13794
J. Phys. Chem. 1996, 100, 13794-13803
Polarization-Modulation Near-Field Scanning Optical Microscopy of Mesostructured Materials Daniel A. Higgins, David A. Vanden Bout, Josef Kerimo, and Paul F. Barbara* Department of Chemistry, UniVersity of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455 ReceiVed: April 3, 1996X
A new polarization-modulation near-field scanning optical microscope (PM-NSOM) is described and demonstrated. Linearly polarized light is rotated through an angle of 180° at a frequency of 2 kHz with an electro-optic modulator and quarter-wave plate combination and is then coupled into the near-field opticalfiber probe. The sample is positioned in the near field of the probe and the near-field light coupled through the sample to the far-field is detected. A 2 kHz modulation is observed in the intensity of the light reaching the detector when the probe is positioned over an optically anisotropic region of the sample. The modulated signal is shown to result from anisotropic absorptions in the sample and from polarization-dependent nearfield to far-field coupling. With lock-in detection of the signal, two optical images are recorded simultaneously as (i) the amplitude, which gives a measure of the magnitude of the anisotropy and (ii) its phase, which yields the characteristic direction of the anisotropy. For strongly absorbing dichroic samples the amplitude and phase of the modulated signal give the spatially resolved anisotropic extinction coefficient and transition dipole orientation, respectively. A more complex contrast mechanism is proposed for nonabsorbing samples, involving the effects of both sample birefringence and anisotropic spatial variations in the refractive index. Nanoscopic characterization of optical materials with the PM-NSOM is demonstrated through resonant imaging of dichroic single crystals of rhodamine 110. Its application to nonabsorbing materials is also demonstrated through nonresonant imaging of the rhodamine crystals, as well as through imaging of defects in fusedquartz cover slips. With PM-NSOM, material defects such as cracks and pits are imaged with high sensitivity, shot-noise-limited signal-to-noise, and better than 100 nm spatial resolution.
Introduction Near-field scanning optical microscopy (NSOM) is a rapidly evolving, high-resolution imaging technique that provides subdiffraction-limited spatial resolution in visible-light images of materials.1-21 The tremendous improvement in the spatial resolution of NSOM images over those recorded by conventional far-field techniques is obtained via the use of a sub-wavelengthsized light source and by holding the sample within the near field of that light source (i.e., at a distance much less than the wavelength of light employed). The most common NSOM light source is a tapered, aluminum-coated, single-mode optical fiber.6 The sample is raster-scanned at a constant distance beneath the NSOM probe, and images are collected one pixel at a time in a manner analogous to the other scanned-probe microscopies. Since visible light is employed as the imaging mechanism in NSOM, a number of different contrast mechanisms are available. Fluorescence represents by far the most sensitive and most easily interpreted contrast mechanism; however, the most general methods simply involve transmission of light through the sample. Contrast in transmission NSOM may result from resonant absorption of the light from the probe, or it may result from complicated near-field effects. Such effects are caused by variations in the refractive index of the material beneath the probe.9,19,22 Incorporation of polarization-dependent imaging techniques in studies of samples with microscopic order on the 50-100 nm (or larger) distance scale provides a valuable means for characterization of local surface or film structure. Several publications have demonstrated the utility of absorption and emission dichroism as a basis for contrast in NSOM experiments.2,3,15,23,24 Those papers employed polarization methods * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, July 1, 1996.
S0022-3654(96)00995-1 CCC: $12.00
to measure molecular order and orientation in highly structured thin film materials. A large body of research using polarization methods for studies of macroscopically ordered samples in farfield experiments also exists.25 In most of the previous applications of polarization-dependent NSOM, entire images were recorded with linearly polarized light of a fixed polarization direction.2,3,7,23,24 While such methods provide useful information, polarization-modulation techniques that rotate the polarization of light from the tip at high frequencies provide much more information in less time.18,26,27 In addition, such modulation experiments move the measurement into a high-frequency regime where there may be much less noise, thus leading to dramatic improvements in the signalto-noise (S/N) ratio observed. Improvements in S/N are expected to be dramatic in PM-NSOM experiments since lowfrequency noise sources such as tip-sample distance fluctuations, laser fluctuations, and fluctuations of the coupling of the laser to the NSOM probe usually dominate over other sources. PM-NSOM has been demonstrated in a previous publication, although the methods used were based on those employed in conventional far-field birefringence measurements and measured only optical anisotropies of a specific orientation.18 In this publication, we report the design and characterization of a new form of PM-NSOM. The apparatus is schematically shown in Figure 1. This PM-NSOM allows for the detailed characterization of optically anisotropic samples via the simultaneous collection of two images which give the magnitude and direction of the optical anisotropy in arbitrarily oriented regions of a sample. The design of the PM-NSOM is presented, and its use is demonstrated in transmission imaging of single microcrystals of rhodamine 110 and in imaging of defects in fused-quartz cover slips. PM-NSOM measurements are performed here by rotating the linearly polarized light coupled into © 1996 American Chemical Society
Optical Microscopy of Mesostructured Materials
J. Phys. Chem., Vol. 100, No. 32, 1996 13795 Nonresonant images of the rhodamine crystals and of fusedquartz cover slips are presented here as examples and are used to characterize the contrast mechanisms and sensitivity of the nonresonant PM-NSOM technique. Although nonresonant images are more difficult to interpret, it is suggested that contrast results solely from near-field effects, providing greater depth discrimination than is available in resonant imaging experiments. Recent theoretical papers have just begun to address these complex contrast mechanisms.9,10,19,22
Experimental Section
Figure 1. Diagram of the PM-NSOM instrument. Laser light is passed through a polarizer oriented at 45° to the fast and slow crystal axes of the electrooptic modulator. A quarter-wave plate oriented with its slow axis at 45° to the crystal axes follows the modulator. When the electrooptic modulator is driven through a full wave of retardation, the system produces linearly polarized light rotating through an angle of 180°. The polarization-modulated light is then coupled into the near-field probe fiber. The sample is positioned on an X,Y,Z piezoelectrically driven stage and is held in the near field of the NSOM probe. The anisotropic optical properties of the sample produce a polarizationdependent modulation in the intensity of the near-field light coupled to the far field detector. An oil immersion objective is used to collect the light and a Brewster plate is used to remove the polarization sensitivity of the aluminum-coated mirrors in the collection path. No output polarizer is used in these experiments. A lock-in amplifier is used to measure the modulated light intensity produced by the sample and detected with a photomultiplier tube.
