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High Extinction Polarimeter for the Precision Measurement of the In-Plane Optical Anisotropy of Molecular Monolayers Guanjiu Fang, Joseph E. Maclennan, and Noel A. Clark* Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309 Received March 19, 2010. Revised Manuscript Received May 24, 2010
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A polarimeter using selected Glan-Thompson polarizers, a spatially filtered probe laser beam, precision polarizer orientation, and spatially filtered output coupling into an optical fiber achieves a static extinction ratio between crossed and parallel polarizer and analyzer orientations of I^/I ≈ 2 10-10. This instrument allows the detection of retardance as small as 0.0015 nm to better than 1%, enabling the first detailed study of the in-plane birefringence of molecular monolayers. We demonstrate the performance of the polarimeter with measurements of the photoinduced birefringence of azobenzene-based monolayers self-assembled on glass.
(1) Fuchs, A.; Kanoufi, F.; Combellas, C.; Shanahan, M. E. R. Colloids Surf., A 2007, 307, 7. (2) Rickert, J.; Weiss, T.; G€opel, W. Sens. Actuators, B 1996, 31, 45. (3) Pope, N. M.; Kulcinski, D. L.; Hardwick, A.; Chang, Y.-A. Bioconjugate Chem. 1993, 4, 166. (4) Kim, D.-H.; Shin, D.-S.; Lee, Y.-S. J. Peptide Sci. 2007, 13, 625. (5) Masuda, Y.; Sugiyama, T.; Lin, H.; Seo, W. S.; Koumoto, K. Thin Solid Films 2001, 382, 153. (6) Somlo, B.; Gupta, V. Mech. Mater. 2001, 33, 471. (7) Laibinis, P. E.; Whitesides, G. M. J. Am. Chem. Soc. 1992, 114, 9022. (8) Hillebrandt, H.; Tanaka, M. J. Phys. Chem. B 2001, 105, 4270. (9) Ichimura, K.; Suzuki, Y.; Seki, T.; Hosoki, A.; Aoki, K. Langmuir 1988, 4, 1214. (10) Yi, Y. W.; Furtak, T. E.; Farrow, M. J.; Walba, D. M. J. Vac. Sci. Technol., A 2003, 21, 1770. (11) Yi, Y. W.; Farrow, M. J.; Korblova, E.; Walba, D. M.; Furtak, T. E. Langmuir 2009, 25, 997. (12) Wang, R.; Guo, J.; Baran, G.; Wunder, S. L. Langmuir 2000, 16, 568. (13) Sagiv, J. J. Am. Chem. Soc. 1980, 102, 92. (14) Schadt, M.; Helfrich, W. Appl. Phys. Lett. 1971, 18, 127. (15) Schiekel, M. F.; Fahrenschon, K. Appl. Phys. Lett. 1971, 19, 391. (16) Soref, R. A. J. Appl. Phys. 1974, 45, 5466. (17) Clark, N. A.; Lagerwall, S. T. Appl. Phys. Lett. 1980, 36, 899.
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liquid-crystal films either by depolarized reflection microscopy18 or by using ellipsometry with oblique incidence.19 Here we describe a visible-light polarimeter for the precision measurement of the in-plane birefringence of subnanometer-thick molecular films deposited on solid substrates, demonstrating its performance by studying the photoinduced optical anisotropy of azobenzene-based molecular monolayers ∼0.4 nm in thickness that are self-assembled on glass.10,11 Azobenzene-based molecules exist as trans and cis isomers, undergoing a reversible transformation between these two forms in the presence of actinic light.20 When orientationally ordered, such dye molecules exhibit anisotropic optical properties because of their anisotropic polarizability. The birefringence of dye-based polymer films can be tuned using orientational hole burning and angular redistribution effects resulting from exposure to actinic light:21 in-plane anisotropy of the refractive index as large as Δn ≈ 0.2 can be achieved by illumination with linearly polarized light (LPL), and the films may be erased (rendered optically isotropic) using circularly polarized light (CPL).22 Here we demonstrate that the erasure process in a self-assembled monolayer (SAM) of the methyl red derivative dMR10,11 with an initial saturated photoinduced birefringence of Δn ≈ 0.13 can be followed as the anisotropy is reduced, down to Δn ≈ 0.001. We can understand the requirements for such measurements by writing down the transmission T = Itrans/Iinc, the ratio of the transmitted to incident intensity, of a birefringent dielectric slab with in-plane birefringence Δn = n - n^ deposited on glass and placed between a crossed polarizer and analyzer. For an anisotropic organic monolayer illuminated with visible light, the retardance is very small and T is well approximated by )
