We present principle and technique to actively stabilize and control the phase differences between multi-laser beams that produce stable and adjustable intensity patterns. This technique is based on a novel optical set-up and on a closed loop control over the phase difference between each pair of the input laser fields. Tunable optical lattices are demonstrated by exciting FeTPPCl-doped liquid crystals with the variable intensity patterns.
© 2007 Optical Society of America
Fabricating photonic crystals with holographic lithography takes advantages of complex intensity patterns from multi-beam interference . This fabrication technique with a sub-wavelength lattice period has a number of desirable advantages including low cost, large area recording and defect-free processing thus it has attracted a great deal of research attention in recent years[2, 3].
Theoretical and experimental effort for holographic lithography has been successfully using a multi-beam arrangement, giving rise to the required spatial intensity pattern. Multi-exposure holographic lithography with discrete phase retardation provided by a quarter or half wave plate between multi-beam configurations has been demonstrated [4, 5]. However, as the nature of the light interference, the environmental disturbances, e.g., vibration, air turbulence and thermal drift, always presents the challenge to the long time stability of the interference intensity patterns. In fact, a single prism was applied to provide and combine the multi-beam in order to assist the alignment and to reduce the experimental instabilities . Phase masks were also applied to improve the sample quality . Active stabilization of the phase differences for multi-beam holographic lithography has not been reported so far to the best of our knowledge, and precise control of the phase differences between interfering beams should be expected to supply a necessary freedom to tune the lattice parameters for the interference intensities, which should be useful for the nanotechnology in general and for holographic lithography in particular .
In this contribution, we demonstrate the use of optic-electronic-mechanical technique to actively stabilize the interference pattern from the multi-laser fields. We further show that the phase of each interference beam can be independently varied, giving rise to stable and rich intensity patterns. An FeTPPCl [5,10,15,20-Tetraphenylporphineiron (III) chloride]-doped 5CB liquid crystal (LC) is applied to register the variable intensity pattern, showing the practicability of making desirable tunable optical lattices with the phase controlled holographic lithography.
2. Theory and experiment
With Ei, ki, and φi representing the field amplitude, wave vector and phase for the ith field, respectively. It is necessary to point out that the pattern instabilities are caused mainly by the random variation of the phase difference (φi - φj) in laboratory conditions.
2.1 Stabilization experiments
The control of the phase difference between two collinear laser beams is a standard practice for many optical experiments, and it is widely applied for ultrashort light pulse measurement  and for coherent control . The active stabilization and control of the phase difference is usually based on the sensing the phase difference from the two-beam interference and the variation of the optical path difference is compensated by an added phase shift, usually provided by a piezo-actuator . For two laser beams with different propagation directions, the interference is produced only in the overlapping region. However, the interference state can also be observed if the light fields are redirected so that they collinearly propagate and interfere. The translation of the local interference to a collinearly propagating interference was realized by Chen et al. for two-beam interference lithography .
The phase control for multi-beam interference is in general more difficult because of the speckles in the interacting region, apart from the increased experimental complexity. Here we design a single device and a fringe lock feedback system to lock the phase difference of two beams marked as beam 1 and beam 2, as shown in Fig. 1. The tri-angled prism redirects the light fields of two laser beams to propagate collinearly along the direction 3 and produces the interference fringes. This single device introduces negligible additional random variation of the phase difference, as both beams are sharing the same optical component and as the prism introduces only constant optics path difference. The phase stabilization system is similar to the feedback loop control adopted in the reference , which consists of the interference pattern magnification, photodiode detection, electronics and piezo control. An aperture with the diameter at 1/20 of the fringe periods is placed before the photodiode. The piezo is control by a Digital Signal Processor using digital proportional-integral-differential control method. The sensed phase shift is detected, analyzed and compensated by the feedback system to overcome the intensity instability.
2.2 Phase control experiments
A three-beam interference configuration is studied in this work, as shown in Fig. 2. Laser output from a He-Ne or a frequency doubled Nd:YVO4 is split into three beams with equal intensities, which are combined to overlap with equal incident angle on the surface of the substrate material. Each pair of the beams are steered to propagate collinearly and to interfere in front of two detectors (shown in Fig. 2). The intensity pattern formed at the substrate is recorded by a CCD camera.
