by solving

Fig. 1 Four-energy-level model for two-wavelength photochemical holographic recording.


Lin et al.: Two-wavelength holographic recording in photopolymer using four-energy-level system. . .


rate equations in Sec. 4 that the optimum ratio is related tothe 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 inthis study is described. The methods for determining thesensitizing and writing wavelengths are proposed and exper-imentally performed.

3 Experiments

3.1 Material

PQ/PMMA photopolymer is used in this study. The materialwas fabricated by a two-step thermo-polymerization method.23

Thickness of the sample is 2 mmwith PQ doping concentrationof 0.7 wt.%. In such PQ/PMMA, the main mechanism for holo-graphic recording is the refractive index change induced byphotochemical attachment between one PQ radical and oneresidual MMA under light illumination.24 The diffusions ofPQ and MMA molecules in polymer matrix can be ignored.

3.2 Wavelength Selection for Sensitizing andWriting Light

Wavelengths of sensitizing and writing lights can bedetermined by absorption spectroscopy. Figure 2(a) shows

a UV-VIS absorption spectrum of PQ/PMMA. In order toidentify absorption characteristics of PQ molecules, theabsorption spectroscopy of dilute solution PQ in MMA(3 × 10−10 mole∕l) is measured and showed in the samefigure. The red curve contains two characteristic absorptionpeaks below the blue wavelength (<450 nm). One peak iscentered 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 forthe pumping of S0 → Sn singlet transition, which will befollowed up by ISC of Sn → T1 to reach metastable levelT1. It has been reported that PQ molecules that reach atT1 level via π → π� transition have longer lifetime thanthose via n → π� transition.22,25,26 This will facilitate moreefficient accumulations of PQ molecules. Thus, the wave-length of sensitizing light is chosen to be 325 nm from anHe-Cd laser.

As shown in Fig. 2(a), the PQ/PMMA samples beforeexposure and after saturated exposure are almost transparentfor wavelengths longer than 550 nm. For nondestructivereadout, the material should not be sensitive to readinglight without illumination of sensitizing light. Hence,wavelengths >550 nm could be used for hologramreconstruction. However, in order to write hologramswith TWP recording, the material should be sensitiveto writing light under simultaneous illumination or preex-posure of sensitizing light. Under these requirements,wavelength for writing light can be found by UV-inducedabsorption spectroscopy.

Figure 2(b) shows spectroscopy curves of 325-nminduced absorption change of PQ/PMMA. The absorptionchange spectroscopy was performed when the sample waspreilluminated for 12 min by a uniform 325-nm He-Cdlaser at intensity of 1 W∕cm2. It is found that there is a sig-nificant UV-induced absorbance change in the wide rangefrom 550 to 700 nm. In addition, as illustrated by theblue curve in Fig. 2(a), the photoproduct PQ-MMA hasalmost no absorption at this range. Thus, the measuredresults indicate that the excited PQ molecules at T1 level pro-vide the absorption change so that this range of wavelength issuitable for writing light. For convenience, a red beam withwavelength of 647 nm from a Krypton laser is chosen forwriting and readout.

3.3 TWP Holographic Recording and NondestructiveReading

The schematic diagrams for TWP holographic recording andnondestructive reading experiments are shown in Fig. 3(a).A uniform beam of intensity 0.33 W∕cm2 from a 325-nmHe-Cd laser is used as the sensitizing light, and two s-polar-ized beams (each of 0.22 W∕cm2) splitting from a 647-nmKrypton laser are used as the writing lights. The writing lightsare incident symmetrically on the sample with an intersectionangle of 28 deg (2θ) in the air. By controlling the opening andclosing of shutters S1, S2, and S3, TWP holographic record-ing and reading 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 (byclosing S2) from time to time and the diffracted intensityfrom 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

Abs

orba

nce

Wavelength (nm)

π π*

PQ in MMA

PQ/PMMA

Exposed PQ/PMMA

Abs

orba

nce

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

-ind

uced

abs

orba

nce

chan

ge

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 × 10−10 mole∕L). (b) UV-induced absorption spectroscopy of PQ/PMMA.




the curve IUV ¼ 0 in Fig. 3(b), where diffraction efficiency isdefined as the ratio between the diffracted and the incidentintensities. It is seen that maximum diffraction efficiency ismuch below 10−3%; thus, holographic recording at only redwavelength is almost negligible compared with that with UVsensitization shown in the following.