1. Introduction Molecular monolayer films are important in a wide variety of materials science and engineering. Organic films self-assembled and covalently bonded onto substrate surfaces are of particular interest, forming the basis for the control of interface properties such as hydrophobicity1 and enabling chemical detection,2 bioselection,3 bioassay methods4 and a host of other active processes.5-11 The structural characterization of such monolayers has typically been carried out using X-ray and optical methods, the latter including ellipsometry,11 absorption and vibrational spectroscopy,11,12 and dichroism.13 A method widely used to probe the structural anisotropy of bulk phases is the birefringence measurement, which is of key importance in the study of liquidcrystal phases, for example, enabling the detection of phase transitions and underlying essentially all of the application development of liquid-crystal displays.14-17 The quantitative measurement of in-plane birefringence, however, has been used only rarely in the structural study of molecular monolayers because the optical path differences for different polarizations are extremely small for typical optical anisotropies and film thicknesses. One context where the in-plane birefringence of organic films that are a few molecular layers thick has been measured quantitatively is in the study of freely suspended smectic
T = sin2 2θf
πΔnd 4nm ½ g2 λ ðng þ1Þ2
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(18) Chattham, N.; Korblova, E.; Shao, R.; Walba, D. M.; Maclennan, J. E.; Clark, N. A. Liq. Cryst. 2009, 36, 1309. (19) Olson, D. A.; Cady, A.; Weissflog, W.; Nguyen, H. T.; Huang, C. C. Phys. Rev. E 2001, 64, 051713. (20) Xie, S.; Natansohn, A.; Rochon, P. Chem. Mater. 1993, 5, 403. (21) Delaire, J. A.; Nakatani, K. Chem. Rev. 2000, 100, 1817. (22) Natansohn, A.; Rochon, P.; Pezolet, M.; Audet, P.; Brown, D.; To, S. Macromolecules 1994, 27, 2580.
Published on Web 06/22/2010
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Figure 1. Schematic diagram of the polarimeter. A polarized 623.8 nm probe beam normally incident on the sample is used to measure changes in the birefringence of a thin anisotropic film. The probe beam is spatially filtered both before and after the sample and illuminates small spots on the Glan-Thompson polarizers (P, A). The analyzer (A) is mounted on a rotating stage with an angular resolution of 0.001. In the setup to test the polarimeter, two 514.5 nm ancillary pump beams, illuminating the sample at a 10 angle of incidence, are used to induce optical anisotropy in a photoactive self-assembled monolayer by photowriting with linearly polarized light (beam 1) and to photoerase (in-plane isotropization) using circularly polarized light (beam 2). The pump beams provide a convenient mode of reversibly controlling the optical anisotropy and optic axis orientation (n) of the monolayers in evaluating the polarimeter. In other experiments, the quarter-wave plate in pump beam 2 is replaced with a half-wave plate, and the pump beams, now both linearly polarized, are used to drive the system between two ordered states with different azimuthal orientations. Ferroelectric liquid crystal (FLC) shutters are used to turn the two pump beams on and off with a switching time of 40 μs.
