"Hi..I was wondering what the speaker system method consists of to deter intrusions?
Thanks B"

Worldwide Campaign to stop the Abuse and Torture of Mind Control/DEWs

Free yourself.. and others by being in front of a strobe..

Go find a xenon strobe.. pulse bursts of chaotic energy stops mind control.. John Travolta and Dance Fever type.. very good 4 you.

Split Ring Ressonator

http://mcvictimsworld.ning.com/forum/attachment/download?id=2301601...

Phase modulation using dual split ring

resonators

Iftekhar O. Mirza*, Shouyuan Shi, and Dennis W. Prather

Dept of Electrical and Computer Engineering, University of Delaware, 151 Evans Hall Newark, Delaware 19716

See the attached file below with the full Descripiton of Phase Modulation using duel Split Ring-

*iomirza@udel.edu

http://www.ece.udel.edu/

Abstract: In this paper, we studied phase modulation numerically using

metamaterials such as stacked structures of dual split ring resonators

(DSRRs). To demonstrate the modulation, a vertical and a planar design

were considered, where the wave vectors were parallel and perpendicular to

the proposed structures creating 70 degrees and 80 degrees of phase change,

respectively. In both of the designs modulation was brought about by

changing the effective index of the structure through switching between the

open and short states of the DSRRs while maintaining high transmission.

One of the attractive features of our design was the thin layers of DSRRs,

where for the vertical and planar models the DSRRs layers were 5 mm and

2.28 mm respectively. The numerical results obtained by simulation

matched well with the theoretical prediction.

© 2009 Optical Society of America

OCIS codes: (160.3918) Metamaterials; (060.5060) Phase Modulation; (070.5753)

Resonators.

References and links

1. V. G. Veselago, The electrodynamics of substances with simultaneously negative values of permittivity and

permeability, Sov. Phys USPEKHI 10, 509 (1968).

2. R. A. Shelby, D.R. Smith, and S. Schultz, “Experimental verification of negative index of refraction,

Science 292, 77-79, (2001).

3. Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, “Three-dimensional

subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies,”

Phys. Rev. Lett. 95, 153901(4) (2005).

4. Z. Sheng and V. Varadan, “Tuning the effective properties of metamaterials by changing the susbstrate,” J.

Appl. Phys. 101, 014909-1, (2007).

5. D. K. Ghodgaonkar, V.V. Varadan, and V. K. Varadan, “Free-space measurement of complex permittivity

and complex permeability of magnetic materials at microwave frequencies,” IEEE Trans. Instrum. Meas.

39, 387-394, (1990).

6. K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis and E. Ozbay, “Investigation of magnetic

resonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).

7. K. Aydin, K. Guven, N. Katsarakis, C. M. Soukoulis and E. Ozbay, “Effect of disorder on magnetic

resonance band gap of split-ring resonator structures,” Opt. Express 12, 5896 (2004)

8. A. A. Zharov, I. V. Shadrivov, and Y.S. Kivshar, “Nonlinear properties of left handed materials,” Phys.

Rev. Lett. 91, 037401 (2003)

9. H. T. Chen, W. J. Padilla, J. Zide, A. Gossard, A. Taylor and R. Averitt, “Active terahertz metamaterial

devices.” Nature 444, 597-600, (2006).

10. V. J. Logeeswaran, A. Stameroff, M. Islam, W. Wu, A. Bratkovsky, P. Kuekes, S. Wang and R. Williams,

“Switching between positive and negative permeability by photoconductive coupling for modulation of

electromagnetic radiation,” Appl. Phys. A 87, 209-216, (2007).

O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett. 84, 1198, (2004).

11.

12. P. He, P. Parimi, C. Vittoria, “Tunable negative refractive index metamaterial phase shifter,” Electon. Lett.

43, (2007).

13. A. Velez, J. Bonache, “Varactor-loaded complementary split ring resonators (VLCSRR) and their

application to tunable metamaterial transmission lines,” IEEE Microwave and Wirel. Compon. Lett. 18, 28-

30, (2008).

#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009

(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5089

14. D. Smith, S. Schultz, P. Markos and C. M. Soukoulis “Determination of effective permittivity and

permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104-1,

(2002).

15. H-T. Chen, J. Ohara, A. Azad, A. Taylor, R. Averitt, D. Shrekenhamer and W. J. Padilla, “Experimental

demonstration of frequency-agile terahertz metamaterials,” Nature Photonics 2, 295-298, (2008).

