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Abstract
A novel optical sensor is proposed and demonstrated with the use of spherical-wave Bragg degeneracy of a volume holographic optical element. Bragg degeneracy can be performed perfectly for a volume hologram written by two plane waves or spherical waves. But only spherical reference light is useful to perform severe shifting selectivity in one direction and Bragg degeneracy in another direction. The experiment corresponding to theoretical simulation was demonstrated in a volume holographic optical element, which was an optical servo for a collinear volume holographic disc. Through clever design, the displacement response of the tracking beam was observed for a magnification magnitude of 980% to the displacement of the probe beam so that the resolution requirement of the photosensor can be reduced. Besides, a high linearity of the displacement response was observed. To discover the design freedom, a theoretical study of the displacement response was done for the servo by two spherical waves. The linearity, the magnification magnitude, and the diffraction efficiency were examined and the property of the Bragg degeneracy was figured out.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Volume holographic storage (VHS), owing to the advantages including high-density storage capacity, various multiplexing schemes, and long life has been extensively studied to perform more than 1TB storage to meet modern archival storage [1–8] with appropriate recording medium [9,10]. The extremely high storage density on a typical size such as a traditional blu-ray disc needs a design of high precise geometrical servo on the disc in the writing and reading process. The development of a low-price high precise geometrical servo is a key issue before the storage technique can be commercialized. The servo issue in VHS becomes more critical. High precision mechanical positioning is a potential approach, but strict tolerance management could pay a big price. The optical approach actually is a good way to sense micro- or nano- displacement and will be a good candidate in precise positioning and servo [11–15]. Besides, in the condition of reading disc from different machine, even the highest precision motor can’t make the disc locating exactly at the writing position [16]. Therefore, only a disc-embedded servo system can approach the writing position. Inphase uses the interfering fringes in the readout image to detect the disc misalignment [3]. Because the detection process requires a whole data page reading time, the shift compensation speed is limited. Collinear system adopted the market proved servo technologies in DVD system, and ensured the high speed sensing [17,18]. However, the combination of DVD layer makes the disc complex and cost more. In this paper, we propose a position servo of holographic data storage system using disc embedded volume holographic optical element (VHOE). It is not only fast in position sensing but also simple and low cost.
Most of the precise optical sensors could apply interferometry to reach sensitivity at the range of optical wavelengths. Similar but also different from an interferometer, volume holographic optical element (VHOE) [19] is an optical component to perform various extraordinary properties, including optical sensing. The mechanism for a holographic sensor is from the selectivity for the diffracted light [20–28]. In a volume hologram, Bragg condition induces high selectivity in the reading light, which includes wavelength selectivity and spatial selectivity [29–31]. Under a certain condition, there exists a condition called Bragg degeneracy, where the Bragg condition is released [29–30]. Bragg degeneracy causes insensitive property in the reading light and usually is not a candidate for a precise sensor. In this paper, we propose and demonstrate a novel scheme to implant a VHOE to serve displacement sensor in a VHS system. Through theoretical simulation and experiment, we present a study of Bragg degeneracy for an open window of a VHOE to perform an optical servo with high design freedom.
2. Bragg degeneracy
Bragg condition is an important factor in volume holographic diffraction [31]. Bragg condition can be satisfied if energy conversion and momentum conservation can be met simultaneously, as shown in Fig. 1(a). Generally, in the reading condition, if the incident angle or wavelength is different from the writing condition, a Bragg mismatch occurs. In some cases, a slight difference will cause dramatic decay of the diffraction efficiency. In the case that the grating is formed by two plane waves, the vertical displacement of the reading light will fall into the window of Bragg degeneracy, as shown in Fig. 1(b), where kg is the grating vector, ks1 and kr1 are the writing beams, kr2 is the reading beam and ks2 is the diffracted beam through Bragg degeneracy. It means that there is no decay in diffraction efficiency when the incident angle of the reading light is changed along the vertical direction. The Bragg degeneracy is not limited to plane wave incidence. However, plane wave reference is suitable for angular selectivity, not for shifting selectivity. When the incident lights are spherical waves, there is not only with severe Bragg condition in one direction but also with Bragg degeneracy in another direction [24–25,32–35], as shown in Fig. 2, where the hologram is written by a spherical wave and a plane wave. To simplify the calculation, the angle between the two writing lights is set 90°. In the case that the thickness of the volume hologram is L, the distance between the point source of the spherical wave and the hologram is zo, through the VOHIL model [32,36–37], the diffraction efficiency along the horizontal and the longitudinal directions can be written [33–34]
Fig. 1. (a) Schematic diagram of Bragg degeneracy in k space. (b) The direction of the Bragg degeneracy shown in the incident plane.
