Measuring Nonlinear Optical Properties of Materials The Experimental Methods

Transcription

1 Measuring Nonlinear Optical Properties of Materials The Experimental Methods Kerensa H. Gimre May 18,

2 Abstract In this project, we seek to develop experimental methods for measuring the loss and coupling efficiency as a function of the index of refraction solutions placed in the holes of holey fibers. We propose an experiment to measure the transmission as a function of refractive index. Transmission data is collected for two lengths of the fiber, assuming the coefficient of loss and the coupling efficiency of the fiber are constant with index of refraction in the holes. From the combination of the data taken at each refractive index, valuable results detailing how loss and coupling efficiency depend on index of refraction can be obtained. Experimental results can be compared to results from theoretical calculations performed by researchers at the University of Maryland [2]. This work will be used to optimize holey fiber technology to achieve improved nonlinear absorption and optical limiting. 2

3 Contents 1 Introduction 4 2 Background & Definition of Key Terms Nonlinear Absorbers Total Internal Reflection The Holey Fiber Experiment Definition of Key Terms Experimental Methods Data Analysis 11 5 Current Results 13 6 Future Work 13 7 Acknowledgements 16 A Equipment Diagram Key 17 B Gaussian Beam and Beam Diameter 17 C LabVIEW Code 17 3

4 1 Introduction Holey fibers have recently been developed as a useful tool in fiber optic systems due to the ease in accurately engineering desired optical properties. Regular fibers are characterized by a central core material with a relatively high refractive index surrounded by a second material with a lower refractive index. Holey fibers, on the other hand, have a solid core surrounded by a hexagonal array of holes. While light is primarily coupled into the core of a holey fiber, a small portion of the light extends into the surrounding holes. The light that bleeds into the holes is referred to as the evanescent tails. Linear transmission is increased in holey fibers because only the evanescent tails interact with the abosrber. Additionally, the nonlinear transmission threshold depends on the extent of the evanescent tails, which in turn depends on the relative refractive index of the glass and holes. The optical properties of the holey fibers can be tailored by filling the holes with various solvents with known refractive indices. As the refractive index of the solvent approaches that of the glass core, the percentage of the light that extends into the holes changes, which alters the energy loss as the light propagates. By measuring the transmission for two lengths of fiber, the coupling efficiency and loss as a function of index of refraction of the holes can be found. There exists extensive theoretical work calculating these values and we seek to validate it with our experimental results [2]. The military and telecommunications industries use sensitive equipment that is easily damaged by high intensity lasers. The Naval Research Laboratory finds it imperative that technology be developed to protect valuable telecom equipment from high energy signal spikes. Recent studies demonstrate that materials exhibiting nonlinear absorption can be paired with optical fiber technology, which is important in data transmission and imaging applications, to protect devices from damaging signals in real time [2]. In this project, we attempt to characterize some of these materials. We will measure transmission in holey fibers for several indices of refraction in the holes. Some data has previously been collected; we wish to add to it and compare to theoretical calculations for the loss as a function of index of refraction in the holes. This research will help develop optical limiters that fit with existing fiber optic systems. 2 Background & Definition of Key Terms The following is an explanation of terms pertinent to the research project. We begin with descriptions of concepts such as Snell s Law and simple phenomena like total internal reflection. Since telecommunications equipment is, in general, easily damaged by high intensity light, it is preferable to interact with these devices using light of lower intensity. Devices that are capable of limiting the transmission of high intensity light for enhanced protection are called optical limiters. In the context of this work, an optical limiter is a device with high absorbance for high intensity incident light, and low absorbance for low intensity incident light. This is analogous to stating the transmission is low for high intensity light and high for low intensity light (where transmission is defined as the ratio of energy out to energy in). This is similar to a photochromic lens. Outdoors, high intensity UV light is incident upon the surface of the lens, causing it to turn opaque and absorb most of the incident light, transmitting very little. Indoors, when low intensity light is incident on the surface, the lens becomes transparent, absorbing very little of the light and transmitting most of it. Albeit, a photochromic lens operates by an entirely different chemical process than optical limiters, and our optical limiters are triggered by visible light (not UV), yet the concept of an optical limiter remains the same. 4

