THREE DIMENSIONAL OPTICAL DATA STORAGE IN POLYMERIC SYSTEMS

By

CHRISTOPHER J. RYAN

Submitted in partial fulfillment of the requirements

For the degree of Doctor of Philosophy

Dissertation Adviser: Dr. Jie Shan

Department of Physics

CASE WESTERN RESERVE UNIVERSITY

May, 2012

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

Christopher James Ryan candidate for the Doctorate of Philosophy degree

Dr. Jie Shan

Dr. Kenneth Singer

Dr. Rolfe Petschek

Dr. Lei Zhu

January 20, 2012 Table Of Contents

List of Tables 4

List of Figures 5

Acknowledgements 7

Abstract 8

Chapter 1 Introduction to Optical Data Storage 9

1.1 Motivation 9

1.2 Features of Optical Data Storage 9

1.3 A Brief History of Optical Data Storage 12

1.4 New Techniques for Optical Data Storage 15

1.5 3D Optical Data Storage 19

1.6 Multilayered Films as Storage Media 22

1.7 Coextruded Polymeric Films 23

1.8 Chapter Content 24

Chapter 2 Two‐Photon Induced Aggregate Switching of Excimer‐Forming Dyes 25

2.1 Introduction 25

2.2 Materials 27

2.3 TPA of C‐18 RG Dye 30

2.4 Experiment 31

2.5 Results and Analysis 32

2.6 Chapter Conclusion 34

Chapter 3 High Density Optical Data Storage in Multilayer Polymer Films 36

3.1 Introduction 36

3.2 Sample Fabrication 39

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3.3 Film Properties 41

3.4 Optical Patterning and Reading 42

3.5 Determination of the Crosstalk 47

3.6 Modeling of the Layer Crosstalk 48

3.7 Comparison to Crosstalk Model 50

3.8 Chapter Conclusion 52

Chapter 4 The effect of Multilayering on the Contrast of 3D Data Storage Media 53

4.1 Introduction 53

4.2 Geometric Restriction to the Data Density 55

4.3 Determining the Signal Contrast and Background Noise 57

4.4 Comparing Multilayered Films to Monoliths 61

4.5 Results 63

4.6 Shot Noise and Dark Current 66

4.7 Chapter Conclusion 68

Chapter 5 Thermal Influence on Biexciton Annihilation in Zinc Phthalocyanine 69

5.1 Introduction 69

5.2 Materials 70

5.3 Experiment 72

5.4 Results 73

5.5 Physical Interpretation of the Time Dependence of the Collision Rate 76

5.6 Thermal Dependence of the ZnPc 80

5.7 Conclusion 83

Appendix A Power Dependence of Photopatterning in C‐18 RG dye 85

A.1 Introduction 85

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A.2 Reading from Subdiffraction Systems 89

A.3 Sample Preparation 90

A.4 Photopatterning at the TPA Wavelength 90

A.5 Photopatterning with Linear Absorption 94

A.6 Appendix Conclusion 97

Bibliography 98

3

List of Tables

Table 5.1 71

4

List of Figures

Chapter 2 Two‐Photon Induced Aggregate Switching of Excimer‐Forming Dyes 25

Figure 2.1 27

Figure 2.2 28

Figure 2.3 29

Figure 2.4 29

Figure 2.5 33

Figure 2.6 33

Chapter 3 High Density Optical Data Storage in Multilayer Polymer Films 36

Figure 3.1 40

Figure 3.2 42

Figure 3.3 42

Figure 3.4 44

Figure 3.5 47

Figure 3.6 48

Chapter 4 The effect of Multilayering on the Contrast of 3D Data Storage Media 53

Figure 4.1 55

Figure 4.2 57

Figure 4.3 60

Figure 4.4 60

Figure 4.5 62

Figure 4.6 64

Figure 4.7 65

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Figure 4.8 66

Figure 4.9 67

Chapter 5 Thermal Influence on Biexciton Annihilation in Zinc Phthalocyanine 69

Figure 5.1 71

Figure 5.2 74

Figure 5.3 74

Figure 5.4 82

Figure 5.5 83

Figure 5.6 83

Appendix A Power Dependence of Photopatterning in C‐18 RG dye 85

Figure A.1 91

Figure A.2 92

Figure A.3 93

Figure A.4 95

Figure A.5 96

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Acknowledgements

A broad range of techniques, skills, and principles are required to create and refine new ideas as related to these multidisciplinary projects. My contributions to the field exist only as enabled by my interactions. Throughout the course of these experiments and inventions, I collaborated with many individuals from the various departments at CWRU.

Here is presented a list of those individuals whose contributions were palpable: Dr. Jie

Shan, Brent Valle, Anuj Siani, Dr. Cory Christenson, Dr. Jack Johnson, Dr. Joseph Lott, Dr.

Kenneth Singer, Dr. Eric Baer, Dr. Anne Hiltner, Dr. David Schiraldi, and Dr. Christoph

Weder.

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Three Dimensional Optical Data Storage in Polymeric Systems

Abstract

by

CHRISTOPHER J. RYAN

Since the late 1980s optical data storage has been a staple for the circulation of digital information. Through the years the storage capacity of these devices has grown to match new demands and applications. However, fundamental optical limitations exist which inhibit the growth of the current paradigm of devices. This work is comprised of experiments and demonstrations related to new optical data storage techniques.

Various results are presented to augment and optimize future iterations of such devices.

Most notably, a 64 layer disk is fabricated and used to store data. This device is fashioned using a polymer coextrusion technique and stores information at a high density on 23 of its 64 fluorescent layers. To understand the significance of such devices, a simulation is used to quantify the benefits of multilayered storage disks over monolithic devices. Noise is shown to be drastically reduced in multilayered structures, while the signal contrast grows under the influence of confinement effects. In the process of making this device, an aggregrochromic dye was chosen as a candidate material. Further experiments characterize how the dye changes phases as a response to photopatterning. As presented, these projects cite specific issues with optical data storage technology and offer options for complexity and growth within the field.

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Chapter 1: Introduction to Optical Data Storage

1.1 Motivation

Since the late 1980s, three‐dimensional (3D) optical data storage has become a significant area of interest to the scientific and engineering communities. As formats progressed from Laserdisc to Compact Disc to Digital Video Device to Blue Ray Disc, 2D storage devices have remained a standard for cheap, stable data storage. With each new generation of devices came in increase in overall storage density. [1]

However, the wave nature of light has imposed fundamental limits to the storage density of such optical devices. There are new methodologies to circumvent these bottlenecks. Expanding storage into the third dimension has produced devices that push density of optical media over a terabyte per disk[2, 3].

1.2 Features of Optical Data Storage

The general operating principles of 2D optical storage formats rely upon modulated reflection patterns. Most commercial disks store information on a thin aluminum film that is housed within a transparent plastic disk. Information is stored on such a device during the fabrication process as the aluminum films are stamped with a pattern. The

9 information is later read by reflecting a focused laser beam at the surface. The disk is spun about its axis, which translates the pattern relative to the laser. The resultant reflection from the disk is modulated with the information from the pattern, and the reflection is captured by a photodiode. As a result the photodiode produces a modulated electrical signal which conveys the information to the next step in the process [3].

These aluminum based disks are the most prevalent kind of write‐once‐read‐many

(WORM) disk. Other materials have been used for variations of this concept. Cyanine, phthalocyanine, and azo based dyes have been layered adjacent to the aluminum or even used as a replacement for it. In this kind of disk, there is no stamping, and the disk is manufactured without a pattern. Instead, writing is done by modulating a laser beam that is focused on this material. Absorption of the modulated light causes heating, and as a result there is a spatial modulation created in the phase of the disk (typically polycrystalline or amorphous). There is a difference in the refractive index of the two phases, so the result is that the disk is patterned with a modulated reflection coefficient.

This type of disk is read in the same way as its stamped counterparts. The benefit is that the disk is writable post fabrication[3, 4].

For later versions of this device, the disk is also erasable. In such disks, the active material is typically a semimetal alloy such as GeSbTe. The basic principles are the same,

10 but by further exploitation of the material’s phase behavior, the disks are made rewritable. When heated above the material’s crystallization temperature (~ 150 C), an amorphous region becomes polycrystalline and more reflective. By taking any region, polycrystalline or amorphous, above its melting temperature (~600 C), it melts and cools rapidly to an amorphous solid. During photopatterning, the laser power is controlled to utilize these properties. A low power mode is used to write data on a blank region of the disk, and a high power setting is used to erase written regions. The resultant photopattern is later read with reflection based methods[5].

The wave nature of light has imposed a fundamental limit to the data storage density

(DSD) of all optical storage formats thus far[6]. The radius of the narrowest part of the beam is called the beam waist (0). Diffraction limits the minimum size of 0 based upon the wavelength () of the light being focused and the numerical aperture(NA) of the lens that is used to focus it . There exists a simple proportionality relation between them (Eq1)

(1)

The beam waist also defines the resolution of a typical reading system. Features with separation smaller than 0 cannot be easily discriminated with linear microscopy methods. The minimum resolution of the system then sets an upper limit on the DSD, as data packed more densely than the beam waist cannot be resolved. The maximum

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DSD of a 2D storage system is thus proportional to . Note that for a given disk, the writing and reading processes do not necessarily use the same so 0 may be different for each process.

As the standard format of optical storage has changed, the DSD has increased significantly. Since 0 limits the DSD, each successive format has reduced the wavelength and increased the NA of the optics involved.

1.3 A Brief History of Commercial Optical Data Storage

A brief history of mainstream optical data storage starts with the Laserdisc(LD)[7, 8].

Originally produced by Pioneer, LDs and their hardware were the first commercially available optical data storage systems. The LD itself was an aluminum sheet of 30 cm in diameter which was mounted in a plastic cylinder. Data was stored in the device during fabrication as each aluminum disc was stamped with a pattern. For consumer video storage, this pattern contained an analog video signal and a digital audio signal. The pattern is read with either a 632 HeNe laser or 800nm diode.

The LD device family was replaced by the Compact Disc (CD) player. CDs occupy a significantly smaller form factor than LDs. The CD is a thin plastic cylinder with diameter of 12 cm and height of 1.2 mm. The bulk of CDs are WORM disks with an aluminum film.

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Later writable and rewritable disks were manufactured. CD players use a 780 nm diode laser and optics with a NA of 0.45. The features on the disk are larger than 0.5 um in each dimension and separated by 1.6 um. The overall capacity is ~700 MB [9].

The next major format of 2D optical data storage to be widely produced was the Digital

Versatile Disc (DVD). The DVD follows the same size and form as the CD. Similarly writable and rewritable formats are available for DVDs. The mechanics of a DVD player are the same as a CD player; however, a shorter wavelength laser and stronger optics are used. For a DVD system a 650 nm diode laser is used with a lens of .65 NA. The features on the disk are typically 0.32 m wide, 0.4 m long and 0.12 m tall. The bumps are separated by about 0.74 m which leads to a device capacity of 4.7 GB.

Versions of the DVD are now made with 2 layers of storage rather than a single aluminum layer, a second layer of semitransparent reflective material is used. Either layer can be selected by changing the position of the focal point. Intuitively, the addition of a second layer multiplies the storage by a factor of 2. DVD disks are also sometimes made 2 sided; by essentially taking 2 disks and gluing them back to back, the capacity is doubled yet again. However to read the other side of such a disk, it must be turned over in the player.

The most recent commercial format for optical data storage is the Blu‐Ray Disk (BD).

