J. Phys. Chem. B 2001, 105, 1763-1769
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Simultaneous Determination of Average Direction of Molecular Orientation and Effective Second Order Nonlinear Optical Constant (|d eff|) by Phase Measurements of Second Harmonic Generation Hiromi Kimura-Suda,*,† Takafumi Sassa,‡,| Tatsuo Wada,†,‡,⊥ and Hiroyuki Sasabe†,‡,§ Core Research for EVolutional Science and Technology (CREST), Japan Science and Technology Corporation (JST), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan, Frontier Research Program (FRP), RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan, and Chitose Institute of Science and Technology, 758-65 Bibi, Chitose, Hokkaido, 066-8655, Japan ReceiVed: September 11, 2000; In Final Form: December 12, 2000
We present a new analytical method of molecular orientation in films using a phase measurement of second harmonic generation (SHG) with a theoretical curve fitting. The new analytical method provides the average direction of molecules and the absolute value of the effective second-order nonlinear optical constant (|d eff|) simultaneously. In conventional methods, the average direction of molecules in a sample has been relatively determined with that in a standard sample having preknown molecular direction. The second harmonic (SH) interference fringe obtained between a reference having preknown molecular direction and the sample has been compared with that between the reference and the standard sample. In the new method, however, the average direction of molecules can be obtained without the standard sample. The value of |d eff| is calculated through the fitting process, the average direction of molecules is determined by the sign or the phase of d eff, which is introduced by a reference. Complete expression with physical meanings is given for the valley points and the contrast of SH interference fringe. There, effect of a lens to focus a fundamental wave to a sample is also taken into account. The new phase measurement of SHG with the curve fitting has been carried out with poled poly(methyl methacrylate) films doped with 2 wt % of p-nitroaniline (PNA/PMMA), which were used as a reference and also as a sample. The accuracy of the new method has been demonstrated in comparison of the value |d eff| of the sample with that determined by Maker fringe measurement. The determined average direction of molecules for the sample was confirmed by experimental geometry of the reference and the sample and also from the poling geometry for the sample. We have shown that the phase measurement of SHG and the curve fitting are useful tools to investigate the molecular orientation.
Introduction In recent years, development of better nonlinear optical (NLO) materials has been attractive in the field of optoelectronics.1,2 In particular, the second-order NLO responses of organic and polymeric materials are an important subject of studies in construction of practical devices using thin films, and still larger second harmonic generation (SHG) is the most important topics.3-7 Toward this subject, it is certainly important to develop molecules possessing larger first-order hyperpolarizability. Moreover, how to increase the degree of polar alignment in the media and how to keep its stability are two questions of importance.8 Spontaneous polar alignment is also an attractive subject in this field. To date, there are some studies on this subject: the polar alignment of molecules unsuited for an electric field poling has been carried out without the poling, and the polar alignment is thermodynamically stable.9,10 Appearance of spontaneous * Corresponding author:
[email protected]. † Japan Science and Technology Corporation (JST). ‡ RIKEN (The Institute of Physical and Chemical Research). § Chitose Institute of Science and Technology. | Present address: Department of Material Science & Engineering, University of Washington, Seattle, WA 98195. ⊥ Present address: Supramolecular Science Laboratory, RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
polar alignment is dependent on the molecular structure, and designed by their surroundings, i.e., temperature, solvent, steric hindrance, hydrogen bond, van der Waals force, and so forth. Consequently, it is important to investigate molecular orientation in the media in order to explore the mechanism of spontaneous polar aliment and improve its performance. Measurements of molecular orientation have been also the subject of a number of studies.11-13 Phase measurements of SHG are used widely for determination of the average direction of molecules.14-21 Although, in conventional phase measurement of SHG, the average direction of molecules in a sample has been relatively determined in comparison with that of a standard sample having preknown molecular direction, our method enables to obtain the average direction of molecules without the standard sample. Moreover, our method does not only provide the magnitude of NLO response, i.e., absolute value of the effective second-order nonlinear optical constants (|d eff|), but it reduces measurement time and allows the acquisition more information without changing the target. The purpose of this work is to improve the phase measurement of SHG by refining the optical alignment using a more accurate characterization method. First, we will describe the basic concept for the phase measurement of SHG based on SHG interferometry to determine the average direction of NLO molecules and the value of |d eff|.
