Patent Grant
8340486
The invention relates to optical devices employing nonlinear optical materials.
The field of nonlinear optics is extremely rich in results, and has been around for many years. Basically the premise of nearly all measurements in the field is that one introduces a sufficiently high power flux (or “fluence,” a term of art) in an optical material, it is often possible to excite nonlinear behavior, meaning that the properties of the material change with the input optical power. This kind of effect is very often described through the use of, for instance. Chi2 (χ2) and Chi3 (χ3) which are material dependent constants that describe the strength of two of the relevant nonlinear optical activities of a material. Some nonlinearities, which are material dependent, will work at the full optical frequency, while others are slower. Recently, engineered organic materials have begun to be used for nonlinear optics, because they can be designed to have extremely large χ2 and χ3 moments.
In one aspect, the invention relates to a method for controlling the nonlinear moments of a nonlinear optical material of an electrooptical device. The method includes controlling an optical mode region of the electrooptical device by providing a time varying signal to the electrooptical device via one or more electrodes of the device and affecting the nonlinear moments of the nonlinear optical material of the electrooptical device by providing a time independent bias to the device. In one embodiment, the nonlinear optical material includes a χ3 material. In another embodiment, the method includes employing the time independent bias to bias the χ3 material such that the χ3 material behaves in a manner analogous to a χ2 material. In yet another embodiment, the method includes employing the time independent bias to dynamically bias the nonlinear optical material. In yet another embodiment, the method includes employing the time independent bias to dynamically phase match the nonlinear optical material and an optical signal. In yet another embodiment, the method includes controlling a multi-wave process via the electrooptic device and employing the time independent bias to control the effective index of optical signals in the multi-wave process. In one embodiment, the time independent bias includes a DC bias of 50V or more. In another embodiment, the step of affecting the nonlinear moments further includes providing the time independent bias via the one or more electrodes used for providing the time varying signal.
In one embodiment, an electrooptical device is configured to perform the aforementioned method for controlling the nonlinear moments of the nonlinear optical material. In one embodiment, the electrooptical is configured to perform at least one of electrooptic modulation or difference frequency generation. In another embodiment, the electrooptical device includes a slot waveguide having a slot region and being arranged to provide a DC field of at least 1×108 V/m in the slot region. In one embodiment, the nonlinear optical material is a χ3 material that covers the slot region of the slot waveguide.
In another embodiment, a controller is configured to perform the aforementioned method for controlling the nonlinear moments of the nonlinear optical material. In one embodiment, the controller is arranged to provide the time varying signal to the electrodes via one or more signal paths between the controller and a slot region of the electrooptical device, and the controller is further arranged to provide the time independent bias via the one or more signal paths. In another embodiment, the controller is further arranged to provide dynamic phase matching between the optical signal and the nonlinear optical material. In one embodiment, the controller and the electrooptical device are located on the same chip.
The foregoing and other objects, aspects, features, and advantages of the invention will become more apparent from the following description and from the claims.
The objects and features of the invention can be better understood with reference to the drawings described below, and the claims. The drawings are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the invention. In the drawings, like numerals are used to indicate like parts throughout the various views.
We describe hereinbelow method, devices, and systems for controlling the nonlinear moments of a nonlinear optical material of an electrooptical device. We begin with a brief technology overview followed by a description of exemplary methods, devices, and systems according to principles of the invention.
Nonlinear optical polymers can provide a unique and powerful platform for building a number of useful optical devices. Traditionally, they have been used in all-polymer waveguiding systems, which have had a number of severe practical limitations. Silicon has recently become a popular material for integrated optical systems, but it lacks strong nonlinear properties. By combining nonlinear optical polymer claddings and silicon waveguides in a hybrid system, we show that a number of significant advantages are obtained. In particular, fabrication can be done using conventional CMOS processing, with the polymer added as part of back-end processes (after all of the high-temperature processing is completed), and the waveguide structure can also serve as an ultracompact set of electrodes. We also describe the use of second-order nonlinear polymers with silicon for parametric amplification and oscillation.
Unlike many conventionally used optical gain elements, such as erbium doped fiber amplifiers, the wavelength of nonlinear polymer based gain elements are limited only by the material absorption and guiding abilities of the waveguide system.
