Imaging Using Phase Conjugation Lens Techniquesphase conjugation technology can be advantageous in multipath rich environments. In multipath environments the numerical aperture of

Forum for Electromagnetic Research Methods and Application Technologies (FERMAT)

1

Abstract—This paper details a summary review of

previously reported work carried out at the Queen’s

University of Belfast (UK) into the topic of nonlinear

frequency selective surfaces as a means for imaging in the

far, or in, the near-field using the principle of phase

conjugation. We detail some of the main theoretical and

practical issues surrounding this topic. Emphasis is placed

on an active dual-sided lens topology based on microwave

phase conjugating circuitry and a single layer nonlinearly

loaded pumped wire array technology. This paper is

intended as a means for rapid assimilation of this topic. It

is also hoped that others will wish to expand on the original

material which has been created in this area.

Index Terms—phase conjugation, nonlinear frequency

selective surface, imaging, spatial data encryption.

I. INTRODUCTION

By conjugating the phase of an incoming electromagnetic

wave front it is possible to automatically cause the incoming

wave front to re-propagate exactly back along the path or

paths along which it originally traversed without prior

knowledge of its point of origin provided the propagation path

properties remain stationary during such a two way signal

pass, [1]. This property can be exploited in a variety of

scenarios that are useful to the physics and engineering

communities. For example in adaptive optics [2] phase

conjugation is exploited in order to remove atmospheric

induced aberrations.

The classical approach used to create a phase conjugate

signal at optical wavelengths is to use four-wave mixing in an

optically suitable nonlinear media [3]. This creates a low

power phase conjugated version of an incident optical wave

front after mixing. Whenever more than one signal at the same

frequency is present phase conjugating surfaces automatically

split the retransmitted signal into multiple beams, with each

returned along the path they arrived [4]. Therefore the use of

phase conjugation technology can be advantageous in

multipath rich environments. In multipath environments the

numerical aperture of the phase-conjugating surface appears

to increase with respect to the aperture presented by a non-

phase conjugating surface of the same physical area, this

results in superior focusing.

Direct translation of the approach used for generation of

phase conjugated signals at optical frequencies to microwave

through sub-millimeter frequencies requires a rethink in

respect of the enabling technologies and physical architectures

used for their effective production. The core issue here

involves establishing what type of physical media lends itself

to providing efficient phase conjugation that is appropriate to

the frequency at which the required application occurs. In

addition the effect that the technology choice induces on the

overall phase conjugation process has to be capable of

assessment either by analytical and/or numerical

electromagnetic simulation means. This is necessary so that

structure optimization and synthesis by repeated optimization

can be obtained prior to media construction, characterization

and eventually, operational deployment.

Applications for phase conjugation technologies at

microwave through millimeter frequencies are wide ranging.

Examples of prototype communications and radar systems

have appeared in the published literature e.g. [6, 7]. In these

applications finite numbers of receive and re-transmit arrays

are used such that the incoming wave front to be phase

conjugated is spatially sampled. The use of phase conjugation

technology for retrodirective arrays in wireless

communications applications has been extensively reviewed

in [8].

In nearly all cases the actual uptake of phase conjugation

technology into actual operational equipment has largely

failed to materialize. Mainly this is thought to be due to the

effectiveness of the phase conjugation media in dealing with

the very small signal levels of the incident wave front signals

to be conjugated. One recent notable exception occurs in [9]

where phase locked loop technology is used such that incident

signal power levels as low as -120dBm can be phase

conjugated to a high degree of accuracy. Phase locked loop

implementation technology opens the way for the first fully

robust engineered solutions for low complexity self-aligning

self-tracking satellite communication terminals, [10].

Other than the above approach the types of media that are

currently used for phase conjugation in microwave through

submillimeter regimes do not vary significantly, all are based

around discrete sampling of the incident wave front. This is

followed by processing through nonlinear components by

mixing the signal sample to be phase conjugated normally

with the second harmonic of the incoming signal frequency.

This method was first reported by Pon [11] and becomes

increasingly more difficult to implement as frequency

increases. This is because the method requires the availability

of a spectrally pure 2nd harmonic pump signal of sufficient

power to operate each mixing element in the array square low

fashion such that a sideband of sufficient power for post

processing can be generated. A second harmonic pump

waveform is used so that the phase conjugated intermediate

Imaging Using Phase Conjugation Lens Techniques

Vincent Fusco and O Malyuskin

ECIT Institute, Queen’s University Belfast

NI Science Park, Queens Island, Queens Road, Belfast, BT3 9DT, UK (Email: [email protected], [email protected])


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frequency, IF, appearing after mixing occurs at the same

frequency as the incoming signal. This imposes significant

complexity on the mixer design in order to minimize RF to IF

leakage. Such feed-through will act to impair the

retrodirective capability of the array.