the NSOM probe through an angle of 180° at a frequency of 2 kHz. The anisotropic optical properties of the sample (whether due to dichroism, birefringence, or anisotropic spatial variations in the refractive index) produce a polarization-dependent modulation (at 2 kHz) in the intensity of near-field light coupled through the sample to the far-field detector. Using lock-in detection, two optical images are then recorded as the amplitude and phase of the polarization-dependent response of the sample. The amplitude image provides a direct measure of the degree of anisotropy (of arbitrary direction) in local regions of the material while the phase image yields the characteristic direction of the anisotropy. For PM-NSOM imaging of samples which absorb the probe wavelength (referred to as “resonant PM-NSOM”), the amplitude image provides a measure of the local anisotropy of the extinction coefficient, as is demonstrated for the rhodamine 110 crystals. The phase image is shown to yield the transition dipole orientation in these experiments. The measured extinction in these resonant PM-NSOM experiments is influenced by both near-field and far-field effects but is shown to have an approximately linear dependence on the thickness of the rhodamine crystals. It is further demonstrated that PM-NSOM can be employed to image nonabsorbing samples (referred to as “nonresonant PM-NSOM”) provided the refractive index of the sample in the near field is anisotropic. Contrast in such images results from the dependence of the near-field intensity (and its coupling to the far-field) on the refractive index of the material directly beneath the NSOM probe. Such effects therefore yield a polarization-dependent signal in experiments on birefringent samples and also in experiments on samples which simply show sub-wavelength-scale spatial variations in local refractive index. It should be noted that the contrast mechanism employed for imaging birefringent samples is based solely on near-field effects28 and does not measure rotation of the polarization of the light passing through the sample, as is done in traditional far-field birefringence measurements.29
PM-NSOM Apparatus: Detailed Description. A modified Topometrix Aurora NSOM was used to record all of the nearfield and topographic images presented here. A diagram of the instrument and the optical path employed is shown in Figure 1. Either the 514 nm line of an argon ion laser or 633 nm light from a HeNe laser was used in all PM-NSOM imaging experiments. Linearly polarized light from the laser was focused through a two-crystal electro-optic modulator (Lasermetrics Model 3079FW) which was followed by a quarter-wave plate (Special Optics). The electro-optic modulator was aligned so that the incoming polarization vector bisected the fast and slow axes of the crystals. The quarter-wave plate following the modulator was positioned so that its slow axis was aligned approximately parallel to the polarization vector of the laser prior to the modulator. At 514 and 633 nm, the electro-optic modulator was determined to have half-wave voltages of 175 and 220 V, respectively. The modulator was driven at twice this amplitude by a Trek high-voltage amplifier (Model 601) which amplified the output of a Stanford Research digital function generator (Model DS335). The function generator was used to produce a linear voltage ramp (sawtooth) at 2 kHz to drive the modulator through a full wave of retardation. From simple Jones calculus, this system can be shown to produce linearly polarized light rotating through an angle of 180° at 2 kHz.30 The polarization-modulated laser beam was coupled into the cleaved end of a ≈ 0.5 m long single-mode optical fiber (Thorlabs FS-SN-3224), at the other end of which was the tapered, aluminum-coated near-field probe, originally developed by Betzig et al.6 After exiting the near-field probe, the light passed through the sample, which was mounted on a piezoelectrically driven sample stage with X, Y, and Z motion. The sample was positioned within 5-10 nm of the near-field probe and was maintain at this distance to better than (1 nm with the shear-force feedback mechanism described in detail elsewhere.31 Collection of the light passing through the sample was accomplished with a 1.25 numerical aperture oil immersion objective (Zeiss Model 440280) followed by a series of three aluminum-coated mirrors and an achromatic lens. No output polarizer was used in these experiments. The lens produced an image of the end of the near-field probe (at 100× magnification) on a 100 µm pinhole mounted in front of a 1P-28 photomultiplier tube (PMT). The output of the PMT was demodulated and analyzed with a Stanford Research digital lockin amplifier (Model SRS-830). Light levels reaching the PMT were typically (2-5) × 108 photons/s with 100-500 µW coupled into the probe fiber. The amplitude (R) and phase (θ) of the modulated signal from the PMT were measured by the lock-in with a time constant of 10 ms. To further remove fluctuations in the system, the amplitude was ratioed to the buffered, averaged (10 ms filter time constant) dc signal from the PMT. The ratioed amplitude signal was then output to the Topometrix control and data collection electronics.