10.1021/jp003202q CCC: $20.00 © 2001 American Chemical Society Published on Web 02/10/2001
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Second, we will present the configuration of the SHG interferometer adopted in the measurement and the theoretical analysis of interference fringes as well. Then, we will show experimental results of the poled polymer films by means of the phase measurement of SHG and perform the theoretical curve fitting to the data. Finally, we will discuss the accuracy and the advantage of our fitting program. Theory for Phase Measurement of SHG Basic Concept for Defining Average Direction of Molecules. Here, we explain how the average direction of molecules in a polar thin film can be expressed through an electric field of an SH wave generated in the medium. In the following model, i-j-k laboratory axes are considered. For simplicity, the collinear interaction along the i-axis is treated between a nonlinear polarization wave and an SH wave, both propagating in z direction in the film, one of which surface is at z ) 0 and the other at z ) L. The film is assumed to be transparent for all the related light waves. Generally, solving Maxwell’s nonlinear wave equation, with applying a slowly varying amplitude approximation, gives the SH wave (E ˜ 2ω i (z)) generated in the medium as follows:
E ˜ 2ω i (L) ) -iC
-ik ∫0LP˜ 2ω i (z)e
2ω(L-z)
i
dz
(1)
where k2ω denotes the phase velocity of the SH wave and i (z) indicates a nonlinear polarization wave for SHG, reP ˜ 2ω i 2ω 2ω 2 spectively. C is a constant given by (k2ω 0 ) /(2ki ) (k0 : wavenumber for the SH wave in a vacuum). In general, the nonlinear polarization wave has a different phase velocity (kNL i ) from that of the SH wave due to wavelength dispersion of the medium and can be expressed as -i(ki P ˜ 2ω i (z) ) Pi(0)e
NLz+φ
0)
(2)
where φ0 indicates an initial phase of the nonlinear polarization wave at z)0. Pi(0) denotes the amplitude of the nonlinear polarization wave and involves information about the average direction of NLO molecules and the value of |d eff|. It is explained in detail later. Finally, from eqs 1 and 2, we can obtain the generated SH wave using Pi(0) and φ0 by -i(φL+φ0) E ˜ 2ω i (L) ) -i2CPi(0){sin(∆k‚L/2)/∆k}e
(3)
where ∆k ) kNL - k2ω and φL ) (k2ω + kNL i i i i )(L/2). ∆k represents a phase mismatch between the nonlinear polarization wave and the SH wave, and φL represents a phase change generated in the medium for the SH wave. Here, we focus on the coefficient Pi(0). For simplicity, we consider that the medium is composed of an NLO molecule having a rigid rod-like structure with one primary charge-transfer (CT) axis, and those molecules are almost aligned in one direction. When the medium is pumped with a fundamental wave with an amplitude Ei, Pi(0) can be expressed by using the oriented-gas model22
Pi(0) ) β/KKK〈cos3[K,ei]〉{Ei}2
(4)
where ei is a unit vector for the i-axis. K shows the unit vector along the molecular axis (CT-axis) and defines the direction of / each NLO molecule included in the medium. βKKK indicates the first-order hyperpolarizability component of the molecule, including local field factors. The brackets represent the degree
Figure 1. Configuration of the SHG interferometer. The fundamental beam irradiates the reference with an incident angle (θR), and both the fundamental beam and the SH beam are incident on the sample with an incident angle (θS). The phase generator is rotated along an axis perpendicular to the optical axis with an angle θPG. Meaning of symbols: θPG,in, angle of refraction in the phase generator; LPG, a thickness of phase generator; lRS, a distance between the reference and the sample.
of the contribution of all the NLO molecules to the exiting field / 〈cos3[K,ei]〉 indi{Ei}2. Therefore, the absolute value of βKKK cates the magnitude of the nonlinear polarization wave excitation and corresponds to |d eff|. If the sign of the brackets is / 〈cos3[K,ei]〉 ) |d eff|eiδ considered, it can be rewritten as βKKK (δ ) 0, π). Keeping in mind that generation of NLO properties is based on noncentrosymmetric properties of the medium, the brackets indicate how large the noncentrosymmetry is represented along the i-axis, or in other words, it indicates the degree to which the averaged molecular axis 〈K〉 is projected on the i-axis. Therefore, the sign of the brackets, or the phase δ, represents direction of 〈K〉 compared to that of the i-axis. If the sign is negative 〈cos3[K,ei]〉 < 0, or δ ) π, it indicates that 〈K〉 and ei orient in the opposite direction, and the positive sign 〈cos3[K,ei]〉 > 0, or δ ) 0, in the same direction. As these two situations can change the sign of Pi(0), it results in the phase shift of P ˜ 2ω i (z) (eq 2) by δ. This means that, from eq 3, those two situations result in the phase shift of the generated SH wave. Hence, the evaluation of δ from the SH wave leads us to the determination of the average direction of NLO molecules with respect to the direction of the i-axis, and can be performed by phase-detection techniques based on SHG interferometry. In the SHG interferometry technique, a reference material or an oscillator is introduced to generate an SH wave (reference SH wave), which interferes with an SH wave generated from a sample (signal SH wave). There, the phase shift δ has been determined by comparing the SHG interference fringe obtained from a standard sample having preknown molecular direction with the fringe from a sample having unknown molecular direction. In this study, we directly evaluate both δ and |d eff| for a sample by analyzing the SHG interference fringe obtained between a reference and a sample. In the next section, the theoretical analysis of the fringes is described. Configuration of the Phase Measurement of SHG. Figure 1 shows the configuration of the SHG interferometer used in the present experiments. The p-polarized reference SH wave and the p-polarized signal SH wave interfere with each other, and the interfered power is evaluated at the point A. In this configuration, the sample material surface and the reference material surface are set to be opposite each other.