This disk follows the same form as the previous standards. They are plastic cylinders of

13 the same dimensions of CDs and DVDs. Blu‐Ray technology takes its name from the ultraviolet laser that is used in it. By reducing the wavelength of the beam to 405 nm and increasing the NA of the optics to 0.85, the BD offers a significant improvement in

DSD over its predecessors. The beam waist for such a device is about 0.15 um. As such, the features on the disk are no smaller than 0.15 um, and the overall capacity is 25 GB.

There are also dual layer BD that are analogous to the dual layer DVDs described above[10].

As mentioned above, the trend of decreasing the wavelength of the laser and increasing the NA of the focusing optics has practical limitations. The best multielement lenses available have a NA of nearly 1.4 if oil immersed and 0.95 if dry. This means that there is less than a factor of 2 in improvement in the DSD of future devices from increasing the NA. The practice of decreasing the wavelength of the laser is also restricted. While light exists with wavelengths much shorter than 405 nm, there are no good diode laser sources of such light. To continue the trend toward smaller  either new high band gap semiconductor materials must be developed, or other low cost methods of laser generation must be found. While using the current paradigm of devices, there is little opportunity to increase the DSD[2, 6].

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1.4 New Techniques for Optical Data Storage

New techniques are being developed to circumvent the limitations of the current technology. However, these approaches stem from three basic ideas. Firstly, if each feature on the disk could represent a wide range of numbers, rather than just 0 or 1, the density would increase significantly. Secondly, if the size of the features could continue to shrink, the DSD would increase. Finally, if the entire volume of the disk could be used rather than just a single plane, then the DSD would rise as well.

Regardless of the techniques used, the general task is the same for all optical storage devices. First one must create localized changes to the optical properties of a material.

These changes must be made so that they can later be detected and resolved. To realize such devices, proper mechanisms for reading and writing of data are imperative.

As such, this research requires significant contributions from multiple fields including chemistry, physics, and material science. Because this work is so multidisciplinary, there are a multitude of unique approaches to such a device. However, the general task imposes constraints and thus commonality arises between designs.

The information on the current disks is stored as binary. Each feature on the disk represents either a 1 or a 0. By changing the features to instead represent a wider range of numbers, the DSD can be greatly enhanced. For example, if each bump on a

15 current disk could be replaced by feature on the disk had 20 different detectible configurations, then the DSD would increase 10 fold. Data throughput would also be significantly increased, as each number written and read holds more information than that of a binary system. Of course, such a change would require a more refined detection system. Two methods which utilize this idea are multilevel storage and holographic storage[11‐13].

In Multilevel Storage systems the overall structure of the disk and drive are very similar to the aluminum stamped optical disks that have been a standard for years. However, the binary features are replaced by bumps of multiple discrete magnitudes. One way to achieve this is to use an array of different heights; each one would reflect the beam to a unique point in space. The detector from a typical optical drive is replaced by an array of detectors, so the position of the reflection is accurately resolved. An alternative would be to replace each of the bumps with features of varied discreet reflection coefficient. Then the detector could interpret the magnitude of the reflected beam to represent an array of numbers. Clearly this method increases the storage density of a given disk by a multiple of the number of different heights that it uses[13].

In a holographic storage system features within the disk are written to a disk by interfering 2 beams of light. One of these beams is encoded with information through spatial light modulation. The material holds the information in the form of a diffraction

16 grating. Later, a reading beam is passed through this grating to reproduce the spatially modulated pattern. By imaging this beam onto a CCD, the spatial pattern is resolved and a large digital number. This process typically allows the features to hold between 8 and 16 bits of information, rather than a single bit. The overall storage density is therefore multiplied by this factor[11, 12].

Another approach to denser data storage involves decreasing the size of the data features even further. As stated earlier, improvements to  and NA are near their limits.

However, by using materials with nonlinear responses such as materials with threshold, the features could be written with size smaller than the beam waist . This technique has been well applied to photoresists to get features as small as While there are a few optical storage mechanisms that are threshold processes, none of them have been fully exploited yet[14, 15].

The ODS density is also limited by the reading process. One way of resolving features below the diffraction limit is to use near field microscopy. By placing its detector very close to its specimen, a near‐field scanning optical microscope (NSOM) uses the properties of evanescent waves to get resolution far smaller than the diffraction limit.

In such a system, the resolving power is limited by the size of the detector rather than the wavelength of light that is used for illumination. NSOM has been demonstrated to detect and resolve features with 0.02 um lateral spacing and 0.002 um height. However,

17 this kind of detection is limited in its scope. To detect features they must be on the surface of the sample.

Another way to the beat the diffraction limit is through stimulated emission depletion microscopy (STED). This technique is restricted to systems that contain fluorescent dye, so the reflection paradigm of disks would need to change to utilize STED. STED improves the resolution of a microscope by quenching the fluorescence in parts of the focal volume that are not at its center. When an excitation pulse is absorbed by the fluorescent dye, it creates an excited carrier population within the dye. This population inversion typically decays exponentially with time on the nanosecond scale as the excitations spontaneously emit fluorescence. However, a second pulse can be used to stimulate emission, and by selective shaping of this pulse, the spontaneous fluorescence is quenched outside of the central region. This technique has resolved features on the order of 6 nm. STED microscopy is not limited in the same way as NSOM, as STED techniques can penetrate the surface of the disk[6, 16].

Structured illumination microscopy has achieved similar resolutions. The sample is imaged while being illuminated with a spatially periodic light source. Images are recorded as the source is translated and rotated through the sample. A series of images are produced that are convoluted with the known periodic light source. By performing a deconvolution an image of the sample is produced with very fine detail, and resolutions

18 similar to STED have been demonstrated. Image processing provides resolution better than 10 nm. Because it is computationally heavy, such a method is not useful for optical data storage [17].

1.5 3D Optical Data Storage

Since the detection methods for subdiffraction data features bring problems of their own, it remains pertinent to consider other options. As seen with DVDs, the DSD of a disc can be doubled by adding a second plane of data. In fact, the density is multiplied by the number of layers of information. This method of using the depth of the disk as a storage parameter is the basis of 3D optical data storage. Rather than storing data on a plane within a disk, the goal of 3D data storage is to use the entire volume of the disk.

Clearly, an issue arises here, as when reading deep into a disk the information that is stored on other planes will contribute to the signal[1].

The principles of confocal microscopy are necessary to resolve data from densely packed volumes. As such, the only storage mechanisms with 3D utility are those that create localized changes to either fluorescence or reflectance. A multitude of devices exist as examples for each of these detection methods. However, fluorescence has a greater potential for a large number because the refractive index mismatch in reflection based systems leads to stronger optical aberrations when reading and writing [1].

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The problem of 3D data storage, however, is more complex than just reading the disk.

To properly demonstrate the principle, one must produce a disk with differential optical properties that are distributed throughout the volume of the medium. There are generally two approaches to this problem. In many cases, data is written during the fabrication process, and the disk cannot be changed afterward. However for more flexibility in use, writable disks are fabricated blank and data is later written by photopatterning [1].

The current industry standard WORM (write once read many) disks operate based on reflection. Data is stamped onto disks as they are injection molded. The best commercial disks available can store 30GB per layer and have 2 layers. Using the same process, Pioneer has fabricated a multilayered disk of 20 layers of data with buffer layers in between. Such a device has the potential to store over 500GB. The ability to focus onto each layer is demonstrated, neither the writing data nor reading data has been shown in such a disk[3].

All designs which demonstrate the ability to create 30 or more planes of data utilize multiphoton absorption. These disks are produced blank, and data is written post fabrication. A multiphoton process is necessary as it localizes the absorption of light to

20 a single plane. Most schemes involve 2‐photon absorption, and a few claim higher order effects. In most of these cases, the multiphoton absorption directly induces a change in optical properties. However, there are many devices where the absorption instead initiates a sequence of events that result in such a change.

Most of the designs in the scientific literature utilize photochromic molecules. As a general term, a molecule is photochromic if it can be transformed from species to species by the absorption of a photon. In data storage devices, a photochromic dye with a significant two‐photon crossection is dissolved into some polymer matrix. Upon illumination, the dye changes its optical properties. In some cases, the absorption and fluorescence properties of the material are locally changed enough to make a basis for data storage[18‐21].

For ease of production, most of the devices in this field are fabricated as homogenous, monolithic disks. High data storage densities, stable storage lifetimes, and rewritability are all demonstrated in a variety of papers using such devices. Even with such success, there is motivation to make inhomogeneous, multilayered disks instead[22‐24].

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1.6 Multilayered Films as Storage Media

Though there are many issues with their fabrication, there is still much research done involving multilayered disks. To create these devices, most groups spin coat alternating layers of photoactive and inactive materials. This process, while easy to do, produces films with poor uniformity and also does not scale well to larger number of layers. A less popular technique involves fabricating individual layers and later adhering them together. Uniformity of these disks is much better than spin coating, but this comes at the cost of a more labor intensive fabrication process. This method is also much more difficult to scale into disks involving thirty or more layers. While issues exist with the production of multilayered disks, researchers continue to work with them as they boast many benefits over the monolithic disk[22‐24].

The benefits of multilayer systems are multifaceted. The major arguments for multilayered disks include reduced materials costs, increased contrast, and reduced aberration. Because the active material is the most costly ingredient in these designs, spatial confinement of the active region reduces the amount of the expensive ingredient and reduces the overall cost of the disk. Furthermore the spatial confinement increases the contrast of the written data regions whence compared to the unwritten areas. This in turn augments the signal to noise ratio (SNR) and doubles the potential storage density. Finally spatial confinement of the active layers reduces the phase aberrations of a wavefront traveling through the disk. This allows for random accessibility during

22 writing, and furthermore, the reduction of aberration leads to smaller focal volumes and an overall increased working depth of the disk[22‐24].

Even with the benefits of multilayering, the difficulties of established methods for manufacturing such disks make them an unlikely candidate for real application. This creates opportunity for other technologies and processes to attempt to solve this problem. Here we use the polymer coextrusion technique with die based multipliers to create multilayer polymeric films to use as 3D storage media.[25, 26]

1.7 Coextruded Polymeric Films

In the polymer coextrusion process, two polymers are heated to matching viscosities.

As they are extruded through the same nozzle, they are spread into a bilayer film. The ratio of the thickness of one layer to the other is a controlled by adjusting the rate at which each polymer flows. The overall thickness of the bilayer is also controlled by adjusting the flow rate of the polymers. Dies are then used to cut, stack and spread the film. As this is done the number of layers is multiplied while the overall thickness remains the same [25, 26]. Further description of coextrusion can be found in section

3.2 as well as a figure of the process and a resultant roll.

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Films made in such a manner are produced in rolls. These films are characterized by their overall thickness, number of layers, and ratio of bilayer thicknesses. Film variance is usually less than 5% from layer to layer. The films exist with 2 to 4096 layers with bilayer thickness as small as 10nm. This process scales easily to mass production as it is already used to make films on the square mile scale. By focusing on this method, we hope to alleviate difficulty of manufacture that has thus far outweighed the practical benefits of using multilayered systems as data storage media.[25, 26]

1.8 Content

The bulk of this work demonstrates the design and characterization of a coextruded multilayer polymer film for use as a 3D optical data storage system. The working WORM disk is presented in Chapter 3. Chapter 2 covers the characterization of the materials chosen for this disk and a photo induced aggregrochromic effect. Chapter 4 contains a simulation of the contrast to noise ratio of multilayered and monolithic disks which quantifies some of the benefits of multilayered disks. Chapter 5 contains the results of a mostly unrelated paper on the charge transport properties of Zinc Phthalocyanine

(ZnPC). The appendix contains information on photopatterning and far field microscopy below the diffraction limit as well as an experiment designed to yield this effect.

