Compensation of Group Delay with Tunable SlowFast Light
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Compensation of Group Delay with Tunable Slow/Fast LightForm-Birefringent Metamaterial StructuresWeiguo YangDepartment of Engineering & Technology, Kimmel School, Western Carolina University, Cullowhee, NC 28723, USAe-mail: wyang@John D. GrahamCenter for Rapid Product Realization, Kimmel School, Western Carolina University, Cullowhee, NC 28723, USARobert P. Ingel and Michael A. FiddyCenter for Optoelectronics and Optical Communications, University of North Carolina at Charlotte, Charlotte, NC28223, USAAbstract: We demonstrate the compensation of slow light by tunable slow/fast light structure made of form-birefringent metamaterial structures. Employing full compensation, the slow light structure can effectively be made to disappear over a significant frequency range.© 2010 Optical Society of AmericaOCIS codes: (050.2555) Form birefringence; (160.3918) Metamaterials.1. IntroductionIt has been shown that one-dimensional periodic stacks of anisotropic layers, for a given frequency range and polarization, can exhibit an anomalous phase response where the group index of refraction is negative. This anomalous phase response is equivalent to an effective negative index of refraction and it has been predicted that it also leads to anomalous shifts of the center of gravity of the beam similar to the effect of a slab of material exhibiting a negative index of refraction (NIM) [1]. It has been predicted and confirmed experimentally that this anomalous phase effect is present in structures composed of a single anisotropic layer [1,2]. Furthermore, such structures are capable of providing a tunable group index of refraction from negative values associated with fast light to positive values corresponding to slow light [2]. With these tunable slow/fast light modules, one can compensate for a structure or device where the light is significantly slowed down or equivalently undergoes a sequence of operations resulting in an excessive group delay compared to that of an empty path, to the degree that the group delay can be fully compensated as if nothing other than free space lay in between the transmitter and receiver. In this paper, we report experimental demonstrations of this sort of transmission invisibility, where two tunable slow/fast light modules made from form-birefringent metamaterial structures are used. For example, the he first one can be set to generate a slow light effect in a specified frequency range, simulating the structure or the device that introduces an excessive group delay. The second tunable slow/fast light module is then employed to compensate the first slow light module. By virtue of the tunability, we have demonstrated all cases of over-compensation, full-compensation, as well as enhanced slow light effects depending on the second tunable slow/fast light module. To the best of our knowledge, this is the first experimental demonstration of this sort.2. Experiment and ResultsFigure 1a shows the experimental setup of this demonstration. The tunable slow/fast light modules are made of single layer form-birefringent disks. One such disk is shown in Figure 1b. In our experiments, we used a Stratasys® FDM rapid prototyping machine and created form-birefringent disks using common engineering plastics, such as(a) (b)Figure 1: (a) Experimental setup for the demonstration of transmission invisibility. (b) The form-birefringent disks made of ABS. These disks are building blocks for tunable slow/fast light modules.Vector NetworkAnalyzer (VNA)Slow Light ModulehornhornTunable Slow/Fast Light Module978-1-55752-890-2/10/$26.00 ©2010 IEEEABS, for metamaterial structures targeted for X-band (8GHz-12GHz) operation [2]. FDM processes have a minimum feature size of about 120 μm and are suitable for fabrication of metamaterial structures in microwave frequencies of 300 GHz or lower. The index contrast for ABS form-birefringent disks can easily achieve 0.14. With further surface treatment, index contrasts as high as 0.7 have been reproducibly achieved. In the current experiment, as shown in Figure 1a, a 9-cm thick ABS tunable slow/fast light module has been used to set up a slow light effect in a specific frequency range. Another 2-cm thick surface-treated tunable slow/fast light module is used to demonstrate the compensation of the slow light effect originating in the first module. The measurement is performed in the frequency domain by using the vector network analyzer (VNA, Agilent Technology N5230A). The transmission spectrum is referenced to a through calibration (Thru-Cal). Accordingly, a flat spectral phase response represents the empty path between the transmitting and receiving horn antenna. It can be seen from Figure 2a that the first tunable slow/fast light module is used to set up a slow light effect between 9.5 GHz to 10.5 GHz (dotted trace). The group index of refraction is estimated to be 2.6 as compared to 1.2 of the disk. Tuning the second tunable slow/fast light module one can compensate this slow light effect, as seen in Figure 2a. One can tune through over-compensation (dashed trace), full-compensation (solid trace), and slow light enhancement (dot-dashed trace). The fullyeffectively cancelling the effect of the first slow light structure as well as the compensating module. Both the enhanced slow light effect and the over compensated case show the expected shift of center frequency of the slow/fast light effect due to the change in the total thickness of the birefringent layers involved. Figure 2b shows the corresponding spectral intensity response. It can be seen that although the spectral phase exhibits essentially a flat slope similar to an empty path after the full compensation, the total transmission in these experiments was reduced, suffering loss from 10 dB to 20 dB within the frequency range of interest. Unlike the doubly-negative NIM case [5], this loss can be in principle compensated for by introducing gain without losing any fast/slow light characteristics.3. Discussions and ConclusionsIn conclusion, we have demonstrated for the first time the compensation of a slow light effect with a tunable slow/fast light module made of form-birefringent metamaterial structures. At full compensation, the spectral phase response exhibits the same slope as an empty path between the transmitter and receiver, effectively hiding the combined slow/fast structures in between. The spectral intensity response still suffers a loss from 10 dB to 20 dB in these experiments because of the inherent loss in the dielectrics used. This loss can in principle be compensated by creating larger index differences by mean of form birefringence in higher dielectric constant materials or by introducing gain in these media.4. References[1] A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, “Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials,” Phys. Rev.B70, 165107 (2004).[2] K. Sinchuk, et.al., “Tunable Negative Group Index in Metamaterial Structures with Large Form Birefringence,” Opt. Ex. (Accepted, 2009).[3] D. H. Raguin and G. M. Morris, "Antireflection structured surfaces for the infrared spectral region," Appl. Opt.32, 1154-1167 (1993).[4] E. B. Grann, M. G. Moharam, and D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am.A11, 2695 (1994).[5] M. I. Stockman, “Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality,” Phys. Rev. Lett. 98, 177404 (2007).。
