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A continuous multiple exposure diffraction grating (CMEDG) is fabricated holographically on polymer dispersed liquid crystal (PDLC) films using two-beam interference with multiple exposures. The grating is fabricated by exposing a PDLC film to 18 repeated exposure/non-exposure cycles with an angular step of ~10°/10° while it revolves a circle on a rotation stage. The structure of the sample thus formed is analyzed using a scanning electron microscope (SEM) and shows arc-ripples around the center. From the diffraction patterns of the formed grating obtained using a normally incident laser beam, some or all of the 18 recorded arc beams can be reconstructed, as determined by the probing location. Thus, it can be applied for use as a beam-vibration sensor for a laser.
©2010 Optical Society of America
1. Introduction
Holographic lithography, a method that combines holography and photoinduced polymerization, has attracted considerable attention recently in the fabrication of mesoscale structures or photonic crystals (PCs). PCs exhibit some unique optical characteristics, which can be summarized as photonic band-gap (PBG), band-edge effect and anomalous dispersive properties [1]. Fourteen Bravais PC structures can be formed by the interference of three (or multi) non-coplanar beams (ITNB) that have the same polar angle along an azimuthal plane [2–5]. Additionally, non-periodic structures that do not have a complete photonic band gap, such as photonic quasi-crystals (PQCs), can be produced by ITNB [6] or multi-exposures [7]. The holographic technique that utilizes two-beam interference with multi-exposures can simplify experimental setup for fabricating PCs holographically. Particularly, it provides us the benefit of avoiding complex alignment and inaccuracy associated with the differences between the optical path lengths and angles of the interference beams [8].
The present authors have reported unusual refraction from hexagonal PCs based on holographic polymer-dispersed liquid crystals (H-PDLCs) by three-beam interference [9] and introduced multi-exposures to replace the multi-beam interference fabrication process [10]. Multi-exposures are usually performed to fabricate PQC structure using point-by-point holographic recording, in which the sample is set on a rotation stage and exposed repeatedly to two beam interference while the sample being rotated an angle. The motivation of the study is to achieve a simple but distinct position-sensitive H-PDLC film for use as a beam-vibration sensor for a laser. Two approaches for fabricating H-PDLCs films are examined. One is the PQC utilizing point-by-point multi-exposures of two-beam interference, and the other is defined as a continuous multiple exposure diffraction grating (CMEDG), which adopts a novel two-beam interference with multiple continuous exposures to yield a circular interference pattern. The H-PDLC fabricated from latter approach provides us a good beam-vibration sensor for a laser beam, since the diffraction of formed grating probed by a normally incident laser beam, re-constructs some or all the recording 18 arc beams depending on the probing location. However, the reconstruction from PQC is not sensitive to the probing location. The fabrication mechanism of a CMEDG involves multi-exposures in peristrophic holographic recording, which was developed to increase the storage capacity [11–16].
2. Experiments
Experimentally, the recording medium is a PDLC film, which consists of liquid crystal (18 wt% E7, Merck), polymer (81 wt % NOA81, Norland) and photo-initiator (1 wt% R.B., Aldrich). Drops of homogeneously mixed compound are sandwiched between two indium-tin-oxide (ITO)-coated glasses that are separated by ~20 μm glass spacers to produce a sample.
For the approach of two-beam interference with point-by-point multi-exposures or multiple continuous exposures, the sample is exposed to the light interference using the off-axis holographic setup that is shown in Fig. 1 [15]. A TE-polarized CW diode pumped solid state (DPSS) laser beam (Verdi, λ=532 nm) is expanded and divided by a beam splitter into two TE-polarized beams, the reference (~500 mW/cm2) and object beams (~400 mW/cm2), that simultaneously illuminate the sample. The former is incident normally onto the sample, while the latter is incident at an angle ~39° to the normal. The sample sits on a rotation stage that revolves in the x-y plane.
Fig. 1 Experimental setup for holographic recording based on two-beam interference with multiple exposures. The intersection angle (θ) between the two beams is ~39°. M and B.S. represent mirror and beam splitter, respectively.