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2. Experiments The polarimeter shown in Figure 1 was designed to measure tiny changes in the birefringence of thin films. The probe light from a 632.8 nm helium-neon laser is spatially filtered, polarized, and focused onto a 40-μm-diameter spot on the sample. The transmitted beam passes through an analyzer and is focused onto a diffraction-limited spot on a single-mode optical fiber that leads to the photocathode of a photomultiplier tube (PMT). This fiber, with 3.5/125 μm core/cladding diameters, is selected to block the stray and reflected light from optical components in the system and to improve the extinction ratio further. The signal from the PMT goes to a time series recorder and from there to a computer. For the study of photoactive monolayers, two 514 nm pump beams with their own polarization control components are arranged to be incident on the sample with an angle of 10 with respect to the probe beam. The pump beams can be turned on or off individually in 40 μs by applying square waveforms to ferroelectric liquid-crystal optical shutters. The collimated pump
beams are 1.67 mm in diameter, which is much wider than the probe beam, so that the probed region is essentially uniformly illuminated. The polarizer and analyzer used for the probe beam are GlanThompson polarizers with a nominal extinction ratio of 5.0 10-5 for white light. We have found that much higher extinctions (I^/I ≈ 10-9 to 10-10) can be achieved for a probe laser beam that is spatially filtered on its input and output as described above. The analyzer is mounted on a rotation stage controlled with a stepping motor with an angular resolution of 0.001, a requirement for reliably achieving high extinction. The extinction ratio (I^/I ) of the polarimeter is a measure of the relative transmission intensities when the Glan-Thompson polarizer and analyzer are parallel and crossed, respectively. I is too intense to be measured directly by the PMT, but in practice, the extinction ratio may be determined by scanning the analyzer orientation ψ in small angular steps (δψ ≈ 0.001) through the extinction orientation ψ = 90 and recording the transmitted intensity I(ψ) without a sample, as shown in Figure 2 for a 0.7 mW probe beam. The intensity variation is then fit with the function I = I cos2(ψ) þ Ipl, giving an extrapolated value of I ≈ 3.8 1012 counts/s and Ipl = I^ ≈ 900 counts/s, corresponding to an extinction ratio of Ipl/I ≈ 2.4 10-10, where Ipl is termed the polarimeter leakage (pl). The fitted values of I agree well with those measured directly by orienting the analyzer and polarizer parallel and inserting neutral density filters into the beam. For small uncrossing angle δψ = ψ - π/2, the polarimeter transmission T(δψ) is given by T(δψ) ≈ [δψ]2 þ Tpl, where Tpl = Ipl/I is the polarimeter leakage transmission. For the birefringent film in the example above (T ≈ 8 10-8), the transmitted intensity is T ≈ 3 105 counts/s, about 300 times the leakage level. The background transmission, which is equivalent to that of a weakly anisotropic SAM with a retardance )
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where a principal optic axis is along the mean in-plane molecular orientation of the monolayer (n), θ is the angle between n and the polarization of the probe light, d is the slab thickness, ng is the index of refraction of the glass substrate, and nm = (n þ n^)/2 is the mean refractive index of the slab. For a monolayer with anisotropy typical of a liquid crystal (nm = 1.6, ng = 1.5, Δn = 0.13, d = 0.4 nm, and λ = 633 nm), we have (4nm/(ng þ 1)2) ≈ 1, and with θ = 45 to get the maximum transmission, we find T ≈ 8 10-8. From this, we see that a polarimeter with a high extinction ratio much better than 10-8 is desirable for the precision measurement of monolayer birefringence.
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Figure 2. Transmitted intensity of the polarimeter with no sample as a function of the angle between the polarizer and the analyzer, showing the experimental data (black and blue squares) and best fit (red curve). The corresponding extinction contrast, the ratio of the transmission intensities for the parallel and crossed Glan-Thompson polarizer/analyzer pair, is I^/I = 2.4 10-10 in this example.
Figure 3. (a) Depolarized transmitted intensity and transmission vs time when a dMR-SAM between crossed polarizers initially with in-plane anisotropy is rendered isotropic by illumination with precisely circularly polarized light. Open blue squares, raw transmission data in units of PMT counts/3 ms. Solid black points, transmission data with polarimeter leakage with a sample in place of IplS = 3.35 ( 0.02 counts/3 ms (red line, calculated from an average of the last 10 000 points), subtracted out. (b) Birefringence obtained from the absolute polarimeter transmission. Note that Δn (transmission)1/2. The inset shows the structure of dMR. of ∼0.003 nm, can be reliably fit to and subtracted from the raw intensity data as we will show below, leaving only photon counting (N)1/2 fluctuations to limit the data at small Δn. The performance of the polarimeter was assessed by studying the dynamics of the photoinduced birefringence of the dMRSAM (azo-SAM) system10,11 shown in the inset of Figure 3b. We have performed extensive investigations under different writing and thermal and photoerasing conditions that will be reported in detail elsewhere. In these experiments, the two pump beams and the probe beam are directed such that the three beams are concentric on the measured sample. Pump beam 1 for anisotropic writing is linearly polarized light (LPL), rotated -45 from the 11688 DOI: 10.1021/la101117n
probe beam polarizer axis (Figure 1), inducing an in-plane mean molecular orientation and principal optic axis n oriented at θ = þ45 from the probe beam polarization. Pump beam 2 for erasing is circularly polarized light (CPL) with an eccentricity smaller than 1%, controlled using a variable waveplate. This eccentricity adjustment is critical and is set most precisely by probing the resulting anisotropy induced by CPL in the monolayer. The analyzer orientation is adjusted to obtain the extinction of the probe beam when no sample is present. The sample, initially a thermally randomized (in-plane isotropic) azo-SAM, is aligned normal to the incident probe beam and is translated laterally to find a position where the probe beam encounters minimal birefringence from the ∼1-mm-thick glass substrate. This adjustment is essential because at some places on the sample spurious phase shifts due to intrinsic strain birefringence of the glass are comparable to that of the fully written azo-SAM. The magnitude of the birefringence and the optic axis orientation of the glass vary over the surface, and regions of the glass/thermally randomized SAM surface may be found, having IplS, the depolarized transmission signal with the sample in the probe beam, close to Ipl, the dark transmission of the polarimeter with no sample.
