4 Double Resonant Frequency (DRF) DSRR 1
4.4 Discussion and Conclusions
In the process of seeking key points for counterpoising the power insufficiency of meta -materials, two methods of SDSRR and IDSRR endeavor to solve this problem.
All the procedures from sample design to practical experiment are depicted in Sec.4.2 and Sec.4.3 respectively.
Basing on the concept of SDSRR, there is still a great chance applying such a mechanism to compensate the power loss although direct evidence is not yet available. An over loosen structure of DRF-DSRR may prohibit the generation of flowing currents on the surface of metallic DSRRs, thus a high density of DRF-DSRR structure (more small DSRR cells in per large DSRR cell) is necessary for further demonstration. Now, a DRF-DSRR sample is going to be fabricated through semiconductor process; its resonant frequencies will locate at X-band and 1550nm infrared region by considering the limitation of existing facilities. The behavior of this sample at X-band will provide sufficient facts that determine whether the idea of SDSRR is useful or not. Moreover, if it works, the cooperative response of
microwaves and infrared light on the same piece of sample is worthy for studying as well. The intrigued interaction may inspire additional inspirations in the future.
As for the idea of IDSRR, the experiment data of DRF-DSRR basing on IDSRR have claimed the failure for counterpoising power loss of metamaterials. The inverse DSRRs can only induce reflection effects while they are placed regularly at certain angle. When small DSRRs change to sporadic formation, this phenomenon would not exist anymore and is useless for predicted purpose. Therefore, applying IDSRR on DRF-DSRR is not a realistic method to reach our target in this chapter. The experiment data indicate the possibility of implementing IDSRR for DRF-DSRR approaches to zero.
Chapter 5
Optical Response of Metamaterials
In the previous two chapters, the operating frequency is about several GHz, and all patterns are designed under the restriction of X-band. The ultimate destination, however, is realizing metamaterials for modern optical system. Hence, samples and their response corresponding to extremely high frequency (about tera-hertz) are important for this study. In this chapter, some metamaterials samples provided by Industrial Technology Research Institute (ITRI), including DSRRs and metallic wires, will be investigated in optical spectrum. The experiment results will be analyzed and compared with theoretic assumptions to see if there is any possibility for the accomplishment of metamaterials within infrared region.
5.1 Experiment Setup
The optical experiment setup is a little different from the microwave one. A tunable laser (Agilent, 81682A Tunable Laser Module; operating frequency range is from 1400-1580 nm) connecting to a power amplifier (Erbium-Doped Fiber Amplifier, 1530nm to 1562nm) with 22dB gain is used to produce coherent and steady light source with essential power as shown in Fig. 5.1 (a). After magnified by EDFA, the output light is connected through an optical fiber with a fiber pigtail. A set of lens following the fiber pigtail is used to collimate the divergent source so it would almost
tend to be plane waves after passing the lens set. At this time, the beam diameter of the operating light is 4mm.
(a)
(b)
Figure 5.1: (a) Top view of the experiment Setup for infrared region. The angle is set to be 0 while the sample is perpendicular to the incident light. (b) Photograph of practical experiment setup.
Next, in order to force the electric field coinciding with the desired direction (perpendicular to the optical table), a polarizer is introduced on the optical path. A beam splitter following the polarizer can separate the source into two parts. One is taken as the monitoring light for reference, and another one is propagating directly into the sample. Meanwhile, two sets of detectors and powermeters (Newport, 1830-C Optical Power Meter with 818 IR detector; HP, Infinium Oscilloscope with Newfocus 1611 High-Speed Photoreceiver) are applied in this experiment for simultaneously detection. For the observed sample, a rotation stage (Newport, ESP 300 Motion Controller/Drive with VP-25XA Precision Compact Linear Stage) is constructed under the sample to change the relative angle between incident light and our pattern. The rotation angle is set to zero when the incident light is perpendicular to the sample surface. During the experiment process, the angle will start rotation from 80 to 100 degree. Behind the sample, a lens is used to collect light beam to prevent any diffraction phenomenon.
5.2 Sample Specification
Before start descriptions of the design details about our samples, the issue concerning manufacture should be emphasized first because conventional process may not meet our request. In a standard semiconductor process, the most common material is silicon. Such a material will introduce about 50% significant reflection while it was applied at infrared band, which may reflect most of the incident beam before it encounters the patterns. Then it is totally impossible for the pattern to interact with the electromagnetic waves at all. Moreover, heavy reflection will also cause heavy power loss besides the intrinsic metamaterials properties, and the power efficiency will be more difficult to solve. Due to the requirement of substrate material, another material which has minute reflection would be the best choice. Fortunately, cooperative ITRI group has invented a new fabricating process consisting of nano-imprinting and lift-off techniques [19] so that the substrate can be made by acrylic polymer which is transparent and subtle reflecting for 1550nm. Thus all samples in this experiment will be constructed on the acrylic substrate in the following sections. Furthermore, acrylic substrate is convenient except for preventing
significant power loss in the optical system when it is combined with other optical components, such as lens, in the future.