Molecular Orientation Measurement
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First, we consider that the fundamental wave has large enough beam width whole through the pass, so that we do not have to take into account overlap of beam cross sections between the reference SH wave and the signal SH wave. This assumption gives insight as to how δ and |d eff| are theoretically involved in the interference fringe. Then, later we expand it to a general case in which a lens is used to focus a fundamental wave to a sample. Incident angles of the fundamental wave to both the reference and the sample are represented as θR and θS, respectively. A phase generator is located between the reference and the sample and is rotated with an angle θPG to modulate the interfered SH power. The incident angle of the reference can be changed to adjust the reference SH power compared with the signal SH power. Taking into account reflection losses at all of the boundaries and optical path changes induced by the phase generator and by film of both the reference and the sample, the reference SH wave (E ˜ 2ω ˜ 2ω R ) and the signal SH wave (E S ) observed at point A can be expressed as
E ˜ 2ω R (θR,θPG,θS)
)
2ω 2ω T2ω R (θPG,θS)ER (θR)exp[-i{φR (θR) + φ2ω l (θPG) + φ0R + δR}]
φωl )
( )
2π ω ω [nairlRS + (LPG/cos θPG,in ){nωPG - nωair cos(θPG ω λ ω )}] (10) θPG,in
where λω is a wavelength of fundamental wave, and n2ω air and nωair are refractive indices of air at the SH wave and the fundamental wave, respectively. lRS indicates the distance between the sample and the reference. LPG represents a thickness 2ω ω and θPG,in are angles of refraction of the phase generator. θPG,in in the phase generator for the SH wave and the fundamental ω wave, respectively. n2ω PG and nPG denote refractive indices of the phase generator for the SH wave and the fundamental wave, respectively. Here, if we assume that the thickness of the reference and the sample are thin enough to give negligible phase retardation 2ω (φ2ω R (θR) and φS (θS)), the interfered SH power at the point A 2ω (Ptotal) can be expressed as
(5)
(x )
0/µ0 [A(θR,θPG,θS) + 2 ω B(θR,θPG,θS)cos{φ2ω l (θPG) - 2φl (θPG) + δR - δS)}] (11)
P2ω total )
where
and 2 2ω ω 2ω E ˜ 2ω S (θR,θPG,θS) ) {TS (θR,θPG)} ES (θS)exp[-i{φS (θS) +
2ω 2 A(θR,θPG,θS) ) [T2ω R (θPG,θS)ER (θR)] + 2 [{TωS (θR,θPG)}2E2ω S (θS)] (12)
2φωl (θPG) + φ0R + δS}] (6) and respectively. T2ω R (θPG,θS) indicates the field transmittance for the reference SH wave, and TωS (θR,θPG) for the fundamental 2ω wave. E2ω R (θR) and ES (θS) indicate amplitudes of the reference and the signal SH waves, respectively, and they can be expressed, according to W. N. Herman et al.,23 as follows: eff ω 2 E2ω R (θR) ) AR(θR)|dR (θR)|{E0 }
(7)
eff ω 2 E2ω S (θS) ) AS(θS)|dS (θS)|{E0 }
(8)
valley ω valley φ2ω l (θPG ) - 2φl (θPG ) + δR - δS ) (2m + 1)π/2
Equations 7 and 8 are essentially the same as (2C{sin(∆k‚ L/2)/∆k}) in eq 3 except that they include reflection losses for both the fundamental wave and the SH wave and that they include no phase terms, which are involved in eqs 5 and 6. 2ω φ2ω R (θR) and φS (θS), in eqs 5 and 6, indicate a phase retardation generated in the reference and the sample, respectively, and correspond to φL in eq 3. φ0R and 2φωl (θPG) + φ0R indicate the initial phase of the nonlinear polarization wave of the reference and the sample, respectively, and correspond to φ0 in eq 3. The phase shifts obtained from the average direction of NLO molecules are indicated by δR and δS for the reference and the sample, respectively, and they can have the value of 0 ω or π, as was explained before. φ2ω l (θPG) and φl (θPG) indicate phase retardation generated by both the phase generator and the air between the reference and the sample for the SH wave and for the fundamental wave, respectively. They can be given as follows:
( )
(13) Equation 11 shows that SH power includes two components; one is the DC component and the other is the modulated AC component with respect to the rotation angle θPG of the phase generator. The latter component varies the SH power sinusoidally and gives a fringe form. There, the valley points of the fringe (θvalley PG ) are given by