13796 J. Phys. Chem., Vol. 100, No. 32, 1996 A second input on the Topometrix electronics monitored the phase signal from the lock-in. The phase angle was recorded relative to that measured for a reference dipole absorbing light polarized along the vertical direction in the images presented below. Amplitude, phase, and topographic images were all recorded simultaneously as the sample was raster scanned over 5 and 10 µm distances at a rate of 10 s/line. The pixel time in these images was 50-100 ms. PM-NSOM: Optical Characteristics and Signal-to-Noise. The polarization properties of the modulated laser beam were verified both before and after coupling into the near-field probe. Prior to coupling into the probe, a polarizer and detector were placed after the modulator/quarter-wave plate combination. Full modulation (to better than 100:1) in the intensity was observed at 2 kHz for all orientations of the polarizer. Rotation of the polarizer through 180° produced a continuous 360° change in the measured phase of the modulation but no change in the depth of modulation. These results prove that the system was producing linearly polarized light varying through 180° in time. No modulation (less than 1%) in the intensity was observed when the polarizer was removed. The sawtooth waveform used to drive the modulator produced a singularity at the end of each ramp when the voltage switched to its starting value. This singularity was measured to be 20 µs wide and led to no measurable effects since it was well outside the detection bandwidth employed in the lock-in amplifier. Once the light was coupled into the near-field probe, imperfections in the aperture of the probe led to the production of elliptically polarized light from the tip (as measured in the far field). The quarter-wave plate was adjusted to partially compensate for the tip effects and to produce approximately linearly polarized light from the tip rotating at 2 kHz through 180°. The purity of polarization was determined to be at least 20:1 at all polarizations. This extinction ratio was obtained by placing a polarizer in the far field of the tip and measuring the depth of modulation in the intensity of light passing through it. Once again, rotation of the output polarizer through 180° was used to verify that the light was linearly polarized (within 20: 1) throughout the full range of modulation. Lock-in detection of the modulated signal (with the polarizer in place) showed that only the phase of the modulation changed as the polarizer was rotated and the amplitude of modulation stayed constant to within 5%. No higher harmonics (2nd and 4th) were observed in the modulated signal. Removal of the output polarizer prior to the PMT showed that the PM-NSOM instrument had an inherent polarization sensitivity caused by the three aluminum mirrors employed in the microscope and by tip aperture, taper, and coating imperfections. These effects were dominated by the polarization sensitivity of the mirrors, which led to a background modulation signal of ≈20% of the average light level reaching the detector. Compensation for the effects of the mirrors was accomplished by inserting a Brewster plate (a glass slide) into the beam path between the collection objective and the PMT, as shown in Figure 1. The Brewster plate was tilted to reflect varying amounts of the light polarized normal to the plane of incidence with the metal mirrors. The background modulation signal in the absence of dichroic absorbers was reduced to ≈1-2% of the average light level with this method. The remaining background modulation was caused by imperfections in the tips that were produced and characterized in-house by methods discussed extensively in the literature.2,3,32 These imperfections led to a few nonidealities. First, as noted above, the tip behaves as an arbitrary wave plate, an effect partially compensated for with the quarter-wave plate, yielding a slightly reduced polarization purity of light from the tip (≈20:
Higgins et al. 1). Second, pinholes, which are sometimes found in the aluminum coating and always limit the quality of near-field images due to the introduction of stray light, are particularly problematic in PM-NSOM. The coupling of light from pinholes is highly dependent on the polarization state of the light within the fiber. Stray light reaching the detector from any pinholes therefore leads to anomalous modulation signals. Imaging of the tip onto the 100 µm pinhole placed prior to the PMT dramatically reduced such effects. Finally, the aperture itself can have a slight polarization sensitivity, leading to the residual background signal of ≈1-2% of the average light level. Signals produced by sample features were easily observed above this small background due to the high S/N ratios obtained in both the amplitude and phase measurements. The noise of the amplitude signal from the lock-in was determined to be at the shot-noise limit for small signals. For the light level used here ((2-5) × 108 photons/s), the shot-noise limited S/N is expected to be ≈500:1 (in a 100 Hz bandwidth), giving an expected detection limit of about 0.2% modulation. Actual measurements of the noise level in both the amplitude and phase signals were obtained by recording the background signals with the NSOM probe in feedback. A clean, fused-quartz cover slip was used as the sample and was held stationary during these measurements. The noise in the amplitude signal was found to be 0.2% of the average light level, a value consistent with expectations. The noise in the phase angle was measured to be (7°. Such noise figures indicate that transmission imaging of weakly absorbing, ordered films is possible with the polarization-modulation technique. For example, a close-packed monolayer of an organic dye such as rhodamine 110 will absorb ≈3% of the light from the NSOM probe, giving an expected S/N of better than 10:1 in the amplitude image. Sample Preparation. The rhodamine 110 (Exciton) crystals used here were grown by slowly evaporating a small drop of a 10 mM rhodamine solution in methanol, at a temperature of ≈5 °C, on a clean fused quartz cover slip (Quartz Scientific). The surface of these evaporated films was found to be highly heterogeneous as viewed under an optical microscope at 600× magnification. Crystals of the type imaged below were found in small regions on the surface near the edge of the film. These crystals appeared in the shape of a parallelogram. No crystal structure for these rhodamine crystals could be found in the literature. Background High signal-to-noise images of the magnitude and direction of optical anisotropies (due to dichroic and/or birefringence effects) in local regions of samples are provided by the PMNSOM methodology presented here. The theory behind resonant PM-NSOM imaging of dichroic samples will be addressed first since the contrast mechanism is more easily interpreted. In these experiments, the sample produces a polarization-dependent modulation in the intensity of the light reaching the far-field detector. This modulation is produced primarily by the polarization-dependent absorption of the sample. Amplitude (extinction) and phase (direction of the absorbed polarization) images obtained via lock-in detection of this signal provides the means by which the absorption anisotropy of local sample regions can be characterized with spatial resolution routinely better than 100 nm. In PM-NSOM experiments, the polarization of light from the tip is modulated linearly in time through an angle δ (δ ) π here) so that the polarization angle of the near-field light at any point in time is defined as δνt, where ν is the frequency at which the polarization is modulated (2 kHz) and t is time. The intensity at the PMT after passage of the near-field light through