The basic principle of phase conjugation through mixing is

expressed in (1).

( ) ( )

( )( )[

( )( )]φωω

φωω

ωφω

+++

−−=

+=

t

tVV

tVtVV

RFLO

RFLOLORF

LOLORFRFIF

cos

cos2

1

coscos

(1)

Of the sidebands produced in the mixing process the lower

sideband is useful as its phase is conjugated with respect to the

phase of the incident signal. In general to enhance RF-IF and

LO-IF mixer isolation a suitable LO signal frequency is

selected such that an output frequency that is close to, but not

identical with, the RF frequency is obtained. This raises a

collateral issue of re-directed beam pointing error. Beam

pointing error occurs when an RF and LO frequency offset

f∆ is present in the mixing process [12] hence giving rise to

a difference between the incident wave angle of arrival θin and

the retransmitted wave sending angle θs as given in (2), inf is

the carrier frequency of the incident signal,

in

in

s

in

f

ff ∆−=

θ

θ

sin

sin (2)

As will be discussed later in this paper the phase

conjugation techniques established above for wireless

communications applications can be extended for the purpose

of microwave lensing. This is possible since a type of lens can

be made to bend incoming divergent ray paths along phase

conjugated, i.e., negative refraction paths, in order to form a

convergent beam.

Extension of the wave front point sampling techniques

described above uses finite 2D periodic grids point loaded

with non-linear lumped elements. These have been evaluated

for their potential as suitable phase conjugation media. This

approach leads to applications such as super resolution near

field imaging and high resolution far field imaging. Both of

these topics are to be discussed in this paper.

Imaging and the ability to collimate energy into highly

localized spatial regions is a core area which demands

attention as it impacts into a diverse range of advanced

applications. Precision delivery of radiotherapy treatment into

highly confined spatial regions, the ability to track and guide

microprobes for automated surgery, enhanced sub-

wavelength photolithography for next generation

semiconductor manufacture, increased resolution microscopy,

enhanced resolution remote sensing and manipulation of

nano-particles are but a few examples. In this context the

phase conjugating lens appears to have considerable merit

since the lens can be flat, or conformal, and they can be made

to be very thin.

In this paper we offer a survey of our efforts to date in trying

to obtain a clearer understanding of some of the critical path

theoretical and practical issues surrounding this area of

technology.

Section 2 describes the basic mathematical tools that have

been created for the analysis of wire element frequency

selective surfaces, FSS that use lumped non-linear elements

for the purpose of phase conjugation, PC. Section 3 describes

how negative refraction can be devised using these structures.

The experimental means for evaluating the phase conjugation

properties of the structures in section 2 and 3 is described in

section 4, while section 5 describes various aspects of the

lenses target localization and image manipulation properties.

Section 6 details how the lenses operate when processing

amplitude and phase modulated signals. In section 7 we

discuss how spatial data encryption can be made to occur

within the intermediate space between two phase conjugating

lenses. Finally in section 8 we draw some broad conclusions

from the work presented.

II. ANALYSIS OF WIRE GRID PHASE

CONJUGATING FSS LENS

In [13] we described a means for analyzing a doubly

periodic array of thin wires loaded with any type of lumped

linear impedance element and we derived generic closed form

expressions for its scattering properties. The resulting

expressions can be evaluated rapidly and thus provide the

means for synthesis by repeated analysis.

This work was extended to establish a rigorous full-wave

theory for nonlinearly loaded wire arrays that had properties

that would permit microwave phase conjugation and negative

refraction [14]. Here a mathematical description of the full-

wave scattering properties of a two-dimensional double

periodic array of wires loaded with nonlinear lumped elements

was developed in order to represent the arrangement in Fig. 1.

The simulation results for the array when pumped by a

spatially fed local oscillator wave front showed evidence of

the production of a phase-conjugated wave. The mechanisms

accounting for energy lost to specular reflection as well

grating lobe formation were described. The result in Fig. 2

shows that the production of phase conjugation by this process

is inefficient, only 2%. This is due to the assumed weak

nonlinearity, selected so that we could deploy Volterra series

analysis. In principle adding a stronger nonlinearity and using

a mathematical procedure such harmonic balance could be

adopted to give a framework within which more efficient

designs could be developed.