A number of advances in both design and synthesis of nonlinear optical polymer material systems have been previously achieved. Polymers with a second-order optical nonlinearity, with r33 values of 200 μm/V, have been demonstrated. This r33 is around an order of magnitude larger than that of many conventional nonlinear optical materials, like lithium niobate, which has an r33 of 30 μm/V. Third-order nonlinear optical polymers have also been synthesized, with Kerr coefficients of 7×10−14 cm2/W, around twice that of silicon. At the same time, great advances have been made in the field of silicon photonics; low-loss waveguides, high-Q resonators, and electrically pumped all-silicon modulators have been built into chip-scale systems.
Nonlinear optical polymers and silicon waveguides can be combined to provide a hybrid platform with unique advantages. The nonlinear polymer can provide a flexible source of large second- and third-order optical nonlinearities. At the same time, the silicon can provide tight optical confinement due to its high index of refraction and optically invisible electrical contacts to the active regions. Moreover, fabrication technology for silicon is quite advanced due to the significant investments made by the silicon microelectronics industry. It is likely that a silicon-polymer hybrid system will prove to be an attractive platform for a number of optical devices, including integrated optical parametric oscillators, broad-band optical amplifiers, low-Vπ modulators, and all-optical switches. Additional details are provided in Baehr-Jones et al., “Polymer Silicon Hybrid Systems: A Platform for Practical Nonlinear Optics,” J. Phys. Chem. C 112, 8085 (2008), hereby incorporated by reference herein in its entirety.
Silicon Photonics
The low-loss properties of crystalline silicon in the near-infrared have been known for decades. Over the past several years, in particular, the field of silicon photonics has witnessed significant growth. For linear optics, silicon waveguides have proven extremely versatile, in that advanced lithographic and processing techniques have enabled feature sizes as small as 40 nm to be realized and Q values of 300 k to be obtained. This has been achieved, moreover, in planar, lithographic processes that are compatible with commercial silicon foundries, suggesting that manufacturing costs in quantity will be very modest. Modulation at speeds up to 10 GBit/sec has also been demonstrated on the basis of the free-carrier plasma dispersion effect, with Vπ values of 1.8 V obtained. Surprisingly, even all-silicon photodetection at high speeds is possible through the introduction of specifically tailored lattice defects.
Silicon-based nonlinear optics is a young field. This is largely due to the absence of an appreciable second-order nonlinearity due to inversion symmetry in the silicon lattice. Attempts have been made to strain the silicon layer in order to achieve second-order nonlinearities, but these experiments have not resulted in a large r33 value nor any practical devices to date. While parametric gain has been achieved through third-order optical nonlinearities in silicon, the requisite pump powers are extremely large, around 11 W. These high power levels, which are well in excess of the damage threshold of silicon waveguides, require that devices be operated in pulsed mode and greatly limit the devices' utility. The picture is similar for Kerr-effect-based all-optical switches; the amount of gate optical power needed for π radians of phase shift, which we will refer to as Pπ, is typically on the order of 100 W. While lower switching powers have been obtained through the use of two-photon absorption (TPA) to generate free carriers, these devices are not ultrafast, with bandwidth limitations of around 1 GHz or less.
Nonlinear-Polymer-Based Modulators
The most familiar application of nonlinear optical polymers is electrooptic modulation. Nonlinear polymer modulators are based on the Pockels effect, in which an electric field changes the refractive index of a poled material, generally for near-infrared radiation. Mach-Zehnder modulators and ring modulators can both be built on this principle. Waveguides are generally built by performing photolithography on a series of different polymer materials, creating a multilayer, low index contrast guiding system. Nonlinear-polymer-based devices have conventionally been built using multilayer photolithographic processes in all-polymer systems with metal electrodes.
Conventional nonlinear polymer modulators are already quite competitive with modulators based on other material systems. One of the most important characteristics of an electrooptic modulator is the Vπ, or level of external voltage that is needed to induce π radians of phase shift in a Mach-Zehnder. This corresponds to switching from complete optical transmission to complete extinction. A lower value is desirable because it makes the supporting electronics cheaper and significantly reduces the amount of power that is consumed by the modulator; the on-chip power dissipation for electrooptic modulators is an important limitation toward achieving massive integration. With nonlinear polymers, Vπ values of 0.65 V have been demonstrated. For comparison, modulators based on lithium niobate, a nonlinear optical crystal, have only achieved Vπ values of around 2 V to date. Lithium niobate devices are the most common Mach-Zehnder modulators available commercially today.