and
φ2ω l )
2 2ω ω 2ω B(θR,θPG,θS) ) 2T2ω R (θPG,θS){TS (θR,θPG)} ER (θR)ES (θS)
2π 2ω 2ω [n2ω air lRS + (LPG/cos θPG,in){nPG λω/2 2ω n2ω air cos(θPG - θPG,in)}] (9)
(14)
where m indicates an integer. The modulation depth of the fringe curve shown by the term B(θR,θPG,θS) includes |d eff| of the reference and the sample through eqs 7 and 8, respectively. If |d eff| of the reference is already known, |d eff| of the sample can be obtained from analyzing the modulation depth of the fringe. The valley points of the fringe include information about the average direction of molecules of both the reference and the sample. If the average molecular direction of the reference, that is δR, is already known, the value of |δR - δS| gives the average direction for the sample. That is to say, |δR - δS| ) 0 indicates that the average direction of the sample is in the same direction with the reference with respect to the polarization direction of the fundamental wave, and |δR - δS| ) π indicates that in the opposite direction. Here, we consider a general case in which a lens is introduced to focus the fundamental wave to the sample. In this case, the lens creates differences in both beam width (spot size) and power density of the fundamental beam between the reference and the sample. These two factors affect the contrast of the fringe (ratio of the AC component to the DC component). That is to say, the beam width difference generates an uninterferred SH wave from the reference which affects the DC component of the
1766 J. Phys. Chem. B, Vol. 105, No. 9, 2001
Figure 2. Schematic of corona poling system. The wire is positioned above ground electrode on which PNA/PMMA film is heated. Corona discharge is achieved by high voltage power supply. Positive ions are created and deposited on the top of the surface. Two kinds of poling geometry are carried out by laying film face down (a) and the film face up (b).
fringe, and the power density difference gives different amplitudes of the reference and the signal SH waves which affect both the AC and the DC components. Taking the ratio S of the SH beam width at the sample to the reference, these factors can be included in eq 12 as follows: 2 2ω A(θR,θPG,θS) ) [T2ω R (θPG,θS)ER (θR)] + 2 (1/S)[{TωS (θR,θPG)}2E2ω S (θS)] (15)
This term shows that introducing a lens or letting S be either smaller or larger than 1 makes the contrast of the fringe lower. Experimental Section Poled Polymer Film Preparation. Thin films of poled poly(methyl methacrylate) (PMMA) doped with p-nitroaniline (PNA) are used as a reference and as a sample (PNA/PMMA films). Both films for the reference and the sample were prepared to have almost the same film properties including the second harmonic coefficients. PMMA (Grade: H-1000B, Mn ) 3.1 × 104, Mw ) 5.8 × 104) was obtained from Kyowa Gas Kagaku Kogyo. Glass transition temperature (Tg) of PMMA was 92 °C. PNA (purity 99+%) was purchased from Tokyo Kasei Organic Chemicals. PMMA was completely dissolved in chloroform and mixed with PNA. PNA concentration was 2 wt % in PMMA. After mixing, the solution was poured onto a clean slide glass plate and cast at 3000 rpm for 10 s by a spin coating method. These films were dried at 60 °C (near the boiling temperature of chloroform) for 24 h under the vacuum condition in order to remove residual solvent. The direction of the dipole moment of PNA in PMMA was controlled by a corona discharge technique (corona poling),24-26 as shown in Figure 2. Two kinds of poling geometry were employed using positive corona discharge: laying the film face down (a) and laying the film face up (b). The PNA/PMMA films were heated with a heater for 30 min at 100 °C (> Tg of PMMA) with an electric field, and then the films were quickly cooled to room temperature under the field to freeze the dipolar alignment of PNA. In both geometries, PNA molecules can be aligned in one direction perpendicularly to the film surfaces. The film thicknesses were measured by a surface roughness measurement system (ULVAC, DEKTAK IIA).