16. M. K. Karkkainen and P. Ikonen, “Patch antenna with stacked split-ring resonators as artificial magneto-

dielectric substrate,” Microwave Opt. Technol.Lett. 46, 554–556, (2005).

17. S. Oh, L. Shafai, “Artificial magnetic conductor using split ring resonators and its applications to

antennas,” Microwave Opt. Technol.Lett. 48, 329–334, (2006).

18. S. Maslovski, P. Ikonen, I. kolmakov and S. Tretyakov, “Artificial magnetic materials based on the new

magnetic particle: metalsolenoid” Prog. Electromag. Res. 54, 61-81, (2005).

19. N. Katsarakis, T. Koschny and M. Kafesaki, “Electric coupling to the magnetic resonance of split ring

resonators,” Appl. Phys. Lett. 84, 2943-2945, (2004).

20. J. B. Pendry, D. Schurig, D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780-1782,

(2006).

21. M. Kafesaki, T. Koschny, R. Penciu, T. Gundogdu, E. Econonou and C. Soukoulis, “Left-handed

Metamaterials: detailed numerical studies of the transmission properties, J. Opt. A: Pure and

Appl. Opt. 7, S21-S22, (2005).

22. D. Dudley, W. Duncan, J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc.

SPIE 4985, 14-25 (2003).

23. K. Aydin, E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl.

Phys. 101, 024911-5, (2007).

24. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer and H. Giessen, “ Three-dimensional photonic

mtamaterials at optical frequencies,” Nature Materials 7, 31-37, (2008).

25. C. Balanis, Antenna Theory, third edition (John Wiley & Sons, 2005), Chap. 6.

26. T. Hand, S. Cummer, “Controllable magnetic metamaterial using digitally addressable split-ring

resonator,” IEEE Ant. Propag. Lett. (to be published).

1. Introduction

Recently metamaterials have drawn a lot of attention in the research arena [1, 2, 20]. The

ability of this class of materials to respond to an electromagnetic field and bring about

changes in a material’s fundamental properties has opened up doors for new applications such

as flat lens, antenna miniaturization and artificial magnetic conductors to name a few [3, 16,

17]. One of the advantages of these artificial materials is that they can also be tuned over a

frequency range by effectively changing the substrate properties, the geometry of the

resonating metamaterial structure, or by changing the external fields with non linear

dielectrics [4, 6, 7, and 8]. Another effective way of tuning resonating metamaterials such as

the split ring resonators is by changing the resistance properties of the rings using capacitors

that can be controlled by an applied voltage [11]. As these tunable structures are scalable with

the wavelength, they can be used for modulation for any desired frequency range. In

particular, a Terahertz modulator was demonstrated where the metamaterials were grown on a

conductive substrate and the amplitude of the incoming wave was modulated using electrical

controls to change the resistivity of the metamaterial on a GaAs substrate [9, 15]. Also

recently, another research group demonstrated phase shifting with tunable negative refractive

index metamaterials using variable external magnetic field [12]. Similar work was also done

with negative index material by means of photoconductive coupling [10]. Complementary

split ring resonators and their applicability in tuning frequency has also been studied [13].

Although these works had been successful in bringing out the idea of frequency and

amplitude modulation, little investigation has been carried out in terms of phase modulation

using metamaterials. Also a major challenge in working with metamaterials has been the

inherent loss that arises from their resonating nature. To address such issues, in this paper we

demonstrated phase only modulation using tunable metamaterials, namely the DSRRs. We

mitigated the issue of material loss by employing thin resonating metamaterials operating at

an off-resonant frequency to demonstrate a high degree of phase modulation with very

minimal loss. Particularly, in our paper we demonstrated phase modulation using two

#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009

(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5090

different polarizations for the DSRRs: in the first configuration, the polarization of magnetic

field, H, was perpendicular to the DSRRs as shown in Fig. 1 (a), whereas in the second

configuration, shown in Fig. 1(b), the wave vector k was perpendicular to the ring. The