Then, TWP holographic recording with sensitizing light(by opening S3) is performed. The result is shown as thecurve IUV ¼ 0.74I0 in Fig. 3(b), where I0 represents thesum 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 ordersof magnitude than that without UV light. Thus, the signifi-cance of material sensitization induced by sensitizing light isfully demonstrated.

After holographic recording, the Bragg selectivity curveof the hologram was measured by rotating the samplemounted on a rotational stage. Figure 4(a) shows a typicalcurve for a hologram with ∼40% diffraction efficiency. Itcan be seen clearly that the selectivity curve of the hologramfits well with the Kogelnik’s formula27 without consideringthe absorption at 647 nm. This result indicates that a uniform2-mm-thick hologram has been recorded by TWP method inour PQ/PMMA. In addition, in order to test the persistenceproperty of the TWP hologram, a holographic reconstructionexperiment 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 diffractionefficiency was measured by using detector D1. Figure 4(b)shows the result. It is seen that diffraction efficiencyremains 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 TWPhologram.

4 Four-Energy-Level Model of TWP HolographicRecording

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 equationsfor the population density of PQ molecules at each level canbe written as

dN0

dt¼ −qUV0σUVρUVN0 þ

N2

τ20þ N1

τ10; (1)

dN1

dt¼ qUV0σUVρUVN0 −

N1

τ12−N1

τ10; (2)

dN2

dt¼−qUV2σUVρUVN2−qRσRρRN2þ

N3

τ32þNB

τB2þN1

τ12−N2

τ20;

(3)

dN3

dt¼ qRσRρRN2 −

N3

τ32− k3pN3M; (4)

dNB

dt¼ qUV2σUVρUVN2 −

NB

τB2− kBPNBM; (5)

Sample

BS

MirrorKrypton laser

Krypton laser 2θθ

HeHe--CdCd laserlaserS3

S2

S1

D1

D2

(a)

0 200 400 600 800 10000

5

10

15

20

IUV

= 0.74 I0

IUV

= 0

Writing time (min.)

Dif

frac

tion

effi

cien

cy (

%)

x4000

(b)

Fig. 3 Experimental results. (a) Optical setup. (b) Comparison ofdiffraction efficiency between with and without sensitizing light.

-0.10 -0.05 0.00 0.05 0.100

5

10

15

20

25

30

35

40Experimental data Theoretical

Nor

mal

ized

dif

frac

ted

pow

er

Detuning angle (Deg.)(a)

0 4 8 12 16 20 240

1

2

3

4

5

6

Dif

frac

tion

eff

icie

ncy

(%)

Reading Time (hr.)

(b)

Fig. 4 Experimental result. (a) Bragg selectivity curve of a two-wave-length photochemical (TWP) hologram with diffraction efficiency of40%. (b) Nondestructive readout of the TWP hologram.




whereN0,N1,N2,N3, and NB are population densities (mol-ecules·cm−3) of each level, respectively. M is the concentra-tion of residual monomer, MMA. ρUV and ρR are photon flux(photons · s−1 · cm−2) of UV sensitizing light and red writ-ing light, with definition ρ ≡ I∕ðhνÞ, where h is the Planckconstant, I is the intensity, and ν is the frequency of light.σUV and σR are molar absorption cross-sections (cm2) ofUV and red lights, respectively. qUV0 is the quantum yield(molecules per photon) of UV light for the transitionS0 → Sn. Similarly, qR and qUV2 represent quantum yieldsof red and UV lights, respectively, for the transitionT1 → 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 thefree PQ radicals and MMA at level Tn to form photoprod-ucts. The rate equation of growth of photoproduct densityNPcan be written as

dNP

dt¼ k3PN3M þ kBPNBM: (6)