Kimura-Suda et al.
Figure 3. Optical arrangement for phase measurement of SHG. Meaning of symbols: F1, color filter; F2, CuSO4 filter; F3, laser line filter (λ ) 532 nm); L, lens; P, polarizer; PG, phase generator; PM, photomultiplier tube; Ref, reference; Sa, sample.
Linear Optical Analysis. Optical absorption spectra of both unpoled and poled thin films were measured by a UV-VISNIR scanning spectrophotometer (Shimadzu, UV-3100PC). The decrease of absorption peaks due to PNA can be observed if the PNA molecules are oriented perpendicular to the substrate. The refractive indices of films were determined by a polarization modulated spectroscopic ellipsometer (JASCO, M-150). SHG Measurement. The second harmonic coefficient of the poled PNA/PMMA films was determined by a rotational Maker fringe method23,27 using a Q-switched Nd:YAG laser (SpectraPhysics GCR-230) operating 10 Hz repetition rate and 10 ns pulse width. Either the p-polarized or s-polarized fundamental beam operating at a wavelength of 1064 nm was passed through a color filter and then introduced to the PNA/PMMA film. The p-polarized SH signal (λ ) 532 nm) obtained in transmission was passed through a laser line filter (λ ) 532 nm), and it was detected by a photomultiplier tube and averaged by a boxcar integrator. The SH signals (Maker fringes) from the poled PNA/ PMMA films were measured at room temperature with incident angles from -80° to 80°. A y-cut quartz crystal plate (d11 ) 0.3 pm/V) was employed as a reference. The second harmonic coefficients were determined from the Maker fringe measurement, and then values of |d eff| corresponding to the experimental geometry were calculated both for the reference and the sample,23 in which d31 ) (1/3)d33 was assumed. The |d eff| of the reference was to be used in the fitting process of the interference fringe, and that of the sample was to be used for comparison of that obtained from the phase measurement of SHG. Phase Measurement of SHG. The new optical arrangement of the phase measurement of SHG was improved from a system of Kajikawa et al.,28 as shown in Figure 3. In the former system, the average direction of molecules in a sample was relatively determined in comparison with that of a standard sample having preknown molecular direction. The SH interference fringe obtained between a z-cut quartz as a reference and the standard sample was compared with that obtained between the quartz and the sample. In the measurement, the average direction of molecules in both the reference and the standard sample was required to determine that of the sample. However, the new method enables to obtain the average direction of molecules in a sample without the standard sample. The average direction of molecules in the sample is determined through fitting process
Molecular Orientation Measurement to SH interference between the reference and the sample. Moreover, the new method also provides the magnitude of NLO response, i.e., |d eff|, at the same time. The value of d eff of the reference is required to calculate |d eff| in the sample. The fundamental beam source was a p-polarized Q-switched Nd:YAG laser, and the p-polarized SH signal was detected as mentioned above. An SH interference fringe was obtained by the new SHG interferometer. The fundamental beam, after passing through a color filter, was radiated onto the reference with incident angle θR. A certain amount of fundamental wave was converted to an SH wave by passing through the medium of reference, and the rest of the fundamental wave was passed through the reference without converting to the SH wave. A sample was placed behind the reference at incident angle of θS. Both incident angles θR and θS were varied to optimize the contrast of the SH interference with attention paid to the influence of physical conditions, e.g., surface defects and the rotational axis, and then both incident angles were fixed during the measurement. The distance between the reference and sample was measured by a ruler as 280 mm. A glass plate inserted between the reference and sample acted as a phase generator. By varying the incident angle of the phase generator, the SH intensity was oscillated in a periodic fashion, as described in the theory section. The incident angle of the phase generator (θPG) was changed from -50° to 50°. In the optical arrangement, the lens with 500 mm focal length was put before the reference to focus the fundamental beam, and then the effect of the lens was investigated. In this measurement, the poled PNA/PMMA film was employed instead of a quartz plate as the reference, because the film preparation was easy and the contrast (modulation depth) of SH interference could be simply optimized by the concentration of PNA and/or the incident angle of the