Optical Microscopy of Mesostructured Materials
J. Phys. Chem., Vol. 100, No. 32, 1996 13797
an anisotropically absorbing sample is then given by
Iout )
I0 + I I0 - I cos(2(θ - δνt)) 2 2
(1)
The angle θ is the orientation (in the plane of the surface) of the absorbing dipole with respect to some reference. All angles are measured relative to the vertical direction on the images presented below. The minimum intensity of light measured during the modulation cycle is I, while I0 is the maximum. The amplitude of modulation measured by the lock-in amplifier, which effectively removes the time dependence in eq 1, is ratioed to the average signal from the PMT. Thus, the amplitude signal recorded in the images is given by:
R)
I0 - I I0 + I
(2)
The phase angle measured by the lock-in is 2θ (again, θ is the orientation of the absorbing dipole), as shown by eq 1. With the assumption that Beer’s law remains valid for nearfield experiments, the anisotropic extinction coefficient can be obtained from the amplitude image, as given in eq 3:
)
1-R -1 log bc 1+R
(
)
(3)
where is the molar extinction coefficient in M-1 cm-1, b is the sample thickness, and c is the concentration of absorber in the sample. This equation is valid in general for far-field polarization-modulation experiments. As will be discussed below, the assumption that Beer’s law remains valid in nearfield experiments is tenuous at best. Application of these equations in PM-NSOM experiments will be demonstrated below. Apparent adherence to Beer’s law and the expression given in eq 3 will also be shown for a limited range of absorption. Equations 1-3 are valid for the case where the absorption of the sample dominates over any birefringence effects. When birefringence becomes important, difficulties in interpretation of the signals arise from complex near-field effects. The electric-field strength in the near field of the probe is strongly dependent on the refractive index of the material beneath the probe. As has been shown in theoretical work on purely dielectric media, the intensity of light coupled from the probe is known to increase with the dielectric constant of the material.9 Since a birefringent material has different refractive indexes along different directions in the crystal, the intensity of light in the near field will depend on the polarization of the light from the tip, as will the intensity of light reaching the detector. Therefore, variations in field strength as a function of sample position and near-field polarization render I and I0 in the above equations ill-defined quantities. Quantitative measurements of the absorption strength are difficult in such situations. However, the dipolar orientation can still potentially be determined, as is shown in the nonabsorbing samples section of the experimental results. The theory behind these complicated contrast mechanisms requires comprehensive modeling of the tip-sample geometry with a complete 3-dimensional solution of Maxwell’s equations. A number of theoretical works which have just begun to address such issues have recently appeared in the literature.9,10,19,22 While birefringence effects and spatial variations in the refractive index of the sample limit the quantitative measurement of absorption strengths with the PM-NSOM method, they do in fact provide contrast in “nonresonant” transmission images via the complex near-field effects described above. Again,
measurements from such images cannot be made in a quantitative manner without sophisticated mathematical modeling of the near-field regime. Qualitative results can however be obtained from the high S/N images. It should be noted that the local birefringence of samples has indeed already been utilized for imaging in a different PM-NSOM designed specifically for such measurements.18 The methods presented here differ markedly from the more conventional methods used to measure birefringence in this previously published work. Results Absorbing Samples: Rhodamine 110 at 514 nm. The implementation of PM-NSOM for imaging of strongly anisotropic absorbers is demonstrated here by imaging single crystals of rhodamine 110 with 514 nm light. The topographic image of the rhodamine crystal sample acquired with the NSOM instrument is shown in Figure 2a. A number of crystals are seen in this image with thicknesses varying from about 10 to 140 nm. Anisotropic transmission images recorded with the PMNSOM and corresponding to the region shown in Figure 2a are presented in Figure 2b,c. These images are reported as the amplitude (b) and phase (c) of the modulated intensity of light reaching the detector. As noted earlier, the linearly polarized light from the NSOM tip is rotated linearly in time through 180° in these experiments. A polarization-dependent intensity at 2 kHz (the frequency of the polarization modulation) is detected after passage of the light through an anisotropic region of the sample. With the exception of a small background (see above), this modulated signal is produced primarily by the dichroism of the sample at this wavelength. The background signal in this image is ≈3% of the average intensity at the detector and the maximum modulation depth is ≈83%. The magnitude of the absorption anisotropy plotted in Figure 2b is defined by eq 2. The amplitude of modulation produced by these crystals correlates well with their apparent thicknesses, as is expected when the absorbance of the sample dominates the contrast; a more quantitative correlation is presented below. The amplitude image shows surprising structure within several of the crystals, as is especially visible in the crystal in the bottom right-hand corner of the image in Figure 2b. These features, which appear as dark lines in the crystals are ≈1 µm long and ≈150 nm wide and demonstrate that the spatial resolution in these images is better than 150 nm. The origin of these features is unknown; however, they are not readily apparent in the topographic image and are most likely due to small cracks in the crystals. It is also possible that they represent density (concentration) variations in the crystal which lead to variations in the local absorption strength, or they may be due to disordered regions which are less anisotropic. Finally, as has been discussed elsewhere, these features may also be due to changes in the refractive index of the crystal (from density or order variations) beneath the NSOM probe. Variations in the intensity of light coupled from the near-field regime to the detector are produced by such effects. The phase image shown in Figure 2c gives a local measure of 2θ directly, as defined in eq 1. The angle θ gives the orientation of the transition dipoles relative to the vertical direction on the image. An absorbing sheet polarizer placed prior to the PMT was used to calibrate the phase measurements and was removed prior to imaging the sample. The orientation of the transition dipole for each crystal was obtained directly from the phase image. A second copy of the phase image with white arrows appended to represent the directions of the transition dipoles is shown in Figure 2d. The dipole orientations were determined from the average phase measured beneath the
13798 J. Phys. Chem., Vol. 100, No. 32, 1996
Higgins et al.