DSRRs consisted of single split rings packed very closely where the adjacent rings’ split gaps

were alternated in orientation. The key advantage of the DSRRs in the first configuration was

that the rings could provide an off-resonance high permeability value when excited by the

magnetic field [18]. Whereas in the second configuration the symmetric nature of the

alternate rings could avoid electric coupling from the magnetic resonances that might lead to

cross-polarization effects [21] when excited by the electric field .The key advantages in both

of our designs were the constituent elements which could be readily manufactured using

standard lithography processes and simple electrical connections could be used to regulate

between the two states of the modulation using very thin layers of DSRRs in the propagation

direction. Compared to conventional phase modulators, metamaterial-based phase modulators

operating in transmission mode, promise to produce enhanced phase modulation in terms of

exhibiting a high degree of phase change within a small volume. Moreover, being physically

small it can ensure ease of structural integration and can offer scalability with wavelength that

can reduce design constraints while operating in different frequencies. We believe these

modulators can be the building block for spatial light modulators in the microwave frequency

regime that can add significant advantage over conventional modulators by simplifying future

Digital Micromirror Devices (DMD) and phased array antenna design by controlling each

element of the array or pixel electronically [22, 25].

The first step in the recipe to build a tunable phase modulator was to design the DSRRs

that could provide the resonant frequency around which the phase modulation would occur.

Standard numerical techniques were used to retrieve the constitutive parameters and the

effective refractive index information of the unit cell of the DSRRs for the two different states

of modulation: electrically open and closed rings [5]. The difference in the value of the

effective index for the two different states was used to calculate the phase change. We also

calculated the change in phase using the volumetric field data obtained inside the

computational region and explained the differences with the calculated theoretical result. In

the following sections we will provide the details of the numerical setup, extraction of the

relevant parameters to calculate the modulation and discuss the simulated results with a

conclusion for improvement and our plan for experimental verification.

E

k

E

k

H

H

Transmission plane Reflection plane Transmission plane

Reflection plane

3.81 mm

5 mm

z

y

x

15 mm

15 mm

y

1m

m

(a) (b)

3.63 mm

z

x

Fig. 1. (a). Configuration 1: H-field perpendicular to the DSRR. (b) Configuration 2: k vector

perpendicular to the DSRR

#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009

(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5091

2. Design and modeling

The DSRRs needed to be designed in such a way so that it could operate for a particular

frequency where the values of the effective permeability and permittivity of the DSRR’s

would meet the following criteria: a) numerically large to create appreciable phase change

through a change in the effective index, b) impedance matched interface, and c) minimize the

power loss. This is formalized in terms of the Figure Of Merit (FOM) = nreal / nimaginary, where

nreal and nimaginary are the real and imaginary parts of the refractive index respectively. The

goal will be to achieve a high FOM for each state for both of the configurations.

In order to meet these requirements we carried out several numerical simulation using the

commercial software HFSS to obtain an optimal design. Two different orientations of the

DSRRs with respect to the wave vector were considered: case1) wave vector, k, parallel to the

structure and case 2) wave vector, k, perpendicular to the structure. The setup in Fig. 1(a),

shows the unit cell analysis for the configuration 1 which will be discussed in the following.

The dimensions of the DSRR were 3 mm x 3 mm with a gap and strip width of 0.33 mm. The

thickness of the metal was 0.02 mm printed on a 0.25 mm thick Duroid substrate (ε = 2.2).

The unit cell of dimension 5 mm x 1 mm x 3.63 mm was placed in between the waveports

with a perfect magnetic conductor (PMC) boundary condition in the y-direction and

perpendicular to the ring and a perfect electric conductor (PEC) boundary condition in the z-

direction and parallel to the ring. By doing so, we were able to simulate a two dimensional

periodic structure along both y and z directions with minimal computation. A similar setup

was used in [4]. Based on this orientation, the DSRRs were excited by the magnetic field

which was perpendicular to the DSRRs. The dense stack of DSRRs acted as metalsolenoid

which helped to concentrate the magnetic flux inside the structure giving rise to a strong

magnetic resonance. Similar design was considered and discussed in [18] where it was

highlighted that the main benefit of this design was that a high value of permeability could be

obtained away from the resonance. The large off-resonance permeability value leads to a

large effective index at the same frequency for the DSRRs which could be exploited for

maximum phase modulation. The reflection/transmission spectra results obtained from the

simulation were used to extract the effective index of the DSRR using the formulation

described in [4, 5].

