Modeling Photobleaching of Optical Chromophores: Light-Intensity

Department of Chemistry, and Department of Materials Science and Engineering, ...... Moshrefzadeh , R. S.; Misemer , D. K.; Radcliffe , M. D.; Francis...
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J. Phys. Chem. C 2008, 112, 8051–8060

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Modeling Photobleaching of Optical Chromophores: Light-Intensity Effects in Precise Trimming of Integrated Polymer Devices† Greeshma Gupta* and William H. Steier Ming Hsieh Department of Electrical Engineering, UniVersity of Southern California, Los Angeles, California 90089-0483

Yi Liao,‡ Jingdong Luo, Larry R. Dalton, and Alex K.-Y. Jen Department of Chemistry, and Department of Materials Science and Engineering, UniVersity of Washington, Seattle, Washington 98195 ReceiVed: December 1, 2007; ReVised Manuscript ReceiVed: December 25, 2007

We present a model for the photobleaching of nonlinear optical (NLO) chromophores, via photo-oxidation, using either high-intensity or low-intensity light sources. A closed-form expression is derived for calculating the temporal evolution of bleaching-induced refractive index change, averaged over the thin-film depth. The averaged values are appropriate for analytically calculating corresponding changes in the effective index of optical waveguides. This applies to precise trimming of the resonant wavelength and coupling in chromophoredoped polymer microring resonator (MRR) devices. In high-intensity (few kW/cm2) laser photobleaching experiments for trimming of MRR coupling, the observed refractive index changes are nearly 1 order of magnitude less than those predicted by low-intensity bleaching curves, for the same total exposure energy. An in-depth review of the photophysics and photochemistry of photo-oxidation of aromatic molecules is presented here, revealing that a high-intensity excitation source is likely to cause chromophore ground-state depopulation, due to the long lifetime of the triplet state. This theory also explains why photobleaching efficiency can be increased by pulsing the excitation, because the chromophore ground-state is allowed to replenish between bleaching pulses. For the first time, to our knowledge, the concept of saturated absorption is applied to model the effect that high-intensity light has on photobleaching-induced index change. The values of the photostability figure-of-merit and saturation intensity for π-conjugated NLO chromophores, such as CLD-1, are obtained here by fitting experimental data. We also note that light-intensity is known to affect the rate of varied photoreactions, such as laser ablation of polymers and human tissue and plant photosynthesis, which share striking photophysical similarities with photobleaching. 1. Introduction Organic molecules such as laser dyes and nonlinear optical (NLO) chromophores undergo photobleaching when excited by a UV, visible, or infrared light source. Photobleaching or photodegradation may be undesirable or, on the contrary, may be useful in different photonics applications. For the case of lasers and optically pumped amplifiers based on dyes, as well as for polymer electro-optic devices based on NLO chromophores, photobleaching due to the pump or input light source causes device performance to deteriorate with time.1,2 On the other hand, photobleaching is very useful for patterning lowloss NLO polymer waveguides3,4 and for postfabrication trimming of NLO polymer devices.5–8 In the context of photobleaching being detrimental, there is great interest in estimating the photostability of the absorbing molecules.2,9–11 With regard to photobleaching used for defining and/or trimming thin-film polymer waveguides, the interest goes further, into the domain of modeling the change in material refractive index as bleaching progresses.12–14 We point out two limitations of the existing models. First, refractive index changes are calculated as a function of both † Part of the “Larry Dalton Festschrift”. * Corresponding author. Tel: 213-740-4408. Email: [email protected]. ‡ Current address: Department of Chemistry, University of Central Florida, Orlando, FL 32816-2366.