5 Figure 1: A diagram demonstrating an optical limiter and its similarity to a photochromic lens. As low intensity light is incident on the optical limiter (central block), there is high transmission (analogous to the photochromic lens turning translucent). When high intensity light is incident, there is little transmission (in the example, the photochromic lens turns opaque). In the diagram, the thick arrow represents high intensity light, and the thinner arrow represents light of lower intensity. 2.1 Nonlinear Absorbers For an optically linear device, absorption increases linearly with increased incident intensity. In our case of nonlinear absorption, however, a solution is carefully engineered so absorption increases nonlinearly with increased intensity. If we plot the input energy versus the output energy, we observe a proportional relationship for an object exhibiting linear absorption. For our nonlinear absorber, this relationship is not proportional and transmission decreases as input intensity increases 1. Figure 2: A plot of the difference between a linear and nonlinear absorber. Note decreased transmission with increased input energy for the RSA non-linear device and the non-proportional relationship. We want to make optical limiters compatible with fiber optic systems for enhanced protection. To accomplish this, a nonlinear absorbing material is combined with an optical fiber to create an optical limiter in a fiber. It is very well understood in current fiber optic technology how to accomplish this. For this reason, we will be focusing on holey fibers, which are less understood and show promise as the new frontier of fiber optics. 1 We use compounds exhibiting Reverse Saturable Absorption (RSA). Most nonlinear absorbers exhibit Saturable Absorption, implying that transmission increase with increasing input energy. 5

6 One of the benefits of using holey fibers is that they are easily integrated into fiber optic systems. Additionally, specific properties are simply engineered so holey fibers can be tailored to the desired needs. Figure 3: On the left is an image of a regular fiber, and on the right, a holey fiber. Note that both of these are cross-sectional views. In the regular fiber (left, above) the core (bright central region) is surrounded by the cladding of different material. In the holey fiber (right, above), the core is solid silica glass, the cladding is the hexagonal array of holes surrounding the core, and solid silica glass encloses all of this. Since we are interested in studying optical limiting in fiber optics, we must first understand the physics behind fiber optics. 2.2 Total Internal Reflection The first concept we need to introduce is index of refraction, n. The refractive index, n, describes the speed of light in a material by the equation n = c v where c is the speed of light in a vacuum and v is the speed of light in a material [1]. How refraction occurs in a material and how light is refracted through a surface is determined by n. Snell s Law describes the relationship between refraction and the angle of incident light. Specifically, Snell s Law states that light traveling in a medium of index n 1, incident on another medium of index n 2 at an angle of θ 1 from the normal, will then travel through the second medium at an angle of θ 2 from the normal: n 1 sin(θ 1 ) = n 2 sin(θ 2 ). If n 2 > n 1, then the angle of refraction, θ 2 is less than the angle of incidence, θ 1. 6

7 Figure 4: A picture depicting a light ray traveling through a region of index of refraction n 1, hitting a surface (central vertical bar) and transmitted to the second region of index of refraction n 2. Here n 1 < n 2. Consider the case where n 2 < n 1, so that θ 2 > θ 1. If θ 1 is large enough, θ 2 approaches 90 and the transmitted light propagates along the interface. If θ 1 is larger than this critical angle, then the light reflects off the surface and no light is transmitted. This is called Total Internal Reflection. Figure 5: On the left, the incident ray approaches at an appropriate angle for the light to be refracted through the surface. On the right, total internal reflection occurs. So, the critical angle is the angle of incidence which causes the angle of refraction to be 90. Solving Snell s Law for an expression for the critical angle (θ c ) gives: θ c = sin 1 n 2 n 1 Total internal reflection occurs when light strikes a surface at an angle larger than the critical angle. This results in most of the light being reflected and some transmitted. As stated, this occurs when n 1 is larger than n 2. Fiber optics rely on total internal reflection for their operation. For total internal reflection to occur in a fiber optic, and for light to travel the length of the fiber down the core, the refractive index of the core must be higher than that of the surrounding cladding (n 1 > n 2 ). 7