For a normally incident wave in free-space, at the air-sample boundary the scattering

parameters, namely the S11 and S21 can be related to the reflection ( Γ ) and transmission (T)

coefficients [5] as:

Γ = R ± R2 −1 (1)

where,

S 2 − S 2 +1

R = 0.5 11 21 (2)

S11

and

S + S −Γ

T = 11 21 (3)

1 − ( S11 + S21 )Γ

ncomplex = nreal + nimag ,

Following this, the complex refractive index can be formulated as

2mπ − arg(T ) − log(| T |)

nreal = and nimag = . The parameter d indicates the slab

where

dk0 dk0

2π

, where λ0 is the operational

thickness in the direction of propagation and k0 =

λ0

#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009

(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5092

wavelength in free space. In our studies, m was set to zero as the wavelength inside the

DSRRs was larger than the slab thickness. Detailed discussion of the parameter m can be

found in [4]. The extracted data are shown in Fig. 2(a), where the real and imaginary parts of

the effective index for the open and closed cases of the DSRRs were plotted. From the graph,

at 4 GHz the real part of the effective index was 5.9 for the open state DSRRs while for the

closed state the value of the real part of the effective index was 1.6. The closed state had a flat

real part response and minimal loss since the DSRRs were off-resonance within the frequency

range of 3.5 – 4.5 GHz. The closed state for the DSRR was achieved by effectively shorting

the gaps in the DSRRs by placing a piece of metal inside the gap. Due to the large index

difference between the two states, we chose a frequency band centered at 4 GHz for our phase

modulation application. Although, at resonance the real index was at a maximum which

would provide the maximum phase modulation, the imaginary part which indicated the loss of

the structure was also very high that could potentially degrade the overall performance of the

device. In particular, the transmission data as shown in Fig. 3(a) indicated that for

configuration 1 the transmission was -1.6 dB and -2.8 dB for the open and short case

respectively. The value of the imaginary parts for both the cases at this frequency was

negligibly low and the difference in the real parts of the effective index was calculated as 5.9-

1.6 = 4.3. The calculated FOM for the open state was 5.9/0.325 = 18.2 and for the closed state

the FOM was 1.6/0.0003 = 5.3 x 103. As expected the FOM was much higher for the closed

state because of the absence of a resonance.

Freq: 4GHz

Go find a xenon strobe.. pulse bursts of chaotic energy stops mind control.. John Travolta and Dance Fever type.. very good 4 you.

Split Ring Ressonator

http://mcvictimsworld.ning.com/forum/attachment/download?id=2301601...

Phase modulation using dual split ring

resonators

Iftekhar O. Mirza*, Shouyuan Shi, and Dennis W. Prather

Dept of Electrical and Computer Engineering, University of Delaware, 151 Evans Hall Newark, Delaware 19716

See the attached file below with the full Descripiton of Phase Modulation using duel Split Ring-

*iomirza@udel.edu

http://www.ece.udel.edu/

Abstract: In this paper, we studied phase modulation numerically using

metamaterials such as stacked structures of dual split ring resonators

(DSRRs). To demonstrate the modulation, a vertical and a planar design

were considered, where the wave vectors were parallel and perpendicular to

the proposed structures creating 70 degrees and 80 degrees of phase change,

respectively. In both of the designs modulation was brought about by

changing the effective index of the structure through switching between the

open and short states of the DSRRs while maintaining high transmission.

One of the attractive features of our design was the thin layers of DSRRs,

where for the vertical and planar models the DSRRs layers were 5 mm and

2.28 mm respectively. The numerical results obtained by simulation

matched well with the theoretical prediction.

© 2009 Optical Society of America

OCIS codes: (160.3918) Metamaterials; (060.5060) Phase Modulation; (070.5753)

Resonators.

References and links

1. V. G. Veselago, The electrodynamics of substances with simultaneously negative values of permittivity and

permeability, Sov. Phys USPEKHI 10, 509 (1968).

2. R. A. Shelby, D.R. Smith, and S. Schultz, “Experimental verification of negative index of refraction,

Science 292, 77-79, (2001).

3. Z. Lu, J. A. Murakowski, C. A. Schuetz, S. Shi, G. J. Schneider, and D. W. Prather, “Three-dimensional

subwavelength imaging by a photonic-crystal flat lens using negative refraction at microwave frequencies,”

Phys. Rev. Lett. 95, 153901(4) (2005).

4. Z. Sheng and V. Varadan, “Tuning the effective properties of metamaterials by changing the susbstrate,” J.

Appl. Phys. 101, 014909-1, (2007).

5. D. K. Ghodgaonkar, V.V. Varadan, and V. K. Varadan, “Free-space measurement of complex permittivity

and complex permeability of magnetic materials at microwave frequencies,” IEEE Trans. Instrum. Meas.