Figure 2. Topography (a), modulation amplitude (b), and modulation phase (c) and (d) images of single crystals of rhodamine 110. The color scale at the bottom left applies to the topographic image and the amplitude image, while the scale at the bottom right is a continuous scale which applies to the phase images. The unprocessed PM-NSOM images were recorded with 514 nm light which is strongly absorbed by the crystals. The crystals are highly dichroic, causing the polarization-dependent intensity modulation which is reported here as the amplitude and phase images generated by lock-in detection of the modulated signal. The amplitude image provides a measure of the magnitude of the dichroism and the phase image gives the transition dipole orientation. The orientations of the dipoles were calculated from the phase image and are shown by the arrows in d. The dipoles are oriented parallel to the short face of the crystals.
region in which each arrow is placed. As can be seen in the figure, the dipoles were found to be aligned parallel (0° ( 10°) to the short edge of the crystals. Deviations of the dipole from parallel to the short edge appear in some places and are most likely due to distortions in the image caused by nonlinearities in the piezoelectric scanner. As is shown by eq 3, it is possible that PM-NSOM measurements can be employed to measure the anisotropic extinction coefficient for samples such as these. An absorbance image is shown in Figure 3b. A plot of absorbance vs crystal thickness was generated from this image and is shown in Figure 3c. The absorbance appears to vary linearly with crystal thickness for absorbances smaller than ≈1. From the linear
region of this plot, assuming a concentration of 2.5 M for the dye in the crystals, an anisotropic extinction of ≈30 000 M-1 cm-1 at 514 nm is calculated. The apparent linearity of the absorbance vs thickness plot suggests that the deceptively simple relationship given in eq 3 can be used for such quantitative measurements. However, a number of effects limit adherence to Beer’s law and the validity of eq 3. Some of these effects result from experimental difficulties. For example, the light from the probe is slightly elliptically polarized, as evidenced by the reduced polarization purity (≈20:1) of the light reaching the far field. The residual light of orthogonal polarization reduces the maximum possible modulation to about 95% and suggests that a break in the
Optical Microscopy of Mesostructured Materials
Figure 3. Topography (a) and calculated absorption image (b) of rhodamine 110 crystals. The absorption image was obtained from an amplitude image (similar to Figure 2b) using eq 3 and assuming Beer’s law is valid in near-field experiments. (c) Absorbance vs thickness plot derived from b showing apparent adherence to Beer’s law. As noted in the text, the relationship is actually much more complicated than is suggested by this plot. The break from linearity that occurs for crystals thicker than 100 nm is due mostly to the instrumental limitations presented in the text.
absorbance vs thickness plot should occur at an absorbance of about 1.3. Stray light from small pinholes and other sources
J. Phys. Chem., Vol. 100, No. 32, 1996 13799 may contribute as well and further reduce the point at which the break occurs. Variations in the optical properties of the material being imaged may present further, fundamental limitations to the validity of Beer’s law in NSOM experiments. As noted above, the intensity of light in the near field and the intensity of light coupled to the far-field detector are highly dependent on the refractive index of the material in the near field of the NSOM probe. The near-field regime extends about half the optical probe diameter (≈50 nm) into the sample;10 in this region, the variations in the near-field and far-field intensities caused by variations in the sample’s refractive index will compete with absorption by the sample. In fact, the two effects are expected to be of opposite sign, with an increase in refractive index coupling more light to the far field and an increase in absorption coupling less. Beyond the near-field regime, absorption of the light becomes the dominant mechanism. The amplitude images (anisotropic absorption) presented above are complicated by such effects since the light must pass through both near-field and far-field regions of the sample. I and I0 in eqs 1 and 2 are not easily defined in such a situation. The next section will present a dramatic demonstration of these effects. While such problems limit quantitative absorption measurements, future advances in production of near-field probes will dramatically reduce some of the experimental limitations. Even with these limitations, quantitative dipole order and orientation information as well as qualitative absorbance images are easily obtained. These images are obtained rapidly and require only simple mathematical analysis for interpretation. Most importantly, order and orientation information can be obtained on samples of arbitrary orientation. All such measurements can be made with high S/N and are even possible on very weakly absorbing monolayer or submonolayer samples. Nonabsorbing Samples: Rhodamine 110 at 633 nm. The complex dependence of the near-field to far-field coupling efficiency on the dielectric properties of the near-field sample is shown here to be a valuable means for obtaining images of nonabsorbing, optically anisotropic samples. Such samples might include transparent samples which are locally birefringent, such as polycrystalline materials or glasses with strain-induced defects. Nonresonant images of the rhodamine single crystals are presented here as an example of such systems. Figure 4 shows the topography, unpolarized NSOM transmission images, and PM-NSOM images (phase and ratioed amplitude) of crystals similar to those imaged in Figures 2 and 3. The images presented in Figure 4 were acquired with 633 nm light. As is immediately apparent from Figure 4b, strong contrast is observed in the unpolarized NSOM image even though the crystals absorb only weakly at 633 nm. The complex contrast mechanisms which lead to the features observed in this image will be addressed first, as this will aid in the understanding of the PMNSOM images to be presented later. The effects that contribute to contrast in the unpolarized transmission image in Figure 4b are based on the refractive index effects (both isotropic and anisotropic) discussed throughout this article. These effects have been addressed both theoretically9 and experimentally21 in the past. Again, it is known that the coupling efficiency of light from the near field to the far field increases with an increase in the refractive index of the material in the near field of the NSOM probe.9 Sample topography can lead to contrast via such a mechanism. As a topographic feature is crossed during the acquisition of an image, the distance between the NSOM probe aperture and the sample changes.21 Tip/sample distance changes cause changes in the optical properties (i.e., from those of the sample
13800 J. Phys. Chem., Vol. 100, No. 32, 1996
Higgins et al.