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Chapter 2: Two‐Photon Induced Aggregate Switching of Excimer‐Forming Dyes

2.1 Introduction

Current commercial optical data storage technologies use linear absorption processes to write and read data.[27, 28] Information is written by making localized changes to the optical properties of the disk to produce a spatially modulated reflection pattern. The overall data storage density of a disk is determined by the spacing between the written features. The minimum width of the features on a disk is limited by the diffraction of the light used to write it. Typically new formats of commercial storage emerge by using shorter wavelengths and optics with larger numerical aperture (NA). However, there is little room to continue this trend without advances in optics and laser materials.

New methods are required to further increase the storage density of disks. The most prevalent approach for doing so involves writing data into the depth of the disk. Some models of DVD and Blu Ray disk exemplify the potential of this concept, as they are fabricated to have up to four individually addressable storage layers. However, complexity of producing and using multilayer systems increases with the number of layers. To facilitate denser storage still, others turn to nonlinear optics.

Two‐photon absorption (TPA) is the most common tool for enabling 3D data storage.[20,

29] Since this processes scales quadratically with the incident light intensity, optically‐

25 induced changes are restricted in depth even when focusing light into a bulk material.[30, 31] Here we report a novel, readily‐manufactured ODS system that relies on the optically‐induced switching of the aggregation state of an excimer‐forming, fluorescent TPA dye in a polymer matrix.

Well‐defined voxels with dimensions of 3x3x6 m were written individually by exposing the material to a focused, modulated laser pulse train. The light pulses had duration of

10ns, energy of 55 nJ, and were centered about 675 nm to correspond to the dye’s TPA absorption maximum. Once written, the data was read by confocal laser scanning microscopy. Three‐dimensional ODS systems based on this approach promise a storage capacity of up to several Tbytes on a DVD‐size disk, which is two orders of magnitude higher than that of current commercial ODS technologies.[32]

The majority of the systems designed for 3D ODS employ photochemical processes to enable storage. Typical reactions include photoisomerizations,[33‐35] photo‐induced dimerizations,[36, 37] photodecompositions,[38] and photopolymerizations.[39, 40]

Fluorescent photochromic systems have attracted particular interest, because the photophysical processes are fast, efficient, and reversible.[19, 41, 42] However, it has been challenging to create fluorescent photochromic materials, which combine high stability, high fluorescence quantum yield, and large TPA cross‐section.

26

Here we demonstrate an approach to 3D ODS materials that relies on the switching of the aggregation state of an excimer‐forming fluorescent dye. The dye has an appreciable TPA cross‐section, and it is blended in an inert host polymer. It is shown elsewhere this material changes fluorescence colors as a response to heat [43‐46] chemicals,[47, 48] or mechanical forces,[49‐53] The optical changes arise from induced changes of the aggregation state of the dye molecules. We surmised that such changes are elicited in small volumes by TPA‐induced local heating.

2.2 Materials

We explored a melt‐processed blend of poly(ethylene terephthalate glycol)

(PETG)and 1.1% w/w of 1,4‐bis( ‐ cyano‐4‐octadecyloxystyryl)‐2,5‐ dimethoxybenzene (C18‐RG, Figure

2.1) as TPA‐addressable ODS medium.[43, 45] C18‐RG was selected on account of its significant changes in absorption and emission spectra upon aggregation/dissociation, its high thermal and photochemical stability, and, as demonstrated here, its appreciable TPA cross‐section.

27

PETG was chosen as the matrix due to its glassy nature and excellent optical properties.

Its glass transition temperature (Tg) of 78 ˚C, which defines the write/erase temperature(vide infra) is sufficiently above ambient temperature and provides excellent stability of the storage medium as discussed below. The solubility phase diagram and aggregation kinetics of C18‐RG/PETG blend sand similar materials have been previously investigated.[43, 45]

Figures 2.1 illustrates the aggregation state and optical properties of the 1.1% w/w C18‐

RG/PETG blend films as a function of thermal history. The corresponding normalized absorption and fluorescence spectra are shown in Figure 2.3. The dissolution temperature at which the dye is thermodynamically soluble is ca. 130 ˚C for 1.1% w/w of C18‐RG in PETG, Figure 2.1; note that the dissolution temperature is a function of the dye content. Thermodynamically unstable, but kinetically trapped molecular mixtures of the dye and the polymer can be produced by quenching a thermodynamically miscible, melted mixture of the two components (230 ˚C for a blend comprising 1.1% w/w dye) to

28 below Tg. In this state, the blend film appears yellow (peak wavelength of the

abs absorption spectrum max = 447 nm, Figure 2.3) and displays the green

fl fluorescence(peak wavelength of the fluorescence spectrum max = 508 nm, Figure 2.2,

2.3)that is characteristic of a molecularly mixed blend. Subjecting the quenched blend to temperatures above Tg but below the dissolution temperature leads to stable and

abs pronounced changes in absorption (orange appearance, max = 387 nm, Figure 2.3) and

fl fluorescence (orange, max = 542 nm), due to aggregation of the chromophore molecules; these changes are retained if the blend is cooled back to ambient temperature (Figures 2.2,2.3).The original state can be restored by subsequently heating the phase‐separated blend to above the dissolution temperature(all erase experiments reported here were carried out at 160 ˚C) (Figures 2.1,2.2,2.3).Thus, the above data document that the blend employed here can be used as a rewritable, optically readable storage medium, in which local exposure to well‐defined temperatures allows one to write and erase information in two dimensions with microscopic resolution.

29

In principle, two different modes of operation are possible. The first begins with a quenched blend (in which the dye molecules are dissolved)into which data is written through annealing above Tg but below the dissolution temperature, and erased through heating above the dissolution temperature. Alternatively, the second process starts with a phase‐separated material into which data is written by heating above the dissolution temperature and is erased by annealing above Tg. The cycles illustrated in Figure 2.2 and

2.3 show that either starting point is a viable option and in principle, many write/read/erase cycles are possible.

2.3 TPA of C‐18

The choice to utilize C18‐RG for the present optical data storage systems was based on the expectation that this dye, like other cyano‐substituted oligo(phenylene vinylene)s[53‐57] possesses an appreciable TPA cross‐section, so that the above‐

30 described write/erase schemes could be achieved by TPA‐induced local heating. The TPA cross‐section of C18‐RG was measured using the open‐aperture Z‐scan method.[58, 59].

Figure 2.4 shows the TPA cross‐sections of C18‐RGas a function of wavelength in the range of 625 to 725 nm, where the linear absorption is negligible (Figure 2.3). The TPA cross‐section of the dye varies between 0and 650 GM with a maximum at 675 nm. A very similar behavior was found for C1‐RG (Supporting Information). These experiments reflect a significant nonlinear absorption, which is comparable to that of similar molecules reported in the literature.[53‐57]

2.4 Experiment

For TPA‐based writing experiments, 1.1% w/w C18‐RG/PETG blend films of a thickness of 150 m were annealed at 90°C for 2 days to ensure complete aggregation of the chromophores. Data writing was accomplished by using a Nd:YAG laser in combination with an optical parametric oscillator (OPO), which produced light pulses of a center wavelength of 675 nm, duration of 10 ns, and energy of 3 mJ. The pulse‐to‐pulse energy stability was ~ 20%. These pulses were attenuated and focused onto the storage medium through an oil‐immersed objective lens with a numerical aperture of 0.85. The resulting Gaussian beam was measured to have a waist of 3 m and Rayleigh range of

10m. Each data spot was written by exposing the samples to a single laser pulse. The samples were moved in 3D by a computer‐controlled 3‐axis translation stage. In initial experiments, the average pulse energy was systematically varied. For each trial, a set of

31 spots was written while the average pulse energy was held constant. At pulse energies above 100 nJ permanent localized damage was observed, while pulse energies below 25 nJ brought about no visible optical changes. The energy range of 50‐65 nJ was found to afford the desired changes. An average pulse energy of55 nJ was used for the data writing experiments presented below. Confocal laser scanning microscopy was used to characterize the voxels written into the C18‐RG/PETG blend films using the above approach. A continuous wave laser operating at a wavelength of 400 nm was used to excite the samples and the fluorescence was recorded in two channels corresponding to the integrated intensity in the spectral ranges of 500 – 525 nm and

650 – 800 nm, respectively. These spectral windows are sensitive to and thus were chosen to monitor the aggregated and dispersed state of the chromophores.

2.5 Results and Analysis

Confocal microscopy images of a representative sample show eight written data spots of

10m below the surface of the film in Figures 2.5 and 2.6. The variations in these data spots were caused by the pulse‐to‐pulse energy variation of the output of the OPO.

Figure 5a shows the raw intensity image of the sample after the application of a low pass filter in a plane parallel to the film surface (XY plane) for fluorescence in the spectral range of 650 – 800 nm. Orange excimer emission of aggregated dye molecules is observed across the entire sample, except for the written spots, which appear as darker areas, indicative of dispersion of the dye aggregates due to the TPA‐induced local

32 heating. The result is further confirmed by the corresponding fluorescence intensity image recorded for the spectral range of 500 – 525 nm (Figure 2.5). The image shows a complementary behavior, i.e. the written spots appear bright, reflecting an increase of the green emission in these areas. In addition, we did not observe any appreciable photo‐induced degradation of the films during writing. In previous studies, the ratio of the emission intensities in the above short and long wavelength windows has found to represent a good measure of the aggregate states.[43, 45, 50, 53] Thus, we used the ratio of the intensity of the images shown in Figure 2.5, with their respective backgrounds subtracted, to generate a composite image, which indeed shows a significantly improved contrast. The image contrast can be further enhanced by applying a low pass filter. The choice of the low pass filter removes the effect of the dye aggregates from the image. Further processing could easily convert the signal to binary.

33

As is evident from Figure 2.5, the spot sizes written with the setup employed here have a diameter of ~3 m in the XY plane. Figure 2.6 shows the emission intensity profile of the top 4 spots from Figure 2.5c as recorded in the ZX plane. The dimensions of the data spots in the ZX direction (~6 m) are a bit larger than those in the XY‐plane (~3 m), which are mostly limited by the size of the beam focus. Note that because the writing process requires a threshold temperature, it is possible to achieve a data spot substantially smaller than the writing beam size, the result of which will be reported elsewhere.[60] The current results reveal clearly that the TPA‐based writing process allows one to write voxels that are microscopically localized in all 3Ds.

34

Finally we comment on the stability of this new storage medium. Below the polymer’s Tg, the molecular mobility of the system is negligible and the morphology of the dye/host systems is stable for years. In this regard, the Tg of the chosen host polymer dictates the stable operating temperature regime of the system. This indicates that written features remain intact at ambient conditions, but leaves open the possibility of erasing data by supplying sufficient thermal energy to heat the sample above Tg and re‐aggregate the chromophores, as has been illustrated in Figure 2.2.

2.6 Conclusion

In summary, we have demonstrated a new ODS system that relies on the optically‐ initiated, thermally induced switching of the aggregation state of an excimer‐forming, fluorescent TPA dye in a polymer matrix. Such blends can easily, inexpensively and rapidly be fabricated in large quantities using simple melt‐processing techniques. Well‐ defined voxels with dimensions of ~3x3x6 m have been written through the exposure of the blend to single laser pulses. The voxel size is comparable to the focal point volume of the writing laser, suggesting that thermal transport does not place a lower limit to the voxel size, at least not at the length scales used here. A diffraction limited laser beam can be achieved by optimizing the optical setup. In that case the volume for efficient TPA is limited to a space slightly smaller than 0.4 m in each dimension given the wavelength and numerical aperture used. Such a scheme can be used to potentially write several terabytes of binary data in a disk of size of the common CDs and DVDs.