39, 387-394, (1990).

6. K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis and E. Ozbay, “Investigation of magnetic

resonances for different split-ring resonator parameters and designs,” New J. Phys. 7, 168 (2005).

7. K. Aydin, K. Guven, N. Katsarakis, C. M. Soukoulis and E. Ozbay, “Effect of disorder on magnetic

resonance band gap of split-ring resonator structures,” Opt. Express 12, 5896 (2004)

8. A. A. Zharov, I. V. Shadrivov, and Y.S. Kivshar, “Nonlinear properties of left handed materials,” Phys.

Rev. Lett. 91, 037401 (2003)

9. H. T. Chen, W. J. Padilla, J. Zide, A. Gossard, A. Taylor and R. Averitt, “Active terahertz metamaterial

devices.” Nature 444, 597-600, (2006).

10. V. J. Logeeswaran, A. Stameroff, M. Islam, W. Wu, A. Bratkovsky, P. Kuekes, S. Wang and R. Williams,

“Switching between positive and negative permeability by photoconductive coupling for modulation of

electromagnetic radiation,” Appl. Phys. A 87, 209-216, (2007).

O. Reynet and O. Acher, “Voltage controlled metamaterial,” Appl. Phys. Lett. 84, 1198, (2004).

11.

12. P. He, P. Parimi, C. Vittoria, “Tunable negative refractive index metamaterial phase shifter,” Electon. Lett.

43, (2007).

13. A. Velez, J. Bonache, “Varactor-loaded complementary split ring resonators (VLCSRR) and their

application to tunable metamaterial transmission lines,” IEEE Microwave and Wirel. Compon. Lett. 18, 28-

30, (2008).

#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009

(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5089

14. D. Smith, S. Schultz, P. Markos and C. M. Soukoulis “Determination of effective permittivity and

permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104-1,

(2002).

15. H-T. Chen, J. Ohara, A. Azad, A. Taylor, R. Averitt, D. Shrekenhamer and W. J. Padilla, “Experimental

demonstration of frequency-agile terahertz metamaterials,” Nature Photonics 2, 295-298, (2008).

16. M. K. Karkkainen and P. Ikonen, “Patch antenna with stacked split-ring resonators as artificial magneto-

dielectric substrate,” Microwave Opt. Technol.Lett. 46, 554–556, (2005).

17. S. Oh, L. Shafai, “Artificial magnetic conductor using split ring resonators and its applications to

antennas,” Microwave Opt. Technol.Lett. 48, 329–334, (2006).

18. S. Maslovski, P. Ikonen, I. kolmakov and S. Tretyakov, “Artificial magnetic materials based on the new

magnetic particle: metalsolenoid” Prog. Electromag. Res. 54, 61-81, (2005).

19. N. Katsarakis, T. Koschny and M. Kafesaki, “Electric coupling to the magnetic resonance of split ring

resonators,” Appl. Phys. Lett. 84, 2943-2945, (2004).

20. J. B. Pendry, D. Schurig, D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780-1782,

(2006).

21. M. Kafesaki, T. Koschny, R. Penciu, T. Gundogdu, E. Econonou and C. Soukoulis, “Left-handed

Metamaterials: detailed numerical studies of the transmission properties, J. Opt. A: Pure and

Appl. Opt. 7, S21-S22, (2005).

22. D. Dudley, W. Duncan, J. Slaughter, “Emerging digital micromirror device (DMD) applications,” Proc.

SPIE 4985, 14-25 (2003).

23. K. Aydin, E. Ozbay, “Capacitor-loaded split ring resonators as tunable metamaterial components,” J. Appl.

Phys. 101, 024911-5, (2007).

24. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer and H. Giessen, “ Three-dimensional photonic

mtamaterials at optical frequencies,” Nature Materials 7, 31-37, (2008).

25. C. Balanis, Antenna Theory, third edition (John Wiley & Sons, 2005), Chap. 6.

26. T. Hand, S. Cummer, “Controllable magnetic metamaterial using digitally addressable split-ring

resonator,” IEEE Ant. Propag. Lett. (to be published).