Silicon-based modulators have also not reached the levels of performance exhibited by nonlinear polymer modulators, with Vπ values of only 1.8 V achieved. In Green et al., “Ultra-Compact, Low RF Power, 10 Gb/s Silicon Mach-Zehnder Modulator,” Optics Express 15, 17106 (2007) it has been shown that a very low VπL value can be obtained if one offsets the switching signal with a DC bias, suggesting that improvements to this might be possible; however, these designs are predicated on a large amount of current flowing through the device, suggesting that even if lower switching voltages are obtained, power usage may remain unacceptably high. By contrast, very little current flows through a nonlinear polymer modulator, as the nonlinear polymers usually have low conductivities.
When integrated with a silicon platform, however, polymer-based modulators achieve even greater advantages. Devices are fabricated by defining a series of waveguides and optical structures on a silicon-on-insulator substrate. The polymer can then be spin coated to obtain a high-quality film. This has the advantage of requiring high-resolution lithography to be done only with silicon rather than polymer. The main device complexity in such an approach is captured in the silicon layer, which is fabricated using standard CMOS processing steps. Additional details are provided in Baehr-Jones et al., “Optical Modulation and Detection in Slotted Silicon Waveguides,” Optics Express 13, 5216 (2005), hereby incorporated by reference herein in its entirety.
Polymer-Silicon Slot Waveguide
The integrated nonlinear polymer-silicon design involves a slot waveguide, which consists of two distinct silicon strips. As shown in
It is important to note that the silicon in this case is being used only as an optically transparent conductor and, as such, is uniformly doped near the optically active regions. As discussed in Baehr-Jones et al., “Optical Modulation and Detection in Slotted Silicon Waveguides,” Optics Express 13, 5216 (2005), some of the inventors work in the past has involved lightly doped p-type silicon with 1015 boron/cm3. The only significance of the doping level is that it decreases the resistivity compared to that of intrinsic silicon and can cause increased optical loss in high quantities.
Slot waveguides have been fabricated with low optical losses through electron beam lithography; losses of better than −4 dB/cm have been obtained. Slot waveguide modulators including polymers have also been built; ring-based modulators have been built, which exhibit tuning of 5.2 GHz/V, around five times more responsive than modulators designed with similar polymers on a nonslotted architecture. When used in a Mach-Zehnder configuration, we have previously obtained VπL values of around 0.5 V·cm; this suggests that Vπ values below 250 mV could be obtained in a device of several cm of length in a push-pull configuration without any improvement in material performance. A recent design study suggests that it should eventually be possible, by using the best nonlinear polymer materials available today and scaling down the slot size of the silicon guides, to obtain further improvements; slot-waveguide-based modulators with Vπ values of 10 mV or less should be possible, an improvement over current typical Vπ values by nearly 2 orders of magnitude. Additional details are discussed in Hochberg et al., “Towards a Millivolt Optical Modulator with Nano-slot Waveguides,” Optics Express 15, 8401 (2007), hereby incorporated by reference herein in its entirety.
Nonlinear Polymer all-Optical Modulators
All-optical modulators built in silicon have been the subject of increased interest. Such devices are usually built based on a Mach-Zehnder geometry; a signal optical mode goes through both arms, and a gate optical mode is introduced into one of the arms.
By analogy to the Vπ value reported for the electrooptic modulator, it is possible to characterize the response strength of an all-optical modulator in terms of Pπ, the instantaneous power required to obtain an induced it radians of phase shift in one arm. Lower values for ππ are better as they correspond to more responsive modulators that require less gate power. Nearly all optical waveguides have a certain amount of optical power that can be tolerated (a damage threshold); higher values than this lead to device breakdown, often due to the effects of heating. Achieving lower Pπ values is an important step toward practical all-optical modulators since it is desirable to build devices that can function with continuous-wave optical inputs.
One approach to lowering the Pπ is to use a nonlinear material with a stronger response. Nonlinear polymers show significant promise in this area; ultrafast nonlinear coefficients double that of silicon have already been demonstrated. In fact, polymers with around 10 to 100 times the third-order nonlinear coefficient of silicon are likely to be demonstrated.