35

Chapter 3: High Density Optical Data Storage in Co‐extruded Multilayer Polymer Films

3.1 Introduction

New transformative concepts for optical data storage applications are needed to meet the future requirements of applications in multimedia, archiving, security, and many others. Commercial data storage technologies are moving to three‐dimensional materials, but the known concepts suffer from limited addressability and high fabrication costs. We demonstrate here that storage systems based on co‐extruded multilayer films can overcome these problems and allow for terabyte level bit‐by‐bit optical data storage. Stratified films with 64 storage and 64 buffer layers, with a period of 3.4 m, were fabricated by a readily scalable continuous roll‐to‐roll process at 200 meters per hour. Information in the form of complex patterns and individual bits was recorded in up to 23 superimposed layers by photobleaching a fluorescent dye via one‐ photon absorption. The optical resolution and cross‐talk were examined. The results demonstrate that the fabrication process, which is far simpler than current approaches, allows one to fabricate Blu‐ray compatible, high‐density multilayer storage media with storage capacities that are orders of magnitude higher than the state of the art.

High capacity optical data storage (ODS) is required for robust archiving, security tags, and even new media formats for three‐dimensional (3D) displays, and many other applications [61]. Conventional two‐dimensional ODS has advanced to allow 25 GB/layer storage in blu‐ray (BR) discs©, which is sufficient for high definition video storage.

36

However, the storage capacity is limited by diffraction of the writing beam, the cost of many‐layered media, as well as the number of layers that can be fabricated and addressed [62]. Shorter wavelengths or higher numerical aperture (NA) optics offer some improvements, but substantial advances can only be achieved by utilizing multi‐ dimensional methods including spectral and polarization multiplexing [63, 64], holographic recording [65], and in particular, the efficient use of the axial dimension to overcome the limits of surface storage [20]. The capacity of 3D storage media has currently progressed toward terabyte (TB) levels [2].

Localizing data in a 3D storage medium is often achieved by activating the particular material response using two‐photon absorption (TPA) by high power sources, such as near‐infrared pulsed lasers. The use of this nonlinear optical process greatly reduces the optical changes outside the region of interest [2, 18, 66‐70]. In these schemes, data planes are written either in monolithic materials [2, 19, 71], or in materials with discrete active layers. The former are easy to fabricate, while the latter allow further confinement of the data within a layer. This reduces cross‐talk during writing/reading, as well as the amount and cost of the recording material. However, the multilayer (ML) discs reported in previous efforts were fabricated through either sequential spin coating

[15, 21] or lamination [3, 24, 72], which are labor intensive and cannot economically scale to large numbers of layers.

While easy, low‐cost multilayer fabrication is one important roadblock, other system‐

37 level issues are also impeding the transformation to commercial TB ODS. This transformation will be best addressed by a evolving the system from the present commercial state of the art. In particular, it would be desirable to develop a TB read/write system using existing BR laser diode technology and that conforms to existing requirements. Optical aberrations in the read/write system limit the addressable depth so that the current BR specification of a total thickness of the storage medium to 140μm significantly limits the number of layers possible with a reflective storage scheme as a reflective scheme requires large layer separation to avoid coherent reflection effects. Thus, TB multilayer storage requires a medium and storage scheme that simultaneously confines the data to tight axial dimensions and allows reading and writing with minimum crosstalk.

We report here on an approach that successfully addresses all of these issues and paves the way for future high performance, low‐cost, easily scalable and manufacturable TB

ODS media. First, we have developed a novel, robust, and simple approach for digital

3D ODS in ML polymer films that were fabricated in a continuous, melt co‐extrusion, roll‐to‐roll process. This is truly low‐cost and easily scalable both in film area and number of layers. In addition, permanent storage is demonstrated in 23 superimposed data layers utilizing fluorescence (FL) quenching of an novel oligo(p‐phenylene vinylene) dye organic dye upon one‐photon absorption. This was achieved with a sub‐milliwatt continuous wave (CW) 405 nm diode laser, enabling operation with current compact BR sources. Finally, a high axial data density (3 m/layer), low crosstalk scheme was

38 realized using a FL reading scheme, which, in combination with writing at the diffraction limit of the BR laser, promises TB storage capacity within commercial disc thickness specifications.

3.2 Sample Fabrication

The co‐extrusion technique [73, 74] used to manufacture these films is illustrated in

Figure 3.1a. In this process, which has already been successfully applied to the fabrication of photonic crystals [75], lasers [76], and gradient refractive index lenses [77], two thermoplastic polymers (A and B) are heated to form a melt with matching viscosities, and then coextruded into a bilayer feedblock. The AB bilayer is sent sequentially through a series of multiplication dies. Each die cuts, spreads, stacks the melt and doubles the number of layers. Films with over four thousand layers and layer thickness as low as 10 nm have been produced using this technique [74, 78]. The laboratory process employed in the present study allows fabricating films up to 36 cm in width at a speed of approximately 200 m/hr, though much higher speeds and widths are possible in commercial production lines employed for other commercial applications.

39

The chromophore C18‐RG was synthesized as previously described [45]. PETG Eastar

6763 and spectroscopic grade toluene were obtained from Eastman Chemical Company and Burdick & Jackson and were used as received. A blend of C18‐RG and PETG (nominal dye content 2 wt.%) was prepared using a Haake Rheocord 9000 batch mixer at 230°C for 5 minutes. To co‐extrude the PETG solution with the PVDF, both materials were heated to 230°C where the polymers have matching viscosities. The bilayer produced by the co‐extruder was sent sequentially through 5 dies. Each die cut perpendicular to the bilayers, spread, and stacked the film to multiply the number of layers by 2. The final film produced was a system of 64 layers with an overall thickness of approximately 200

m. Co‐extrusion also permits the manufacture of periodic films with more than two distinct types of layers (i.e., ABC or ABCB) to accommodate more sophisticated designs

[74].

Using this technique, we fabricated a storage system consisting of 64 data and 64 buffer

40 layers, which serve to confine the bits within discrete layers. A photograph of the roll of the film produced in this study is shown in Figure 4.1b. Data storage layer A is composed of a transparent host polymer, poly(ethylene terephthalate glycol) (PETG) that is doped with 2.0 wt.% of the fluorescent chromophore 1,4‐bis( ‐cyano‐4‐octadecyloxystyryl)‐

2,5‐dimethoxybenzene (C18‐RG) (13). Buffer layer B consisted of poly(vinylidene fluoride) (PVDF), is optically inactive and refractive index‐matched to layer A. This material is particularly useful to limit diffusion of the dye during processing [79]. The average thicknesses of layers A and B are 0.3 and 3.1 m, respectively. The production process and writing/reading system has much broader applicability than the particular material reported here.

3.3 Film properties

C18‐RG is a cyano‐substituted oligo(p‐phenylene vinylene) dye with aggregochromic properties [45]. The structure is shown in Figure 3.2. Previous studies on thermodynamically immiscible blends of this dye and various host polymers have demonstrated significant changes of fluorescence (FL) properties upon exposure to light, heat, chemicals, or mechanical forces, which are attributed to excimer formation or breakup [45]. The usefulness of this particular dye for optical data storage has already been demonstrated by two‐photon switching of the excimer‐monomer transition in monolithic films [70]. We prepared the dye‐doped polymer layers in a molecularly mixed blend following the procedure described in [70]. The absorption coefficient of

41 layer A is 0.1 m‐1 at 405 nm, whereas both the PETG matrix and the PVDF buffer layer are transparent in the visible spectrum.

Figure 3.3 shows the FL spectrum of a single active layer under 405 nm excitation, taken with a spectrometer and CCD fiber‐coupled to the confocal microscope. An area 2.5 x

2.5 m was scanned in about 100ms at 0.01 mW/m2. The monomer and excimer fluoresce at 410 and 445 nm, respectively. Upon exposure to CW light of high fluence, bleaching of the FL is observed with no shift of the peak, indicating that the dye does not aggregate to form excimers under these conditions.

3.4 Optical Patterning and Reading

The data writing was performed by FL quenching of the storage medium C18‐RG upon one‐photon absorption of a CW laser beam at 405 nm focused onto the chosen layer.

This becomes possible because of the axial confinement of the data in the ML films. The reading, on the other hand, was done by FL detection as opposed to reflection, an approach commonly used for single and few‐layer storage media. As we show below, FL

42 detection significantly increases the axial layer packing density and thus the storage capacity. If molecularly dispersed in PETG, C18‐RG displays absorption and FL spectra with maxima at 445 nm and 510 nm, respectively. An intensity on the order of 0.1 mW/m2 or greater is required to obtain measurable quenching with sub‐ms exposures.

The changes were observed to be permanent and stable over the time period of more than 2 years.

Figure 3.4 depicts FL images written into the top 23 storage layers of the 64‐layer films described above. The written regions correspond to areas of reduced FL intensity (black).

To write the data, the output of a CW 405 nm diode laser was focused into the film through an Olympus M Plan Apochromat, 100x, 1.4 NA oil‐immersed objective. Patterns were recorded using an Olympus FV1000 confocal microscope by scanning the laser beam along a customized path at a rate of 75 nm/ms. Writing was performed layer‐by‐ layer from the lowest to the topmost storage layer. The incident power was about 130

2 2 W and the intensity was varied between 1.5 mW/m (topmost) to 2.0 mW/m

(lowest layer). The same confocal microscope and laser source subsequently collected

3D FL images of the sample at a reduced fluence and increased scan rate (0.01 mW/m2 at 5 m/ms).

43

The use of the FL detection schemes allows smaller layer spacings compare to schemes relying on phase changes and reflection, as discussed. Another limiting factor is the response function of the reading system itself. The confocal microscope used here, with a 1.4 NA objective, is an extreme case. With these optics, the intensity at the detector plane drops by half if the sample is moved by about 0.1 m axially out of the focal plane

(for an infinitely small aperture), which is much smaller than the layer spacing [45]. If instead the 0.85 NA objective found in BR players is used, even with an aperture diameter a factor of 10 larger than the spot size at the detector, this figure is still only

0.89 m. Thus, while the factors limiting the minimum layer spacing are relaxed here, the optical limit of the reading system is not yet an issue. There are likely other issues

44 that results in a need for a minimum spacing, such as thickness variation and solubility of the dye.

From the images shown in Figure 3.4, it is evident that data can readily be recorded and retrieved from each of the individual storage layers. The average reduction in the FL intensity throughout the film for the written areas is about 22%. The images show that the quality of the retrieved images decreases for the deeper layers due to aberrations.

However, we demonstrated that it is readily possible to retrieve information from 23 layers, which is the largest number of recorded layers that has been reported in a heterogeneous ML ODS medium. We note that the aberrations depend on the working distance of the objective, and that the quality of storage in the deep layers, and therewith the number for layers from which information can be retrieved, can be further increased up to the BR specification by optimizing the lens system.

State‐of‐the‐art, two or four layer BR discs have an axial spacing of greater than 10 m in order to limit the coherent cross‐talk that occurs due to multiple reflections of the reading beam at the reflective layer and spacer layer interfaces [80]. The FL detection scheme employed here greatly reduces the multiple reflections as well as emitting at a non‐degenerate wavelength, allowing much smaller spacings to be used compared to phase change materials. Thus, the spacing of our layers (3 m) is one of the smallest explored [21].

45

The areal density of ODS is constrained by the beam waist at the diffraction limit. To examine the data bit dimension of our ML films, single lines were written into a monolithic film of the active layer under the same writing conditions as described above.