The photoproduct bears index of refraction different fromother parts of the photopolymer so that the phase hologramcan be recorded as the uniform sensitizing light and thespatially modulated writing light are given. Based on thephotochemical mechanisms in PQ/PMMA, the followingapproximations are made. It is assumed that initially allPQ molecules are at the ground level S0, so at t ¼ 0, N0 ¼NA and N1 ¼ N2 ¼ N3 ¼ NB ¼ NP ¼ 0, where NA is the

doping concentration of PQ molecules. During holographicwriting process, the diffusion of PQ molecules is so smallthat they are distributed among the energy levels purelyaccording to the local intensities of UV and red lights, soNA ¼ N0 þ N1 þ N2 þ N3 þ NB þ NP. Finally, if the writ-ing time is long enough, all PQ molecules will be pumped tobecome radicals at levels Tn and attach with MMA to formfinal photoproduct; thus at t → ∞, NP ¼ 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 sensitizingand writing lights, all the level-relaxation terms in rate equa-tions can be neglected except the term of τ12 for the ISCrelaxation.28,29 For simplicity and without loss of generality,absorption cross-sections for both wavelengths are assumedas unity. This will not affect physical results because actuallyits effect is absorbed in the quantum yield of each level at thatwavelength.

Under these simplifications, population densities of PQmolecules at each level and photoproduct can be solvedand written as

N0ðtÞ ¼ NA expð−qUV0ρUVtÞ; (7)

N1ðtÞ¼qUV0ρUVτ12

1−qUV0ρUVτ12NA½expð−qUV0ρUVtÞ−expð−t∕τ12Þ�;

(8)

N2ðtÞ ¼qUV0ρUVNA exp½−ðqUV2ρUV þ qRρRÞt�

ð−qUV0ρUV þ qUV2ρUV þ qRρRÞð−1þ qUV2ρUVτ12 þ qRρRτ12Þ

þ qUV0ρUVð1 − qUV0ρUVτ12Þ

NA expð−qUV0ρUVtÞð−qUV0ρUV þ qUV2ρUV þ qRρRÞ

−qUV0ρUVτ12

ð1 − qUV0ρUVτ12ÞNA expð−t∕τ12Þ

ð−1þ qUV2ρUVτ12 þ qRρRτ12Þ; (9)

N3ðtÞ ¼NAqRρRqUV0ρUV expð−Mk3PtÞ

ð1 − τ12Mk3PÞðqUV0ρUV −Mk3PÞðqUV2ρUV þ qRρR −Mk3PÞ

−qRρRqUV0ρUVNAðqUV2ρUV þ qRρR −Mk3PÞ−1 exp½−ðqUV2ρUV þ qRρRÞt�


−qUV0ρUV

ðqUV0ρUV −Mk3PÞ1

ð1 − qUV0ρUVτ12ÞqRρRNA expð−qUV0ρUVtÞ

ð−qUV0ρUV þ qUV2ρUV þ qRρRÞ

þ qUV0ρUVτ12ð1 − qUV0ρUVτ12Þ

qRρRNAð1∕τ12 −Mk3PÞ−1 expð−t∕τ12Þð−1þ qUV2ρUVτ12 þ qRρRτ12Þ

; (10)