3. Principle and experiment
In our design, the tracking signal should be detected even when the disc shifts through several pages of data because it can minimize the consumption of recording material. Therefore, the recording of the VHOE and the data stream is independent of each other. It can be easily implemented by different-time recording, different-wavelength recording, or different-polarization recording. The system design of the VHS is shown in Fig. 3, which is a collinear system. In the collinear VHS system, the reference, and the signal displayed in the same spatial light modulator (SLM) are along the same optical axis. The reference light is a ring pattern surrounding the signal. The advantage of the collinear VHS system is free of alignment between the reference light and the signal light. The reference and the signal lights are relayed to the front focal plane of the objective lens by L2 and L4, and are focused onto the recording medium by the objective lens [38–41]. The concept of the collinear VHS system is illustrated through Fig. 4. The SLM in Fig. 4 is actually the relayed image of the SLM in Fig. 3. Note that the transmission setup in Fig. 4 is used to illustrate the recording and reading system which is a reflection-type system, where a reflection layer attached on the back side of the holographic disc so that the diffracted signal will be directed to the camera sensor on the same side of the SLM. The camera sensor in Fig. 4 is actually the conjugate image of the camera sensor in Fig. 3. If the reference is phase encoded, a possible shortage is that the complex reference pattern could cause strict mechanical alignment between different machines in reading the same disc. Through the 3D recording of the interference fringe, one record location on the disc could bear dozens of exposure by shifting multiplexing. This means that the multiplexing is done through rotation of the disc while there is no movement of the reference and signal. The Bragg selectivity relates to the design of the phase encoding structure on the reference area in the SLM.
Fig. 3. The setup of the collinear VHS system. M: mirror, L: lens, QWP: quarter wave plate, PBS: polarized beam splitter.
Fig. 4. The schematic diagram of the principles of the collinear VHS system and the VHOE-servo. (a) The writing process of the VHOE-servo, (b) the reading process of the VHOE-servo.
In such a way, how to identify the location is a key technology. Incorporated with the feedback loop of the driving motor, the optical scheme will be necessary to support the addressing precision. To develop an optical-added servo, we propose to implant a VHOE close to a certain specific recording location, but it is recorded independently from the data stream. The VHOE by using two-beam interference, and it is called VHOE-servo, as shown in Fig. 4. The new setup with the VHOE-servo is shown in Fig. 4. The two beams are from M8 and M9, respectively. The reflected light from M9 is collimated and finally is a convergent spherical wave onto the disc, and this is called the probe beam. The reflected light from M8 is a spherical wave and is collimated by the objective lens, and it is called the tracking beam. The convergent light and the collimated light finally build up the VHOE-servo in the data recording area, as shown in Fig. 5. The two beams are mutually tilted to each other along the y-direction, while the rotation of the disc will cause the effective displacement along the x-direction. It means that the grating could perform Bragg degeneracy when the disc slightly rotates.
When the disc rotates, the equivalent focusing point of the tracking beam is laterally displaced from the original position. As shown in Fig. 1, the diffracted light will be deviated from the original direction and finally causes a lateral displacement on the sensor plane. To enlarge the sensitivity, the focal length of the lens in front of the sensor can be enlarged, so that the displacement of the tracking beam could be enlarged.
In the experiment, we turn off the SLM to simulate a condition of the different-time recording. So the reference beam and the signal beam in the data stream do not interfere with the tracking and the probe beam in the servo system. The focal lengths of the lens are listed below: fL1 = 0.7 cm, fL2 = 20 cm, fL3 = 20 cm, fL4 = 18 cm, fL5 = 20 cm, fObj 2 = 0.4 cm. The laser wavelength was 532nm. The thickness of the recording medium was 2 mm. The probe and tracking beams on the sensor plane are shown in Fig. 6(a). But there was a serious problem observed in the experiment. If the Bragg degeneracy direction of the VHOE-servo is not precisely along the disc moving direction (e.g., y-axis), even a slight difference, serious Bragg mismatch will occur and it causes obvious degradation of the diffraction intensity of the tracking beam. In the simulation, only 2 µm displacement along the x-axis is allowed for effective diffraction. Such strict tolerance was not easy to control in the experiment. One of the solutions is to enlarge the displacement tolerance along the x-axis. Therefore, we changed L5 in the experiment from a spherical lens to a cylindrical lens, which enabled the probe beam to be a spherical wave along the y-axis and a collimated wave along the x-axis. It refined the wave front curvature along the Bragg direction and thus improved the shifting tolerance. The experimentally observed spots on the sensor plane is shown in Fig. 6(b). The phenomenon of abnormal intensity decay of the tracking beam was removed. The disc moving distance vs. the displacement of the tracking beam on the sensor plane is shown in Fig. 7, where high linearity was observed, as the prediction in the simulation. Through the lens effect, we can find that the displacement magnification magnitude was around 980%, so the required resolution of the sensor could become lower.
