Resonant optical cavities have been demonstrated to improve energy efficiencies in Holographic Data Storage Systems (HDSS). The orthogonal reference beams supported as cavity eigenmodes can provide another multiplexing degree of freedom to push storage densities toward the limit of 3D optical data storage. While keeping the increased energy efficiency of a cavity enhanced reference arm, image bearing holograms are multiplexed by orthogonal phase code multiplexing via Hermite-Gaussian eigenmodes in a Fe:LiNbO3 medium with a 532 nm laser at two Bragg angles. We experimentally confirmed write rates are enhanced by an average factor of 1.1, and page crosstalk is about 2.5%. This hybrid multiplexing opens up a pathway to increase storage density while minimizing modification of current angular multiplexing HDSS.
© 2016 Optical Society of America
As internet bandwidth continues to increase, consumers and corporate segments alike are moving their ever expanding data to remote data centers. Everything from personal media libraries to corporate finance data is being stored remotely. Ideally, we would like to store all of this data on the fastest possible medium, and we would like that medium to last as long, cost as little, and have the smallest possible form factor. Unfortunately, no such medium exists. Solid State Drives (SSD) are the fastest but most expensive form of storage, and do not have a very good shelf life. Other contenders are magnetic tapes, magnetic Hard Disk Drives (HDD), bit based optical discs, and Holographic Data Storage Systems (HDSS) under research. With so many options, one of the research focuses of data storage is a matter of matching the right kind of data with the right kind of storage device, which is a matter of “data temperature”. The data on a given storage system which is used most frequently is then the hottest data, and it needs to be stored on the fastest storage medium, such as SSD. The rest of the data then falls somewhere between hot and cold, where the coldest data is rarely used but must be kept in storage. For this cold data, it is possible to use slower media since the data is not in high demand during most of its lifetime.
Among the slower storage options, magnetic tapes and HDDs are the only two media which are easily re-writeable making them suitable for data that falls between hot and cold. Thus HDSS is best suited to archives where Write Once Read Many (WORM) memory is used to store immutable or stable data such as photos, music, medical histories, old financial records, etc. In the WORM field competitors include the SONY/Panasonic Archival Disc (AD) and possibly 5D eternal storage. AD sacrifices data transfer rates—359.65 Mbps—and storage density—250 GB/in3 in a standard 12 disc cartridge—for a ~50 year archive life . 5D storage promises densities as high as 439 TB/inch3 with an archive life on the order of 1020 years, but the data rates of this developing technology are still unknown . HDSS, on the other hand, offers maximum data transfer rates of 2.4 Gbps and a storage density of 720 GB/in3 while maintaining the same ~50 year archive life as AD at one 13th of the total cost of ownership of an AD system . With all of these advantages, HDSS is a promising option of WORM memory in cold data storage.
While HDSS is a very attractive WORM system, it is not very energy efficient: the nature of the holographic recording and readout process wastes 80% to 99.99% of the light provided by its laser source. Moreover, current HDSS storage densities are still well below the theoretical limit. 3D optical data storage is limited to the storage density of 1/λ3 bits/inch3 , which is equivalent to a density on the order of 10 TB/inch3. Reaching this goal will require the use of many Degrees Of Freedom (DOFs) to increase number of multiplexing. Currently, the number of angular multiplexed holograms is limited by the maximum available angular space for the reference beam, 180 degrees, which is already partially occupied by the object angular extent. To further increase capacity in keeping up with improving recording media , additional DOFs are needed to multiplex even more holograms while minimizing the modification of system optics and signal encoding schemes. As demonstrated previously, resonant optical cavities can be employed in readout  and recording  to recover much of the conventionally wasted light allowing for effective gains in energy efficiency, data transfer rates, and storage densities. Cavities can also sustain orthogonal modes for reference beams according to their eigenmodes. These eigenmodes are an inherently orthogonal set of functions, which means that they can be used as orthogonal phase codes to providing another DOF in HDSS multiplexing [8–10], bringing it closer to the 3D limit when effectively combined with angular multiplexing
In this paper we report the experimental demonstration of a cavity enhanced, orthogonal mode-angular hybrid multiplexing, which enables HDSS to accesses more multiplexing DOFs. First, crosstalk of image bearing holograms recorded via a Hermite-Gaussian (HG) 0,0 and a mostly-phase Spatial Light Modulator (SLM) generated HG 1,0 reference beam is evaluated. Second, eigenmode multiplexing of two distinct images at single location is demonstrated. Third, to demonstrate cavity enhanced eigenmode recording, images are recorded using a cavity enhanced HG 1,0 reference beam. Finally, we demonstrate cavity enhanced mode-angular hybrid multiplexing by enhancing the write rate of four distinct images which are successfully recorded and reconstructed by using both angle and mode multiplexing. Sections 2-5 address the experimental demonstration of single page crosstalk, eigenmode multiplexing, eigenmode enhancement of write rate, and cavity enhanced mode-angle multiplexing, respectively. Section 6 discusses crosstalk, the utility of the technology in enhancing data density, and potential limitations of cavity enhanced mode multiplexing when it is applied to HDSS along with angular multiplexing.