5.2.1 DSRR pattern
(a) (b)
Figure 5.2: (a) Schematic layout of DSRR pattern. Linewidth a is equal to 0.2um while lattice constant b is 1.0um. (b) The structure of DSRRs with cut wires whose linewidth is also 0.2um. By inserting discontinuous wires between two DSRRs, the lateral lattice constant c changes to 1.4um.
The design of DSRRs at 1550nm is similar to that at X-band except for extremely small scale, pattern metal and different substrate. As shown in Fig. 5.2, DSRR pattern and DSRRs with cut wires are illustrated clearly. All of the linewidth and intervals are equal to a, which is solely 0.2um therefore the lattice constant in Fig. 5.2 (a) is just 1.0um. In contrast to the identical lattice dimension in both directions for DSRRs alone, the lateral lattice constant of Fig. 5.3 (b) has a little modification. Cut wires are inserted in the middle of two DSRRs and for this reason the lattice constant will increase from 1.0um to 1.4um. Finally, completed DSRR and wire cells are presented in Fig. 5.3 through SEM. All structures are made by gold, and its thickness does not exceed 100nm. The total pattern area of each sample is 2 2× mm2, and the substrate size is 4 4× mm2 while its thickness is 3mm.
Figure 5.3: SEM Photograph of DSRRs and wires. All DSRRs and wires are fabricated by gold, and the substrate is acrylic polymer.
5.2.2 Metallic Wire Line Grating Pattern
The specification of metallic wire line grating pattern is depicted in Fig. 5.4 (a). The width w of linewidth and the spacing between two lines are both 80nm, which implies 40nm wire radius and 160nm lattice constant. The area covered by metallic wires is 40 40× mm2, thus the wire length L is 40mm. Meanwhile, the material used for wires is aluminum while the substrate is glass. Fig. 5.4 (b) shows photographic image of the whole sample. Some external glue is adhered on the plate, but it does not affect the experiment results since light will not pass those polluted areas.
(a) (b)
Figure 5.4: (a) Schematic layout of metallic wire ling grating. Linewidth w is equal to 80nm while lattice constant 160nm. The wire length L is 40mm. (b) Photograph of practical sample whose width and length are both 40mm.
5.3 Experiment Results
5.3.1 DSRR Pattern
The experiment results of nano-scale DSRR pattern now is shown in Fig. 5.5. The experiment starts from 80 degree incident to 100 degree, and the resolution is 0.1 degree. The response of two samples, DSRRs alone and DSRRs with discontinuous wires, are presented together to make an easy comparison. The transmission power of DSRRs increases as the angle increasing from 80 to 90 degree. The power reaches its peak value, 1.37mW, while the rotation angle is 88.3 degree. After the maximum power transmission, the curve starts to decrease while the rotation angle continues to move. The behavior of the whole pattern shows there in no absorption phenomenon at all. If the DSRRs actually bring the effect of negative permeability, then significant absorption is supposed to occur around 90 degree just as what we observed in previous chapters. However, the experiment data gives the evidence that there is neither any power drop nor the activity of negative permeability.
Figure 5.5: Measured transmission power of nano-scale DSRR sample. The response of DSRRs alone is marked by clear circles while the activity of DSRRs with wires is denoted by bold solid line.
Since there is barely response for the DSRR alone, then the transmission curve of DSRRs and wires is supposed to be inactive either. According to the experiment data shown in Fig. 5.5, the pattern of DSRRs and wires has a smooth curve similar to a blank sample. In fact, both responses of DSRRs alone and composite DSRRs are almost identical despite of subtle difference at the peak position. Generally, the uneven faces which are cut manually will introduce uncertainties in the experiment;
including the position of transmission peak. Therefore, the similar curve may be caused by the intrinsic property of acrylic substrate itself, which the incident light will have maximum transmission power when the substrate plate is parallel to the beam. In other words, the predicted absorption of negative permeability does not happen eventually.