The resulting bleaching profile is shown in Figure 3.5. A fit yields a full‐width‐half‐ maximum (FWHM) of 380 nm, which is approximately the minimum bit spacing achievable in this current system, and is consistent with the diffraction‐limited beam size. This places the areal density of our ML films close to that of BR systems, the minimum bit spacing of which is 320 x 150 nm, owing to the threshold nature of the phase change writing process, allowing sub‐diffraction limit writing.

46

3.5 Determination of the Crosstalk

A significant factor that determines the minimum bit spacing in both the axial and lateral dimension is the cross‐talk. One attractive feature of ML films in the context of

3D storage is the confinement of the bits in the axial direction, which reduces cross‐talk between neighboring bits and layers during writing and reading. To directly measure the cross‐talk, an array of bits was written into 10 successive layers and the contrast modulation in the middle (“probe”) layer was read as information was written in the

47 others. Similar writing conditions as described above were employed. The laser was modulated with a square wave generator to produce on‐off bit pairs separated by 1.0

m in both lateral directions, and the total area written (40 x 40 m) was larger than the beam diameter in any given layer, so as not to underestimate the total cross‐talk between any two layers. This also leads to results that are not dependent on which of the 10 layers is chosen as the probe. A subsection of the FL pattern and modulation after select writing steps are shown in Figs. 3.6a and b. The main effect of cross‐talk appears to be an overall reduction in the average FL level.

3.6 Modeling of the Layer Crosstalk

Crosstalk is an issue during both writing and reading in 3D storage systems. Here, the crosstalk during writing is examined for the cases of linear and two photon absorption.

The relevant parameter, physically, is the ratio of the intensity received at a given bit location during explicit writing of that bit relative to that obtained during writing of all

48 other bits in all other layers. The simulated bit array consists of Nz layers with a spacing of z, each consisting of Ny by Nx bits, with spacings of y and x, respectively. The bit array occupies an volume of size Lx by Ly by Lz. The origin is placed at the center of the data array. Assuming a diffraction‐limited Gaussian beam, the reduction in the FL a single bit located at the origin during explicit writing of that bit (the signal, S) should be proportional to some power of the fluence.

p  Nzz  e 2 SC (3.1)  w2 0  where C is a proportionality constant,  is the absorption coefficient, w0 is the beam waist, and p is chosen to be either 1 or 2 to simulate either a linear or quadratic bleaching response. The FL reduction of this same bit during writing of all the other bits

(the noise, N) is given by the sum

p  Nzz 22  N /2 2(ix ) 2( jy ) Nz /2 2 y Nx /2 pp 22 e wwkk NC2 e e S  w kNzyx/2k jN  /2 iN /2  (3.2)

2 and the 1/e beam radius, wk, at the z‐origin when writing layer k is given by

2 kz wk w0 1  nw 2 /  0 (3.3) where n is the refractive index, and  is the writing wavelength. S is subtracted from this to account for the single term in the sum which is defined as the signal. This can be greatly simplified assuming a highly focused beam and a large scan area. However it is more accurate to simply perform the summation numerically (Matlab). The parameters were chosen to correspond to those used in the experiment. The bit spacing was chosen

49 as 1.0 m in both lateral dimensions with all bits being “on” (numerically equivalent to the “on‐off” pattern of 0.5 m spacing produced by the square wave generator), z=3

m, Nx=Ny=40, Nz=10, Lx=Ly=40 m, Lz=27 m, and w0=0.32 m. A beam waist corresponding to the experimentally observed value of 0.32 m is used. The result plotted in Figure 4 is the ratio S/N. S corresponds to the modulation signal, while the total N results in overall constant bleaching, so this ratio can be determined from the

max  min experimental data by calculating 1 max , where max is the average of the peak values in the modulation and min is the average of the troughs.

This calculation is intended only as an order‐of‐magnitude comparison, as there are many other physical processes that must be taken into when designing an optimal ML structure (29), such as multiple reflections. One of the primary differences between experiment and theory here is the fact that the beam is scanned continuously and not discretely. Furthermore, for large intensities the bleaching will become sub‐linear, which is not accounted for in the theory. The light scattered at the interfaces and the inability to control all aspects of the confocal writing system on small scales (such as the retrace and sample positioning) also contribute to the CBR.

3.7 Comparison to Crosstalk Model

The ratio of signal modulation to the background depletion FL (carrier‐to‐background ratio, or CBR) is used to quantify the cross‐talk. The CBR after writing each of the 10 layers (starting with the probe layer) is plotted in Figure 3.6c (triangles). The value

50 decreases from 2 to 0.15 with increasing number of layers, and is in good agreement with numerical simulations. While this is not insignificant, this CBR ratio is more than sufficient to resolve individual bit information, as shown in Figure 3.4. Due to the high

NA of the writing objective and the inert buffer layers, the fluence in the layer adjacent to one that is being written, is reduced by more than a factor of 10. Two theoretical curves for the CBR are also plotted, one assuming the bleaching is related to the linear power of the fluence and one assuming a quadratic dependence (e.g. in TPA scheme).

The theory, which is consistent with the experimental results, indicates nonlinear fluence responses yield significant enhancements in the CBR.

The similarity of the bleached spot size and cross‐talk measurements to the theoretical results based on the beam parameters suggest that the bleaching process may depend in a nearly linear fashion on the fluence; however, as the film reported here has been stored under mercury‐containing fluorescent lamps with weak blue‐violet lines for two years without a measurable decrease in the FL, one may speculate that a threshold exists, below which no bleaching occurs. One‐photon absorption with a nonlinear or threshold fluence response is the preferred method for commercialization, in contrast to the nonlinear optical processes such as TPA which require complex pulsed laser systems or very high power CW diode lasers, and the longer wavelength required to write increases the spot size. Other materials such as Au nanorods [15] or organic photopolymers [81] have already shown potential for a one‐photon initiated nonlinear

51 or threshold response. Work is currently ongoing to incorporate such materials into the co‐extrusion process.

In the future, we will incorporate these one‐photon, nonlinear fluence response writing schemes into the medium described here so that we can expect a 40 layer 1 TB capacity,

0.8 TB/cm3 density disc in the standard areal format. The resulting 136 m thick film is within the 140 m blu‐ray specification compatible with the optics of compact, commercial writing systems, which account for aberration and tilt tolerances[82]. This presents a feasible approach to fabricating a TB‐level storage medium in a large scale at low cost within the material specifications of current writing systems.

3.8 Conclusion

In summation, we have shown that co‐extruded ML films are feasible for use as a 3D

ODS medium. With the commercial systems presently available, the ability to increase the density is limited not only by the optics but also by the cost needed to add and manufacture additional layers. Co‐extrusion removes this serious constraint. We have written films containing 23 active layers with independent images, the largest number of layers of any stratified storage medium. The cross‐talk between layers is also examined, and while not negligible, is small enough to permit demonstration of this film as a storage device. The lateral bit spacing is limited by the diffraction of 405 nm laser, and the axial bit spacing allows TB‐level recording within the thickness specification of current disc players.

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Chapter 4: The Effect of Multilayering on the Contrast and Noise of 3D Storage Media

4.1 Introduction

As new 3D optical data storage technologies are developed, a variety of new disk schematics are created. Typically these disks fit into one of two styles. Monolithic disks are made from homogenous materials and as a result are easier to fabricate than multilayered disks. On the other hand the operational advantages of multilayered disks are often demonstrated by the groups who make them[15, 21, 24]. Some multilayered devices have been shown to offer data storage densities that are not attainable by monolithic disks [21]. The most common claim is that higher contrast to noise ratios

(CNR) are achieved through multilayering[24, 83]. However, the precise nature of the benefits is not well understood.

Previous works show that the contrast to noise ratio(CNR) of a layer within a multilayered disk changes very little when the adjacent layers are written[24]. This result is expected for multiple reasons. In a multilayered system more light should be delivered to the target layer because there is less parasitic absorption from the layers above. Furthermore, there should be less background and noise produced from out of focus layers when reading a multilayered disk.

53

It is the focus of this work to model and compare both the signal contrast and the contrast of the background noise from out of focus regions in both multilayer and monolithic fluorescent disks. In doing so, the benefits of reduced cross‐talk and parasitic absorption are quantified and can act as a guide for the design of future storage media. The effect is examined for various intraplane spacings and various degrees of confinement. Furthermore, the enhancements are examined in the cases when Shot noise and photodiode dark current are the dominant noise sources.

The nature of the signal contrast and background depend heavily upon the writing and reading mechanisms of the disk. For most 3D data storage systems, the fluorescence properties of a material are modified by interaction with a writing beam. Typically a sample is not fluorescent at a particular wavelength, and the application of the writing beam creates fluorescence. However, other disks exist where fluorescence is quenched by the application of the writing beam. Often the change is created by a nonlinear absorption event, however some materials exist which linear absorption leads to nonlinear materials responses. In such systems, the mechanism for change is often thermal or photochemical. Often these mechanisms create threshold based changes, and produce binary spatial modulations. This is the type of device that is considered in this simulation.

54

A three step approach is taken to evaluate the signal contrast and noise contrast of such disks. First the signal generated by a single voxel is calculated for a fluorescent reading process. Next, the total background noise from fluorescent regions surrounding this voxel is calculated determine the maximum possible contrast of the background noise.

Finally, the interplane data spacing (D=a+b) and the ratio of the active layer to the passive layer(Ra=a/D) are varied to compare the signal and noise contrasts for various data densities and systems[figure 4.1].

4.2 Geometric Restriction to the Data Density

In this simulation, signal contrast is compared to the noise contrast as the main determinant of the effect of multilayering. However, geometry suggests a rough

55 estimate of the limit to the density of the disks based simply upon the size of the written spots. The length scales of interest are the thickness of an active layer(a), the thickness of a passive layer(b), and the z radius of the written spots(z0). The parameters of the writing beam determine z0. When writing, the intended layer should be at the center of the beam while adjacent layers should be outside of z0. Under this constraint

2 2 . Two limiting cases emerge for this system. In the monolithic limit, b‐>0, so 2. In this limit, the planes of data are spaced no closer than the twice z0. In the very confined multilayered structure limit, a‐>0 so . In these limits, it is seen that the multilayered structure allows the planes to be spaced about twice as closely as the monolithic limit[figure 4.2]. This estimate is based solely on the constraint that the adjacent layers lie outside of the written spot’s potential diameter. By calculating contrast of the signal and noise, the problem is addressed in a more rigorous manner.

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4.3 Determining the Signal Contrast and Background Noise

The contrast and noise values are calculated as sums over all fluorescent coordinates[equ 4.1]. These are combined to calculate the contrast CNR. The center of the bit of interest is defined at the origin and the position of the confocal pinhole is fixed accordingly. M(r,,z) is the spatial distribution of fluorescent regions within the disk.

I(r,z) represents the intensity profile of the reading beam, which is centered at the origin.

The confocal transfer function, T(z), determines how much of the emitted light from any point is captured by the detector. Other important quantities are the quantum yield(Y)

57 and absorbance() of the dye, and the sensitivity(r) of the detector. So then the current produced in the detector(J) can be found by evaluating an integral:

, , , (4.1)

The term in brackets describes the distribution of the absorbed light and the application of YT(z) determines how much is reemitted into the detector. The integral is done over all space to accumulate the contribution from every point. Application of the photodiode responsivity, rp, converts the captured photons to electric current. The form for each of these functions will be described later as the signal contrast(JS) and noise current(JN) are calculated. When calculating the CNR= JS / JN, the materials properties and detector sensitivity cancel out, and the result is the ratio of the integral of the spatial properties of the system[equation 4.2]. However, the absorbance of the material still affects the shape and amplitude of I(r,z).