fundamental beam. If there are large differences of SH intensity between the sample and the reference, it is difficult to obtain a sufficient contrast. However, the sufficient contrast of SH interference leads to the accurate theoretical curve fitting. Therefore, it is necessary to optimize contrast of the SH interference. For the reference in the new method, the poled PNA/PMMA film is more suitable than the quartz plate. Finally, the SH intensity of the reference was measured without the sample. The fundamental beam passed through the color filter was irradiated on the reference, and both the fundamental and SH beams were incident on the rotating phase generator. Then the SH beam was detected. This measurement was required to determine the amplitude of the fundamental wave in the fitting process, which is described in the next section. Curve Fitting of SH Interference Fringe. We first apply a theoretical curve fitting to the SH interference in order to obtain the average direction of molecules and the |d eff| value simultaneously. The amplitude and valley points of the SH interference are key parameters for the theoretical curve fitting. Figure 4 shows the schematic flowchart of the curve fitting process. First, the positions of valley points are shifted on the axis of θPG to be symmetrical with respect to θPG ) 0. Second, the valley points are fitted to the theoretical valley points described in eq 14. In this step, the average direction of the sample (δS) can be obtained. The fitting is executed using the following variables: the distance between the sample and reference (lRS), the thickness of phase generator (LPG), refractive indices of the phase generator at 532 and 1064 nm (n2ω PG and nωPG), and δS. The other parameters comprising eq 14 are fixed as constant. There, we set the phase shift term of the reference
J. Phys. Chem. B, Vol. 105, No. 9, 2001 1767
Figure 4. Schematic flowchart of the curve fitting process. Meaning of symbols: LPG, the thickness of the phase generator; lRS, the distance between the sample and reference; n2ω PG, refractive index of the phase generator at 532 nm; nωPG; refractive index of the phase generator at 1064 nm; Eω0 , the amplitude of the fundamental beam; δS, phase shift of the sample; δR, phase shift of reference; λω, wavelength of the ω fundamental beam; n2ω air , refractive index of air at 532 nm; nair, eff refractive index of air at 1064 nm; |deff |, absolute values of | and |d R S the effective second-order nonlinear optical constants of the reference and sample; S, beam width ratio of the SH beams at the sample to that at the reference.
Figure 5. Absorption spectra of unpoled and poled PNA/PMMA films. Dotted line, unpoled film; Solid line, poled film.
(δR) as 0. This means that if the obtained δS ) 0, the average direction of the sample is in the same direction as the reference with respect to the polarization direction of the fundamental wave; if δS ) π, it is in the opposite direction. Then, Eω0 , the amplitude of the fundamental beam, is calculated by fitting of SH intensity obtained from the reference without sample with eq 11 with B(θR,θPG,θS) ) 0, taking account |deff R |, determined beforehand by the conventional Maker fringe method. Finally, |deff S | can be calculated by fitting the amplitude of SH interference to the theoretical one described in eq 11, using |deff S | and S as variables. Results and Discussion Linear Optical Properties of PNA/PMMA Films. Figure 5 shows absorption spectra of the unpoled and poled PNA/ PMMA films. A strong absorption is observed near 366 nm, and there is no absorption at 532 and 1064 nm, which indicates that the PNA/PMMA film is transparent at both harmonic and fundamental frequency. The absorption peak near 366 nm is decreased after corona poling. This means that the PNA chromophore is oriented to the surface normal in PMMA.3
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TABLE 1: Parameters for Theoretical Curve Fittinga LPG (mm) LRef (µm) LSa (µm) lRS (mm) lair (mm)
λ (nm) nRef nSa nSub nPG
1.09 2.51 2.50 280 118 ω
2ω
1064 1.4950 1.4950 1.5194 1.5194
532 1.4970 1.4970 1.5367 1.5367
a
LPG; thickness of the generator, LRef; thickness of the reference film, LSa; thickness of the sample film, lRS; distance between the reference and the sample, lair; coherence length of air, λ; wavelength, nRef; refractive index of the reference film, nSa; refractive index of the sample film, nSub; refractive index of substrates.
Figure 6. SH intensities of the reference film passed through the phase generator as a function of rotational angle of phase generator. P-polarized fundamental beam is radiated to the reference, SH beam and fundamental beam are passed through the phase generator. P-polarized SH signals are detected.