NBðtÞ ¼NAqUV2ρUVqUV0ρUV expð−MkBPtÞ

ð1 − τ12MkBPÞðqUV0ρUV −MkBPÞðqUV2ρUV þ qRρR −MkBPÞ

−qUV2ρUVqUV0ρUVNAðqUV2ρUV þ qRρR −MkBPÞ−1 exp½−ðqUV2ρUV þ qRρRÞt�


−qUV0ρUV

ðqUV0ρUV −MkBPÞ1

1 − qUV0ρUVτ12

qUV2ρUVNA expð−qUV0ρUVtÞð−qUV0ρUV þ qUV2ρUV þ qRρRÞ

þ qUV0ρUVτ121 − qUV0ρUVτ12

qUV2ρUVNAð1∕τ12 −MkBPÞ−1 expð−t∕τ12Þð−1þ qUV2ρUVτ12 þ qRρRτ12Þ

; (11)




NPðtÞ ¼ NA −NAqRρRqUV0ρUV expð−Mk3PtÞ

ð1 − τ12Mk3PÞðqUV0ρUV −Mk3PÞðqUV2ρUV þ qRρR −Mk3PÞ

−NAqUV2ρUVqUV0ρUV expð−MkBPtÞ

ð1 − τ12MkBPÞðqUV0ρUV −MkBPÞðqUV2ρUV þ qRρR −MkBPÞ

þ�

Mk3PqRρRðqUV2ρUV þ qRρR −Mk3PÞ

þ MkBPqUV2ρUVðqUV2ρUV þ qRρR −MkBPÞ

�

×qUV0ρUVNA exp½−ðqUV2ρUV þ qRρRÞt�

ðqUV2ρUV þ qRρRÞð−qUV0ρUV þ qUV2ρUV þ qRρRÞð−1þ qUV2ρUVτ12 þ qRρRτ12Þ

þ�

qRρRMk3PðqUV0ρUV −Mk3PÞ

þ qUV2ρUVMkBPðqUV0ρUV −MkBPÞ

�×

1

ð1 − qUV0ρUVτ12ÞNA expð−qUV0ρUVtÞ

ð−qUV0ρUV þ qUV2ρUV þ qRρRÞ

þ�−

qRρRMk3Pð1∕τ12 −Mk3PÞ

−qUV2ρUVMkBPð1∕τ12 −MkBPÞ

�×

qUV0ρUVτ12τ12NA expð−t∕τ12Þð1 − qUV0ρUVτ12Þð−1þ qUV2ρUVτ12 þ qRρRτ12Þ

: (12)

NpðtÞ represents temporal evolution of the concentrationof photoproduct that governs the dynamics of TWP holo-graphic recording. Before proceeding to investigation ondynamics of holographic recording, several observationscan be made. First, above solutions show that, withρUV ¼ 0, N0 ¼ NA and N1 ¼ N2 ¼ N3 ¼ NB ¼ Np ¼ 0for all time, no matter what the value of ρR is, i.e., whenthere is no UV light, all PQ molecules will stay at groundlevel and the material is not sensitive to red light. This con-firms the requirement that sensitizing light is necessary forenabling the TWP holographic recording.

Further, τ12 is so quick that the terms involved with expo-nential term of τ12 in Eqs. (9) to (12) can be neglectedcompared with other terms of the solution. Under these sim-plifications, it can be seen that Np (thus, TWP holographicrecording) is mainly conducted by the quantum yields of thematerial, i.e., qUV0, qUV2, and qR as well as photon flux ofsensitizing and writing lights, ρUV and ρR. In the next sec-tion, the methods for finding these material parameters ofPQ/PMMA through light-induced absorption experimentsare described. Then, dynamics of TWP holograms can beinvestigated by adjusting intensity ratio of sensitizing andwriting lights.