waveguide depth and bleaching time. In order to focus on the time-evolution of macroscopic device parameters such as effective index and coupling between waveguides of directional couplers or microring resonator (MRR) devices, we would like to encapsulate the depth-dependence. This can be done by considering the average value of refractive index, averaged over waveguide depth. It is this averaged value of refractive index that we calculate in this paper. Using this we can analytically solve for time-evolution of macroscopic quantities, without the need for a mode-solver. Second, to the best of our knowledge, the experimental data modeled to date12–14 was always obtained using UV or visible bleaching light sources of low intensity, of the order of up to a few hundred mW/cm2. We found that these models fail to predict the refractive index changes observed in our experiments of high-intensity (few kW/cm2) laser bleaching of MRR coupling regions. The (visible) wavelength of the laser source used was near the linear absorption maximum of the chromophore. The bleaching time is only between a few seconds and a minute, but the high intensity results in total exposure energy of the order of a few kJ/cm2. In spite of this large amount of energy, the observed refractive index change, ∆n, is 1 order of magnitude lower than that predicted by curve fitting of lowintensity bleaching data, for a bleaching time corresponding to the same total exposure energy. Moreover, for equal amounts

10.1021/jp711359j CCC: $40.75  2008 American Chemical Society Published on Web 05/08/2008

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Figure 2. Chemical structures of (a) the YLD161b chromophore and (b) the AJL8 chromophore.

Figure 1. (a) Chromophore-doped bus waveguide vertically coupled to passive MRR, bleached by a circular green laser beam spot of diameter 10 µm. (b) Lateral coupling of ring and waveguide, both made of chromophore-doped polymer, bleached simultaneously by an elliptical red laser beam spot 2 µm wide and 7 µm long, by scanning the laser beam relative to the sample at a constant speed of 100 µm/s.

of total light energy incident on similar chromophores, we found that ∆n is nearly 1 order of magnitude greater for the case when we wait 10 s between repeated 20 ms bleaching pulses, as opposed to bleaching continuously. Postfabrication trimming of Mach–Zehnder interferometers using high-intensity light has been demonstrated earlier,6,7 but the refractive index change was not modeled. In order to understand and predict the changes in refractive index caused by high-intensity photobleaching, a model is required that takes into account the saturation effects inherent in the use of high-intensity light. Development of such a model is the subject of this paper, a preview of which is presented in the following paragraphs. We have successfully applied photobleaching to precisely trim the coupling in MRR devices. A laser beam spot of intensity on the order 1–10 kW/cm2 was tightly focused onto the coupling region of polymer microring resonator devices, as illustrated in Figure 1. This was used to trim the ratio of power coupled between the MRR and the vertically or laterally coupled bus waveguide, via photobleaching-induced change in the refractive index of the chromophore-doped polymer material. The host polymer is amorphous polycarbonate (APC). The chromophores used are YLD161b and AJL8, which have peak absorption wavelengths in the visible region. The chemical structures and absorption spectra of these chromophores are shown in Figures 2 and 3, respectively. They are similar to π-conjugated polyenebased CLD-1 in chemical structure.15 Hence, in the presence of ambient oxygen-containing air and an excitation light source of wavelength in the peak absorption band of the chromophore molecules, the predominant mechanism of photochemical bleaching would be photo-oxidation by singlet oxygen2,15 and not trans–cis isomerization.10,16 The photophysics and photochemistry of the photo-oxidation process are detailed in section 2, with emphasis on the effects of high light-intensity. Regardless of the exact mechanism of photodegradation, the resulting decrease in material refractive index with time is modeled using the Beer–Lambert law and a local photobleaching rate equation, as reviewed in section 3. Conventionally, the

Figure 3. (a) Absorbance of the YLD161b chromophore in chloroform. The absorption maximum in APC is expected to be in the green wavelength region, at about 565 nm. (b) Absorbance of AJL8 in APC, with a red absorption peak wavelength of 711 nm.

refractive index is evaluated as a function of polymer film depth and bleaching time. However, here we derive a simple closedform expression for the refractive index averaged over film depth and as a function of time only. This enables easy, efficient, and accurate prediction of the corresponding evolution of thin-film device parameters such as MRR power coupling ratio and resonant wavelength, during postfabrication trimming. Considering device fabrication using photobleaching, this can provide a good estimate of the time within which certain design goals would be met, for example, desired phase-matching conditions for NLO devices. In section 4, we verify the above for the case of low-intensity bleaching. We note that ref 16 suggests that high-intensity photobleaching leads to rapid oxygen depletion in the polymer film, which in turn is the cause for a bleaching rate different from that of