The PQC sample is set on a rotation stage and exposed repeatedly to two beam interference while the sample being rotated an angle. In this experiment, the sample is exposed to two-beam interference for eighteen times with the sample being rotated with 20°, i.e. exposed at 0°, 20°, 40°,…340°. For a CMEDG sample, a shutter is placed in front of the beam splitter to control the duration of exposure. Since the shutter is opened and closed periodically, the sample experiences repeated exposure/non-exposure cycles while it revolves on the rotation stage. A motor rotates the stage in a circle (through 360°) in ~72 s; the recording duration is ~2 s for each exposure. Hence, the sample goes through 18 repeated exposure/non-exposure cycles with an angular step of ~10°/10°. The pattern of two-beam interference with multiple exposures is recorded on a PDLC sample, forming a circular diffraction grating. Restated, a CMEDG sample experiences 18 exposures at 0°-10°, 20°-30°, 40°-50°,…, and 18 non-exposures at 10°-20°, 30°-40°, 50°-60°,…etc. The phase separation between the LC and the polymer takes place in the sample after being irradiated, and then forming periodic structures under two-beam interference when the shutter opens. However, photo-polymerization does not occur during the cover interval. The interference region in the sample is a circle of diameter ~1 cm, as determined from the beam size of the recording beam. The polymer structure formed in the sample is studied using a scanning electron microscope (SEM). A SEM sample is prepared as follows. One of the glass substrates is split away from an H-PDLC sample. Care is taken in splitting the sample to ensure that the polymer structure is not damaged. The H-PDLC film is immersed in n-hexane solution for a week to remove all LCs. The sample is then placed in the air to evaporate off the n-hexane solvent. Finally, it is coated with a thin gold film to produce a SEM sample.
3. Results and discussion
The total intensity accumulated intensity of the two-beam interference with continuous exposures can be expressed as [15],
where I(x,y,z) is the total interference intensity; n is the number of exposures; ϕ is the exposure angular step (0°-10°, 20°-30°, 40°-50°, etc…); θ is the incident angle of the object beam during recording; r(x,y) and are the electric field of the reference and object beams, respectively, and k is the modulus of the k-vector. In the simulation process, variables n and θ are set to 18 and 39°, respectively.Figure 2(a) presents the simulated interference intensity profiles on the x-y plane of a PQC. It is clear to see from Fig. 2(a) that the iso-intensity profile consists of circular bands (inner part) and circular clusters of points (indicated by solid lines) arranged in a circle with 18-fold rotational and mirror symmetry to the center. Further, the clusters at the outer region are arranged quasi-periodically in circles. Figure 2(b) gives the interference intensity profile simulated using Eq. (1) for a CMEDG sample. As seen in Fig. 2(b), it exhibits a 18-fold central symmetry and a radial arc-form ripple pattern. Such a profile is reasonable, since it is a holographic sample, and recorded using 18 repeated exposure/non-exposure cycles with an angular step of ~10°/ 10° as it revolves. Notably, the interference intensity profile comprises three different classes of profile. First, the inner region of the pattern contains circular bands. Eighteen holes correspond to regions of lower-intensity around a circle with a radius of ~2-3 μm (Fig. 2(c)). Finally, the profile presents polygons that are nearly concentric rings with a spacing of ~0.8 μm in the outer region (Fig. 2(d)). These concentric rings function as a 1-D grating across the x-y plane (with coordinates in Fig. 1). From the simulated results (Fig. 2(b)), based on holographic theory, the reconstructed images are expected to include 18 arcs in a circle when a beam probes normally incident on the sample in the direction of the reference beam (Fig. 1), since the application of the reference beam reconstructs the 18 object beams (Fig. 4(c) ). Comparing the intensity profiles of Figs. 2(a) and 2(b), we can find that the interference profiles do not include quasi-periodic at outer region for the CMEDG sample fabricated under continuous exposures. The PQC structure would expect to produce additional diffraction beams at inner side. On the contrary, the sample under the continuous multiple exposures is expected to produce a much simpler diffraction pattern due to the lack of quasi-period (long-range translation) as existed in a sample under point-by-point multiple exposures.