In addition to selecting a stronger material, the nonlinear response of a device can be enhanced by concentrating the optical modes into a smaller propagation area. In such a situation, a larger electric field will be induced by the optical mode, which will, in turn, lead to a larger shift in the nonlinear material. The amount of all-optical modulation obtained in a waveguide can be written as:
Here, Aeff is the effective area for the optical modes involved, the E and H fields are for the modal patterns, and L is the length. In a standard fiber optic cable with a mode field diameter on the order of 10 μm, the effective area would be approximately 100 μm2. However, a ridge silicon waveguide with dimensions of 0.5×0.1 μm, such as that shown in
Utilizing this silicon-polymer hybrid geometry, we have previously demonstrated an all-optical modulator with terahertz bandwidth. A Pπ of 2 W was obtained and discussed in more detail in Hochberg, et al., “Terahertz All-Optical Modulation in a Silicon-Polymer Hybrid System,” Nat. Mater. 5, 703 (2006). By contrast, in all-silicon devices, typical values were obtained for an ultrafast Pπ range from 50 to 100 W. As nonlinear polymers continue to increase in strength, they can be easily integrated into the polymer-silicon hybrid system used devices. It is likely that Pπ values of less than 1 W will eventually be possible, even without resonant enhancement.
Nonlinear Polymer Optical Amplifiers and Parametric Oscillators
A significant goal for silicon photonics is the development of optical amplifiers and lasers for the near-infrared. A number of advantages can be obtained by using a nonlinear polymer cladding with a silicon waveguide system. The most important benefit is the additional nonlinearity available from the polymer as compared to the nonlinearity from silicon alone. The χ2 moment that can be obtained from nonlinear polymers is quite large; an r33 of 200 pm/V corresponds to a χ2 moment of around 8.3×10−10 m/V. The induced nonlinear polarization moment for a 1×107 V/m electric field, typical for the 0.5×0.1 μm silicon ridge waveguides described here is then 8.3×104 V/m. By contrast, the χ3 moment of silicon is 1.7×10−19 m2 V−2, corresponding to an induced nonlinear polarization of only 170 V/m. This analysis presumes, of course, that the r33 encountered for electrooptic modulation is, in fact, an ultrafast effect. The polymer response bandwidth has been shown with conventional modulators to be at least 165 GHz. Through optical rectification, however, it has been established that at least some nonlinear polymers do show a relatively flat r33 value to even the optical frequency, as discussed in Baehr-Jones et al., Optics Express, “Optical Modulation and Detection in Slotted Silicon Waveguides,” 13 5216 (2005).
As discussed in Yariv, Quantum Electronics, 3rd ed. New York: Wiley, 1988, equation 2 below predicts the gain coefficient available for a waveguide with a second-order nonlinearity.
As for the third-order nonlinearity, a smaller effective area leads to a larger nonlinear effect and, in this case, higher gain. Typical effective areas for a second-order nonlinear process in a ridge silicon waveguide will be around 0.5 μm2. In this case, the approximate gain coefficient for parametric gain in a χ2 nonlinear polymer with signal and idler near 3 μm would be 104 cm−1 W−1/2 for a polymer with r33 of 200 pm/V, implying that a gain of 1 dB/cm could be obtained with only 10 μW of optical power in the pump beam. Note that the gain coefficient in the case of a second-order nonlinearity depends on the square root of the optical power, in contrast to the Raman gain coefficient reported previously.
Clearly, a large amount of optical gain can potentially be obtained with a far lower power pump beam through the use of nonlinear polymers than can be obtained with the Raman effect. This can be used as the basis for optical amplifiers with very low pump power. However, another significant advantage is the intrinsically broad-band nature of the nonlinear polymer response. Unlike the Raman effect, no resonance is involved with the parametric gain process in a χ2 polymer. As a result, in principle, a single pump wavelength could be used to provide optical gain to signals at a wide array of frequencies. Similar to a conventional material with optical gain, when the gain exceeds the loss in a polymer system, spontaneous emission is then amplified, and coherent output can be created through the use of a resonator. With a nonlinear optical system, such a device is known as an optical parametric oscillator (OPO).
The threshold of such a device depends heavily on the waveguide loss that is present. The lowest threshold Raman lasers have been built into systems with waveguide losses of 0.2 dB/cm and achieve a threshold of 26 mW. If losses of 5 dB/cm were obtained with a polymer-silicon waveguide system with the previously calculated gain, then the threshold for a nonlinear polymer-based OPO with an r33 of 200 pm/V could be around 130 μW, even if no substantial resonant enhancement of the pump is assumed. Of course, lowering the waveguide losses toward the level obtained in the silicon system would lower the threshold power as well.
Effective χ2 Due to Electric Bias Field
One issue with χ2 materials is that material processing is substantially more difficult than with χ2 materials, due to the fact that the χ2 material must be poled, that is, the nonlinear moments of the microscope constituent material must be oriented in a particular direction.