Figure 4. Topography (a), unpolarized transmission NSOM (b), modulation amplitude (c), and modulation phase (d) images of rhodamine crystals imaged off resonance, with 633 nm light. The color scale at the bottom left applies to the topographic, unpolarized NSOM, and modulation images, while the scale at the bottom right is a continuous scale which applies to the phase image. The contrast in these unprocessed optical images results from complicated near-field effects in which the detected intensity depends strongly on the refractive index of the material beneath the tip. For the thin crystals in these nonresonant experiments, the detected polarization-dependent intensity modulation is caused mostly by their birefringence. For the thicker crystals, the residual dichroism of the crystals begins to dominate the contrast, as is shown by the nonmonotonic dependence on crystal thickness of the unpolarized NSOM image in b. The phase image shows that the direction of maximum extinction is the same as the direction of maximum refractive index, i.e., parallel to the short face of the crystals.
to those of the ambient medium) of the near-field regime and hence will lead to changes in the intensity of light reaching the detector. Such effects are observed through the rapid intensity variations in the unpolarized NSOM transmission image shown in Figure 4b as a rhodamine crystal edge is crossed. In the absence of large topography, the difference in refractive index between a sample and the surrounding substrate material can also cause variations in the intensity of light reaching the detector. This effect is also observed in Figure 4b for the two thin crystals in the lower left corner of the image. As can be seen, both of these crystals yield an increased intensity in
comparison to the fused-quartz background. For the thicker crystals in the image, a decrease in intensity is observed and is apparently due to the small residual absorption of the rhodamine crystals. The nonmonotonic response of these crystals as a function of thickness points to the competition between the nearfield refractive index effects and near- and far-field absorption. For the thicker crystals, only a small fraction of their thickness is in the near-field of the probe, and the refractive index effects rapidly “saturate” as crystal thickness increases beyond the nearfield regime (≈50 nm).10 Conversely, the absorption of the crystal continues to increase with thickness in an approximately
Optical Microscopy of Mesostructured Materials linear fashion. Note that in the absence of absorption, these results suggest that nonresonant near-field experiments are potentially much more sensitive to the properties of the sample in the near field than resonant NSOM experiments. Nonresonant NSOM may therefore discriminate better between the near-field region of a sample and the bulk. While unpolarized transmission NSOM will yield contrast in nonresonant images, PM-NSOM images provide much more information and with better signal to noise. Figure 4c,d shows nonresonant PM-NSOM images acquired on the rhodamine crystals. Once again, contrast in these images is produced by the effects of the anisotropic optical properties of the sample, namely, its birefringence and anisotropic spatial variations in the refractive index. Since PM-NSOM is sensitive only to the anisotropic properties of the sample, topographic features have a different effect than in unpolarized NSOM images. Topographic contrast is observed here because the edge of each crystal presents a front of rapidly varying refractive index along a certain direction. Such a feature leads to a small variation in modulation amplitude at the crystal edge, as is seen in Figure 4c, and to a change in the phase of the detected modulation, depending on the orientation of the edge, as seen in Figure 4d. Similar effects are also observed for the defects in the thicker crystals shown in Figure 4. These defects appear as streaks in the crystal images and appear dark in Figure 4b and bright in Figure 4c. They show strong contrast and were described above as resulting from cracks, concentration variations, or disordered regions within the crystal. They appear long and narrow, with widths smaller than the size of the near-field probe. The contrast mechanism is likely due to the anisotropic refractive index effects discussed above. In uniform regions on the crystals themselves, a weakamplitude signal is observed, as shown in Figure 4c. The amplitude signal results from one of two effects, the changes in near field coupling efficiency caused by the birefringence of the crystal in the near-field regime, or the residual dichroic absorption of the crystal in both near- and far-field regimes. The amplitude image alone cannot distinguish between these two contrast mechanisms and requires simultaneous acquisition of the topographic image, the phase image, and/or the unpolarized NSOM transmission image. In any case, both birefringence and dichroism lead to an increase in the modulation amplitude of the detected light. Figure 4c shows this as an increase in the brightness. The apparent decrease in modulation amplitude for the crystal at the bottom of the image is caused by interference from the residual background. The phase image of the crystals is presented in Figure 4d. The crystals for which birefringence effects dominate the contrast are made apparent through the unpolarized NSOM image shown in Figure 4b. Namely, these crystals are the thin crystals which couple more light to the far-field detector than the substrate. For these crystals, the phase image can be used to measure the characteristic direction of the birefringence. This determination is analogous to the measurement of transition dipole orientations described above in the resonant imaging of the rhodamine crystals. In the nonresonant phase image (for the thin crystals only) the phase of the intensity modulation is shifted by 180° from that measured previously in the resonant absorption images. This result indicates that the direction of maximum refractive index is the same as the direction of maximum extinction. Such a result is expected if the main electronic absorption centered at 530 nm dominates the optical properties in this region of the spectrum. The 180° phase shift occurs because a greater refractive index produces a higher intensity at the detector, whereas a greater absorption decreases the intensity. Therefore it is concluded that both the crystal