2. Crosstalk of single holograms read out by orthogonal cavity eigenmodes
The orthogonality of image baring holograms is tested by using HG, optical cavity, eigenmodes as write reference beams. We record a single image bearing hologram at its own location in the crystal by either an HG 0,0 or an HG 1,0 reference beam. The image is reconstructed with one of the two orthogonal beams and the diffraction efficiencies are compared when the hologram is read out with each beam. Crosstalk is evaluated by taking the ratio of the diffraction efficiency of the matched reference beam to that of the orthogonal reconstruction beam.
As seen in Fig. 1 an SLM (Model LC 2012, Holoeye) is setup in the reference arm of a holographic recording geometry and illuminated with a 532 nm wavelength beam from a frequency doubled Nd:YAG laser (Compass 315M, Coherent). The recording setup is downstream of a 340 mm focal length lens. This lens Fourier Transforms (FT) the reference beam from the SLM with an additional phase and scaling factor , and creates a beam with a 1/e field radius of ~304 μm in the crystal. The linear polarizers and λ/2 plates around the SLM are set to operate the SLM in the “mostly phase” modulation mode . The term “mostly phase” refers to a coupling of phase and amplitude modulation in the SLM. In particular, if we normalize the transmission of the SLM such that the minimum transmission is unity, then maximum phase modulation corresponds to a roughly 9 times higher transmission. The reference beam then passes through the Fresnel beam sampler, which is used in the trials of Section 4 for enhancement monitoring. The signal arm expands a Gaussian beam to a collimated beam with an approximate diameter of 5 mm. This collimated signal beam passes through the transmissive object to be recorded. The transmissive object is then FTed by a microscope objective lens with f = 53mm (Model 80.3020, Rolyn Optics). The two beams intersect inside of a 0.015 mole % Fe:LiNbO3 crystal (Deltronic Crystal Industries, Inc.) with the c-axis perpendicular to the reference beam and parallel to the plane of the recording beams. The crystal is 5 mm thick, 10 mm wide, and 20 mm tall. Since the signal and reference beams are vertically polarized and the crystals optical axis is horizontal, all beams in these experiments encounter only the ordinary refractive index. Consequently there are no effects from the birefringence of LiNbO3. Upon readout of the hologram a CMOS camera (DCC1445M, Thorlabs) is placed in the readout beam to record the reconstructed image. Diffraction efficiency is also measured at this point with a power meter (Newport 1918-R unit with a 918D-SL-OD3 detector).
The mode of the reference beam is controlled by setting the SLM to either a vertically split screen or a uniform screen. The split screen uses bit values of 0 and 157 to create a 0 to π phase step that bisects the incident Gaussian beam converting it to a HG 1,0 beam. The uniform screen uses a bit value of 157 over the entire SLM to make sure that the reference beam has the same power inside the Fe:LiNbO3 crystal. This is possible because of the “mostly phase” modulation of the SLM which has some amplitude modulation coupled to the phase. The profiles of the reference beams at the location of the Fe:LiNbO3 crystal depicted in Fig. 1 are shown in Fig. 2.