Modeling Photobleaching of Optical Chromophores low-intensity bleaching. However, as explained in section 2, we propose that depopulation of the ground-state of chromophores is the factor that limits photo-oxidation under conditions of high-intensity bleaching. Intense laser radiation causes a large number of aromatic molecules to be “trapped” in the first excited triplet state, which can have a relatively long lifetime of up to 1–20 s in rigid polymer matrices.17 This is a case of saturated absorption of light, a nonlinear optical effect that is fundamental to the operation of dye lasers18 and optical limiters.19 In section 5, we enhance the bleaching model of section 3, by applying the concept of saturated absorption in order to account for the effect of high-intensity photobleaching. By considering the intensity-dependence of the absorption crosssection, we are able to successfully explain data obtained from our experiments on high-intensity photobleach trimming of MRR coupling. By using our models to fit experimental data, we obtain values of the photostability figure-of-merit and saturation intensity for the chromophores considered here. These values can be used to predict low- and high-intensity bleaching rates of these and similar π-conjugated NLO chromophores in photobleaching experiments for trimming and/or fabrication of electro-optic as well as passive polymer devices. The effect of light-intensity on photobleaching of NLO chromophores doped in polymer microphotonic devices is studied for the first time here, to the best of our knowledge. However, extensive studies have been carried out on the effects of light intensity on various other photoreactions, such as, laser ablation of man-made polymeric materials as well as human tissue20–22 and photosynthesis in chlorophyll-containing plant cells.23–26 The analysis here is partly inspired by, and may contribute back to, a deeper understanding of the interaction of light with organic molecules in analogous systems of physical, chemical and/or biological interest. This is discussed in section 6. 2. Photophysics and Photochemistry of Bleaching NLO Chromophores The physics and chemistry of photoreactions of aromatic organic molecules have been studied widely. Studies have shown that singlet oxygen plays an important role in photobleaching of aromatic molecules. Singlet oxygen is well-known to be formed by triplet energy transfer from the excited triplet state of aromatic molecules.27 This would encompass π-conjugated NLO chromophore molecules,28 including the stilbene- and polyene-based chromophores.10 The most common mechanism by which singlet oxygen causes bleaching is photoperoxidation of ground-state electron-accepting aromatic molecules, which include condensed aromatics such as anthracene27 and dyes and chromophores.29 Hence, as indicated in ref 16, we believe that the oxidation mechanism for π-conjugated chromophores containing electron-accepting CdC bonds would also be peroxidation of the ground-state chromophores. However, prior to the actual chemical reaction, there is a series of photophysical processes initiated by the absorption of incident light, in which the magnitude of light intensity can play an important role.27 This is what we review and apply here. We note that highintensity light is not likely to cause two-photon absorption in our experiment. This is because the wavelength of the monochromatic bleaching laser is close to the linear absorption maximum of the chromophore. Hence, bleaching is due to onephoton absorption.30,31 Referring to Figure 4, the overall photobleaching mechanism may be explained as follows.

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Figure 4. Electronic states of a chromophore molecule, with the respective valence electron spins and state lifetime, τ, and the various interstate processes. Intersystem crossing (ISC) is the only process not involving photons and is indicated by dashed arrows.

By absorption of incident UV or visible light photons, chromophore molecules in the ground singlet state S0 are excited to the first excited singlet state S1 (S0 f S1). The singlet states have paired valence electron spins, whereas, in the triplet state, the valence electron spins are unpaired. In the presence of highintensity incident light, higher excited singlet states may be formed, which relax back to S1,17 and although spin-forbidden, significant S1 f T1 intersystem crossing occurs, leading to a larger number of molecules in the triplet state.17,27 Interaction of S1 and T1 states with dissolved oxygen, which naturally occurs in the paramagnetic triplet state (3O2), enhances S1 f T1 and T1 f S0 intersystem crossing (ISC).27 Hence, the following processes lead/contribute to and/or compete with the formation of singlet oxygen (1O2), as outlined in ref 32, which presents studies on aromatic molecules used as sensitizers for photo-oxidation.