Refractive indices of unpoled PNA/PMMA film were measured as a function of wavelength by the ellipsometer. The refractive indices at 532 and 1064 nm are 1.497 and 1.495, respectively. The thicknesses of PNA/PMMA films as the reference and the sample are 2.51 and 2.50 µm, respectively. SH Interference Fringe of Poled PNA/PMMA Film and Curve Fitting. The Maker fringe measurement as described in the preceding section cannot show an average direction of the molecules. A complete description of the molecular orientation is only obtainable by the phase measurement of SHG. The reference and the sample were both prepared by the poling geometry (a) in Figure 2. The SH signals were monitored as a function of incident angle θPG with every 0.2° in order to obtain complete valley points of interference fringe, because the features of the valley are important to evaluate the shift of the fringe. The SH intensities at θR ) θS ) 45° were chosen to check our measuring system and fitting program. Note that in this condition, since both the reference and the sample had almost the same film property (Table 1) and almost the same effective second-order coefficients as indicated below, E2ω R (θR) and E2ω S (θS) in eqs 7 and 8, respectively, had the same values. Figure 6 shows the SH intensity as a function of the rotation angle of the phase generator obtained for the reference without the sample. The SH intensity is decreased with increase of the incident angle θPG, because the fundamental beam is slightly reflected by the phase generator, and the reflectivity is increased with increase of the incident angle θPG. The amplitude of the fundamental wave was obtained by fitting this result with |deff R (45°)| of 0.28 pm/V obtained from the Maker fringe measurement.
Figure 7. SH interference fringe between the two poled PNA/PMMA films and its curve fitting. The SH interference is obtained with the lens. Open circles are plots of the experimental result. Solid line is a curve fitting.
Figure 8. SH interference fringe between the two poled PNA/PMMA films and its curve fitting. The SH interference is obtained without the lens. Open circles are plots of the experimental result. Solid line is a curve fitting.
Figures 7 and 8 show the SH interference fringes and the fitted curves with and without the lenses, respectively. Even at the valley points, the SH signals are not vanishing (nonzero). This result indicates that SH intensity of the sample is slightly different from that of the reference. The interference fringe is shifted by π when a sign of the incident angle θR or θS is changed or when the poling geometry is changed ((b) in Figure 2). The lens creates differences in both spot size and power density of fundamental beam between the reference and the sample. The fringe curve without the lens showed the DC component being close to 0 and gave higher contrast. It can be explained by letting A(θR,θPG,θS) ≈ B(θR,θPG,θS) in eq 11, which gives the DC component to be 0. This approximation is reasonable, because generally the field transmittance ω (T2ω R (θPG,θS), TS (θPG,θS)) is roughly 1 in such a small angle between -50° and 50°. On the other hand, introducing the lens lowered the contrast. This is because the lens made the spot size of the fundamental waves different on the reference and the sample, leading to a low contrast, as explained previously. However, in the case without the lens, the accuracy of the fitted curve near 0° was not in good agreement with the experimental data, whereas the case with the lens gave good agreement through the entire scanned range. Enlarging the spot size by removing the lens introduced inhomogeneity of the films, such as thickness and the molecular orientation variations, which deviated from the theory. In our model, the lens to focus the spot size performed an important function to obtain good quality SH interference. From the fitting of the curve with the lens, |deff S (45°)| of 0.30 (45°)| ) 0.28 pm/V. On the pm/V was obtained by using |deff R other hand, |d eff| of the sample at an incident angle of 45° was calculated to be 0.30 pm/V from the analysis of the Maker fringe