The largest number ‘2’ on a resolution bar target (USAF-1951 RES-1, Newport) is used as the object to be recorded. The original image is taken with the CMOS camera and the image is written once with a HG 0,0 reference beam and once at a separate location 1.5 mm apart with a HG 1,0 beam. The holograms are read out via both the HG 0,0 and 0,1 beam and the images are captured. The images can be seen in Fig. 3.
The diffraction efficiency of each hologram is recorded when illuminated with each reference beam. The hologram recorded with an HG 0,0 reference beam has a diffraction efficiency of 0.581% under HG 0,0 readout and 0.014% under HG 1,0 readout. Similarly, the hologram recorded with an HG 1,0 reference beam had diffraction efficiencies of 0.0066% and 0.393%. Taking the ratio of those diffraction efficiencies we find that recording with the HG 0,0 beam has a single page crosstalk of 2.5% and the HG 0,1 recording has a crosstalk of 1.7%.
Furthermore, this test was repeated with six other holograms at separate locations in the crystal for a total of eight holograms. Crosstalks were similar for HG 0,0 and 0,1 recording, so we report the mean of all eight crosstalks as 2.48% with a standard deviation of 1.17%.
While, the crosstalks are low, readers should notice the blur in the reconstructed images. This is a result of low pass filtering during recording. Since the extent of the signal beam inside the recording material is a FT of the illuminated object, the recording process naturally cuts off higher spatial frequencies as the reference beam acts as a low pass Coherent Transfer Function (CTF). In particular the Gaussian apodization caused by the reference beam would blur a reconstructed image under a one-to-one imaging condition which is our experimental case. The extent of the blur can be calculated by convolving the image with a Gaussian spot with a 1/e field diameter ofFig. 3.
Readers should also notice narrow dark lines in the images. The lines are defects in the CMOS camera used to capture the images. The vertical line present in the reconstructions is not visible in the original object because the crystal shifts the beam path as a plane parallel plate would. The original object was recorded without the crystal in the path, thus when the holograms were recorded the signal beam was shifted relative to the CMOS defects. While the vertical line is not present in both object and reconstructions, the horizontal line is. This further supports the fact that the lines are a result of CMOS defects, and a shift in the signal beam path rather than some unknown optical phenomenon.
Returning to the blur in the image, the broad dark lines in the reconstructions are likely due to the biased nature of the CTF created by the overlap of the reference beam and signal beam. The vertical extent of the reference beam’s interaction with the signal beam is consistent throughout the volume of the hologram, but the horizontal angle between the reference and signal beam effectively widens the CTF in the horizontal direction. Thus the resolution of the system is higher in the horizontal direction than in the vertical. This can be seen it the way that the top and bottom of the “2” are more washed out than the more vertical lines in the middle of the “2”. A secondary reason for the existence of the large dark regions in the reconstructions is the fact that this is a coherent imaging system. Any phase errors from misalignment will show up in the image as interference patterns.
3. Image multiplexing with Hermite-Gaussian reference beams
Using the experimental setup of Fig. 1, an image of the largest number “0” on the USAF test chart is recorded using a HG 0,0 reference beam, and an image of the largest number “1” is recorded at the same location using a HG 1,0 reference beam. The exposure times are adjusted to equalize the diffraction efficiencies of the two holograms. After recording, the two holograms are illuminated by each of the two reference beams, and the resulting images are captured.
Figure 4 shows the captured images from the multiplexing experiment. This clearly demonstrates the low crosstalk of HG mode multiplexing as the “1” does not show up in the “0” image and vice versa. In this case we would expect crosstalks similar to those measured in Section 2.1. In fact, Fig. 4 (a) shows a maximum crosstalk of 2.58% and Fig. 4 (b) has a maximum crosstalk of 1.25%. Both crosstalks agree nicely with the 2.48% average crosstalk of Section 2.