S1 + 3O2 f T1 + 3O2

(1)

S1 + 3O2 f T1 + 1O2

(2)

S1 f T1

(3)

T1 + 3O2 f S0 + 3O2

(4)

T1 + O2 f S0 + O2

(5)

3

1

Processes 2 and 5 involve the transfer of electronic energy from the excited-state of the chromophore to the oxygen molecule, resulting in the formation of singlet oxygen. In processes 1 and 4 there is simply an exchange of vibrational energy. Chromophore molecules, M, in the ground-state S0 react with singlet oxygen to give peroxide, which is believed to be the main bleached product

M(S0) + 1O2 f MO2

(6)

We note that reaction 6 is the actual bleaching reaction, in which (singlet) oxygen is consumed. Also, only ground-state chromophores can participate in this reaction. In the presence of high-intensity light, S0 f S1 excitation is very rapid: the lifetime of the absorbing ground state is ∼1 µs, as shown in section 5. Some S1 state molecules relax back to the S0 state by fluorescence, but due to intense laser radiation, a large fraction of the S1 state molecules transition to the T1 state by the abovementioned processes, up until process 3. For aromatic molecules dissolved in rigid polymer matrices, the lifetime τ of the S1 state is a few nanoseconds, whereas the lifetime of the T1 state is of the order of a few milliseconds to a few seconds.33,34 Due to the long lifetime of the triplet state, normal phosphorescence

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Gupta et al. in turn reduces the optical susceptibility.39 This translates to a decrease in refractive index of the material. 3. Modeling of Photobleaching-Induced Refractive Index Change

Figure 5. Calculated normalized concentration of oxygen, C(x ) 0, t)/C1, as a function of diffusion time, at the base of a spin-cast polymer film of thickness 2 µm. The oxygen concentration just within the top surface is C1 ) Sp, where S is the solubility of O2 in the polymer and p is the partial pressure of O2.

(T1 f S0) and the relaxation processes (4) and (5) are relatively delayed. Hence, the ground-state S0 is temporarily depleted,17 and reaction 6 is inhibited until the S0 state is replenished. We would like to point out that, at any time, reaction 6 is not likely to be limited by the depletion of oxygen. Oxygen diffuses into the polymer film continually and fairly rapidly. For a spin-cast film of thickness l as depicted in Figure 5, the oxygen concentration C versus diffusion time can be estimated at a particular depth x within the film, given the initial O2 concentration C0 within the volume, and the constant O2 concentration C1 at the permeable top surface that is exposed to a source of oxygen35,36 (ambient air in our case). C1 ) Sp, where the solubility S of oxygen in polycarbonate-like polymers has an average value of ∼0.1 cc(STP) cm-3 atm-1,37 and the partial pressure p of atmospheric O2 is 0.21 atm. For the extreme case of complete oxygen depletion within the bleached polymer volume, C0 ) 0. The oxygen diffusion coefficient D, in amorphous polycarbonate with 25 wt % chromophore, would be close to the value of 2.4 × 108 cm2/s, quoted in Table 2 of ref 38. Using the equation for diffusion in an infinite plane sheet, for small times,36 we find that oxygen diffusion into a 2 µm thick polymer film is greater than 70% complete in 100 ms, as shown in Figure 5. We note that in reality, the bleached volume is not infinite, and is also surrounded on all four sides by polymer (cladding material and/or unbleached core region) with oxygen concentration ≈C1, indicating that the actual diffusion time is less than that estimated above. In section 5, by fitting high-intensity bleaching data, we find that the triplet state lifetime of the chromophores considered here is greater than or close to the above diffusion time of 100 ms. Hence, although certain molecules are trapped in the excited triplet state, oxygen diffuses into the thin film at a fairly fast rate, replenishing amounts used up for the production of singlet oxygen via process 2. Hence processes 4 and 5 would not be inhibited by the absence of oxygen. Triplet state molecules relax via these processes to replenish the ground-state molecules, which are then oxidized by existing 1O2 or with process 5 generated 1O2, to yield peroxide, as per reaction 6. Photoperoxidation occurs at the sites of the CdC double bonds in the “bridge” that connects the donor and acceptor groups of the chromophore molecules considered here (Figure 2). This disrupts the conjugated π system of the chromophore, causing the molecular hyperpolarizability to decrease, which