5.3.2 Metallic Wire Line Grating Pattern
The measurement optical response of metallic wire line grating pattern is shown in Fig. 5.6 as rotating from 80 to 100 degree with the resolution is 0.1 degree. By
viewing the experiment data, the estimated absorption while the incident beam is parallel the periodic wires does not happen. Instead of that, a strong transmission, whose peak value is 6.69mW, occurs in the range from 91 to 93 degree. On the other hand, the power measured at remaining degrees is extremely minute because of the heavy reflection of the sample itself. The light source passes the sample only when it is almost parallel to the sample plane, where smallest reflection occurs. Therefore, the curve of our metallic periodic sample without any absorption is simply the activity of a single opaque plate. Comparing to the smooth curve in Fig. 5.5 due to transparent acrylic substrate, the sharp curve in Fig. 5.6 is caused by the heavy reflection of the metallic substrate. Otherwise, a power drop is supposed to happen while the incident wave encounters numerous metallic periodic wires in the propagating direction.
Figure 5.6: Measured transmission power of nano-scale metallic wire structure from 80 to 100 degree.
5.4 Discussion and Conclusion
According the experiment results mentioned above, we can conclude that neither DSRR pattern nor wire structure has the predicted response. The reason why they can
not achieve the target of negative property can be discussed in details below.
First we start to figure out the failure factors of DSRR sample itself. Due to prior knowledge, the lattice constant of DSRRs should be 1/6 of operating wavelength; that is, absorption only happens while the lattice constant is around 1/6 of the resonant frequency. In this experiment, operating wavelength is 1550nm thus the lattice constant of effective DSRR pattern should be about 258nm, which is much smaller than 1um. The absorption does not occur in this experiment since the resonant phenomenon is supposed to appear at lower frequency (longer wavelength). In fact, the corresponding resonant frequency of a DSRR pattern with 1um lattice constant is 5 10× 13Hz (6um operating wavelength) results the power drop not appearing.
Furthermore, another factor, the total number of cells, should be included for concern as well. On the surface of a DSRR sample, there are totally 4 10× 6 cells in the
2 2× mm2 area. The relation of resonant frequency and the total number of cells reminds us that the resonant frequency of nano-scale DSRR pattern will shift significantly to lower frequency again (longer wavelength), thus it even pushes the resonant toward the spectrum lower than 5 10× 13Hz. In summary, two main factors that control the position of resonant frequency both show the intendancy of frequency shifting towards lower spectrum. For seeking the presentation of negative permeability, a light source with larger wavelength should be used to obtain the desired experiment results.
As for the metallic wire line grating sample, some formulas should be reviewed first. In the process of developing the estimation of plasma cutoff frequency of metallic wires, there are actually three different assumptions. One has been mentioned in Eq.3.1. Here all of them are listed below.
Pendry:
Maslovski:
where fp is the plasma frequency, a is the lattice constant, r is the wire radius and
light
c is the speed of light in vacuum. For the metallic wire sample, a = 160nm and r = 40nm. If these parameters are replaced into Eq.5.1 to Eq5.3 and Eq.3.2, then the effective permittivity, the plasma frequency and its corresponding wavelength could be obtained in table 5.1.
Table 5.1: Calculation effective permittivity and plasma frequency through three different formulas
As shown in the table, two of the three formulas give the plasma frequency far above the operating one (1550nm, 1.94 10× 14Hz), which means the metallic structure can present negative permittivity property in the experiment. Also, the effective value of permittivity is shown in the table. However, the plasma frequency by calculating through Eq.5.2 is not available because close ratio of lattice constant to wire radius gives negative value of Eq.5.2, and the plasma frequency becomes imaginary. Thus it is impossible for such a metallic structure to have the character of negative permittivity in Sarychev’s estimation
By introducing the experiment data and comparing them to the calculation data, the one computed through Eq.5.2 is most practical since there is no absorption around 90 degree in the realistic measurement. The experiment data demonstrate Sarychev’s
estimation is the most precise formula for calculating the plasma frequency of metallic wires. In fact, the accuracy of Sarychev’s deduction comes from its consideration of varied potential vector which is assumed to be constant in Pendry’s and Maslovski’s concept. By introducing the R-dependent potential vector [20], the effective permittivity will change thus the square of plasma frequency with a factor will be obtained through replacing ln( / )a r in Eq.5.1 by ln( ) 3
2 2 a r
+ −π . In such an equation, the ratio of lattice constant to wire radius must not exceed 5.9 to ensure the existence of plasma frequency and negative permittivity.
In conclusion, the experiment results of DSRR and wire samples do exhibit neither negative permeability nor negative permittivity characteristics in optical spectrum. More samples matching the requests are necessary for advanced demonstration.