,,, (4.2) ,,,

Where MS and MN are the forms of M for regions producing signal and background, respectively. For the simulation of the microscope’s illumination, the reading beam was set to a wavelength() of 400nm and a numerical aperture(NA) of 0.85. I(r,z) was assumed to be the shape of a Gaussian beam with decaying intensity in absorbing regions[equ 4.3].

58

, (4.3)

Here L(z) is the effective path length through the material with absorption coefficient

at location z. This is used to approximate the attenuation of the light as it penetrates the sample. z0 is the Rayleigh range of the beam and w0 is the beam waist. These two parameters are directly related to NA and  by equation 4.4. The absorbance and quantum yield of the dye was chosen to match the dye used for our data storage based experiments in the other papers[60, 84]

(4.4)

Geometric optics determine the transfer function T(z). The amount of light from each point source that makes it to the detector is determined by comparing the size of the image of each point source at the confocal pinhole to the size of the confocal pinhole.

Interference effects in the point spread function were ignored, and the resulting approximation of T(z) was a Lorentzian in z, centered on the focal plane [figure 4.3]. To examine the effect of the pinhole on CNR, simulation was done once with the pinhole matched to the size of Airy disk of the fluoresced light and later with the pinhole 5 times larger than the Airy Disk.

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To find Js and JN , M(r,z) was designed for a material with a threshold response to the illumination.[15, 68] As such, the functions are populated with values of 1 in coordinates that are written and 0 for the unwritten coordinates. The CNR will be identical for systems where written regions are represented by quenched fluorescence.

Near the beam focus, equipotential surfaces of I(r,z) are roughly ellipsoidal, so the spots were assumed to be ellipsoidal with radius w0 and z0 in the r and z directions, respectively. For this disk, only seven layers of data are simulated. The noise contributions from additional layers decrease as the inverse square of the distance from the focus because T(z) has as a Lorentzian form. Contributions beyond the first few layers are very small, and the sum converges rapidly [figure 4.3].

To simulate Js, only the center voxel is permitted to fluoresce [figure 4.4A]. The background noise, JN , is determined by examining the variance of the background. To

60 calculate the maximum possible background(Jmax), all surrounding voxels are considered to be written[figure 4.4B]. In a real, written disk each voxel has a 50% chance of being written. The average background is then Jmax/2, as half of the surrounding voxels are expected to be written. The variation of this background is the main source of noise.

Because the bits are either on or off, they can be described by a binomial distribution.

I(r,z) and T(z) are sharply peaked, so the voxels that contribute the most to the background and its variance are adjacent to the bit of interest. This is seen in figure 4.3 as the central peaks are much larger than the others. Most of the background comes from these two bits, so the background is approximated by a binomial distribution with

2 trials. The variance in the background related to the maximum background as JN =

3/2 Jmax/2 . In systems with larger contributions to the noise come from other layers, JN will still be proportional to Jmax. However, the proportionality constant will be smaller.

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4.4 Comparing multilayered films to monoliths

This process is repeated for disks with varying z‐axis separation between voxels and also varying levels of confinement in the z axis through multilayering. The ratio Ra was varied from 100% to 1% in increments of 0.1%. This provided CNR values for monolithic systems was as well as multilayered systems of varied confinement. In each case, the multilayer effect was accomplished by applying a spatial filter in the form of a square wave to the corresponding M. Varying values of Ra were simulated by varying the duty cycle of these square waves. [figure 4.3]. Data density was varied by simply decreasing

D. D was varied from 2z0 to z0 so then simulation would span the most common designs from experiments in the literature.

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4.5 Results

To better understand what happens as the parameters are changed, one can examine the signal and crosstalk noise individually [figure 4.4A]. In the figure, the simulated contrast and background noise are normalized to the simulated contrast and background noise(respectively) of a monolith in the geometric limiting case of D=2z0.

While holding D constant, a few trends are apparent in figure 4.6. For large values of Ra ,

JS increases as Ra decreases. This is because more of the reading beam is delivered to the focal region as the other regions cause less parasitic absorption. That is, for smaller

Ra, the light has a shorter path length through the dye in layers above the bit of interest.

However at small Ra, JS reaches a max and begins to decrease with decreasing Ra. This happens when the bit of interest becomes smaller than the confocal region. JN, however, continuously decreases as the Ra is decreased. The noise decreases because there is less fluorescent material outside of the focal region to contribute to the noise.

As the pinhole size is increased, the behavior of JN remains unchanged. JS behaves similarly for both large and small pinholes. However, for the large pinhole the peak is shifted to larger Ra. This is a direct consequence of the widening of the confocal region.

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In the absence of the any other noise sources, the CNR continuously increases as the active layers are made thinner [figure 4.7]. There is a monotonic increase in the CNR with decreasing values of Ra. It is also notable that the CNR decreases monotonically as

D is decreased. Even with multilayering, more light from adjacent layers is delivered to the detectors as the spacing is decreased. The behavior is similar in both the large and small pinhole cases. However, the enhancement is stronger when the pinhole is smaller.

In the figure, the CNR values are normalized to the CNR for a monolithic device in its closely packed geometric limit. These monolithic CNR values are 625 for the small pinhole and 127 for the large pinhole.

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So from the above it is seen that multilayering can produce a palpable enhancement to the CNR. This enhancement can instead be spent on increase of data storage density. A monolith becomes unreadable as the data spacing is made closer than the radius of the data spots. However, there are multilayered samples with readable CNR values at the same data density. For each Ra there is a corresponding separation that has a CNR that matches the monolithic device with no spot overlap. As such, the multilayering process can increase the data storage density while leaving the CNR constant. This property is exemplified in figure 4.6. The density is capped because the separation has a lower limit of approximately D/z0=1. Even with multilayering, when the plane spacing is smaller than the written spot diameter, the information becomes imprinted on the adjacent layers during writing. This adds noise to the layer at the focus of the beam, and it cannot be filtered by the confocal system.

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4.6 Shot Noise and Dark Current

Thus far, the only noise term described has been the crosstalk. This result is an ideal limit rather than an expectation. Other significant sources of noise for these devices will come from the detector. The photodiode dark current and the Shot current both contribute to the overall CNR. The Shot noise will vary directly as the square root of the generated photocurrent. The photodiode dark current noise values are constant and do not scale with the amount of light taken in. As long as JN is large when compared to the dark current and Shot Noise, figure 4.7 should predict the effect of axial confinement in multilayered disks. However, when the JN is similar in size to the other terms, multilayering produces much less enhancement[figure 4.9]

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In figure 4.9 when other noise sources are dominant, the CNR enhancements seen in figure 4.7 are all but eliminated. This is because most of the enhancement in figure 4.7 is the result of reducing JN. While reduction of the active layer has little effect in these cases, increasing the power of the reading beam or the sensitivity of the detector will boost the CNR of systems. However, the CNR of a monolith scales in the same manner as the CNR of a multilayered disk as the beam power is increased, so there remains no enhancement from multilayering. Although, JN scales linearly with beam power and detector sensitivity while DC is constant and Shot noise scales as the square root. From this, it is possible to retain the enhancements of multilayering by increasing the signal

67 and noise currents so that they are large when compared to the Shot noise and dark current.

4.7 Conclusion

Overall a clear improvement in CNR is seen as the confinement effects are increased in these simulations. When the crosstalk noise is the dominant term, the multilayered disks offer a considerable enhancement to the CNR of a disk. Increasing the reading beam power does not offer any benefit in this case because the signal and crosstalk noise both scale linearly with power. When the pinhole size is increased, the enhancement is not as strong. However, increasing the pinhole size increases the photocurrents significantly. When dark current and Shot noise are the dominant terms, there is no enhancement to the CNR from multilayering. However increasing the generated photocurrent can make the background noise the dominant term.

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Chapter 5: Thermal Influence on Biexciton Annihilation in Zinc Phthalocyanine Films

5.1 Introduction

Metallo‐phthallocyanine (MPC) dyes are noted for their nonlinear optical properties and electronic structure. Common features include large values of chi‐3, a columnar crystalline form, liquid crystalline mesophases, and absorbance bands that span the visible spectrum.

While inorganic semiconductors have filled the role in the past, the mass production capability of organic materials places them as strong candidates for active media in the next generation of optoelectronic devices. Other works present these dyes as active media for femtosecond Kerr gates, photovoltaics, optical data storage, and optical limiters.[85‐88]

For each application, carrier transport and lifetime are of paramount importance.

Various authors have measured ultrafast exciton dynamics in MPC samples.[89‐91]

Many report biexciton annihilation at high excitation densities. In their analyses, the exciton‐exciton crossections are extracted from dynamics measurements and are then used to calculate the intermolecular hopping times. In all cases, the crossection is found to vary like time‐1/2, while the intermolecular hopping times range from 10 to 400 fs.

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These calculated hopping times are derived from the interpretations of the dimensionality of the biexciton interaction. The phenomenon of 1D diffusion of excitons along MPC chains is often presented as an explanation of the result; however a quasistatic population of excitons interacting in 3D can produce the same time dependence. The main purpose of this work is to properly discriminate these models.

In doing so, I intend to explain the excitonic behavior in both crystalline phase and the first mesophase.

The femtosecond dynamics for thin films of zinc phthalocyanine (ZnPC) are presented.

This work characterizes the temperature dependence of exciton behavior in both crystalline and liquid crystalline phases of the ZnPC. The measured exciton population dynamics do not scale linearly with the initial population density, and this behavior is accurately described by a biexciton recombination model. The biexciton recombination crossection and intermolecular hopping time are presented at temperatures from 90‐

400K. Here the exciton hopping time is reported to vary significantly with temperature in both phases. This thermal dependence is in disagreement with the model that the biexciton annihilation arises from 3D interaction of static carriers. The dependence strongly suggests that the interaction is restricted to an exciton population undergoing

1D diffusion. From this, the role of temperature and structural order in the exciton hopping time is clear.

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5.2 Materials

ZnPC powder was purchased from Aldrich and purified via thin layer chromatography.

The resultant powder was placed onto a thin sheet of quartz. Then it was heated beyond its melting point and pressed against another sheet of quartz. The thickness of the sample was set by a one micron spacer. The film was then characterized optically with linear spectrum measurements. The phase transition temperature of a powder of this sample was then measured to be near 375K with differential scanning calorimetry.

The absorbance spectrum of the film was fit using a Lorentz oscillator model.[92‐98] A fit of seven states was chosen as there are seven distinguishable features in the absorption spectrum(figure 5.1). The extracted resonant transition energies and their broadening factors are listed in table 5.1.

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Linear spectrometer measurements confirm a band structure similar to MPC films studied in other papers[92‐98]. The lowest energy peak is understood to be the first pi‐

>pi* molecular transition.[98] The symmetry of the absorption and photoluminescence spectral lines confirms that the next highest energy peak is electronically the same.

However, this state includes an optical phonon mode.[98, 99] Both of these states are commonly present in ZnPC solutions and films.[92, 96, 98, 99] Photoconductivity measurements of ZnPC films have confirmed this state to function as a Frenkel exciton.[97, 98]

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5.3 Experiment

Ultrafast pump‐probe spectroscopy was used to study the exciton dynamics of these

ZnPC films. An amplified titanium sapphire laser provided illumination for time dependant measurements. By use of a thermal stage, the temperature of the sample was controlled and monitored.

Carrier lifetime measurements were made with excitation fluence from 1‐10 mJ/cm2 at temperatures from 80‐450 K. A fundamental output beam of 800 nm (1.55 eV) wavelength was used as a probe with a frequency doubled 400nm (3.1 eV) pumping pulse to produce dynamic absorption measurements. Pump and probe beams intersected at a 30o angle and had radii of 200um and 50 um, respectively. Data was measured over a range of 180 ps with a 260 fs resolution.