According to principles of the invention, we describe methods, devices, and systems for affecting the nonlinear moments of nonlinear optical material. Embodiments of such methods, devices, and systems may be incorporated into the structures, devices, and systems described above as well into other structures, devices, and systems.
In one embodiment, we describe a way to create an “effective” χ2 material from a χ3 material through the use of a DC bias. χ3 materials have a nonvanishing second order moment in the Taylor expansion relating the nonlinear polarization field to the applied electric field. These optical materials exhibit a nonlinear respond due to the following relationship:
P=ε0(εE+χ3E3)
A third order nonlinear response has typically been used for all-optical modulation, four-wave mixing, and other processes. Often, a simple scalar relationship such as is found in the above relationship will hold for a particular component of the electric field, but a more general tensor relationship can also hold.
Materials that exhibit a χ2 effect have typically been used for electrooptic modulation and difference frequency generation. The fundamental relationship governing such a material is:
P=ε0(εE+χ2E2)
Consider now the behavior of a χ3 material, as described above, in the presence of a very strong DC field.
P=ε0(εE+χ3EDCE3)
Here, E is now the optical field, while EDC is the DC electric field induced on the material from an external, time independent bias. Note that this material now behaves quite similar to the behavior of the χ2 material described above. The affected χ3 material can be used for electrooptic modulation, or any other application that χ2 materials might be used with.
Slot waveguides have recently been used to achieve exceptionally low drive voltage χ2 based modulators. The electrodes of the slow waveguide, in addition to providing a time varying signal for modulation, can also be held at a constant voltage offset, to induce a DC field.
A controller/voltage source can be coupled to electrodes for providing the DC bias. The electrodes may be electrically coupled to the slot region via conductive regions or conductive arms between the electrodes and the slot region. In one embodiment, a controller can be arranged to provide a time varying signal for controlling the optical mode region and a time independent bias for affecting the nonlinear moments of a nonlinear optical material. In another embodiment, a controller can employ the same signal paths between the controller and the slot region for providing the time dependent bias and the time independent bias.
Processor-readable (executable) storage media can be employed to automatically or semi-automatically control the application of the time varying signal(s) and/or the time independent signal(s) based on feedback from the electrooptical device 100 and/or manual input. Processor-readable storage media that can be employed by the controller include electronic, magnetic and/or optical storage media. As is known to those of skill in the processor-readable storage media arts, new media and formats for data storage are continually being devised, and any convenient, commercially available storage medium and corresponding read/write device that may become available in the future is likely to be appropriate for use. Also, it is understood that memory used by the controller can reside in memory physically inside of a microcomputer chip or in memory external to the microcomputer or in a combination of internal and external memory. Similarly, analog signals can be digitized by a standalone analog to digital converter (“ADC”) or one or more ADCs or multiplexed ADC channels can reside within a microcomputer package. It is also understood that field programmable array (“FPGA”) chips or application specific integrated circuits (“ASIC”) chips can perform microcomputer functions, either in hardware logic, software emulation of a microcomputer, or by a combination of the two. In one embodiment, portions of the controller or the entire controller may be located on the same chip as the electrooptical device 100.
Embodiments of the electrooptical device 100 can be built for optical radiation with free space wavelength ranging from 1400-1600 nm. This structure could be part of a Mach-Zehnder modulator, and could be part of a telecommunications system, for example. The structure could also be part of a ring oscillator or other structure. Also, embodiments of the electrooptical device 100 may have a variety of other configurations. For example,
Embodiments of the affected χ3 material can create very strong, “effective” χ2 materials. For example, silicon has a χ3 moment on the order of 10−19 (m/V)2. Taking the breakdown voltage for the material to be on the order of 5×108 V/m, which is close to the breakdown field of fused silica, then even using silicon, a relatively weak χ3 nonlinear optical material, a χ2 moment of 5×1011 (m/V) is obtained. This corresponds to a χ2 material with an r33 value of 11 pm/V, close to the strength of Lithium Niobate, a commonly used χ2 material. χ3 nonlinear materials that are several orders of magnitude more nonlinear are possible, which result in r33 values of 1000 pm/V or higher, which is superior to the present state of the art.
Note that these high fields do not necessarily require a large voltage. If a 100 nm slot is used, then the 5×108 V/m field can be obtained with a DC bias of 50V, which can be easily obtained. Depending on the slot configuration, other field strengths can be obtained, such as a field strength of 1×108V/m.