Fig. 2 Simulated patterns of two-beam interference with (a) PQC and (b) CMEDG (top view). The gray bars indicate intensity of interference; (c) and (d) are the patterns corresponding to regions (c) and (d) in Fig. 2(b).
Fig. 4 (a) The illustration of the normally incident probing beam positions (P(0)- P(3)) on the sample; (b), (c), (d) and (e) are the diffraction images of P(0), P(1), P(2), and P(3) from PQC, respectively; (f), (g), (h) and (i) show the diffraction images probed at positions P(0), P(1), P(2), and P(3) on a CMEDG sample, respectively; (j) shows the diffraction image with the probe beam being incident at a distance of 100 μm under the center.
Figure 3 shows a top-view SEM image (on the x-y plane at the coordinates in Fig. 1) of the polymer pattern formed in region (d) marked in Fig. 2(b). The structure of polymer surface contains grooves (polymer-rich region) and voids (LC-rich region), which fact is consistent with the simulated results (Fig. 2(d)). The spacing between the grooves is ~0.8 μm and the diameter of the voids is of the order of submicrons.
Fig. 3 Top-view SEM image of polymer structure in region (c) of Fig. 2(b). Scale bar represents 5 μm.
Figure 4(a) illustrates the probing positions of a normally incident laser beam (λ=532 nm, DPSS laser with beam diameter of ~1 mm) onto the sample at four positions P(0), P(1), P(2) and P(3) in the x-y plane. A movement stage is used to control the displacement of PQC and CMEDG samples. The point, P(0) is at the center, and P(2) is ~0.5 mm below the center. The lateral displacement between points of P(1) and P(2) (or P(2) and P(3)) is ~0.5 mm. Figures 4(b) and 4(f) show the diffraction patterns of the sample under point-by-point exposures (PQC) and continuous multiple exposures (CMEDG) with the probe beam being incident normally onto the center of the sample (P(0), as shown in Fig. 4(a)), respectively. As seen in Fig. 4(b), the diffraction pattern shows 18 diffraction beams and is consistent with that obtained from simulation (Fig. 2(a)). Figures 4(c), 4(d) and 4(e) are the diffraction patterns observed when the probe beam is normally incident onto the PQC sample (point-by-point exposures) at P(1), P(2) and P(3), respectively. The diffraction patterns of these probing positions are similar. However, it is clear to see from Fig. 4(f) that a CMEDG sample (continuous multiple exposures) generates 18 diffraction arcs when probed at the center P(0), and presents the images shown in Figs. 4(g), 4(h) and 4(i) at the probing positions P(1), P(2) and P(3), respectively. Notably, these diffraction patterns include only some arcs. Restated, the diffraction patterns reconstruct the writing object beams that form the interference pattern at the probing location. Notably, Fig. 4 (h) presents more diffraction arcs than Figs. 4(g) and 4(i), because the probed point is closer to the center than in the other two cases. Thus, it clearly gives very distinct diffraction patterns depending on the probing position on the H-PDLC sample, and can be applied for sensing laser-beam vibration. Briefly, the laser beam can be aligned to be normally incident onto the center of the formed CMEDG sample. It gives the diffraction pattern shown in Fig. 4(f). Once it deviates from the center, the diffraction pattern changes. The farther the laser beam deviates from the center, the less diffraction arcs are re-constructed as shown in Figs. 4(g)-4(i). The difference between PQC and CMEDG is believed to result from the fact that the structure (from the interference profile shown in Fig. 2(a) and 2(b)) of PQC has long-range translational symmetry, while it is not for a CMEDG sample.