Chapter 6
Conclusion and Future Work
6.1 Conclusion
Except for fundamental knowledge introduced in chapter 2, two main topics are discussed through a series of design, experiment data and simulation results in this thesis.
A coplanar structure consisting of symmetric DSRRs and discontinuous wires is purposed for advanced manufacturing semiconductor process. The ultimate destination for this coplanar sample is fabricating metamaterials on a single plane which can solve alignment problem since it is extremely difficult for such a small scale. The experiment results shows that symmetric DSRRs, wire1, wire2, and wire3 do have their own predicted properties such as negative permeability and permittivity property separately while the cut wire4 has some kind of gratting character out of prior assumption. If symmetric DSRRs and short wires are put together, the original trait of wires will be covered by the property of ring structure. On the contrary, the wire structure will dominate the character of whole pattern when symmetric DSRRs is combined with wire4, the longest wire. Therefore, the idea of implementing a single symmetric DSRR and wire to build up metamaterials in an independent cell is not applicable although they do have their estimated features seperately.
In chapter 4, two different mechanisms, split DSRR and inverse DSRR, are used to construct DRF pattern for compensating power consumption. Some preliminary
experiment data indicate that there is still a great chance for the first mechanism, SDSRR, to reach the target of DRF. The fractal-like SDSRRs can also have a high frequency resonant even when they are not placed regularly in a square layout. Some patterns through semiconductor process are going to be fabricated now; more clearly conclusions can be made after obtaining further experiment data. In contrast to the positive results for SDSRR, the second mechanism, IDSRR, gives negative conclusion. A series data gathered from different samples demonstrates excavated small DSRRs only showing some reflection effects at 50 degree, and in the schematic array formation. The feature of them is not benefit at all because they are designed for counterpoising transmission power originally.
6.2 Future Work
There are two available research directions extending from our present work:
z DRF-DSRR basing on SDSRR. As mentioned in chapter 4, the chance for accomplishing a power compensating metamaterials by SDSRRs is highly estimated. Its resonant frequency regions are set for X-band and infrared. If it does has response at X-band, then myriad applications is applicable.
z Metallic wires in infrared region. For the technique of modern semiconductor process, it is not difficult to manufacture a metallic wire structure whose permittivity is negative at infrared region such as 1550nm. A sample with a r/ ≥6 such as 100nm linewidth with lattice constant of 300nm or 400nm can approach our target without extremely difficulties.
Bibliography
[1] V. G. Veselage, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and μ,” Sov. Phys.-Usp. 10, 509 (1968).
[2] http://www.darpa.mil/dso/thrust/matdev/metamaterials/program.html
[3] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[4] R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental Verification of a Negative Index of Refraction”, Science 292, 77 (2001).
[5] R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave Transmission through a Two-Dimensional, Isotropic, Left-Handed Metamaterial,” Appl. Phys. Lett. 78, 489 (2001)
[6] J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966 (2000)
[7] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely Low Frequency Plasmons in Metallic Mesostructures,” Phys. Rev. Lett. 76, 4773 (1996)
[8] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low Frequency Plasmons in Thin-Wire Structures,” J. Phys. : Condens. Matter 10, 4785 (1998) [9] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz,
“Composite Medium with Simultaneously Negative Permeability and Permitvitty,” Phys. Rev. Lett. 84, 4184 (2000)
[10] Y. C. Huang, Y. J. Hsu, J. S. Lih, and J. L. Chern, “Transmission Characteristics of Deformed Split-Ring Resonators,” Jap. J. Appl. Phys. 43, L190 (2004)
[11] Y. C. Huang, Y. C. Huang, J. S. Lih, and J. L. Chern, “Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials,” J.
Appl. Phys. 96, 1979 (2004)
[12] E. Ozbay, K. Aydin, E. Cubukcu, and M. Bayindir, “Transmission and Reflection Properties of Composite Double Negative Metamaterial in Free Space,” IEEE Trans. Antennas Propagation 51, 2592 (2003)
[13] B. B. Mandelbrot, “The Fractal Geometry of Nature,” W. H. Freeman and Company, 1983
[14] K. Falconer, “Fractal Geometry – Mathematical Foundations and Applications,”
Wiley, 1990
[15] P. Markos, and C. M. Soukoulis, “Absorption Losses in Periodic Arrays of Thin Metallic Wires,” Op. Lett. 28, 846 (2003)
[16] T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective Medium Theory of Left-Handed Materials,” Phys. Rev. Lett. 93, 107402-1
[16] T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective Medium Theory of Left-Handed Materials,” Phys. Rev. Lett. 93, 107402-1