4.2 Light-Induced Experiment for Determining LevelParameters

According to the four-energy-level modeling, sensitizinglight is absorbed by PQ molecules both at levels S0 andT1, and writing light is absorbed only by PQ molecules atlevel T1. Molecules that absorb photons will be pumpedto higher energy levels S1 and Tn, respectively. Followingthis consideration, light intensity absorption constant αUVðtÞcan be derived as

αUVðtÞ ∝ qUV0N0ðtÞ þ qUV2N2ðtÞ þ α0: (13)

In the above equation, αUVðtÞ represents light intensityabsorption coefficient of UV light, and α0 accounts forthe material intrinsic absorption coefficient that does not con-tribute to population change, such as PMMA polymer matrixabsorption. Defining absorbance as DUVðtÞ ¼ αUVðtÞd,where d represents material thickness, and substitutingN0ðtÞ and N2ðtÞ from Eqs. (7) and (9) into Eq. (13), theabsorbance can be written as

DUVðtÞ ≈ qUV0NAd

�1þ qUV2ρUV

ð1 − qUV0ρUVτ12Þð−qUV0ρUV þ qUV2ρUV þ qRρRÞ�expð−qUV0ρUVtÞ

þ qUV2NAdqUV0ρUV exp½−ðqUV2ρUV þ qRρRÞt�

ð−qUV0ρUV þ qUV2ρUV þ qRρRÞð−1þ qUV2ρUVτ12 þ qRρRτ12ÞþD0

≡ A1 expð−t∕τ1Þ þ A2 expð−t∕τ2Þ þD0; (14)

where coefficients A1 and A2 are related to quantum yieldsqUV0, qUV2, and qR, and photon flux ρUV and ρR. Also, τ1and τ2 are time constants of the light-induced absorbance,which can be written as

1

τ1¼ qUV0ρUV;

1

τ2¼ qUV2ρUV þ qRρR: (15)

These time constants can be obtained by light-inducedabsorbance experiments; then, by curve fitting, the quantumyields can be found. The setup described in Fig. 3(a) wasused for the absorbance measurements. Two measurementswere 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 intensity0.583 W∕cm2, and the transmitted power was monitoredevery 4 s by UV detector D2 located behind the sample.Experimental result is shown by the curve of small blackcircles in Fig. 5. By curve fitting with solid line, it was foundthat τ1 ¼ 625� 7.2 s and τ2 ¼ 12435� 15.6 s. By settingρR ¼ 0 and ρUV ¼ 9.53 × 1017 s−1 cm−2 in Eq. (15), quan-tum yields of UV light at levels S0 and T1 were obtained tobe qUV0¼1.68×10−21 and qUV2¼8.44×10−23, respectively.

Then, UVabsorbance was measured when the sample wassimultaneously illuminated with UV and strong red lights(shutters S3 and S1 open and S2 closed). UV intensity




was 0.583 W∕cm2 and red intensity was IR ¼ 8.32 W∕cm2

(ρR ¼ 2.71 × 1019 s−1 cm−2). In this situation, red photonswere competing with UV photons for molecules at T1

level; thus, the UV absorbance would be reduced.Experimental result confirmed this prediction, as shownby the curve of small blue squares in Fig. 5. By curve fittingwith dashed lines, it was found that τ1 ¼ 623� 6.8 s andτ2 ¼ 5155� 26.5 s. By using values of qUV0 ¼ 1.68 ×10−21 and qUV2 ¼ 8.44 × 10−23, the value of qR ¼ 4.19 ×10−24 is obtained. These parameters will be used for thefollowing 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 writing light isa spatial variation of interference between object and refer-ence waves, which is written as

IRðxÞ ¼ I0

�1þm1 cos

�2π

Λx

��; (16)

where I0 is the sum of intensity of the object and referencebeams; Λ and m1 are the period and the modulation depth ofthe interference pattern, respectively. After substituting lightintensities IUV and IRðxÞ as well as level parameters qUV0and qUV2, and qR, which were found in Sec. 4.2, intoEq. (12), temporal evolution of the spatial distribution ofphotoproduct PQ-MMA, NPðx; tÞ, can be calculated numeri-cally. Since the main mechanism for holographic recordingin the PQ/PMMA is the refractive index change inducedby photochemical attachment between one PQ radical andone residual MMA, hence, the photo-induced refractiveindex change, or the phase hologram, Δnðx; tÞ, which isproportional to density of photoproduct, can be found asNpðx; tÞ and, thus, can be written as