In refs 1 and 9, a simple physical model is used to obtain the temporal evolution of the concentration of dye molecules in a sample, as it is bleached. This is then used to calculate the change in transmission through the sample. Here, we use this model to calculate the temporal evolution of refractive index due to photobleaching of chromophore molecules, using a monochromatic (laser) source. Similar to the analysis in ref 9, we consider light to be incident in the z direction, with z ) 0 at the top interface of the waveguide core layer of thickness L. At time t ) 0, when exposure begins, we assume chromophore molecules are uniformly distributed with an initial concentration of N0 mol/ m3. As bleaching progresses, the chromophore concentration varies with depth z and time t. At a particular time t, the volumetric concentration at depth z is denoted by N(z, t) and the chromophore concentration per unit area, within a thickness or depth z of the core layer is denoted by J(z, t). If we denote the volumetric concentration of the remaining chromophore and the bleached product by Nc and Nb, respectively, we have Nc(z, t) + Nb(z, t) ) N0. For both molecular species, their concentration per unit area, in a depth z is given by

∫0z Nc(z ′ , t) dz′ z Jb(z, t) ) ∫0 Nb(z ′ , t) dz′ Jc(z, t) )

(7) (8)

The initial condition is

Jc(z ) L, t ) 0) ) N0L ) J0

(9)

The intensity of bleaching light, denoted by I, is in units of W/m2. The corresponding photon flux or photon irradiance is given by

ip )

1 I (hc ⁄ λb) NA

(10)

which is in units of mol/(s m2). Here h, c, and NA are the following physical constants: Planck’s constant, speed of light, and Avogadro’s number, respectively. λb is the wavelength of the monochromatic bleaching laser. The photon flux or photon irradiance at depth z and time t is exponentially related to the density of absorbing molecules via their absorption cross-sections, and may be written as

ip(z, t) ) ip0 exp[-σcJc(z, t) - σbJb(z, t)]

(11)

where ip0 is the incident photon flux corresponding to the incident intensity I0 at z ) 0 and σc and σb are the absorption cross-sections of the chromophore and bleached product respectively (in units of m2/mol). Here ip, ip0, σc, and σb denote values measured at the single bleaching wavelength, λb. We note that the bleached product (peroxide) is nearly transparent or very slightly absorbing at the bleaching wavelength, as indicated for AJL8/APC in ref 40. We would expect the same for the YLD161b/APC system, as the two chromophores are similar. At a particular bleaching wavelength λb, each chromophore molecule absorbs an average of B photons before it undergoes reaction 6 to give a bleached product. That is, an average molecule goes through a cycle of absorption, excitation and

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relaxation back to S0, B number of times before it reacts with singlet oxygen to be bleached. B is called the bleaching number and 1/B is the related probability or the quantum efficiency for bleaching.1 B/σ is the photostability figure of merit. The local rate equation for bleaching is

∂Nc(z, t) ) -σcNc(z, t)B-1ip(z, t) ∂t

(12)

Integrating both sides of eq 12 and using eq 11 and then eq 7, we obtain -1

dJc(L, t) σcB ip0 ) dt ∆σ

L

∫ 0

∂ [-∆σJc(z, t)] × exp[-∆σJc(z, t)] × ∂z exp(-σbN0z)dz (13)