In order to estimate the sensitivity of a CMEDG sample as a laser-beam vibration sensor, the sample is probed at various points displacing from the center in both vertical and lateral directions. Experimentally, the size of the probe beam is decreased to ~0.75 mm in this part of experiment. Figure 4(j) shows the diffraction image with the probe beam being displaced a distance of 100 μm vertically from the center. It is clear to see from Figs. 4(f) and 4(j) that, once it deviates from the center a distance of ~100 μm, the number of arcs of the diffraction pattern decreases significantly. Thus, the sensitivity of a CMEDG sample as a beam vibration sensor is within ~100 μm. Similar result is also found in the lateral direction.
In two-beam interference with multiple point-by-point exposures, the diffraction efficiency of the probe beam that is incident at the center is given by [17],
where d is the cell thickness and λ is the writing wavelength. The refractive index modulation, Δn, between LC (extraordinary refractive index) and the polymer is ~0.15. The index modulation ΔnM of Mth exposure is assumed to be ~Δn/M, since, in point-by-point multi-exposures, the monomer concentration decreases as exposure time increases, the structures formed by prior-exposure hinder the diffusion of un-reacted monomers, causing the index modulation ΔnM and the intensities of the diffraction beams to vary among the exposures. The result in Fig. 4(b) shows that the diffraction efficiency does, indeed, decrease with the number of exposures [18]. However, the diffraction efficiency at each point of arc diffraction beams of CMEDG structure is similar (as seen in Fig. 4(f)), because the sample does not expose in a particular position for a long time. Moreover, the diffraction efficiencies of 18 arc diffraction beams from continuous exposures exhibit slight decay. During multiple continuous exposures, the refractive index modulation associated with the Mth continuous exposure, the average refractive index modulation ΔnCM can be approximated by summing it of point-by-point exposures, and expressed aswhere σ is the coefficient of degree of polymerization that is determined by the rate of rotation of the motor. Mn is the nth time of continuous exposure. The value of ΔnCM under multiple continuous exposures does not decrease as rapidly as under point-by-point exposures. The calculation assumes that each continuous exposure with an angular step of 10° (for example 0°-10°) is analogous to n times point-by-point exposures. Here, more than 25 point-by-point exposures are as the sample rotates from 0° to 10° with an exposure time of ~2 s. In the fabrication using the two-beam interference of the present PDLC sample, the complete curing of monomer requires ~1 s. Additionally, the diffraction efficiency can be reasonably assumed to be approximately proportional to the exposure time. Therefore, the estimated degree of polymerization that is analogous to a point-by-point exposure reaches ~10% when the exposure time is ~0.08 s. Restated, the index modulation should be divided by a factor of ten, and the coefficient σ is estimated here to be ten. The cell gap and the wavelength of the probe beam are ~20 μm and 0.532 μm, respectively. Using these parameters, ΔnCM, calculated from Eq. (3), is ~0.00193. Substituting this index modulation into Eq. (2) yields the estimated maximum efficiency of the first exposure (angles of 0°-10°), ~5.1%. The measured maximum diffraction efficiency of the diffracted beam is ~2.7% when the probe beam is normally incident onto the center of the grating, and is lower than the simulated value, probably because of the scattering of the boundary of LC balls and the mismatch of the refraction indices between the LC balls and the polymer matrix. Notably, the efficiency also depends on the fabricated structure and the position of the probe with respect to the center.4. Conclusion
In conclusion, H-PDLC films are fabricated using point-by-point and continuous multi-exposures of two-beam interference. These generate photonic quasi-crystal (PQCs) and continuous multiple exposure diffraction grating (CMEDG). The structure of the CMEDG sample, observed using a SEM, exhibits radial symmetry, and is consistent with the simulated structure. Diffraction patterns from the formed CMEDG sample that is probed by a normally incident laser beam can be used to reconstruct some or all the recording arc beams, depending on the probing location. Thus, a CMEDG can be applied for use as a beam-vibration sensor for laser beams. Experimentally, the sensitivity of the sample as a beam vibration sensor is measured to be within ~100 μm.
Acknowledgement
The authors would like to thank the National Science Council of the Republic of China, (Taiwan) for financially supporting this research under Contract No. NSC 98-2112-M-006-001-MY3 and 98-2923-M-006-001-MY3. Ted Knoy is appreciated for his editorial assistance.
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