One substantial benefit to this approach is the ability to provide dynamic phase matching. A problem in nonlinear optics is that several of the waves involved in a multi-wave process will often have different effective indices. This causes phase mismatch to build up over time and prevents optimal nonlinear optical performance from being obtained. With the inventive biasing approach, the orientation and the periodicity of the “effective” χ2 material can be changed dynamically without the need for new materials processing. This can enable a nonlinear optics device to be tunable over a wider range of frequencies.
In some embodiments of the invention the optical devices are implemented in a silicon-on-insulator (SOI) configuration. Silicon is a useful material because of its low cost as compared to many other semiconductors, and because it has a very well developed and well understood processing technology. Nevertheless, other semiconductor materials might in principle be used instead of silicon in an electrooptic polymer semiconductor waveguide optical amplifier. For some optical wavelengths, other materials might be advantageous as compared to silicon. In alternative embodiments, amorphous silicon and other semiconducting materials including various crystalline and non-crystalline III-V semiconductor compounds, such as GaAs, GaAs/AlGaAs, InP, and the like can be used to implement an electrooptic polymer semiconductor waveguide optical amplifier according to the principles of the invention. In these materials, the wavelength for optical radiation transmitted through the waveguide can also be different and includes but is not limited to NIR, MIR and FIR such as radiation in the bands 1310 nm, 1490 nm, and the range of 1 μm to 30 μm.
In optical communication systems, modulated optical signals can be used to encode a digital signal as a series of intensity pulses. The optical signals used are typically near 1550 nm in free space wavelength, but other wavelengths are possible. For example, commercial fiber optic-based telecommunication systems use signals in the vicinity of 1310 nm, 1490 nm and 1550 nm. In coarse wavelength division multiplexing (CWDM), a channel spacing grid using the wavelengths from 1270 nm through 1610 nm (revised to 1271 nm to 1611 nm) as center wavelengths with a channel spacing of 20 nm is an agreed ITU standard. Dense wavelength division multiplexing (DWDM) is another system used for standardized optical fiber-based telecommunication. In standard commercial systems, optical signals are converted to electrical signals for modulation, and are then converted back to optical signals for transmission. All optical operation such as the electrooptic polymer semiconductor optical gain element of the present invention has advantages in terms of ease of use and speed of processing.
In operation the magnitude of the intensity modulation of the transmitted radiation is sufficient to distinguish a 1 in a digital data stream from a 0 in the digital data stream. By way of example, in various telecommunication systems that operate according to standards set by the ITU or other standard setting bodies, the signal defining a 1 and the signal defining a 0 in the data stream are specified as to their characteristics, which are published so that systems built and/or operated by different vendors can communicate with each other. It is contemplated in this disclosure that the magnitude of the signal variation associated with the modulation will depend on the implementation details of the modulator as part of a specific telecommunications or data processing environment, and that to be effective, the modulator will have to provide signals that are compatible with the associated standards. While the input data stream is described as digital data, the voltages applied across the pairs of electrical contacts can be digital in nature, or can be analog voltages. In the situation where one member of an electrical contact pair is connected to a reference signal or voltage (for example ground potential, “zero volts,” or some other fixed potential) a signal representing a differential voltage relative to the reference voltage can be applied to only the second electrical contact, and that signal can be effective to control the poling. The differential signal can in principle vary above and/or below the reference voltage.
Theoretical Discussion
Although the theoretical description given herein is thought to be correct, the operation of the devices described and claimed herein does not depend upon the accuracy or validity of the theoretical description. That is, later theoretical developments that may explain the observed results on a basis different from the theory presented herein will not detract from the inventions described herein.
Any patent, patent application, or publication identified in the specification is hereby incorporated by reference herein in its entirety. Any material, or portion thereof, that is said to be incorporated by reference herein, but which conflicts with existing definitions, statements, or other disclosure material explicitly set forth herein is only incorporated to the extent that no conflict arises between that incorporated material and the present disclosure material. In the event of a conflict, the conflict is to be resolved in favor of the present disclosure as the preferred disclosure.
While the present invention has been particularly shown and described with reference to the structure and methods disclosed herein and as illustrated in the drawings, it is not confined to the details set forth and this invention is intended to cover any modifications and changes as may come within the scope and spirit of the following claims.
This application claims priority to and the benefit of co-pending U.S. provisional patent application Effective χ2 on the Basis of Electric Biasing of χ3 Materials Ser. No. 61/268,187, filed Jun. 9, 2009, which is incorporated herein by reference in its entirety.
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| Number | Date | Country | |
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| 61268187 | Jun 2009 | US |