Fig. 6. The probe and tracking beams on the sensor plane, with (a) a spherical lens, and (b) a cylindrical lens of L5.
Fig. 7. Measurement of the displacement of the tracking beam vs. the lateral displacement of the optical disc. Five measurements were done at each condition.
4. Design freedom of the optical servo
The application of Bragg degeneracy on an optical servo is a new approach. Besides, there is design freedom to make the whole system at low cost and/or more compact. The Bragg degeneracy exits perfectly when the grating is made by two plane waves for angular selectivity and could exit for the grating interfered by two spherical waves if the radius of the curvature of the wavefront is large. In the application of position servo, the probe beam should be spherical wave to using shifting selectivity, the tracking beam could be either spherical wave or plane wave. Study with simulation to figure out when using two spherical waves to build up the VHOE-servo will be shown below. The simulation is based on the VOHIL model, where a volume hologram is regarded as a volume scattering object. Every point in the volume could scatter the incident light, with a specific phase transformation according to the recording fringes inside the volume [30,34–37,40–41].
Figure 8(a) shows the schematic diagram of the VHOE-servo, which is constructed by two convergent spherical waves. The control parameters are the focusing distance of probe beam (ZP) and tracking beam (ZT), the lateral shearing distance of the two spherical waves α, the thickness of the VHOE-servo t, the width of the VHOE-servo lx and ly. The first simulation is to check the linearity and diffraction efficiency variation with the fixed parameters: lx= ly = 200 µm, t = 1000 µm, ZP= ZT=2000 µm, when α is 500 µm, 1000 µm, and 2000 µm, respectively. The simulation shows that the displacement response of the tracking beam is linear with respect to the displacement of the probe beam. But the slope of the displacement becomes lower when α is larger, where the displacement of the tracking beam is 49.19 µm, 46.89 µm to 43.51µm, respectively when the probe beam reaches 50 µm. In addition, the diffraction efficiency of the tracking beam goes down obviously when α reaches 2000 µm. This means that larger separation between the two spherical waves will cause a breakdown of the Bragg degeneracy.
Fig. 8. Simulation of the Bragg degeneracy for displacement of the tracking beam vs. the probe beam with the incident condition shown in (a) in case of (b) α=500 µm, (c) α=1000 µm, (d) α=2000 µm. (e) Normalized diffraction efficiency vs. probe beam displacement.
The Bragg condition is related to the thickness of volume hologram. Thus we try to change the VHOE-servo thickness while α is fixed 1000 µm and keeps the other parameters unchanged. The simulation result is shown in Fig. 9. Not only that the Bragg degeneracy is worse than those in the thinner VHOE-servo but also that the displacement of the tracking beam departs from the linear line when the thickness of the VHOE-servo is as large as 2000 µm. This means that the thickness of the VHOE-servo needs to be controlled in a finite range or the radius of curvature of the spherical wave should be as large as possible.
Fig. 9. Simulation of the Bragg degeneracy for displacement of the tracking beam vs. the probe beam with the incident condition shown in (a) in case of (b) t = 500 µm, (c) t = 1000 µm, (d) t = 2000 µm. (e) Normalized diffraction efficiency vs. probe beam displacement. The grey lines in (b)-(d) are linear reference lines.
The axial focusing distance is also a design factor for VHOE-servo, and it seems that we can control the displacement of the tracking beam by changing the axial focusing distance. However, the unequal focusing distances of the spherical waves will cause a slanted grating vector and has a negative impact on Bragg degeneracy. In the next simulation, we introduce unequal focusing distances of the two spherical waves. The first is to extend the focusing distance ZP and to see what happens. Figure 10 shows the simulation result. The fixed parameters include lx= ly = 200 µm, t = 1000 µm, ZT=2000 µm, α=1000 µm, and ZP is set 2000 µm, 3000 µm, and 4000 µm, respectively, which correspond to 100%, 150% and 200% of ZT., which is called focusing ratio. The displacement response of the tracking beam is linear to the displacement of the probe beam, but the magnification magnitude of the displacement response becomes smaller when the focusing ratio is larger. The displacement magnification magnitude is 46% when the focusing ratio is 200%. In the three simulation conditions, the diffraction efficiency drops in a similar manner as the disc is laterally displaced, owing to the large radius of curvature of the spherical wave of the probe beam.