Molecular Orientation Measurement measurement. The value from the interference fringe fitting showed good agreement with that from the Maker fringe analysis. From this fitting, δS of 0 was also obtained. This result showed that the sample had the same average direction of NLO molecules compared with that of the reference with respect to the polarization direction (p-polarization) of the fundamental wave, and it coincided with the relation between the average molecular directions of the reference and of the sample shown in the experimental configuration in Figure 3. When the sample poled with the geometry (b) in Figure 2 was mounted with 45° incident angle, the fitted result gave π for δS. These results confirmed the validity for determination of the average molecular direction with the fitting. It is concluded from these results that the fitting curve reproduced the measured interference fringe well and also brought a reliable, effective second-order nonlinear optical constant and the average direction of NLO molecules for the sample. Conclusion We have shown a new analytical method of molecular orientation in films by a phase measurement of SHG and the theoretical curve. The analytical method makes it possible to determine the average direction of molecules and the value |d eff|, and they are simultaneously calculated by the theoretical curve fitting to the SH interference. We have demonstrated the curve fitting to the poled PNA/PMMA films, because the polarity of films could be easily controlled by corona poling. In our SHG interferometer, the SH interference is generated between the reference and the sample films, and modulated by rotating the phase generator inserted between the two. We have shown physical meanings of curve fitting performed to the SH interference fringe. The fitting program was applied to the SH interference, and it was demonstrated that our curve fitting was in good agreement with experimental data in the poled PNA/ PMMA films. Moreover the fitting program taking account of the different of the spot size is useful in our optical arrangement. The resultant value of |deff S | was verified by that obtained from Maker fringe analysis. The average direction of molecules of the sample determined by the fitting coincided with that determined by the poling geometry. In conventional phase measurement, the average direction of molecules in the sample has been relatively determined with a
J. Phys. Chem. B, Vol. 105, No. 9, 2001 1769 standard sample having preknown molecular direction. In our method, however, the average direction of molecules and the value of |deff S | can be obtained by fitting process to the SH interference between the reference and the sample without the standard sample. Thus, our phase measurement of SHG and the curve fitting program procedure can be widely used as an effective method for investigation of NLO molecules. References and Notes (1) Weder, C.; Wrighton, M. S.; Spreiter, R.; Bosshard, C.; Gu¨nter, P. J. Phys. Chem. 1996, 100, 18931. (2) Tykwinski, R. R.; Gubler, U.; Martin, R. E.; Diederich, F.; Bosshard, C.; Gu¨nter, P. J. Phys. Chem. B 1998, 102, 4451. (3) Page, R. H.; Jurich, M. C.; Reck, B.; Sen, A.; Twieg, R. J.; Swalen, J. D.; Bjorklund, G. C.; Willson C. G. J. Opt. Soc. Am. B 1990, 7, 1239. (4) Brouye`re, E.; Persoons, A.; Bre`das, J. L. J. Phys. Chem. A 1997, 101, 4142. (5) Simpson, G. J.; Rowlen, K. L. J. Phys. Chem. B 1999, 103, 3800. (6) Ashwell, G. J.; Jackson, P. D.; Crossland, W. A. Nature 1994, 368, 438. (7) Twieg, R. J.; Dirk, C. W. J. Chem. Phys. 1986, 85, 3537. (8) Marder, S. R.; Perry, J. W. AdV. Mater. 1993, 5, 804. (9) Kimura-Suda, H.; Wada, T.; Zhang, Y.; Sasabe, H. Nonlinear Optics 1999, 22, 91. (10) Kimura-Suda, H.; Zhang, Y.; Sassa, T.; Wada, T.; Sasabe, H. AdV. Mater. 2000, 12, 1196. (11) Goh, M. C.; Hicks, J. M.; Kemnitz, K.; Pinto, G. R.; Bhattacharyya, K.; Eisenthal, K. B.; Heinz, T. F. J. Phys. Chem. 1988, 92, 5074. (12) Campbell, D. J.; Higgins, D. A.; Corn, R. M. J. Phys. Chem. 1990, 94, 3681. (13) Higgins, D. A.; Byerly, S. K.; Abrams, M. B.; Corn, R. M. J. Phys. Chem. 1991, 95, 6984. (14) Kemnitz, K.; Bhattacharyya, K.; Hicks, J. M.; Pinto, G. R.; Eisenthal, K. B.; Heinz, T. F. Chem. Phys. Lett. 1986, 131, 285. (15) Berkovic, G.; Shen, Y. R.; Marowsky, G.; Steinhoff, R. J. Opt. Soc. Am. B 1989, 6, 205. (16) Huang, J. Y.; Lewis, A. Biophys. J. 1989, 55, 835. (17) Sato, O.; Baba, R.; Hashimoto, K.; Fujishima, A. J. Electroanal. Chem. 1991, 306, 291. (18) Higgins, D. A.; Abrams, M. B.; Byerly, S. K.; Corn, R. M. Langmuir 1992, 8, 1994. (19) Liu, X.; Liu, L.; Lu, X.; Zheng, J.; Wang, W.; Fang, Y. Thin Solid Films 1992, 217, 174. (20) Tang, Z.-R.; McGilp, J. F. J. Phys.: Condens. Matter 1992, 4, 7965. (21) Smiley, B. L.; Vogel, V. J. Chem. Phys. 1995, 103, 3140. (22) Zyss, J.; Oudar, J. L. Phys. ReV. A 1982, 26, 2028. (23) Herman, W. N.; Hayden, L. M. J. Opt. Soc. Am. B 1995, 12, 416. (24) Pauley, M. A.; Guan, H. W.; Wang, C. H. J. Chem. Phys. 1996, 104, 6834. (25) Eich, M.; Sen, A.; Looser, H.; Bjorklund, G. C.; Swalen, J. D.; Twieg, R.; Yoon, D. Y. J. Appl. Phys. 1989, 66, 2559. (26) Guan, H. W.; Wang, C. H. J. Chem. Phys. 1993, 98, 3463. (27) Jerphagnon, J.; Kurtz, S. K. J. Appl. Phys. 1970, 41, 1667. (28) Kajikawa, K.; Wang, L.-M.; Isoshima, T.; Wada, T.; Knoll, W.; Sasabe, H.; Okada, S.; Nakanishi, H. Thin Solid Films 1996, 284, 612.