Equation 13 cannot be solved analytically. However, with the approximation that σbN0L 1800 s. The index change derived from MRR coupling ratio change was ∆n ) 6 × 10-3, nearly 1 order of magnitude higher than the case of high-intensity bleaching of YLD161b. This may seem surprising considering that the total exposure energy in both cases is the same: 48 000 J/cm2. However, our model based on the long lifetime of the triplet state and resulting saturated absorption can explain this as follows. As shown in Table 2, τg is very short; at high intensities, ground-state molecules absorb very quickly. Due to the relatively long lifetime of the excited triplet state, during a single exposure period of 20 ms, the AJL8 ground-state population is essentially depleted, i.e., absorption is saturated. Waiting for 10 s or longer between each laser scan allows for the triplet state molecules to relax back to the ground state, without excessive light energy being expended. Triplet state relaxation also leads to the production of more singlet oxygen, via process 5 mentioned in section 2. Thus, during the wait periods of nonexposure, bleaching continues. Hence, the wait time is productive, while light energy is conserved. Thereby the “scan and wait” or pulsed method of bleaching is more efficient than continuously bleaching one spot at a time. We understand that this comparison has been made for two different chromophores. However, they are very similar in structure and the host material is the same. Since AJL8 was not bleached continuously in time, we cannot obtain fitted values of Is and other parameters for this case. CLD-1 high-intensity bleaching data was obtained from ref 16, as part of experiments carried out for bias trimming of Mach–Zehnder devices.7 For experimental parameters as summarized in Table 2, continuous bleaching of one arm of a CLD1/APC Mach–Zehnder for 12 s caused a bias shift of 16°,16 which corresponds to ∆n ≈ ∆neff ≈ 3.1 × 10-4. Is ) 41 mW/ cm2 fits this data well, yielding τe ) 74 ms, and the estimated bleaching curve shown in Figure 11. Referring to Table 2, the fitted values of Is for YLD161b and CLD-1 are physically appropriate, because by using eq 22, they yield values of τe ≈ τT that fall within the several ms-s range of measured triplet state lifetimes of aromatic molecules in rigid media.33,34 Also, for both chromophores, the value of τe ≈ τT is close to or greater than 100 ms, which is the time in which oxygen diffusion is more than 70% complete. This validates our supposition that the relatively long triplet state lifetime limits the high-intensity bleaching rate. We note that the accuracy of the fitted value of Is depends on the accuracy of the previously obtained B parameter. The value BCLD for CLD-1 was obtained in section 4 by a good fit to low-intensity experimental data, whereas for YLD161b, BYLD was estimated to be the same as that of CLD-1. It would be more accurate to estimate that (1/2)BCLD e BYLD e 2BCLD. This would lead to an error of nearly a factor of 2 in the fitted value of Is (from eqs (26) and (15)). With the range considered, the maximum value for B would be 2.4 × 104, yielding Is ) 25.2 mW/cm2, and a minimum value of τe ) 162 ms, which is still greater than 100 ms.

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TABLE 2: High-Intensity Bleaching: Summary of Bleaching Experiment Conditions and Resulting Refractive Index Change and Values of Relevant Parameters Required for/Obtained from Theoretical Fitting chromophore B/σeff (in APC with ip0 J0 σc Is τe (τT) w ) 1/3) λb (nm) I0 (kW/cm2) (101 mol s-1 m-2) tb (s) L (µm) (10-4 mol/m2) (m2/mol) ∆n (10-4) τg (µs) (mW/cm2) (ms) (1028 m-2) CLD-1 AJL8 YLD161b

660 655 532

0.018 16.0 0.8

0.1 88.0 3.6

12 3 60

2.5 2.0 0.85

6. Discussion 6.1. Axial Chromophore Molecules and Effect of Polarized Bleaching Light. Dye and chromophore molecules are not isotropic as assumed in the analysis presented here.1 Rather they are axial and preferentially absorb light polarized along their long dimension. When bleached by polarized laser light, as done in our experiments, molecules normal to the optical electric field are the last to be dissociated. Considering the angular distribution of molecules with respect to the E field, it can be analytically shown that fitted B/σ for the axial case would simply be 9/5× that of the isotropic case.1 This involves considering the mean absorption cross-section, which is one-third the value of the peak cross-section for a molecule that is oriented along the field. 6.2. Intensity Effects on Photoreaction Rates in Analogous Organic Systems. Photoreactions of organic molecules span a wide spectrum, ranging from photosynthesis in chlorophyllcontaining living plant cells, to laser ablation of human tissue, to photobleaching of man-made chromophore-doped polymers, used in modern microphotonic devices. As mentioned in the Introduction, our supposition that light intensity has a nonlinear effect on absorption of NLO chromophores, and hence on their photoreaction rate, was in part inspired by similar effects observed in polymer and tissue ablation20,22 and also in photosynthetic reaction centers.26 Further, we found that the photophysics of excited states, formation of singlet oxygen, and photochemical bleaching of chlorophyll are an important part of photosynthesis-related studies.26 This underlying unity between seemingly diverse systems of chlorophyll-containing plant cells and chromophore-doped man-made polymers resonates with similar views expressed by Sir Jagdish Chandra Bose, when he found striking similarity in the response curves of metallic tin and muscles:53,54 an example of philosophic truths proffered by developing modern science.54 6.3. Role of Triplet State in Photoreactions of Varied Chromophores. The role of the excited triplet state in photoreactions has been studied for decades.55 The study of excited-