Fig. 10. Simulation of the Bragg degeneracy for displacement of the tracking beam vs. the probe beam with the incident condition shown in (a) in case of (b) ZP=2000 µm, (c) ZP=3000 µm, (d) ZP=4000 µm. (e) Normalized diffraction efficiency vs. probe beam displacement. The grey lines in (b)-(d) are linear reference lines.
The second is to extend the focusing distance ZT from 2000 µm, 3000 µm, to 4000 µm, corresponding to 100%, 67% and 50% of the focusing ratio, while ZP is fixed 2000 µm, and the other parameters are the same as the simulation shown in Fig. 10. The results are shown in Fig. 11. Similar to the previous case, the displacement response of the tracking beam is linear to the displacement of the probe beam, but the magnification magnitude of the displacement response becomes larger when the focusing ratio is smaller. The displacement magnification magnitude reaches 182% when the focusing ratio is 50%. The diffraction efficiency also drops as the disc is laterally displaced, but the behavior is different, where larger ZT causes larger decay in diffraction efficiency. The reason is that the shorter the focusing distance is, the more deviation of the wavefront of the probe beam to the original writing beam will be when the disc rotates.
Fig. 11. Simulation of the Bragg degeneracy for displacement of the tracking beam vs. the probe beam with the incident condition shown in (a) in case of (b) ZT=2000 µm, (c) ZT=3000 µm, (d) ZT=4000 µm. (e) Normalized diffraction efficiency vs. probe beam displacement. The grey lines in (b)-(d) are linear reference lines.
5. Conclusion
In this paper, we have proposed and demonstrated a novel design of an optical servo by means of volume holographic optical element. The so-called VHOE-servo is suitable to build up in a holographic recording medium, and therefore we proposed to use it in a volume holographic storage disc. The VHOE-servo utilizes the principle of Bragg degeneracy, where the displacement of the probe beam along the direction of Bragg degeneracy could cause effective diffraction of the tracking beam without or with less decay in diffraction efficiency. The displacement of the probe beam is actually induced by the rotation of the holographic disc and must be very tiny and difficult to sense with a low-cost sensor. By clever design on the optical system, the displacement of the tracking beam can be enlarged and be projected on the photosensor, so that a low-resolution photosensor can be used to detect small displacement. We have implanted the VHOE-servo in a collinear VHS system with a collimated tracking beam and a spherical probe beam. To conquer the severe sensitivity along the direction other than the Bragg degeneracy, we changed the probe beam to a cylindrical beam, where the wavefront along the other direction was collimated to release the severe Bragg sensitivity in this direction. Then we successfully observed the displacement of the tracking beam with high linearity of displacement response with respect to the displacement of the probe beam, where the displacement response fits the prediction in the simulation. Through the design of the focus lens on the photosensor, the displacement magnification magnitude is as large as 980%.
We have extended the study of the Bragg degeneracy for two spherical waves for the probe and tracking beams and to see the design freedom. To make a fair and practical comparison, all the key parameters are considered, including the dimensions of the effective volume of the VHOE-servo, the separation between the two spherical waves, the focusing distance of each spherical wave. The simulation shows that the thickness of the VHOE-servo is a key parameter. A thicker volume hologram will cause bigger degradation of the diffraction efficiency, and affect the linearity of the displacement of the tracking beam. If the focusing distances of the two spherical waves are different from each other, there exist complex behaviors. First, the drop of the diffraction efficiency is bigger owing to the slanted grating vector. It means that the displacement of the probe beam is not exactly along the direction of the Bragg degeneracy. Second, the displacement response of the tracking beam is a function of the focusing ratio. The displacement magnification magnitude is 46% when the focusing ratio is 200%, and the displacement magnification magnitude reaches 182% when the focusing ratio is decreased to 50%. Besides, a smaller focusing ratio makes more degradation on the diffraction efficiency.
The simulation indicates three important characteristics. First, in most conditions, the displacement between the tracking beam and the probe beam is linear. This makes the tracking calculation easy. Second, under a fixed disc thickness, e.g., 1 mm, the separation between the probe and tracking beams needs to keep as short as possible; otherwise, the decay of the diffraction efficiency of the tracking beam will suffer from serious Bragg condition. Third, appropriate control on the focusing ratio is a powerful way to enlarge the displacement of the tracking beam so that the sensing sensitivity can be enhanced with the use of a low-cost photosensor.
In summary, the study shows that there is high design freedom of the VHOE-servo, but it should be noticed to avoid serve Bragg condition along the direction other than the direction of Bragg degeneracy when implanting a spherical probe beam. Also, the thickness of the VHOE-servo should be controlled in a finite range.
Funding
Ministry of Science and Technology, Taiwan (108-2221-E-008 -097 -MY3, 108-2221-E-008-084-MY3).
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