4. Cavity enhanced writing with Hermite-Gaussian eigenmodes
A setup similar to that of Fig. 1 in Section 2.1 is used with the addition of monitoring the diffraction efficiency by a pseudo phase conjugate geometry . In Fig. 5, a resonator cavity is formed in the reference beam around the crystal by inserting a 42.8% transmission, planar entrance coupler, and placing a 1 inch diameter, 200 mm radius of curvature, 99% reflective, spherical mirror 100 mm away from the entrance coupler. The reference beam is the HG 1,0 generated by the SLM. The cavity is stabilized during the recording process by a proportional gain feedback loop with the power sampled by the intracavity Fresnel beam sampler as an input and the driving voltage of the spherical mirror’s PZT mount as the output. During recording, the reverse propagating reference beam is used to read out the hologram in the pseudo-phase conjugate geometry, and a Fresnel beam sampler is used to reflect this diffracted readout signal into the condensing lens. Passing the condensing lens the readout signal beam is optically chopped at 190 Hz and detected by a photo diode (DET36A, Thorlabs) which is lock-in amplified (Model 5210, EG&G Princeton Applied Research). The diffraction efficiency is thus measured as a function of exposure time.
The time evolutions of the diffraction efficiencies of a cavity and a non-cavity hologram recorded at adjacent locations and separated by 1.5 mm are then compared by scaling the data to compensate for pseudo-phase conjugate readout and convert the voltage data into actual diffraction efficiency values. The scaling is derived by starting with an expression for the output voltage of the lock-in amplifier:Eq. (3):Eq. (3) we simplify Eq. (2):Eq. (6) to find the time constant τ with which the diffraction efficiency grows :
Taking the ratio of the non-cavity to cavity time constants we get the cavity enhanced write rate. For five trial pairs we get a Write Rate Enhancement (WRE) of 1.13 ± 0.03. The cavity enhancement of irradiance was GF = 1.38 ± 0.07. According to our previous work , the theoretical WRE for a unit splitting ratio is , so we expect a WRE of 1.18 ± 0.03. Thus, we achieved 96% of the theoretical enhancement with the expected range of theory and result overlapping. This synchronicity proves that HG beams can be used in cavity enhanced recording. The results are summarized in Fig. 6 where the cavity enhanced diffraction efficiency evolves faster than normal writing, and the histogram insert shows that all five trials show enhancement.
The single page crosstalk was also measured for three of these trials yielding an average crosstalk of ~6.2%. This increase in crosstalk from cavity recording is likely due to poor mode matching to the cavity. The 340 mm mode matching lens used is sufficient to allow cavity enhancement, but a better choice of mode matching lens would provide better mode purity in the cavity and higher enhancements.
5. Combined angular and mode multiplexing with cavity enhanced writing
Angular and mode multiplexing are combined while enhancing the write rate with a cavity on the reference arm. The experimental setup is similar to that of Fig. 5, except that the first polarizer, wave plate, and SLM have been replaced with a custom phase plate to convert the beam to a HG 1,0 beam. The Fe:LiNbO3 crystal has also been remounted on a goniometer stage for angular multiplexing. The center of rotation of the goniometer is located at the crossing point of the reference and signal beams. Reconstructions are also observed by placing the CMOS camera where the transmissive object had been for pseudo phase conjugate readout.
Four holograms are multiplexed using 0° and 0.6° angles, and an HG 0,0 and an HG 1,0 reference beam. The 0.6° angular separation was chosen by monitoring the diffraction efficiency of a hologram written with a Gaussian reference beam: since Bragg side lobes are expected to be ~1x10−4 of the Bragg matched efficiency , we chose the separation by rotating the hologram to 1x10−2 of the Bragg matched efficiency, at 0.4°, and proceeded to the next increment on the goniometer stage, 0.6°. While this angle is likely still smaller than the first Bragg null, it provides angular crosstalks that are unmeasurable for single pages. Each hologram is written with a cavity enhanced reference beam with an average GF = 1.20. First an image is recorded at 0° with an HG 0,0 beam, second an image is recorded at 0° with an HG 1,0 beam, third an image is recorded at 0.6° with an HG 1,0 beam, and fourth an image is recorded at 0.6° with an HG 0,0 beam. Each of the four images is reconstructed via pseudo-phase conjugate, cavity enhanced readout, and the results of the reconstruction are shown in Fig. 7.