8 Figure 6: For total internal reflection to occur in a fiber optic, the refractive index of the core must be higher than that of the cladding. In a holey fiber, the cladding is the hexagonal array of holes and the core is solid silica glass. Similar total internal reflection behavior is obtained when the index of refraction of the holes is less than that of the core. 3 The Holey Fiber Experiment The absorbance of light in a material can be described by: di = αi 0 dx (1) where α is the absorption coefficient, x is the thickness of the material, and I 0 is the initial intensity. Solving this differential equation leads to: I(α, x) = I 0 e αx (2) If α is a function of x, the substance is nonlinear, but if α is independent of x, the substance is linear. As previously stated, the eventual goal is to combine holey fibers with nonlinear absorbers for use as optical limiters. Our project is an intermediate step in that process. But before using nonlinear absorbers to create an optical limiter, we must first understand the linear properties. Therefore, we will be performing experiments without nonlinear absorbers. We will hopefully verify theoretical calculations of energy loss as light propagates in the holey fiber. By filling the holes with a refractive index less than that of the silica glass, light will be guided in the solid core. Now as the index difference between the silica glass and the solution in the holes decreases (that is, as the indices approach the same value), the coupling efficiency decreases and the propagation loss increases because total internal reflection does not occur for all light. 8

9 Figure 7: A picture of the holey fiber. This image is viewed as if staring straight down the end. As seen, the core of the fiber is solid and surrounded by a hexagonal array of holes. Figure 8: Above is the theoretical curve (the red one) for loss as a function as index of refraction solution in the holes, as predicted by Curtis Menyuk and Jonathan Hu at the University of Maryland Baltimore County [2]. Notice that the loss is plotted on a log scale. When n holes = 1.455, very close to n glass = 1.459, the loss is 1000dB/m, but when n holes = 1.440, the loss is 1dB/m. A db is a decibel; a logarithmic unit of measurement that describes ratios relative to a set initial value. 3.1 Definition of Key Terms We now define the following terms relevant to this research. We specifically desire information about the coupling efficiency and loss. Transmission: ratio of energy out to energy in. This is what we are directly measuring Coupling efficiency: light incident on the end of the fiber that actually makes it into the core. Propagation loss: light lost due to variety of factors. This can include imperfections in the fiber that cause scattering out the sides. Or perhaps the light is not as tightly confined as in a regular fiber. We assume the latter causes the majority of the loss and the former is small enough to be neglected. 9

10 3.2 Experimental Methods To measure the loss, we will collect transmission data for several different index of refraction solutions in the holes. For each index of refraction, we will collect transmission data for two different lengths of the fiber. From this, we will calculate the coupling efficiency and loss. To achieve solutions of different index, we combine dioctyl phthalate (n = 1.486) and diethyl succinate (n = 1.420) in varying ratios. The index of silica glass is 1.459, so we combine dioctyl phthalate and diethyl succinate at the appropriate ratios to create the following five index solutions less than n glass, which are filled in the holes of the holey fiber 2 : Solution n Table 1: A summary of the index of refraction of the solutions that we will fill in the holes of the holey fiber. Note that all index of refraction values were measured with an Abbe Refractometer. We also monitor the solutions over time to ensure stability of index. Note that when using Solution 5 (n 5 = 1.455), we expect the greatest loss since n 5 is very close to n glass = When filling the holes with Solution 1 (n 1 = 1.435), we expect the least loss since n 1 is very far from n glass = We have successfully arranged the optics table to suit all of our experimental needs. A diagram of the setup is shown in Figure 9. Figure 9: A diagram depicting the experimental setup of our optics table. See the Appendix for an equipment diagram key. 2 We use the Abbe Refractometer to measure the index of refraction of the materials at the Sodium D line at room temperature. We also calculate the dispersion with wavelength of these index solutions. 10