Δnðx; tÞ ∝ Npðx; tÞ: (17)

As an example, assuming I0 ¼ 0.44 W∕cm2 andIUV ¼ 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 isseen 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

ZΛ∕2

−Λ∕2Δnðx; tÞ cos

�2π

xΛ

�dx: (18)

Then, as mentioned in experimental results, the temporalevolution of diffraction efficiency η can be calculated byusing Kogelnik’s formula:27

ηðtÞ ¼ sin2�n1ðtÞπdλ cos θin

�; (19)

where d is the thickness of the material, λ is the wavelengthof the writing beam in material, and θin is the incident angleof 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 valuesof the hologram amplitude and diffraction efficiency canbe obtained here because Eq. (17) is in proportionalrelationship.

(a)

(b)

Fig. 6 The simulation results on TWP holographic recording.(a) Optical fringes and normalized grating profiles Δnðx; tÞ.(b) Diffraction efficiency (qUV0 ¼ 1.68 × 10−21, qUV2 ¼ 1.06 × 10−23,qR ¼ 4.19 × 10−24, NA ¼ 1.93 × 1018 cm−3, d ¼ 2 mm, θ ¼ 14 deg,Λ ¼ 1.34 μm, IUV ¼ 0.131 W∕cm2, I0 ¼ 0.44 W∕cm2, M ¼ 1, k2 ¼3.96 × 10−5, k3p ¼ kbp ¼ 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/cm2

Fitting curve for IR

=0

Fitting curve for IR

=8.32 W/cm2

325-

nm a

bosr

banc

e

UV illumination time(sec.)

Fig. 5 UV-induced absorbance at 325 nm. Symbols: experiments.Solid lines: curve fitting.




4.4 Investigations on the TWP HolographicRecording

Following the same procedures described in Sec. 4.3, thetemporal evolutions of TWP holographic recordings arecalculated by using the intensity ratio between UV andred beams at IUV∕I0 ¼ 0.74, where I0 is fixed at0.44 W∕cm2. The result is shown as solid blue line inFig. 7. In order to examine these calculations, TWP holo-graphic recording experiments are carried out with thesame beam conditions. The results are shown as blackopen circles in Fig. 7. It is seen that the general trends ofthe theoretical and experimental curves appear to matchwell. Thus, the experiments and calculations are repeatedby using different intensity ratios. The maximum diffractionefficiencies corresponding to the given intensity ratio and thetime to reach this point for all cases are summarized inTable 1. It is noted that simulation only gives relative values.By setting the maximum diffraction efficiency for the caseIUV∕I0 ¼ 0.74 to be equal to that of the experimentalvalue (14.6%), the simulation results of diffraction efficiencyfor other cases are obtained.

As illustrated in Table 1, the smaller intensity ratio giveshigher diffraction efficiency, and it takes longer time to reachthe maximum. The following paragraph shows that the four-energy-level model can explain these characteristics.

First, the characteristic that weaker sensitizing light takeslonger time to reach diffraction maximum is understandable.Since the writing intensity I0 is fixed, hence, smaller inten-sity ratio means weaker sensitizing beam intensity, which inturn implies slower pumping rate to excite PQ moleculesfrom the ground state to the metastable level. Thus, it will

need longer time to supply sufficient PQ molecules atlevel 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 bythe four-energy-level modeling. For a fixed writing intensityI0, smaller intensity ratio means weaker background of UVintensity; thus, the contrast of optical interference can behigher in this case. Further, it in turn implies less UV photonsto compete with red photons for PQ molecules at energylevel T1. Thus, the population density of PQ radicals pro-duced by red light, N3ðx; tÞ, can be enhanced comparedwith that produced by UV, NBðx; tÞ. As a result, the spatialmodulation of the holograms produced by these radicals canbe higher in this case; therefore, it gives higher diffractionefficiency.

The question is, can the diffraction efficiency keep grow-ing when the intensity ratio keeps reducing to indefi-nitely small?