1. Introduction

Recently metamaterials have drawn a lot of attention in the research arena [1, 2, 20]. The

ability of this class of materials to respond to an electromagnetic field and bring about

changes in a material’s fundamental properties has opened up doors for new applications such

as flat lens, antenna miniaturization and artificial magnetic conductors to name a few [3, 16,

17]. One of the advantages of these artificial materials is that they can also be tuned over a

frequency range by effectively changing the substrate properties, the geometry of the

resonating metamaterial structure, or by changing the external fields with non linear

dielectrics [4, 6, 7, and 8]. Another effective way of tuning resonating metamaterials such as

the split ring resonators is by changing the resistance properties of the rings using capacitors

that can be controlled by an applied voltage [11]. As these tunable structures are scalable with

the wavelength, they can be used for modulation for any desired frequency range. In

particular, a Terahertz modulator was demonstrated where the metamaterials were grown on a

conductive substrate and the amplitude of the incoming wave was modulated using electrical

controls to change the resistivity of the metamaterial on a GaAs substrate [9, 15]. Also

recently, another research group demonstrated phase shifting with tunable negative refractive

index metamaterials using variable external magnetic field [12]. Similar work was also done

with negative index material by means of photoconductive coupling [10]. Complementary

split ring resonators and their applicability in tuning frequency has also been studied [13].

Although these works had been successful in bringing out the idea of frequency and

amplitude modulation, little investigation has been carried out in terms of phase modulation

using metamaterials. Also a major challenge in working with metamaterials has been the

inherent loss that arises from their resonating nature. To address such issues, in this paper we

demonstrated phase only modulation using tunable metamaterials, namely the DSRRs. We

mitigated the issue of material loss by employing thin resonating metamaterials operating at

an off-resonant frequency to demonstrate a high degree of phase modulation with very

minimal loss. Particularly, in our paper we demonstrated phase modulation using two

#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009

(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5090

different polarizations for the DSRRs: in the first configuration, the polarization of magnetic

field, H, was perpendicular to the DSRRs as shown in Fig. 1 (a), whereas in the second

configuration, shown in Fig. 1(b), the wave vector k was perpendicular to the ring. The

DSRRs consisted of single split rings packed very closely where the adjacent rings’ split gaps

were alternated in orientation. The key advantage of the DSRRs in the first configuration was

that the rings could provide an off-resonance high permeability value when excited by the

magnetic field [18]. Whereas in the second configuration the symmetric nature of the

alternate rings could avoid electric coupling from the magnetic resonances that might lead to

cross-polarization effects [21] when excited by the electric field .The key advantages in both

of our designs were the constituent elements which could be readily manufactured using

standard lithography processes and simple electrical connections could be used to regulate

between the two states of the modulation using very thin layers of DSRRs in the propagation

direction. Compared to conventional phase modulators, metamaterial-based phase modulators

operating in transmission mode, promise to produce enhanced phase modulation in terms of

exhibiting a high degree of phase change within a small volume. Moreover, being physically

small it can ensure ease of structural integration and can offer scalability with wavelength that

can reduce design constraints while operating in different frequencies. We believe these

modulators can be the building block for spatial light modulators in the microwave frequency

regime that can add significant advantage over conventional modulators by simplifying future

Digital Micromirror Devices (DMD) and phased array antenna design by controlling each

element of the array or pixel electronically [22, 25].

The first step in the recipe to build a tunable phase modulator was to design the DSRRs

that could provide the resonant frequency around which the phase modulation would occur.

Standard numerical techniques were used to retrieve the constitutive parameters and the

effective refractive index information of the unit cell of the DSRRs for the two different states

of modulation: electrically open and closed rings [5]. The difference in the value of the

effective index for the two different states was used to calculate the phase change. We also

calculated the change in phase using the volumetric field data obtained inside the

computational region and explained the differences with the calculated theoretical result. In

the following sections we will provide the details of the numerical setup, extraction of the

relevant parameters to calculate the modulation and discuss the simulated results with a

conclusion for improvement and our plan for experimental verification.

E

k

E

k

H

H

Transmission plane Reflection plane Transmission plane

Reflection plane

3.81 mm

5 mm

z

y

x

15 mm

15 mm

y

1m

m

(a) (b)

3.63 mm

z

x

Fig. 1. (a). Configuration 1: H-field perpendicular to the DSRR. (b) Configuration 2: k vector

perpendicular to the DSRR

#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009

(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5091

2. Design and modeling

The DSRRs needed to be designed in such a way so that it could operate for a particular

frequency where the values of the effective permeability and permittivity of the DSRR’s

would meet the following criteria: a) numerically large to create appreciable phase change

through a change in the effective index, b) impedance matched interface, and c) minimize the

power loss. This is formalized in terms of the Figure Of Merit (FOM) = nreal / nimaginary, where

nreal and nimaginary are the real and imaginary parts of the refractive index respectively. The

goal will be to achieve a high FOM for each state for both of the configurations.