In Fig. 7, an average crosstalk of 10% is observed in the reconstructions, but careful control of cavity mode matching, and mode generation fidelity should remove this effect. This crosstalk is expected to be on the order of 6% as seen in Section 4, but the change of mode converter is likely responsible for this.
Crosstalk aside, readers may notice that the images of Fig. 7 show fall-off in image brightness with the center of the images being bright and the edges being dim. This is a natural consequence of illuminating the USAF bar target with a collimated Gaussian beam. Thus, the fall-off is Gaussian in nature due to the collimated Gaussian illumination.
Existing theory predicts zero crosstalk for plane wave signal holograms multiplexed using optical cavity eigenmodes , but we see crosstalks at ~2.5% in the single page trials of section 2. This is likely due to the crosstalk inherent in page base holography using image bearing object beams , but this crosstalk could also be due to several other factors: SLM phase error, SLM coupled amplitude modulation, Gaussian beam imperfections, and stray light.
The SLM has limited bit levels to choose from for setting the π phase shift, so some digitization error may be present in the split screen used to create the HG 1,0 beam. Concurrent to digitization error, the SLM used can only be made to operate in “mostly phase mode”, which comes with some amplitude modulation coupled to the phase modulation [12,13]. The combination of these effects are likely responsible for the horizontal spread of the reference beam seen in the HG 1,0 beam profile of Fig. 2, which would decrease the purity of the beam and thus its orthogonality to the Gaussian beam. Similarly, any imperfections in the beam produced by our source would reduce orthogonality.
Crosstalk power readings may also have been influenced by stray light reflecting off of the many surfaces in the system. This is particularly likely as diffracted signals with matched reference and readout beams were on the order of 100 nW while the mismatched signals were on the order of 1 nW. The noise of the power meter was around 0.5 nW in the fully dark conditions that data was recorded, so SNR is on the order of 2 for measuring the diffraction efficiency in the mismatched case.
For the recording of multiplexed images, Bashaw et. all include the effects of dephasing in broadband signal recording and show that orthogonal phase code multiplexing provides overall crosstalk to signal ratios which are a factor of two lower than those of angular multiplexing . Such reduced crosstalk is appealing for reducing bit error rates and increasing recording density, but cavity eigenmode multiplexing cannot completely replace angular multiplexing for two reasons.
First, mode dimensions increase as the square root of the mode number, so the cavity diameter puts an upper limit on the number of modes that can be used . Second, when using an FT recording geometry the mode profile of the reference beam impacts the CTF in a manner similar to Gaussian apodization. If the reference mode contains a field null parallel to the signal and reference beam plane of incidence (e.g. HG 0,1), the reference beam will act like a high pass filter in recording. This further limits the available choices of cavity modes. Thus, reaching the industry goal of hundreds of multiplexed pages is impossible using only cavity eigenmodes.
Nonetheless, cavity enhanced mode multiplexing combined with angular multiplexing is feasible as seen in Section 6, and is an attractive way to increase data density. Adding mode multiplexing to an angular multiplexing scheme provides an additional DOF for system design increasing data densities toward the theoretical limit . Currently, the number of multiplexed pages reported in literature is about 440 which is primarily limited by the angular extent of the reference beam scanning . However, employing an HG 1,0 mode in the reference path in addition to the currently used HG 0,0 mode improves the number of multiplexing by a factor of 2. Although more area is needed due to the larger dimensions of higher order HG modes, the theoretical recording density still increases by about 1.33. Additionally, the reference path optics do not require substantial modifications. As seen in Fig. 2, the mode diameter along the horizontal direction increases by factor of 1.77 while the vertical dimension is unchanged. An ideal HG 1,0 has a 1/e field radius ~1.5 times larger than the HG 0,0 beam, so it is clear that the experimental beam is wider than is should be in theory. This may be a result of the phase error mentioned earlier or the fact that our FT geometry does not place the phase plate at the front focal plane or surface of the mode matching lens . Experimentally, storage density increases by factor of 2/1.77 = 1.13, but in theory increases by 2/1.5 = 1.33. This seems like a small increase until we consider the trend as higher order modes are added, and the growth in beam size more closely matches the square root approximation . The number of multiplexing increases as the maximum mode number plus one, and mode size increases like the square root of the maximum mode number, so the storage density will increase with the number of modes used as shown in Fig. 8, allowing for a factor of 2.1 storage density increase when five modes are used.