J. Phys. Chem., Vol. 100, No. 32, 1996 13801 refractive index and extinction coefficient are greatest parallel to the short face of the crystal. In the case of the thicker crystals, where dichroism starts to compete with the birefringence effects, the phase of the modulation changes by 180° back to that measured in the resonant imaging experiments. This effect can be seen most dramatically in the thick crystal shown in the left-center part of Figure 4d. Figure 4d shows that as the tip moves from a birefringent to an absorbing region (given by a change from light to dark in the unpolarized NSOM image in Figure 4b) the phase changes by 180°, as described above. The same effect is observed in other crystals in these images and between thick and thin crystals. The PM-NSOM can be used to rapidly characterize such effects in near-resonant experiments on ordered samples via the collection of both the amplitude and phase images simultaneously. Nonabsorbing Samples: Bare Fused Quartz. In the two cases described above, the signal levels were large and the images relatively easy to interpret. The PM-NSOM technique, however, can also be used to obtain high S/N images of materials that do not fall in these two well-defined categories. The images presented in Figure 5 represent one such system, that of bare fused-quartz cover slips. As can be seen in Figure 5a, very little topography is observed above the noise in the measurement ((1 nm). The PM-NSOM images (amplitude and phase) shown in Figure 5b,c, however, show many features. These features include the two “scratches” that are barely visible in the topography and what appear to be small pits in the surface of the glass. For comparison, the traditional transmission NSOM image of the same region of the surface is presented in Figure 5d. The features seen in Figure 5b,c are also visible in Figure 5d, but only with much greater noise (2% vs 0.2% of the average transmitted intensity). These results conclusively demonstrate the tremendous enhancement in S/N that is obtained in PM-NSOM experiments. While the capabilities of PM-NSOM in producing images of defects in otherwise optically transparent samples are quite evident from Figure 5, the contrast mechanisms by which these images are produced are somewhat ambiguous. It can be speculated, however, that the contrast results from the spatial variations in the refractive index of the material directly beneath the tip. When imaging a scratch, for example, the refractive index parallel to the scratch does not vary rapidly in comparison to the NSOM probe size, while that perpendicular to it may change very rapidly. Such anisotropic variations in the refractive index most certainly yield the contrast observed in these polarization-dependent images because of the dependence of the near-field intensity on the local refractive index. Conclusions In summary, a new polarization-modulation NSOM (PMNSOM) has been presented and characterized in terms of image interpretation and signal-to-noise concerns. The PM-NSOM allows for direct imaging of samples with arbitrarily oriented anisotropic local optical properties. Images of the magnitude and direction of the anisotropies were obtained with better than 100 nm spatial resolution. Such images are produced by modulating the polarization of the light from the NSOM tip linearly through an angle of 180°. The optically anisotropic sample produces a polarization-dependent modulation in the intensity of light coupled from the near field to the far field. The modulation may result from absorption dichroism in the sample and/or the complicated dependence of the intensity on the refractive index of the material in the near field. Images obtained with this instrument were shown to have shot-noiselimited signal-to-noise ratios for small transmission anisotropy signals.
13802 J. Phys. Chem., Vol. 100, No. 32, 1996
Higgins et al.
Figure 5. Topographic (a), modulation amplitude (b), modulation phase (c), and standard transmission NSOM (d) images of a fused-quartz surface. The contrast mechanism by which these images are produced is not fully understood but most likely results from spatial anisotropies in the features observed. These features are much smaller than the size of the NSOM probe and most likely result in polarization-dependent coupling of the near-field light to the far field. The results demonstrate the greatly improved S/N that is obtained in PM-NSOM experiments (b and c) over standard transmission NSOM (d). The noise in b and c is limited by shot noise, while that of d is limited by fiber coupler noise.
Images of dichroic and birefringent samples were presented here to demonstrate the application of the PM-NSOM technique. The polarization-dependent modulation amplitude of the transmitted light in purely absorbing, dichroic samples was shown to yield a means for measuring the anisotropic absorption strength in local regions of a sample. The absorbance for single crystals of rhodamine 110 was calculated from the modulation amplitude images acquired with the PM-NSOM and was found to depend linearly on the measured thickness of the crystals, showing apparent adherence to Beer’s law. The transition dipole orientation in these crystals was determined to be parallel to the short face of the parallelogram-shaped crystals. This determination was made simultaneously to the absorption strength measurements by recording the phase angle of the modulation signal. Nonresonant images of the same rhodamine crystals were also obtained with the PM-NSOM using the birefringence of the sample as the primary contrast mechanism. Contrast in these experiments was shown to result from a near-field effect in which the intensity of light coupled to the far field is strongly dependent on the refractive index of the material being imaged. These nonresonant PM-NSOM images were used to show that the axis of maximum refractive index could be determined with
this technique. For the rhodamine crystals, the direction of maximum refractive index was found to be exactly the same as the direction for maximum absorption, as was expected. In a final demonstration of the utility of the PM-NSOM technique, bare fused-quartz substrates were imaged with the PM-NSOM signal again recorded as the intensity modulation amplitude and phase. Scratches and other features were observed with shot-noise-limited signal-to-noise in these images. Although the detailed contrast mechanism in such images could not be determined and would require extensive modeling of the electric fields in the tip-sample region, a qualitative description was given. The PM-NSOM technique promises to be valuable in the imaging of microcrystalline samples and for rapidly characterizing their anisotropic optical properties. The technique does not require that the sample be fluorescent and does not require the use of resonant excitation. Furthermore, the modulation and detection methodology employed here will work for samples which have arbitrarily oriented (in the plane of the surface) anisotropic regions. Finally, the PM-NSOM technique was shown to lead to dramatic improvements in signal-to-noise ratios in comparison to standard NSOM.