The response time of closed loop control unit is less than 0.4 ms, which is much faster than the ambient change of the experimental conditions. Furthermore, it is possible to vary independently the phase term for any values between (0, 2π) for each interfering laser beam, giving rise to additional freedom to change the intensity pattern. Tuning of the phase difference is achieved by translating the detector, so as to allow the piezo to move to a new position to translate the interference fringes to a new locked phase difference.
3. Results and discussion
Figure 3(a) shows the intensity pattern recorded within 12 s without the active control unit. The period of interference spot is measured to be 1.2 μm. It is obvious that the intensity pattern becomes unstable as a result of the random phase shift for any of the incident light fields. On the contrary, the pattern recorded over 14 s [shown in Fig. 3(b)] with the active stabilization control unit is very stable, demonstrating the insensitivity of the system to the ambient change. Figure 4 shows the averaged intensity pattern recorded for a period of 9 min with the active control unit, which clearly demonstrates the practicability of the technique for holographic lithograph. The analysis of the CCD recorded pattern shows that the periodic pattern can be stabilized spatially within λ/20, where λ is the wavelength of the laser radiation. Hence with the phase locking unit, no air-suspension optical table is needed, and the exposure time for any photoresistive materials can be extended to many minutes.
The control of the phases for each light field to adjust the intensity pattern is presented in Fig. 3(c). The intensity pattern shifting along the x-arrowed direction with a phase shift from 0 to 5π/3 is presented. Equally, the phase change for another beam can translate the intensity pattern along other directions. These two feedback systems are independent of each other and it is possible to simultaneously lock the pattern and to impose different phases among the interfering beams so as to translate the locked pattern along the desirable direction. This controlled pattern translation is very useful for holographic lithography, as the conventional way to change the exposure spots is to move and rotate the sample . With this technique, no sample movement is required, thus providing greater accuracy for the holographic lithography.
For the demonstration of a tunable Bragg grating, a FeTPPCl-doped 5CB LC  is employed as the material to record the interference pattern. The laser radiation is from frequency doubled Nd:YVO4 at 532 nm and three beams 1 2, and 3, with the same intensity E 2 are coplanarly arranged to interfere in the doped LC, as shown in Fig. 5. Based on Eq. (1), the three-beam interference can be expressed as
With k = 2π/λ , and φ 12 , φ 13 and φ 23 representing respectively the phase difference between beam 1 2, 1 2 and 2 3, where λ, is the wavelength of exciting Nd:YVO4 laser and θ=1.8°. Light-induced grating structure is produced due to refractive anisotropy of LC with a voltage applied across the LC to reduce the intensity threshold. The established phase dependent fringe pattern can be detected by self diffraction or by using a He-Ne laser to monitor the Bragg structure through diffraction. The period of the Bragg structure, which is shown in the inset (a) of Fig. 5, is λ / sinθ for the three beams with equal initial phases. While phase of beam 1 shifts by an amount of π, grating period is reduced to λ/2sin θ (shown in inset (b) of Fig. 5), which in term affects the diffraction of He-Ne. As the response time of the LC is in the order of hundreds milliseconds , a saw tooth voltage driving piezo will provide the change of the phase with a period of 1.25 s, resulting in a real time change of the grating structure. Periodic grating structure shifting from one period to another will then induce the variation of the diffraction intensities.
Figure 6 shows the recorded diffractions as a function of the varying phase shift of beam 1. As phase shift from 0 to π, the grating period becomes twice smaller, which reduces the diffractions of odd orders as ±1,±3 … while enhancing the diffractions from even orders. The perfect inverse variation of diffraction intensity labeled as +1 and +2 in Fig. 5 supports the prediction very well. We can conclude that the variation of diffraction intensity originates from change of grating period, which is controllable through the phase control technique.
We present in this contribution the principle and technique to actively stabilize and control the phase differences between multi-laser beams that produce stable and adjustable intensity patterns. Tunable optical lattices are demonstrated by exciting FeTPPCl-doped liquid crystals with the variable intensity patterns.
The extension of the present technique to more complex multi-beam arrangement is possible with improved experimental arrangement. Furthermore, the demonstration of the variable optical lattice and real time recording with LC opens up the opportunity to a time dependent, or 4-dimensional PC. The phase-induced diffraction intensity change also promises immediate applications, such as the efficient light-controlled light switching.
This work has been supported by the National Key Basic Research Special Foundation (NKBRSF) (G2004CB719805) and Chinese National Natural Science Foundation (10374120).
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