In order to meet these requirements we carried out several numerical simulation using the

commercial software HFSS to obtain an optimal design. Two different orientations of the

DSRRs with respect to the wave vector were considered: case1) wave vector, k, parallel to the

structure and case 2) wave vector, k, perpendicular to the structure. The setup in Fig. 1(a),

shows the unit cell analysis for the configuration 1 which will be discussed in the following.

The dimensions of the DSRR were 3 mm x 3 mm with a gap and strip width of 0.33 mm. The

thickness of the metal was 0.02 mm printed on a 0.25 mm thick Duroid substrate (ε = 2.2).

The unit cell of dimension 5 mm x 1 mm x 3.63 mm was placed in between the waveports

with a perfect magnetic conductor (PMC) boundary condition in the y-direction and

perpendicular to the ring and a perfect electric conductor (PEC) boundary condition in the z-

direction and parallel to the ring. By doing so, we were able to simulate a two dimensional

periodic structure along both y and z directions with minimal computation. A similar setup

was used in [4]. Based on this orientation, the DSRRs were excited by the magnetic field

which was perpendicular to the DSRRs. The dense stack of DSRRs acted as metalsolenoid

which helped to concentrate the magnetic flux inside the structure giving rise to a strong

magnetic resonance. Similar design was considered and discussed in [18] where it was

highlighted that the main benefit of this design was that a high value of permeability could be

obtained away from the resonance. The large off-resonance permeability value leads to a

large effective index at the same frequency for the DSRRs which could be exploited for

maximum phase modulation. The reflection/transmission spectra results obtained from the

simulation were used to extract the effective index of the DSRR using the formulation

described in [4, 5].

For a normally incident wave in free-space, at the air-sample boundary the scattering

parameters, namely the S11 and S21 can be related to the reflection ( Γ ) and transmission (T)

coefficients [5] as:

Γ = R ± R2 −1 (1)

where,

S 2 − S 2 +1

R = 0.5 11 21 (2)

S11

and

S + S −Γ

T = 11 21 (3)

1 − ( S11 + S21 )Γ

ncomplex = nreal + nimag ,

Following this, the complex refractive index can be formulated as

2mπ − arg(T ) − log(| T |)

nreal = and nimag = . The parameter d indicates the slab

where

dk0 dk0

2π

, where λ0 is the operational

thickness in the direction of propagation and k0 =

λ0

#106965 - $15.00 USD Received 30 Jan 2009; revised 4 Mar 2009; accepted 13 Mar 2009; published 16 Mar 2009

(C) 2009 OSA 30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 5092

wavelength in free space. In our studies, m was set to zero as the wavelength inside the

DSRRs was larger than the slab thickness. Detailed discussion of the parameter m can be

found in [4]. The extracted data are shown in Fig. 2(a), where the real and imaginary parts of

the effective index for the open and closed cases of the DSRRs were plotted. From the graph,

at 4 GHz the real part of the effective index was 5.9 for the open state DSRRs while for the

closed state the value of the real part of the effective index was 1.6. The closed state had a flat

real part response and minimal loss since the DSRRs were off-resonance within the frequency

range of 3.5 – 4.5 GHz. The closed state for the DSRR was achieved by effectively shorting

the gaps in the DSRRs by placing a piece of metal inside the gap. Due to the large index

difference between the two states, we chose a frequency band centered at 4 GHz for our phase

modulation application. Although, at resonance the real index was at a maximum which

would provide the maximum phase modulation, the imaginary part which indicated the loss of

the structure was also very high that could potentially degrade the overall performance of the

device. In particular, the transmission data as shown in Fig. 3(a) indicated that for

configuration 1 the transmission was -1.6 dB and -2.8 dB for the open and short case

respectively. The value of the imaginary parts for both the cases at this frequency was

negligibly low and the difference in the real parts of the effective index was calculated as 5.9-

1.6 = 4.3. The calculated FOM for the open state was 5.9/0.325 = 18.2 and for the closed state

the FOM was 1.6/0.0003 = 5.3 x 103. As expected the FOM was much higher for the closed

state because of the absence of a resonance.

Freq: 4GHz

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