11 A ND-YAG laser outputs 355 nm UV light and pumps an OPO containing a harmonic crystal that can be rotated to provide whatever wavelength is required. We use 532 nm green light because eyes are most sensitive in this range. This light passes through a high-power attenuator to reduce the strength of the beam, since there are more photons than needed for our experiments. The beam travels through a Pellin Broca prism to separate short wavelength contamination from the pure beam. Since we couple this light into a fiber, we require a very high quality beam. For this reason, we send it through a spatial filter, which improves the beam quality 3. Finally, the beam travels through a liquid crystal rotator and polarizer that act together as a low-power attenuator. Reflecting the beam around the table once more, the light travels to the holey fiber apparatus (see Figure 10). By using beam splitters and mirrors, we measure the transmission via two energy meters. A picture of the beam can be obtained with a CCD camera 4. The holey fiber apparatus is a system of focusing lenses and the sample holder (Figure 10) containing the fiber. Light is focused into the fiber and guided through. The fiber is placed in between the two metal plates, laying in the two glass holders seen in Figure 10. The two glass tubes are filled with the refractive index solution, to ensure that the core of the fiber is constantly wet. Additionally, this sample holder can be adjusted for different lengths of the fiber. Figure 10: A picture of the sample holder used for the holey fiber experiments. Please note the small scale. 4 Data Analysis As stated earlier, in equation 2, we expect I out = I in e α LL (3) 3 For more information about the quality of the beam and beam shape please see Gaussian Beam and Beam Diameter in the Appendix. 4 This is useful when trying to maximize the light entering the core. By viewing a picture of the light leaving the fiber it is easier to make the appropriate small micrometer adjustments to couple light into the core. 11

12 where L is the length of the fiber and α L is the propagation loss. Transmission, T, is the ratio of I out to I in. So we can rewrite equation (3) as: T = e α LL. (4) Not all the light incident on the fiber couples into the sample. Coupling efficiency, c, represents the fraction of incident light (E incident ) coupled into the sample (E in ). Mathematically, E in = ce incident (5) We wish to determine loss (α L ) and coupling efficiency (c) for each index of refraction solution in the holes.we make the simplifying assumption that these are independent of fiber length, a physically appropriate assumption. Note that we can experimentally determine E B, E A, the fiber length (L), and n holes (index of solution in holes). We collected data to characterize all the optics on the table. We measured the input and output energy when light traversed each optical device to determine the transmission through each piece: Optical Piece Transmission Beam Pickoff 12% sent to detector, 88% sent to first lens Lens # 1 90% Front Fiber Face 96% Back Fiber Face 96% Lens # 2 85% Table 2: The table summarizes the transmission we measured for each optical device. The transmission reported is an average of several data collections. Figure 11: A graphic of how light is lost through the optics. Per Figure 11, we see that 12% of the original light (E 0 ) is measured at detector A. So E A = 0.12E 0. Next, 88% of E 0 is sent through the first lens through which 90% of the light is transmitted. So E 2 = 0.9E 1 = 0.9(0.88E 0 ). Then E 2 is sent through the front face of the fiber where there is a 96% transmission. So E in (the light sent into the fiber is): E in = 0.96cE 2 = 0.96c(0.9(0.88E 0 )), where c is the coupling efficiency of the fiber. We are unable to measure E out directly, but we know there is a 4% loss across the back face of the fiber. 12

13 Therefore, E 3 (the light hitting lens 2) is E 3 = 0.96E out. There is an 85% transmission through the second lens to detector B so Then and We also know E B = 0.85E 3 = 0.85(0.96)E out. E B E A = 0.85(0.96)E out 0.12E 0, E out = 0.12E 0 E B. 0.85(0.96) E A E out E in = e α LL, and we can substitute our formulas for E out and E in. So E out = e αll 0.12 E B = E in 0.85( (6) (0.9(0.88c))) E A In Equation (6), we know E B, E A, and L from direct measurement. Note that there are two unknowns: α L and c. But if we do this measurement for another length of the fiber at the same n holes, α L and c will be the same (since we assume they are independent of fiber length). E B /E A and L will change but this allows us to solve a system of equations for α L and c. In conclusion, experimental determination of the dependence of loss on refractive index solution in the holes is possible. This data will be compared to results predicted by Hu et. al. to hopefully verify their theoretical work. 5 Current Results We have experienced many technical difficulties and have been unable to measure the transmission for two lengths of the fiber at one value of n holes. Currently, we are in the process of refining our experimental technique since there exists very little consistency in our numbers. In order to debug and reassure ourselves that we are not lacking data-collecting finesse, we are attempting to couple light into a regular fiber filled with dioctyl phthalate (n = 1.486) at an efficiency higher than 70%. Our successes include coupling light into fibers, albeit not at quite the efficiency desired. We manufactured a fiber holder that allows us to collect experimental data and ensure that the fiber core is always filled with the appropriate solution. We also discovered some potentially new physics in terms of solution stability. In our unrewarded attempts to collect data, we noticed that once the holey fibers are filled with solution, their output is not temporally stable. On the order of a week or so, the holes begin to guide light, instead of the core, implying n holes > n glass. We suspect that the relative concentration of dioctyl phthalate and diethyl succinate changes in time. This phenomena requires further investigation for a more reliable explanation. 6 Future Work Evidently, the experimental technique needs refinement. This is something we are currently researching. After a reliable process is constructed, data collection must be completed to fully characterize loss and coupling efficiency as a function of index of refraction solutions in the holes. This can then be compared to theoretical results. After fully comprehending these results, the holey fiber can be filled with a solution of an appropriate nonlinear absorber to create an optical limiter. Data has been collected for these devices in the past, but 13