From the sample’s absorption, heat capacity, and thermal conductivity, it was estimated that each pulse heats the sample by 0.3 K. The characteristic time for thermal diffusion across the laser spot of 200um was estimated to be 3 ms. Therefore the pump beam induced heating was expected to have negligible effects on the ps dynamics. The bulk temperature of the sample was expected to be within 3 K of the reading of the thermocouple.

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5.4 Results

To quantify the exciton dynamics, the quantum efficiency of the conversion of absorbed photons to excitons was assumed to be near 100%. Observed photoluminescence measurements by Bala et al suggest that this efficiency varies little as temperature is varied.[98] From the pulse energy and sample absorbance it was clear how many photons were absorbed, and this was taken to be equal to the number of excitons created. The time‐dependant photoabsorbance measurements were calibrated to this standard.

At 293K the initial exciton population is linear with power. However, the population dynamics do not scale linearly with initial concentration (figure 5.2). This indicates exciton‐exciton annihilation is present. [89‐91]

Similar features are observed for all temperatures from 90K‐400K. There is a fast biexciton annihilation over 5‐10 ps. A slower decay from single exciton behavior is

74 noticed over 100 ps. Finally a much slower background term remains nearly constant over a nanosecond, and this likely from self trapped pi* states. [89‐91]

Because the population decay does not scale linearly with population, a biexciton decay model (equation 5.1) is used to fit the data.[89‐91]

2 1 n   (t)n  n (5.1)

Here n is the exciton concentration,  is the single exciton lifetime, and  (t) is the biexciton crossection.

The time dependence of  (t) is based upon the spatial constraints of the system[91]. In

p each case,  (t)takes the form of  (t)   0t where p is some real number and 0 is a constant that depends upon the properties of the system. For high population densities

(  (t)n  1 ) the linear term in equation 5.1 is negligible. This short time approximation is seen in equation 5.2.

1 1 p1 1 n   0 ( p 1) t  n0 (5.2)

This illustrates a way to fit the time dependence of 0 through simple graph methods.

Given correct selection of p, a plot of 1/n vs. tp+1 should be a straight line. Fitting n‐1 to a power law showed that p= ‐1/2. A plot of n‐1 vs t1/2 for all of the measured data sets produces a series of lines as seen in figure 5.3.

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1/ 2 So with the result of p = ‐1/2, the form of  (t) is determined to be  (t)   0t .

Substitution into equation 5.1 allows the carrier population to be solved for all times and concentrations. Solving the equation 5.1 yields equation 5.3.

 t e  n  (5.3) 1 p1   n     erf  t  0 0   

This became a tool to extract the dynamics coefficients under the condition p = ‐1/2.

Note that in equation 5.3 the carrier concentration goes to zero when t >>  . The differential absorption, however, persists on timescales much larger than exciton lifetimes. As such, this portion of the signal is neither from single exciton decay nor biexciton annihilation. Therefore, this long term behavior was subtracted before applying any of the fitting routines. [91]

The time dependence of  (t) exists because the excitons which are closest to each other at t=0 are most likely to annihilate first. At later times, the closest pairs of excitons have already annihilated and the average time for any remaining excitons to annihilate is longer. The form of  (t) is determined by the exciton‐exciton interaction strength and the translational freedom of the excitons.

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5.5 Physical Interpretation of the Time Dependence of the Collision Rate

In the previous sections it was shown that the differential absorption signal was caused mainly by the presence of excitons, and that these excitons undergo a nonlinear annihilation with each other. The biexciton annihilation coefficient, (t) was shown to

‐0.5 2 have the time dependence of (t) = 0t at pumping intensities lower 10 mJ/cm .

There are two interpretations of the excitonic kinetics that predict this result. Such a response is characteristic of quasistatic excitons with long range interactions in 3‐ dimensions. This dependence is also produced by a population of excitons with a short range interaction that are allowed to diffuse in 1‐dimension.[91]

To build these models, it is assumed that the excitons annihilate through dipole‐dipole interaction. The phenomenological description of the annihilation rate for a single exciton, (t), is the integrated interaction between that exciton and any other exciton in the sample[91, 100]. This is represented as

 (t)   d d r(r)g(r, t) (5.4)

Were d is the dimensionality of the system, (r) is the dipole‐dipole interaction strength of the excitons, and g(r,t) is the pair correlation function between two excitations

77 spaced by a distance r at time t. [91, 100] The dipole term, (r) is easily understood as a

Forster type interaction where

6  R  (r)  k  A  (5.5) op  r 

Here RA is the Forster Radius of annihilation and kop is the optical excitation decay rate.

The correlation function can be found with a diffusion equation [91, 100]

g(r, t)  2D2 g(r, t)  2(r)g(r, t)  F(g(r, t)) (5.6) t

Where D is the diffusion constant for the excitons, and F describes higher order interactions. [91, 100] To good approximation,

F(g(r, t))  2n (t)(1 g(r, t))g(r, t) (5.7)

One such interpretation is the static case. In this view each exciton is well localized and does not move significantly over the course of its lifetime. Since the excitons are considered quasistatic, the divergent term is ignored. If the higher order interactions are also neglected, then the solution to equation 5.6 is simply integrated. [91, 100]

g(r,t)  e2(r)t (5.8)

Placement of this function into the definition of (t) provides an integrable expression and reduces to the form

d 1 6  (t)   0t (5.9)

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So clearly this interpretation reproduces the measured behavior when d=3. In making these approximations, it is important to find the constraints under which they hold true.

The higher order interaction term is negligible if F(g(r,t)) << 2(r)g(r,t). [91, 100] Using equations 5.1, 5.7, 5.8, and 5.9, this constraint reduces to t < (4n(t))‐1. Under this constraint, it is also true that t < , so it is self consistent to ignore the linear decay term in equation 5.1. Its solution under these constraints has the form

1 n(t)  (5.10) 1 d / 6 n0  (6 / d) 0 t

d/6 At high intensities when n0 > k d/(6 0) the constraints reduce to 1<6/d which is true for the observation of d=3. This means that the approximations made are self consistent for the observed dimensionality. [91, 100]

To understand diffusion limited annihilation one must instead consider the global rate laws for interacting populations. That is, for times close to t=0, the asymptotic behavior is well approximated by a power law[91, 101]

n(t) ~ t‐h for some h>0 (5.11)

For a particle undergoing a random walk through a structure, we can expect it to visit S sites before reacting with its nearest neighbor.[101] The average spacing between carriers varies inversely with the carrier density, and so

S ~ n‐1 (5.12)

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A well known result of random walker calculations is that the number of sites visited

increases with the elapsed time tel.[101]

f S ~ tel (5.13)

Here f is determined by the dimensionality of the system. For systems of integer value d, f has piecewise form.[102]

d  for d  2 f   2 (5.14) 1 for d  2

So, from equations 5.12‐ 5.14

n ~ S 1 ~ t  f (5.15)

For short times and high concentrations, the linear decay term in equation 5.4 is negligible. Substitution of equation 5.18 allows the time dependence of (t) to be shown

2  f 1 2 f n  n  (t)  t ~ t  (t) (5.16)

In order to produce the same time behavior on both sides of the equation, it is clear that

(t) ~ tf‐1. So using the piecewise definition of f now defines (t)[91],

d  1  t 2 for d  2  (t)   0 (5.17)  0 for d  2

The experimental time dependence of (t)~t‐0.5 shown in the previous section is expected for a one dimensional system (d = 1) in this interpretation.

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So we see that there are two interpretations of the exciton kinetics that predict the observed result. Such behavior is characteristic of quasistatic excitons with long range interactions in 3‐dimensions. [91] A population of excitons with a short range interaction also produces this result when constrained to 1‐dimensional diffusion. [91]

To differentiate between these cases, it is necessary to consider the temperature

dependence of 0 .

5.6 Thermal Dependance of the ZnPc

For the next set of measurements the temperature dependence of the carrier decay parameters was examined. The sample was held at temperatures from 90K‐ 415K while the pump‐probe dynamics were measured at both a high and a low fluence. The low fluence measurements resulted in sufficiently low excitation density so that biexciton annihilation was not observed. These fits were used to accurately determine at each temperature. The high power measurements were then fit to equation 5.3 with 

constrained to extract  0 at the same temperature. The resulting values of  0 and  were plotted in figure 5.4.

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Here a trend is clear in the behavior of  0 . It is seen to rise with temperature in the crystalline phase and then decreases with temperature as the disorder of the system increases. As seen in figure 5.4,  drops by ~20% as the temperature goes from 365 K to 370 K. This shows that there is a significantly larger number of ways for each exciton to scatter and annihilate as the liquid crystal goes through the phase transition.

For a quasistatic system of interacting excitons, the temperature should have little effect on the rate of interaction. The main contribution from a rising temperature would be thermal expansion. As the average intermolecular spacing increases, the rate of reaction would decrease. This prediction does not match these results. The observed rate of reaction increases with temperature in the crystalline phase. Furthermore the intermolecular spacing of ZnPC changes very little as it is heated through the crystalline phase. Thus heating should have little or no effect on the rate of biexciton decay if the

82 system were in such a quasistatic configuration. As such, we know the excitons do not adhere to the quasistatic 3D interpretation. [89, 91]

In this interpretation, the intermolecular hopping time,  h is intrinsically linked to  0

and the molecular density, N. As such,  h was determined for each temperature under

-1 2 the condition that  h = 4  0N [91]. Since the density of the film varies very little

with temperature, the hopping time was determined directly from measurements of  0 and plotted in figure 5.5.

It should also be noted that the intermolecular hopping time and D, the diffusion

‐1 2 constant are inversely related. That is D ~  h ~ 0 . [91, 101, 102] From this relation the diffusion constant D is determined up to a proportionality constant(figure 5.6).

To test this interpretation, we look to the Arrherius equation. This relation is often used to model thermally activated processes. For most systems that undergo diffusion, the

83 temperature dependence of some rate constant, R, is well described as an activated process of activation energy Ea and characterized by the Arrhenius equation,

E a R  R e k B T 0 (5.18)

where T is the absolute temperature of the system, kB is the Boltzmann constant, and R0 is that rate at T=0 K. In this case, the diffusion constant, D, will be fit to the Arrhenius equation(figure 5.6). A fit for an activated process does not work well over the entire range of data. However, if split into 2 segments that correspond to the phases, this model fits 0 well. The model shows biexciton recombination to have an activation energy of 17  2meV in this system.

5.7 Conclusion

So it is clear that the temperature affects both linear exciton decay and biexciton collision rates in ZnPC. From this, the experiment determined that the exciton recombination does not occur under the constraints of a quasistatic system with long range interactions. Instead, the sample is interaction is found to happen at short range for excitons travelling in 1D. It is also found that with increasing temperature the rate of biexciton collision increases. This change has corresponding effects on the intermolecular hopping time and diffusion constant. Furthermore, the complexity of

 0 ’s temperature dependence shows that different phenomena dominate the annihilation rate in each phase.

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Appendix A: Power Dependence of Photopatterning in C‐18 RG dye.

A.1 Introduction

The ability to pattern high density 3D optical storage disks is limited by the shape and size of the written spots. Understanding beams effect on the sample is an important part of optimizing any such disk. Here a series of spots are patterned into a polymer containing a two photon absorbing dye. In separate experiments, the sample is patterned with wavelengths corresponding to its linear and two photon absorption peaks. By varying the power of the patterning beams, the size of these spots is also varied. As the power of the patterning beam is decreased, the spots become smaller and in some cases the patterns are shown to be smaller than the shape of the beam.