3. Results and Discussion In Figure 3, we show a representative example of the measurement of in-plane birefringence of a monolayer versus time, with a dMR-SAM on glass in the polarimeter probe beam. This film, of thickness d ≈ 0.4 nm, was previously written with linearly polarized pump beam 1 to produce in-plane optical birefringence with a refractive index anisotropy of Δn ≈ 0.13 and the optic axis at θ = 45 with respect to the probe beam polarization. The return of the monolayer to in-plane isotropy when illuminated with circularly polarized actinic light is then monitored in time over a period of t ≈ 105 ms. The open symbols in Figure 3a show the measured transmitted intensity of the polarimeter in units of PMT counts/3 ms as well as the transmission T. As can be seen, the dynamic range in transmitted intensity between the fully written SAM and the polarimeter leakage (the signal at long times, ∼IplS) is about 300. The solid points in Figure 3a show the same data with the leakage asymptote (the average of the last ∼10 000 points) subtracted out and the final result smoothed (black curve). The corresponding in-plane birefringence of the monolayer is shown in Figure 3b, from which we see that for this 0.4-nm-thick molecular film Δn can be tracked down to the Δn ≈ 0.001 range. In the case of azo-SAMs, in-plane anisotropy can be induced dynamically along a known direction, which enables substrate birefringence to be distinguished from that of the SAM. We can also measure the static birefringence of organic monolayers, determining the optic axis orientation of the monolayer by rotating the sample about the probe beam axis. This requires the retardance of the substrate to be much smaller than that of the monolayer or to be measured independently. This polarimeter measures the intensity of the depolarized component of the light exiting the sample, a weak signal that arises from specific elements of the in-plane dielectric tensor of the monolayer: (i) the real part of the diagonal elements causes linear birefringence (LB) and a differential Fresnel reflection (DFR) of the incident polarization along and normal to n; (ii) the imaginary part of the diagonal elements causes differential absorption of the incident polarization along and normal to n (i.e., linear dichroism (LD)); (iii) the real part of the off-diagonal elements causes circular birefringence (CB) and thus optical rotation (OR); and (iv) the imaginary part of the off-diagonal elements causes circular dichroism (CD). We now consider the capabilities of the polarimeter in the study of monolayers with these different optical characteristics, in each case estimating from Maxwell’s equations Langmuir 2010, 26(14), 11686–11689
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measurements. (iii) Circular birefringence and differential reflectivity. The transmission due to circular birefringence is TCB ≈ (πΔnCBd/λ)2 ≈ (ORd)2, where ΔnCB = nL - nR is the difference in refractive index for left and right circularly polarized light and OR is the optical rotatory power. This gives a circular birefringence and a retardance corresponding to the polarimeter leakages of [ΔnLCB]pl ≈ 0.0075 and [ΔnCBd]pl ≈ 0.003 nm, respectively. (iv) Circular dichroism. The transmission due to circular dichroism is TCD ≈ (Δεd/4)2 ≈ [(ΔA)(ln 10)/4]2, where Δε is the difference in the monolayer absorptivity for left and right circular polarization and ΔA = AL - AR is the corresponding difference in the circular optical density. Because the polarimeter measures only the depolarized intensity, it cannot, in general, distinguish among effects i-iv. Some complementary understanding of what effects are to be expected is therefore necessary. In the particular case of the dMR-SAM, the molecular structure is achiral so neither ΔOR or ΔCD is expected, and ΔA extrapolated from solution data is found to be very small.