14 for fewer index of refraction solutions in the holes. We wish to extend the data set for more n holes to fully characterize and develop these devices to their maximum potential. 14

15 References [1] Giancoli, Douglas C. Physics. Prentice Hall, Inc, Englewood Cliffs, New Jersey. 2nd ed [2] Hu, Jonathan, R. Menyuk, S. Flom, R. Pong, J. Shirk, T. Taunay, B. Wright, S. Montgomery, S. Sueoka, J. Butler Optical Limiting in Solid-Core Photonic Crystal Fibers Optical Society of America Image of holey fiber from 15

16 7 Acknowledgements It is noted that this work could not be completed without the assistance of Andrew Hutchison. Additionally, the author would like to thank The National Science Foundation, Research Corporation, Pacific University, and the Naval Research Laboratory for funding and previous work on this project. 16

17 A Equipment Diagram Key B Gaussian Beam and Beam Diameter A Gaussian beam is one with a very intense center, and a drop-off in intensity as the radial distance from the center increases. The beam diameter is generally defined as the distance between points where the intensity has dropped to 1 e of its maximum intensity at the center. 2 The equation for the electric field of a Gaussian Beam is and the intensity is w 0 E(r, z) = E 0 w(z) e I(r, z) = E(R, z) 2 2µ r 2 w 2 (z) e ikz ik r2 2R(z) ( ) 2 w0 = I 0 e 2r2 w 2 (z) w(z) where I 0 is the intensity at the center of the beam at the beam waist, µ is a constant characteristic of the medium, r is the radial distance from the center axis of the beam, z is the axial distance from the beam waist, k is the wave number, E 0 is the electric field at the center of the beam at the beam waist, R(z) is the radius of curvature, equal to z[1 + ( z R z ) 2 ], w(0) is the waist size, and w(z) is the radius of the beam, equal to w ( z z R ) 2. It should be stated that z R is the Rayleigh Range; the distance from the waist to the location where the area of the cross section of the beam is 2 wider. Mathematically, this is described as z R = πw2 0 λ C LabVIEW Code Figure 12, on the next page, is a picture of the LabView Code used to collect data. First, the energy meters are initialized. Then we read the RM6600 Data Buffer in ASCII plaintext string. This is the data from the Energy Probes. If the string contains an OR, signaling an Over Range, or an E, indicating data, we 17

18 send this string to an OR tester. If the string does not contain either of these values, a new data string is collected from the energy meters. At the OR tester, we check the data to see if it contains an OR. If it does, the range variable is decremented and a new data string is collected. If the data does not contain an OR, we convert the data string to number format and check to determine if the value is zero. If the value is zero, we collect a new data string. If the value is not zero, we perform an over-range check with a set fluctuation variable. If the number is over-range, we collect a new data string. Finally, if the number makes it past all these checks, it is sent to a data file which stores the measured value. We follow this process until we achieve a complete, reliable data set. 18

19 Figure 12: A picture of the LabVIEW code used to collect data. Graphic courtesy of Mr. Andrew Hutchison. 19