Under simple microscopy, the potential of optical data storage is limited by the wave nature of light. For most common kinds of microscope, diffraction dictates a minimum beam size for both patterning and resolving information. As such the features on a disk cannot be utilized if they are smaller than the focused beam. Therefore a restriction is imposed on the overall DSD of an optical data storage scheme. However, with a bit of finesse, the next generation of optical storage can circumvent these issues.

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Most of the designs for 3D data storage systems rely on two photon absorption processes. This property benefits the storage density, as it creates spots that are smaller than the beam. For a process of n photons and a writing beam with a Gaussian shape, the half width of the written spot is related to the half width of the beam shape

by a factor of in the radial coordinates and 2 1 in the z direction. These relate to palpable increases in the data storage density.

With few exceptions, the mechanisms that enable 3D data storage use photochemical processes. In fluorescence based systems, each two photon absorption event causes a net creation of a fluorescent molecule. This is frequently produced through a ring closing change[66], though more recent methods utilize photoacid generators to cleave the bonds of dye precursors[2]. In many reflection based systems, the index of refraction of a polymer is changed by a photochromic ring closing[21, 24]. While the absorption of the writing beam is nonlinear, the materials’ response to the absorption is linear. As a result, all written spots retain the Gaussian characteristics of the beam that was used to write them. The spots are similar in size to the beam, and have a soft edge.

The use of a material with a nonlinear response to illumination is one way to circumvent this limit. Some photoresist materials are frequently patterned in such a way as to produce  / 4 detail. With further application of material nonlinearities,  / 20 features have been achieved[103]. While in a polymer gel state, these materials are patterned

86 by photoinitiated crosslinking. The crosslinking only happens in regions where the free radical concentrations are taken above a threshold [103, 104] While very interesting for nanotooling and MEMs, photoresist gels do not offer suitable mechanical properties for optical data storage.

A few methods exist to beat the diffraction limit within the context of 3d data storage.

One demonstration of such a restricted the spot size was done by Nakano et al[21]. The authors photopatterned a material with a UV laser to make small writable regions, then later wrote to these regions with an infrared laser. Since the writable regions were confined to the focal region of the UV beam that was used to make them, the response to the IR beam was confined to the same regions. This produced features that were much smaller than the IR beam that was used to write them. Spatial confinement was provided in the third dimension by the multilayering of the material itself. While this method produced clear and useful results, the down side is that it requires photopatterning of each layer during the fabrication process. Furthermore, while the spots are smaller than the IR beam, they are still similar in size to the UV beam.

The most common forms of nonlinear response used for optical data storage are photothermal in nature. Current commercial writable DVD and Blu Ray disks use thermally crystallizable material[3]. By linear absorption of the writing beam, the material is heated and annealed. From the thermal treatment, a local phase change is

87 created. These modulations in the phase of the disks cause a modulation in the reflection coefficient, so the disks are read by reflection. Since the change is phase based, the change is thresholded with temperature. While the diffraction limited spot size of in a Blu Ray system is 580 nm(NA=0.8, =400nm) the written spots are only

150nm in diameter.

Other recent experiments have used threshold based mechanisms for 3D optical data storage. Photoinitiated crosslinking reactions [68] and photothermal annealing of gold nanorods [15] both produce nonlinear responses in the materials optical properties.

Furthermore, for commercial writable optical media, the information is stored through a threshold based phase change[3‐5]. However, subdiffraction patterning is not demonstrated in these devices. 

The benefits of threshold systems are multifacet. Others have shown that a properly controlled threshold process can circumvent the need for 2‐photon based writing processes[15]. The high contrast, spatially confined writing provides higher signal to noise ratios when reading[21]. Furthermore, the size of data spots has been shown to vary as writing power is changed[105]. However, the potential for smaller written spot sizes and higher DSDs has yet to be explored. In a system with these properties, the data can be packed more densely, and so the overall DSD and storage capacity increase.

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An experiment was designed to elicit such a dependence, should it exist, in a material with known thermal threshold properties. In two separate experiments the sample was patterned at wavelengths matching its linear absorption peak at 400 nm and its two photon absorption peak at 675 nm. Spots were written at various powers, the sizes of written spots were measured for various writing powers.

A.2 Reading from Subdiffraction Systems

In order to make use of features smaller than the beam, the features must be resolvable during reading. Modern imaging techniques have significantly increased the resolution of both 2‐D and 3‐D microscopy to suitable levels for this task. Because of the geometry of the detection, near field methods are not suitable for 3D data storage. Multiple far field techniques have matured in the past 10 years to image features smaller than 10 nm. Stimulated Emission Depletion Microscopy (STED) offers the power to resolve features smaller than 6 nm by using stimulated emission to quench the fluorescence of a major portion of the focal volume around the feature of interest[106]. Structured illumination microscopy(STIM) has achieved similar resolutions by using a light grating to illuminate and scan through the sample. Image processing done to the resultant beat pattern provides resolution to better than 10 nm[17]. Both the I5R and 4Pi methods use counter propagating beams to create interference at the focal point and thus further reduce the resolution to 50‐100 nm[107, 108]. A Nonlinear STIM approach relies upon the saturation properties of certain dies to offer a theoretically infinite resolution[109].

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By this method, the resolved volume is greatly reduced, but is limited by the size and concentration of the dye molecules, the sensitivity of the dye, and the stability of the excitation source[6].

A.3 Sample Preparation

A film of PETg with 2 weight % of C18‐RG dye was fabricated as a thin film to be photopatterned [49]. The dye was made in the process outlined in the literature[110].

Then the dye was added to the polymer PETg in its powder form and heated to 200C to form a solution. The solution was mixed and pressed into thin films between glass slides to produce polymer films. After cooling, the films were reheated to 90C and held there for 45 minutes to allow the dye molecules to mobilize and coalesce.

A.4 Photopatterning at the Two Photon Absorption Wavelength

For the first set of photopatterning experiments, the film was exposed to focused radiation from a pulsed laser source. Laser illumination was supplied by a Nd:YAG operating in 10 nanosecond pulse mode. An optical parametric oscillator was used to set the wavelength of each pulse to 675 nm, which is the 2‐photon absorption peak of the dye. Each pulse was then focused by an oil‐immersed lens objective with numerical aperture of 0.85. Through use of a knife edge technique, the beam waist was directly measured to be .9 um while the Raleigh range in the z axis was 2.3 m [figure

90

A.1]. The diffraction limited beam waist for this wavelength and lens is about 300nm, so there must be significant aberration in the optical system.

The sample was translated through the beam focus by a computer controlled 3 axis stage. Single pulse operation of the laser was also controlled by the computer. The material was patterned by first positioning the sample, and then sending a pulse of light into it. The process was repeated to make a pattern of about 15 spots within the sample. The pulse energy was controlled with a series of neutral density filters. Six different patterns were made in all, each with different pulse energy. The energy of the pulses was varied by application of a series of neutral density filters, each with a transmission of 84%.

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Upon the conclusion of patterning, the samples were imaged with a confocal microscope. For these measurements, the illuminating beam was set to 405 nm to make the dye fluoresce. Spectral filters were placed to match the possible fluorescence modes of the dye.

The images of the sample after pulsed photopatterning at 675 nm are seen in figure A.2.

The pattern does not emit light at any of the dye’s fluorescence modes. However, the pattern is visible in a transmission microscope. From these, it is clear that the pattern is a result of thermal decomposition of both the dyes and the host polymer.

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To extract the feature sizes, each spot was fit to a Gaussian shape. Prior to fitting, a low pass filter was applied to remove noise sources that were much smaller than the resolution of the microscope. To account for the power fluctuations within patterns, the reported measurements are based on the average size of the all of the spots in each pattern [figure A.3]. On occasion, a light pulse strikes an imperfection in the film and produces a particularly large, and misshapen spot. Because of this, spots that are particularly asymmetrical are left out when determining statistics.

All of the spots patterned in this experiment are smaller than the beam diameter. The most significant source of the error is the variance in energy from pulse to pulse. The pulse to pulse instability creates uncertainty in the average power used to create each ensemble. This effect leads to a large variance in the sizes of the written spots.

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From the absorbance of the material (Figure 2.3), it is seen that there is no appreciable linear absorption at 675 nm, so clearly the writing cannot be driven by a single photon process when using this wavelength. Given the strong TPA crossection of the dye at

675nm (Figure 2.4) It is expected that the process is driven by TPA.

Even though the process cannot be completely classified from the data, it is notable that there are spots observed smaller than the diffraction limit. Earlier the beam was characterized to have a waist of 900nm. For two photon absorption this value is reduced 640 nm. Many of the observed spots are smaller than this (Figure A.3), and some of the spots are even smaller than 300 nm. Regardless of the fit of the model, it is clear that this process is making spots smaller than the effective beam waist for both linear absorption and TPA.

A.5 Patterning the Sample with Linear Absorption

Following the experiment with the nanosecond system, the single photon response of the system is examined by writing to the sample with a CW source at 405nm. For this experiment, the sample was patterned with lines by the previously mentioned confocal microscope, and then those lines were imaged and characterized in 3D by the same microscope. To pattern the sample, it was first placed into the 3D stage that is controlled by the microscope. The sample was then imaged at a low power to provide a

94 background reference. Next, the microscope was set to sweep the laser across the sample in individual lines at powers ranging from 1 to 100 mW with a scan rate of 80

m/s. Given the beam waist is approximately 130nm for this optical system, each part of the patterned part of the sample is exposed to the laser for about 1.6ms. Lines were parallel and separated by 1 m to avoid crosstalk effects. After writing the lines were images with the same beam as was used to write them, however the power was reduced to 0.1 mW. The confocal microscope imaged the lines in slices that were separated by 100 nm in depth. One such slice is shown in figure A.4.

In the CW experiment, the data is taken from fig A.4. By taking crossections perpendicular to each line, the Gaussian features of the spots can be fit. Thirty crossections are averaged to decrease the image noise for each line prior to fitting (Fig

A.4).

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To find any power dependant trend, the overall dimensions of the spots were extracted from these averaged images. Because of the Gaussian beam shape, the spots were fit by a Lorentzian along the beam axis and a Gaussian perpendicular to this axis. The results of these fits are found in figure A.5. Here the plots show an increase in both the height and width of the spot as power increases. At low powers, the background noise becomes similar in size to the signal. The fitting becomes unreliable and both spot dimensions appear to increase drastically as the power decreases.

Here the detected spot widths are significantly larger than the beam waist. For a

Gaussian beam of 405 nm light that is focused through a lens with numerical aperture of

1, the beam waist is about 130 nm. In the measurements, the smallest radius of the written spots is found to be about 300 nm [figure A.5].

The data has a generally linear trend with power. However at lower energies this trend does not match the data. This is likely because at these lower energies, the signal to

96 noise ratio is small and the fit to a Gaussian shape is not well constrained. Since there is no clear threshold, it cannot be said that a thermal phase change process is present.

The patterned lines are wider than the beam, and they decrease in size as the power is decreased. This sort of behavior is characteristic in systems with a saturated bleaching response.

A.6 Conclusion

Sub diffraction limit patterning is not something that has is frequently used in the context of 3D optical data storage. However, the tools exist to pattern and read information that is smaller than the diffraction limit. Here is shown a 2‐photon based system that created spots smaller than the focused beam diameter. Similar experiments done with a single photon absorption based system do not exhibit the same sub diffraction features, and are likely in a regime of saturated response. Both systems show a trend in the size of the patterned features. While it is not clearly a threshold process, the sample definitely exhibits a nonlinear response to illumination.

When used as part of a storage medium the system could produce both higher signal to noise ratio and data storage density than a system that uses a non‐threshold mechanism [12, 60].

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