iπd 4ðnm þ ikm Þ F ¼ ½ð ÞðΔnLB þ iΔk LD Þ½ λ ðng þ1Þ2
4. Conclusions Without a sample and with the analyzer oriented to near extinction, the polarimeter transmitted intensity is I(δψ), given by I(δψ) = Iinc[δψ]2 þ Ipl, which can be measured by the precision of the uncrossing of the analyzer through the angle δψ. We can define the leakage uncrossing angle to be the angle δψl for which [δψl]2 = Tpl as a measure of the extinction quality of the polarimeter (the smaller the better). In the present case, [δψl]2 = Tpl for an uncrossing of δψl ≈ 1.5 10-5 rad ≈ 0.001. Each of the four optical effects considered above produces a depolarized electric field E^ corresponding to an effective rotation δj of the incident field Einc through δj = E^/Einc. Fundamentally, the polarimeter obtains δj by measuring I(δj) ≈ Iinc[δj]2 and then using Iinc = [I(δψ) - IplS)]/[δψ]2 to eliminate Iinc, where both intensities are measured with the sample in place. In summary, we have designed a sensitive polarimeter with an extinction ratio of up to 2.4 10-10 that can measure optical retardance down to 0.0015 nm to within 1%. The method needs no special structuring or fabrication of the samples but does require substrate media that are only weakly birefringent. The performance of the polarimeter is demonstrated using the in situ anisotropization of an azo-based self-assembled monolayer.
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the minimum detectable value of the characteristic that would correspond to the polarimeter leakage of Tpl = 2.4 10-10 for a monolayer of thickness d = 0.4 nm. The transmission is calculated by assuming a homogeneous dielectric slab23 bounded by air (index na =1) and glass (index ng), including the effects of multiple beam interference and the different reflectivities of the and ^ field components, which rotate the exiting polarization: (i) Linear birefringence and differential reflectivity. For small retardance, the calculated transmission is given by eq 1, where, as noted above, 4nm/(ng þ 1)2 ≈ 1 for the azo-SAM and most organic monolayers. The depolarized transmission due to birefringence is then TLB ≈ (πΔnLBd/λ)2. Using Tpl=2.4 10-10 gives a retardance corresponding to the polarimeter leakage (PL) of [ΔnLBd]pl ≈ 0.003 nm and the birefringence [ΔnLB]pl ≈ 0.0075. We will justify next that the principal contribution to T of the azo-SAM is birefringence, noting here that T ≈ 8 10-8 for the fully written SAM. (ii) Linear dichroism. When the effects of linear dichroism are included, the transmission becomes TLB,LD ≈ Re[FF*], where
and n þ ik is the complex refractive index. For typical monolayers of neat organic absorbers, we have k and Δk < 0.1 so that nm þ ikm ≈ nm and we can again make the approximation that |[4(nm þ ikm)/(ng þ 1)2]| ≈ 1. The contribution of linear dichroism to transmission is then πΔk LD d 2 ΔεLD d 2 ΔA ln 10 2 Þ ð Þ ½ T LD ð λ 4 4
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where ΔεLD = 4πΔkLD/λ is the difference in the monolayer absorptivity ε, where ε = -ln[I(z)/I(0)]/z for polarization parallel to and normal to n and ΔA = A - A^ is the corresponding difference in the optical density. The minimum detectable anisotropy of the monolayer absorption corresponding to the polarimeter leakage is [ΔkLDd]pl ≈ 0.003 nm, [ΔεLD]pl ≈ 1.5 10-4/nm, and the corresponding anisotropy of the optical density [ΔA]pl ≈ 2.6 10-5. The maximum dichroism of the dMR monolayer at λ = 632 nm, extrapolated from absorbance measurements of dMR in solution,11 is ΔA = 5 10-7. Thus, the contribution of linear dichroism to the transmission of the fully written monolayer will be TLD ≈ [(ΔA)(ln 10)]2 ≈ 10-12, which is roughly 300 times smaller than the measured transmission for the fully written azo-SAM, indicating that dichroism can be neglected in the azo-SAM (23) Reitz, J. R.; Milford, F. J.; Christy, R. W. Foundations of Electromagnetic Theory; Addison Wesley: Reading, MA, 1979; Chapter 18.
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Acknowledgment. We thank Matthew Farrow and David Walba of the University of Colorado for material synthesis and Youngwoo Yi and Thomas Furtak of the Colorado School of Mines for their assistance with making SAMs. This work was supported by NSF MRSEC grant no. DMR-0820579 and NSF grant no. CHE-0079122.
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