While mode multiplexing adds another DOF to HDSS design to increase data density, combining it with angular multiplexing raises the question of angular Bragg selectivity for mode multiplexed holograms. The effects of Gaussian apodization are known to reduce the height of the side lobes in angular multiplexing while increasing the angular width of the Bragg selectivity relative to plane wave reference beams [9,16]. The width of the Bragg selectivity decreases as the beam diameter increases, so we would expect higher order modes to create narrower Bragg selectivities relative to Gaussian recording. Thus, overall, Bragg selectivity for higher order mode multiplexing does not negatively affect storage density, but further investigation is required before mode multiplexing can be implemented in commercial systems.
Bragg selectivity aside, the optimum number of reference modes must be investigated while accounting for the tradeoffs in beam dimensions and Bragg selectivity, because higher order modes provide diminishing returns on storage density. Mode dimensions increase proportional to the square root of the mode number, thus an increase in mode number directly increases the spacing of books in the storage medium. At the same time storage density is increased directly by the number of modes used for multiplexing. Thus, storage density increases according to:Fig. 8, the mode size is plotted in units of the HG 0,0 mode waist on the vertical axis, and the storage enhancement is plotted with the multiplicative storage density increase on the vertical axis.
Leaving the topic of storage density, orthogonal mode multiplexing has another advantage when paired with angular multiplexing. Angular multiplexed volume holographic data storage has an issue with beam fanning, which can hinder the use of pseudo-phase conjugate readout when present in the reference arm, but the use of orthogonal reference beams causes the total beam fanning effect to be divided over the all of the reference beams used. Since the reference beams are orthogonal, the beam fanning caused by the self-interference of the reference beams are also matched to the reference beam that created those patterns. Thus beam fanning caused by an HG 1,0 reference is separate from fanning caused by an HG 0,0 reference. This orthogonality of fanning means that fanning of the reference beam should be reduced by a factor equal to or greater than the number of reference beams used.
Moving on from beam fanning, Mikami and Watanabe made use of the polarization states of their recording beams to accomplish mode multiplexing . In this paper we used phase plates to convert the mode of the reference beam directly from Gaussian to HG, but Mikami and Watanabe’s work suggests that it may be possible to accomplish mode multiplexing by altering the polarization states of the signal and reference beams. This would simplify our optical system considerably, as the use of polarization would remove the need for costly SLMs.
Optical cavities in the reference arm make it possible to improve HDSS recording efficiencies, speeds, and data densities when applied with simple Gaussian reference beams. Cavity eigenmodes provide an additional degree of freedom to angular multiplexing for HDSS to increase the recording density. For the first time, to the best of our knowledge, cavity enhanced, eigenmode and angular multiplexing of image bearing holograms is experimentally demonstrated. Currently, single page crosstalks of ~2.5% for unenhanced holograms, and ~10% for cavity mode-angular hybrid multiplexing is confirmed. The total number of multiplexing is increased by the number of eigenmodes supported by the cavity. The trade-off in reference beam area vs. number of multiplexing pages provides diminishing returns on storage density for higher order modes as the beam dimensions increase; however, the use of the first five modes would grant double the storage density. To further increase the recording density, challenges such as mode conversion fidelity, cavity mode matching, and trade-off balancing between angular Bragg spacing and mode size of higher order cavity eigenmodes have to be addressed. Optimization aside, this demonstration provides a pathway to a more complete usage of the available degrees of freedom of three dimensional optical data storage towards the theoretical storage density limit, 1/λ3 bits/inch3.
We would like to thank Hitachi, Ltd. for the use of their Holoeye LC 2012 spatial light modulator.
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