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Fig. 1 Nonlinear Loaded Wire Array Geometry. Inset shows the reference

wire loaded with nonlinear device at Lss = ,

©2006 IEEE. Reprinted, with permission, from IEEE Transactions on Antennas and Propagation, [14].

Fig. 2 Reflected Phase-Conjugated Field as a Function of Incident Signal Frequency dx=14cm, dy=5cm, normal incidence.

©2006 IEEE. Reprinted, with permission, from IEEE Transactions on

Antennas and Propagation, [14].

III. NEGATIVE REFRACTION

In [15, 16] the properties of a dual-sided phase conjugating

surface shown in Fig. 3, were examined. It was shown that

such a structure when illuminated with a plane wave can

generate a phase-conjugated forward-transmitted plane wave

which experiences negative refraction. Focusing in the far-

and in the near-field regions of the lens was demonstrated both

when excited by a plane wave.

For far-field subwavelength operation the lens in Fig. 3 was

augmented with scatterers on its source and image sides, [17].

The scattering elements are straight wire segments that are

loaded with lumped impedance loads at their centers in order

to make them resonant. These scatterers permit evanescent-to-

propagating spectrum conversion on the source side of the

lens and propagating-to-evanescent conversion on the image

side of the lens. Since evanescent information is available at

the image side then some of the sub-wavelength information

encoded into the propagating waves on the source side can be

extracted at the image side. Through this investigation we

showed that phase conjugation alone does not lead to sub-

diffraction resolution imaging since it operates only on the

propagating part of the field with half wavelength spatial

variation. Here the evanescent-to-propagating spectrum

conversion mechanism augments phase conjugating lens

operation. Imaged focal widths in the far field of up to one-

seventh wavelength were demonstrated. The results obtained

indicated a potential practical means for realizing using

conventional materials devices for fine feature extraction by

electromagnetic lensing at distances remotely located from the

source objects under investigation.

Fig. 3 Dual-sided phase conjugating surface illuminated by a plane wave


Antennas and Propagation, [15,16] .

Fig.4 The near field Ey component of two y-oriented Hertzian dipoles in the

transversal xy plane. Transversal separation between the dipoles is λ/4.



The properties of a lumped loaded wire array as a means for

near field focusing using phase conjugation was studied in

[18]. In particular, it is shown that inductive loading of the

constituent lens wire elements is essential for subwavelength

focusing since this leads to the creation of a phase-conjugated

near field, predominantly determined by a convolution of the

array current distribution with the real part of the Greens

Incident plane

wave

θ

Phase

Conjugator

Isolation

Plane

x

y

z


4

function which oscillates at a subwavelength scale. The

characteristic resolution of the lens was shown to be

approximately λ/7 for a single source and better than λ/4 for

two electric dipole sources at source-lens separation distance

λ/10, Fig.4.

IV. EXPERIMENTAL VALIDATION

The arrangements in Fig. 1 and Fig. 3 were experimentally

validated for their capacity to produce microwave phase-

conjugated energy. An experimental means for assessing the

phase conjugate energy production capability for these types

of lenses was given in [19]. This permitted investigations

which enabled the identification of the fundamental

operational characteristics and underlying mechanisms

associated with the production of phase-conjugated energy by

doubly periodic artificial electromagnetic media. The

experimental approach adopted physical unit cell imaging

within a parallel-plate waveguide simulator (see Fig. 5),

yielding an EM periodic array simulation environment for

normal incidence conditions.

Fig. 5 Parallel-Plate Image Waveguide Simulator

©2009 IET. Reprinted with permission of the IET, [19].

Additional details on the design and use of the parallel-plate

waveguide simulator approach developed above were

articulated in [20]. Here a hybrid measurement/3D EM

simulation technique was used to obtain the reflection and

transmission properties of an FSS under normal incidence. It

was shown that a parallel-plate waveguide simulator can have

its behavior accurately computed by using 3D EM simulation.

A de-embedding method was created which yielded results in

agreement with theoretical prediction.

Free-space experimental results were given in [21] for the

focusing capability of an active phase conjugating lens for a

single and a dipole source pair, Fig. 6(a). When an identical

pair of passive scatterers were located symmetrically about the

lens it was shown that imaging with sub-wavelength

resolution is possible, Fig. 6(b). The experimental evidence

obtained and means for realization suggests new possibilities

for advanced MIMO applications on restricted size platforms

or for fine feature extraction at distances remote from the

objects under investigation.