Figure 11. Estimated temporal evolution of depth-averaged refractive index (λ ) 1.55 µm) for high-intensity red laser bleaching of CLD1/APC thin film, based on fitting of experimental data for 12 s of continuous bleaching (inset). B ) 1.2 × 104 and Is ) 41 mW/cm2.

9.6 7.7 5.5

5987 1044 5500

3.1 60.0 7.0

167.0 1.1 5.1

41.0

74

0.054

12.6

325

7.73

state properties of metal-containing chromophores such as, porphyrins including chlorophyll, and carotenoid polyenes, has received much attention recently19,56,57 due to its importance in understanding biological processes and developing photonics applications such as optical limiters and bioinspired energy converters. On the basis of photophysical processes, lifetimes of the excited triplet and singlet states of these chromophores have been measured. However, to our knowledge, such studies have not been carried out for π-conjugated NLO chromophores. The analysis in this paper shows that precise knowledge of the triplet state lifetime of a NLO chromophore can help predict its photobleaching dynamics. We hope the model proposed here encourages excited-state studies for this important class of chromophores. 7. Conclusions In summary, an attempt has been made to gain insights into the finer details of the photophysics and photochemistry of bleaching of π-conjugated NLO chromophores, at the molecular level, which can help us understand observations made at the device level. UV or visible light excitation enables the formation of singlet oxygen, via interactions of excited states of chromophore molecules with triplet oxygen. Ground state chromophore molecules react with singlet oxygen (with a probability ) 1/B) to give a bleached product (peroxide). In the presence of a high-intensity excitation source, the ground-state population is likely to be depleted due to the relatively long lifetime of the triplet state of aromatic molecules in rigid media such as polymer thin films. This condition of saturated absorption limits the bleaching rate. We have applied the photodegradation rate modeling of ref 9, widely used to calculate change in sample transmittance, to now calculate change in refractive index for the first time. The result is temporal evolution of refractive index averaged over film depth. Using this average value, it is very easy to simulate the corresponding change in macroscopic device quantities such as resonant wavelength and power coupling ratio of MRRs. For cases where the photon irradiance ip0 is a few orders of magnitude higher than the chromophore density per unit area, J0, we have further developed the above model to include intensity-dependence of the chromophore absorption crosssection, based on the well-known concept of saturated absorption. Our experimental results for high-intensity bleach trimming of MRR coupling have been modeled well by this enhanced model. Though high light-intensity speeds up bleaching, the same total energy dose causes less refractive index change for the high-intensity case as compared to low-intensity bleaching. This is because, photobleaching, just like photosynthesis, depends on photon flux and not energy flux.58 A major advantage of using high-intensity bleaching sources like laser diodes is that their light can be focused in a very small area, providing trimming of very selective regions on integrated chips. Also, these sources are monochromatic, and modeling bleaching caused by a single wavelength is easier and more accurate, as compared to bleaching with a broadband source such as white light.14