Optical Microscopy of Mesostructured Materials Acknowledgment. The authors acknowledge the support of the Office of Naval Research and the University of Minnesota in these studies. D.A.H. and D.A.V.B. gratefully acknowledge the National Science Foundation Postdoctoral Fellowship Program for their support. References and Notes (1) Higgins, D. A.; Barbara, P. F. J. Phys. Chem. 1995, 99, 3. (2) Higgins, D. A.; Reid, P. J.; Barbara, P. F. J. Phys. Chem. 1996, 100, 1174. (3) Higgins, D. A.; Kerimo, J.; Vanden Bout, D. A.; Barbara, P. F. J. Am. Chem. Soc. 1996, 118, 4049. (4) Reid, P. J.; Higgins, D. A.; Barbara, P. F. J. Phys. Chem. 1996, 100, 3892. (5) Betzig, E.; Trautman, J. K. Science 1992, 257, 189. (6) Betzig, E.; Trautman, J. K.; Harris, T. D.; Weiner, J. S.; Kostelak, R. L. Science 1991, 251, 1468. (7) Betzig, E.; Trautman, J. K.; Weiner, J. S.; Harris, T. D.; Wolfe, R. Appl. Opt. 1992, 31, 4563. (8) Pohl, D. W.; Denk, W.; Lanz, M. Appl. Phys. Lett. 1984, 44, 651. (9) Novotny, L.; Pohl, D. W.; Regli, P. J. Opt. Soc. Am. A 1994, 11, 1768. (10) Heinzelmann, H.; Huser, T.; Lacoste, T.; Gu¨ntherodt, H.-J.; Pohl, D. W.; Hecht, B.; Novotny, L.; Martin, O. J. F.; Hafner, C. V.; Baggenstos, H.; Wild, U. P.; Renn, A. Opt. Eng. 1995, 34, 2441. (11) Du¨rig, U.; Pohl, D. W.; Rohner, F. J. Appl. Phys. 1986, 59, 3318. (12) Harootunian, A.; Betzig, E.; Isaacson, M.; Lewis, A. Appl. Phys. Lett. 1986, 49, 674. (13) Birnbaum, D.; Kook, S.-K.; Kopelman, R. J. Phys. Chem. 1993, 97, 3091. (14) Dunn, R. C.; Holtom, G. R.; Mets, L.; Xie, X. S. J. Phys. Chem. 1994, 98, 3094.
J. Phys. Chem., Vol. 100, No. 32, 1996 13803 (15) Xie, X. S.; Dunn, R. C. Science 1994, 265, 361. (16) Ambrose, W. P.; Goodwin, P. M.; Martin, J. C.; Keller, R. A. Science 1994, 265, 364. (17) Rogers, J. K.; Seiferth, F.; Vaez-Iravani, M. Appl. Phys. Lett. 1995, 66, 3260. (18) Vaez-Iravani, M.; Toledo-Crow, R. Appl. Phys. Lett. 1993, 63, 138. (19) Christensen, D. A. Ultramicroscopy 1995, 57, 189. (20) Jahncke, C. L.; Paesler, M. A.; Hallen, H. D. Appl. Phys. Lett. 1995, 67, 2483. (21) Valaskovic, G. A.; Holton, M.; Morrison, G. H. J. Microsc. 1995, 179, 29. (22) Keller, O.; Xiao, M.; Bozhevolnyi, S. Surf. Sci. 1993, 280, 217. (23) Betzig, E.; Chichester, R. J. Science 1993, 262, 1422. (24) Moers, M. H. P.; Gaub, H. E.; van Hulst, N. F. Langmuir 1994, 10, 2774. (25) Polarized Spectroscopy of Ordered Systems; Samori’, B., Thulstrup, E. W., Eds.; Kluwer Academic Publishers: Dordrecht, 1988; p 578. (26) Gupta, V. K.; Kornfield, J. A. ReV. Sci. Instrum. 1994, 65, 2823. (27) Juang, C.; Finzi, L.; Bustamante, C. J. ReV. Sci. Instrum. 1988, 59, 2399. (28) A related far-field experiment based on confocal microscopy might simply utilize the polarization-dependent reflectivity of the sample to produce similar images. (29) Thulstrup, E. W.; Michl, J. Elementary Polarization Spectroscopy; VCH Publishers: New York, 1989; pp 167. (30) Kliger, D. S.; Lewis, J. W.; Randall, C. E. Polarized Light in Optics and Spectroscopy; Academic Press, Inc.: Boston, 1990; p 304. (31) Betzig, E.; Finn, P. L.; Weiner, J. S. Appl. Phys. Lett. 1992, 60, 2484. (32) Valaskovic, G. A.; Holton, M.; Morrison, G. H. Appl. Opt. 1995, 34, 1215.
JP9609951