(a)

(b)

Fig.6. (a) Dual-sided phase conjugating lens; (b) Measured resolution of two

electric dipole sources with and without evanescent-to-propagating spectrum

conversion.

©2010 IEEE. Reprinted, with permission, from IEEE Transactions on Antennas and Propagation, [21].

V. TARGET LOCALIZATION AND IMAGE

MANIPULATION

Passive target 3D localization requires a pulse signal of

some type. In [22], Fig.7, it was shown that the characteristic

resolution of a single target by a dual-sided phase conjugating

lens operating under Gaussian pulse excitation is

approximately the same as that obtained using UWB synthetic

aperture radar techniques. This property is very useful for

imaging applications where refocusing has to be

accomplished in a real time, i.e., when high speed target

acquisition is necessary. The possibility of imaging dielectric

targets both in free space and behind lossy wall geometries

using a sequentially switched phase conjugating lens was

reported in, [23]. It was shown that a weakly scattering object

can only be detected behind a lossy dielectric wall when the

backscattered field from the wall is eliminated, in which case


5

the possibility for small target high-resolution imaging

becomes possible.

(a)

(b)

Fig.7 Simulated EM field distribution due to the phase-conjugating lens re-

focused on the target behind the wall (a) and field distribution in the dual half-

space (b). Dot shows the position of target behind the wall (a) and its

symmetric image in the dual half-space (b). Copyright the European

Microwave Association EuMA.

As shown in Fig. 8, in accordance with (2), the possibility

of scaling the image produced by a phase conjugating lens as

the frequency of pump wave is changed is illustrated, [24].

Fig.8 Image de-magnification using pump frequency higher than twice the

frequency of source signal. Original source distribution is represented by two

Hertzian electric dipoles of unequal amplitudes radiating at 2.4GHz and

separated by λ/3 in the transversal range, red line. The de-magnified image at

4.8GHz is shown in blue line. It can also be seen that object amplitude

properties are preserved.

©2010 IEEE. Reprinted, with permission, from IEEE Proceedings, [24].

Control of the focusing and displacement capabilities of the

lens result from amplitude and/or phase control of the

transmitted field is also, [25]. In addition the ability of the lens

to image from the near field into the far field without major

loss of resolution exists.

VI. SIGNAL MODULATION HANDLING

CAPABILITY

The possibility of an ultra thin phase conjugating lens

suitable for systems where amplitude, and or phase encoded

signals are required to be processed was studied in [26,27].

Here the characteristics associated with the transfer of

amplitude and phase modulated signals through a phase

conjugating lens was established and it was shown that

multiple amplitude or phase modulated dipole sources can be

distinguished in the far field with subwavelength resolution

without the necessity for numerical post-processing of the

received data in order to separate channel information from

very close proximity sites.

Free space transmission of an on-off modulated sinusoidal

signal through a phase-conjugating lens was examined in [28]

using a combined time/frequency domain approach. The on-

off keyed (OOK) signal was generated by a dipole antenna

located in the far-field zone of the lens. We demonstrated that

electromagnetic interference between antenna elements

creates spatially localized areas of good-quality reception and

zones where the signal is significantly denigrated by

interference. Next, it was shown that destructive interference

and packet de-synchronization effects critically depend on bit

rate.

VII. SPATIAL DATA ENCRYPTION

Recently it has been shown that in order to provide higher

levels of security in wireless transmissions, a physical layer

phenomenon known as spatial encryption may be of value,

[29]. Here the returned phase conjugated wavefronts that are

received at points more than a few wavelengths from the

originating pilot signal location will be spatially de-correlated.

Consequently, the reconstructed data packets at all points

except close to (approximately 2λ) from the pilot position will

be garbled and hence would be very difficult to recover.

The effect has also been shown to occur after signal

transmission through a phase-conjugating lens. The process

renders the signal unrecoverable unless it is passed through

another phase-conjugating lens. Spatial encryption of a BPSK

modulated signal radiated by a dipole-like antenna and

transmitted through a phase-conjugating lens, and through a

system of such lenses, in free space was theoretically studied

in [30]. When the phase-conjugating lenses were modulated

with a phase encoded pump sequence applied at the same rate

as the BPSK information signal, spatial encryption in the

space between the two phase conjugating lenses was

observed. Importantly, the signal can only be decoded in well

defined spatial regions after passing a second phase-

conjugating lens, Fig. 9.