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We also compare two different methods of high-intensity bleaching: continuous bleaching for the case of YLD161b and the “scan and wait” or pulsed bleaching method for an AJL8 device. Laser scanning and waiting between scans is a more efficient method of high-intensity bleaching, as it allows for the absorption to recover, via triplet state relaxation. This paper puts forth a general procedure for calculating how a particular material system will bleach with time, for the case of high-intensity light. The bleaching number B can be derived by numerical fitting of data for low-intensity bleaching experiments, and then the saturation intensity Is can be obtained by fitting highintensity bleaching data. The triplet state lifetime τT can be derived from the value of Is. Conversely, if τT is known for the chromophore, Is can be calculated prior to experimentation, and/or can be verified precisely. To our knowledge, the triplet state lifetime of polyene-based NLO chromophores is derived here for the first time, for the cases of YLD161b and CLD-1. Photostability figure-of-merit values of NLO chromophores YLD161b and AJL8 have been derived here for the first time to our knowledge. In particular, the values of B/σ for AJL8 may be of great interest, as novel binary chromophore systems with very high EO coefficients contain AJL8-type chromophores.59 The nonlinear effects of high-intensity light on photobleaching of NLO chromophores is partly inspired and supported by similar observations in photosynthesis and polymer/tissue ablation. This encourages seemingly diverse fields to gain from each other by exploring their underlying unity. Acknowledgment. We thank Y.-H. Kuo, H. Tazawa, and N. P. Bhatambrekar for their valuable guidance and help at various stages of this work, in both experimental and/or theoretical aspects. We are also grateful to A. Stapleton and Prof. J. D. O’Brien for their help in phase characterization of MRRs, leading to conclusive results regarding photobleach trimming induced changes. This research was made possible by the support provided by the DARPA MORPH program. Note Added after Print Publication. Figures 9 and 10 were incorrect in the version of the manuscript published on the Web on May 8, 2009 (ASAP) and in print (J. Phys. Chem. C 2008, 112, 8051–8060). The correct version was published on June 4, 2009 on the Web, and an Adddition and Correction appears in print (DOI: 10.1021/jp904432s). References and Notes (1) Kaminow, I. P.; Stulz, L. W.; Chandross, E. A.; Pryde, C. A. Appl. Opt. 1972, 11, 1563. (2) DeRosa, M. E.; He, M.; Cites, J. S.; Garner, S. M.; Tang, Y. R. J. Phys. Chem. B 2004, 108, 8725. (3) Kim, S.; Geary, K.; Fetterman, H. R.; Zhang, C.; Wang, C.; Steier, W. H. Electron. Lett. 2003, 39, 1321. (4) Otomo, A.; Stegeman, G. I.; Flipse, M. C.; Diemeer, M. B. J.; Horsthuis, W. H. G.; Mohlmann, G. R. J. Opt. Soc. Am. B 1998, 15, 759. (5) Hwang, W. Y.; Kim, J. J.; Zyung, T.; Oh, M. C.; Shin, S. Y. Appl. Phys. Lett. 1995, 67, 763. (6) Chen, A.; Chuyanov, V.; Marti-Carrera, F. I.; Garner, S.; Steier, W. H.; Mao, S. S. H.; Ra, Y.; Dalton, L. R.; Shi, Y. IEEE Photonics Technol. Lett. 1997, 9, 1499. (7) Kuo, Y. H.; Steier, W. H.; Dubovitsky, S.; Jalali, B. IEEE Photonics Technol. Lett. 2003, 15, 813. (8) Poon, J. K. S.; Huang, Y.; Paloczi, G. T.; Yariv, A.; Zhang, C.; Dalton, L. R. Opt. Lett. 2004, 29, 2584. (9) Dubois, A.; Canva, M.; Brun, A.; Chaput, F.; Boilot, J. P. Appl. Opt. 1996, 35, 3193. (10) Galvan-Gonzales, A.; Belfield, K. D.; Stegeman, G. I.; Canva, M.; Marder, S. R.; Staub, K.; Levina, G.; Twieg, R. J. J. Appl. Phys. 2003, 94, 756. (11) Rezzonico, D.; Jazbinsek, M.; Gunter, P.; Bosshard, C.; Bale, D.; Liao, Y.; Dalton, L.; Reid, P. J. Opt. Soc. Am. B 2007, 24, 2199. (12) Ma, J.; Lin, S.; Feng, W.; Feuerstein, R. J.; Hooker, B.; Mickelson, A. R. Appl. Opt. 1995, 34, 5352.

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