In order to investigate this problem, we followed the sameprocedures to calculate the maximal diffraction efficiency asa function of IUV∕I0. Further, in order to avoid the problemof oscillations in diffraction efficiency that is embedded insine function of Eq. (19), the maximal value of hologramamplitude in Eq. (18), ðn1Þmax, is examined, which corre-sponds to the maximal value of the spatial modulation ofthe radical population density. Figure 8(a) shows the resultsfor the cases I0 ¼ 0.44, 25.2, and 52 W∕cm2, respectively.

It is seen that the three curves almost overlap with eachother, meaning that the hologram amplitude depends only on

0 500 1000 15000

5

10

15

20

Dif

frac

tion

effi

cien

cy (

%)

Writing time (min)

Fig. 7 The experimental result (black circles) and numerical calcula-tions (solid line) for temporal evolution of TWP holographic recording(I0 ¼ 0.44 W∕cm2).

Table 1 Maximum diffraction efficiency and writing time to reachmaximum under different intensity ratios.

ηmax

Writing time toreach 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 1000

1

2

3

4

5 (a)

I0 = 0.44 W/cm2

I0 = 25.2 W/cm2

I0 = 52 W/cm2

IUV

/I0

(n1) m

ax

x10-4

(a)

10-3 10-2 10-1 100100

101

102

103

104

105

(b)

I0

= 0.44 W/cm2

I0

= 25.2 W/cm2

I0

= 52 W/cm2

IUV

/I0

Wri

ting

time

(min

.)

(b)

Fig. 8 Numerical calculations. (a) Maximum hologram amplitude asa function of intensity ratio. (b) Hologram recording time to reachmaximum versus the intensity ratio (qUV0 ¼ 1.68 × 10−21, qUV2 ¼8.44 × 10−23, qR ¼ 4.19 × 10−24).




the intensity ratio and not the beam intensity. This result canbe understood by recalling that amplitude of the hologramdepends only on the difference of the photoproduct densitiesbetween the bright and dark regions. Therefore, a fixedintensity ratio will produce the same value of the spatialmodulation of the refractive index, no matter how thebeam 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 writtenby the attachment of PQ radicals andMMA. The sum of pop-ulation density NBðx; tÞ þ N3ðx; tÞ, which are excited fromPQ at level T1 by UVand red photons, respectively, plays animportant role in determining the concentration of the photo-product NPðx; tÞ. PQ molecules at level T1 are in turnpumped from the ground level S0 by UV photons. If theUV intensity is reduced too much such that the pumpingspeed from S0 → T1 cannot support that for T1 → Tn,then the spatial distribution of the photoproducts becomesdifferent 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 thefundamental grating is decreased. Therefore, the hologramamplitude is decreased if the intensity ratio is reduced toomuch.

Hence, an optimal value exists for the intensity ratioIUV∕I0. The optimal condition can be estimated when thetwo pumping speeds are equal to each other, i.e.,qUV0ρUV ¼ qUV2ρUV þ qRρR, which gives the intensityratio as

IUVI0

¼ qRqUV2

ðλred∕λUVÞðqUV0∕qUV2 − 1Þ : (20)

Taking qUV0 ¼ 2.01 × 10−21, qUV2 ¼ 8.44 × 10−23, andqR ¼ 4.19 × 10−24, which were obtained from light-inducedexperiments, the intensity ratio is 0.0052. This number isvery 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 hologramwriting speed. Figure 8(b) plots the time to reach maximalhologram amplitude as a function of the intensity ratio forthree cases of I0 ¼ 0.44, 25.2, and 52 W∕cm2, respectively.The figure shows that stronger beam intensity takes shorterwriting time to reach the maximal hologram amplitude,which was observed in the experiments.