6

-8 -6 -4 -2 0 2 4 6 8

6

8

10

12

14

16

18

20

x (λ)

z (λ)

41

50

58

BER (%)

(a)

-6 -4 -2 0 2 4 6

14

16

18

20

22

24

x (λ)

z (λ)

0

29

57

BER(%)

(b)

Fig.9 Spatial averaged BER distribution for pseudo random BPSK signals.

(a) In the space between the lenses; (b) In the space after the second lens.



VIII. CONCLUSIONS

It has been shown that for far field imaging applications the

spatial variation of the wavefront to be imaged/negatively

refracted at the PC lens plane is smooth, of the order of a half-

wavelength. Consequently, the spacing’s between the lens

elements can be of the same order and therefore the lens can

be built using classical microwave circuit components

configured for phase-conjugation operation. This approach

leads to high phase-conjugation efficiency.

In the near-field imaging scenario the spatial sampling rate

is of the order of one tenth of a wavelength or less so at the

present level of circuitry miniaturization lenses cannot be

easily constructed using microwave circuitry. The means for

realisation here is to use lumped nonlinear components

embedded into wire elements. The major drawback of this

approach is the intrinsically low phase-conjugation

conversion efficiency. Developing methods for increasing

efficiency in this class of structure is a suggested topic for

future research.

With the lens arrangements described herein, sub-

wavelength imaging and image manipulation as well as target

location are all possibilities in the near field without lens

augmentation. While in the far field the PC lens must be used

in conjunction with complementary pairs of scattering

elements place in the object and image spaces of the lens.

Finally, we have shown that the deployment of phase-

conjugate lenses in pairs can be used as a novel means for

securing encoded wireless transmissions directly in the

physical layer.

The work presented in this paper shows that phase-

conjugating lenses offer the prospect for access to advanced

applications in radar, communications, imaging and security.

The area still needs much work to be done and it is hoped that

this paper will act as a catalyst for other workers to engage

with this topic.

ACKNOWLEDGEMENTS

This work has been funded by UK Engineering and Physical

Research Council EPSRC, the European Space Agency, ESA,

EU FP7, the Queens University Belfast, the Leverhulme Trust

and the N. Ireland Department of Education and Learning.

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2012.

Vincent Fusco currently holds a personal chair

in High Frequency Electronic Engineering at

The Queen’s University Belfast (UK). His

research interests include active antenna and

front-end MMIC techniques. He is head of the

High Frequency Laboratories at QUB.

Professor Fusco has published over 450 scientific papers in

major journals and in referred international conferences. He

holds several patents and has contributed invited chapters to

several books. He is a Fellow of both the Institution of

Engineering and Technology and the Institute of Electrical

and Electronic Engineers. In addition he is a Fellow of the

Royal Academy of Engineers and a member of the Royal Irish

Academy. In 2012 he was awarded the IET senior

achievement award the Mountbatten Medal for services to UK

Electronics.

Oleksandr Malyuskin received the MSc

degree in Radiophysics and Electronics and

the PhD degree in Radiophysics from

Kharkiv National University, Ukraine, in

1997 and 2001 respectively. He joined the

Institute of Electronics, Communications

and Information Technology, Queens University Belfast, in

March 2004 as a Postdoctoral Research Fellow involved in the

development of novel composite materials for advanced EM

applications. His research interests include analytic and

numerical methods in electromagnetic wave theory,

characterization and application of complex and nonlinear

materials, antenna arrays and time reversal techniques. Dr

Malyuskin has published over 50 scientific papers in major

journals and in refereed international conferences, and has

acted as a reviewer for the IEEE publications.


8

Editorial Comment

Sub-wavelength imaging, with a goal to beat the diffraction limit, remains the ultimate challenge to the EM community—the

“holy grail” of high resolution imaging, so-to-speak. Techniques based on the use of Metamaterials (DNG or double-negative

materials), Transformation Electromagnetics (T-EM), and a plethora of other approaches have been proposed for this purpose.

In this paper the author proposes a novel and alternative approach, based on an extension of the classical “Phase Conjugation”

technique to address the imaging problem, which remains of considerable interest, despite a flood of publications on this topic

in recent years.

Documents

Imaging Using Phase Conjugation Lens Techniquesphase conjugation technology can be advantageous in multipath rich environments. In multipath environments the numerical aperture of