It is also worthy to note that in Table 1, the time to reachmaximum diffraction efficiency of the experimental resultsdeviates 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 offree PQ molecules has been neglected. In holographicrecording, the writing time is in the order of 1000 min.The diffusion length of PQ molecules in PMMA matrix atroom temperature can be calculated to be in the order of sub-micrometers,30–32 which is a fraction of typical fringe spacingof the interference fringe. Hence, the spatial modulation ofthe hologram will be affected. Thus, a more detailed inves-tigation to account for the spatial diffusion of molecules isnecessary for improving the accuracy of the modeling.

5 ConclusionsWe have presented a methodology for investigating TWPholographic recording in PQ/PMMA. Samples of thickness2 mm have been fabricated. Absorption spectroscopy wasused to determine the wavelengths for TWP holographicrecording in this material. An He-Cd laser at 325 nm waschosen as the sensitizing light and a Krypton laser at647 nm as the writing light. TWP holograms of 53% diffrac-tion efficiency and nondestructive readout of this hologramhave been demonstrated.

The four-energy-level model for the system has beenillustrated. Rate equations are listed and solutions for theamplitudes of the TWP holograms have been found. It isfound that the key parameters that govern the characteristicsof the TWP holograms are quantum yields (qUV0, qUV2, andqR) of the material and photon flux (ρUV and ρR) of the inci-dent lights. The quantum yields of PQ/PMMA material arefound by the UV-induced absorbance experiments. Then,using these material parameters, the TWP holographicrecording has been theoretically calculated and comparedwith the experimental results for different intensity ratiosof the gating and writing lights. It is demonstrated thatthe intensity ratio between sensitizing and writing lightsdetermines the maximal achievable diffraction efficiencyof the hologram and that the beam intensity determinesthe writing speed of holographic recording.

Confirmation of the numerical calculations with experi-mental results demonstrates the validity of this model forTWP holographic recording in PQ/PMMA. This methodol-ogy for investigating the dynamics of TWP holographicrecording can be extended to other photopolymers with sim-ilar photochemical schemes.

AcknowledgmentsFinancial support by National Science Council, Taiwan,under contracts #NSC 101-2221-E-009-112-MY3 and #NSC101-2221-E-009-111-MY3 are gratefully acknowledged.

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Chun-Hua Lin received his BS in electrophysics in 2001 from theNational Chiao Tung University, an MS in electro-optical engineeringin 2003, and a PhD in electro-optical engineering in 2013 fromNational Chiao Tung University in Taiwan, China. He is currently apostdoctoral fellow researcher at the Department of Photonics,National Chiao Tung University, Taiwan. His research interests arein photopolymer, holographic storage, and liquid crystal optics.

Sheng-Lung Cho received his BS in control engineering in 1986 fromNational Chiao Tung University in Taiwan and his MS in industry engi-neering in 1992 from Tsing Hua University in Taiwan. He is currently aPhD 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 hisMS 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 NationalChiao Tung University. His research interests are in holographic stor-age, optical computing, optical devices, holographic materials, andholography for optical information processing.

Sien Chi received his BSEE degree from National Taiwan University,Taipei, Taiwan, and his MSEE degree from National Chiao-TungUniversity, Taiwan, in 1959 and 1961, respectively. He receivedhis PhD degree in electrophysics from Polytechnic Institute,Brooklyn, New York, in 1971. From 1971 to 2004, he was a professorat National Chiao-Tung University. He is currently a chair professor atYuan-Ze University, Taiwan. He is a fellow of the Optical Society ofAmerica. His research interests are optical-fiber communications, fastand slow light, passive optical networks, and microwave photonics.

Ken-Yuh Hsu received his BS in electrophysics in 1973 and his MS inelectronic engineering in 1975, both from National Chiao TungUniversity in Taiwan. He received his PhD in electrical engineeringfrom the California Institute of Technology in 1989. He is currentlya professor at the Department of Photonics & Institute of Electro-Optical Engineering at the National Chiao Tung University. Hisresearch interests are in the area of optical computing, optical neuralnetworks, and holography for information storage and processing.




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