Hindawi Publishing CorporationAdvances in Optical TechnologiesVolume 2013, Article ID 738427, 8 pageshttp://dx.doi.org/10.1155/2013/738427

Research ArticlePhotonic Processing for Wideband Cancellation and SpectralDiscrimination of RF Signals

David M. Benton

L-3 TRL Technology, Unit 19 Miller Court, Severn Drive, Tewkesbury, Gloucestershire GL20 8DN, UK

Correspondence should be addressed to David M. Benton; david.benton@l-3com.com

Received 9 July 2013; Revised 16 October 2013; Accepted 16 October 2013

Academic Editor: Augusto Beléndez

Copyright © 2013 David M. Benton. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Photonic signal processing is used to implement common mode signal cancellation across a very wide bandwidth utilising phasemodulation of radio frequency (RF) signals onto a narrow linewidth laser carrier. RF spectra were observed using narrow-band, tunable optical filtering using a scanning Fabry Perot etalon. Thus functions conventionally performed using digital signalprocessing techniques in the electronic domain have been replaced by analog techniques in the photonic domain. This techniquewas able to observe simultaneous cancellation of signals across a bandwidth of 1400MHz, limited only by the free spectral range ofthe etalon.

1. Introduction

Photonic signal processing offers a new paradigm for pro-cessing high bandwidth signals and opens up possibilities fordirectly processing signals that are modulated onto an opticalcarrier. The ability to process and manipulate ultrawidebandsignals enables high-resolution, reconfigurable processingof potentially the entire RF spectrum of signals. It is thispotential that has received a lot of attention over the past fewdecades [1, 2] and is suitably demonstrated through devicessuch as wideband adaptivemicrowave filters enabled throughcoherence and phase control [3]. Photonic technologies area natural source for delivering increased bandwidth, butalso the low loss of fibre optic transmission systems hasseen developments in transmitting Radio over Fibre (RoF)and antenna remoting [4, 5]. As requirements for increaseddata bandwidth develop and as spectral densities increase,with congestion becoming an issue, the need for ever morepowerful digital signal processing (DSP) is a constant driver.This has inevitable consequences for size, weight, and power(SWaP) considerations, especially in RF signal monitoringand characterisation equipment. With the RF signal in pho-tonic form and the inherent bandwidth benefits that ensue,there is a natural opportunity for implementing analog signalprocessing (ASP) techniques and making the processing aninherent part of the optical link [6].

Signal cancellation is conventionally implemented byengineering a version of the target waveform that is matchedin amplitude but 180∘ out of phase (negative feedback) suchthat the interference of the target and engineered waveformsresult in cancellation. This approach can be performed withanalog or digital signals but is likely to be limited in itsoperational bandwidth by frequency dependent phase shifts.Photonic carriers modulated by RF signals are not limitedby these frequency dependent phase shifts in circuitry andhence can operate across a much wider bandwidth. Photonicsignal processing (the manipulation of light waves ratherthan digitised signals) can be used to cancel out commonwideband RF signals enabling weaker signals to be identified.Whilst cancellation is common in photonic signal processingit has tended to be targeted at sideband removal [7–10].Suppression of modulation signals in photonic systems withsome specific examples of signal cancellation was shownthrough inversion in an optical amplifier [11]. Single sidebandsuppression is a common technique in which the signal ismade to interfere with a phase shifted version of itself, helpingto remove the power residing in the (unmodulated) carriercomponent.

There have recently been reports of photonic based RFcancellation systems that claim impressive levels of cancel-lation [12–15], typically 40 dB for broadband signals and a

2 Advances in Optical Technologies

very impressive 70 dB for single tones. These systems repr-esent the current state of the art in photonic cancellationbut have significant differences from the system discussedin this paper. Applications of this technique have focussedon removal of cosite interference where a close proximitytransmitter will pose significant problems for a receiver,particularly relevant where jammers are being used andcan overwhelm a receiver, significantly reducing its abilityto observe weak signals. However, the pairwise nature ofsignal generation for cancellation does not specifically requireone signal to be the reference to be removed. Where thetwo signal sources are independent cancellation will seek toreduce signal contributions that are common to both sources.Conversely signal contributions unique to one source onlywill be unaffected and can emphasise the differences betweenthe two sources, which can help with signal gradiometry andsource location. In this paper photonic processing techniques(equivalent to ASP) are implemented to demonstrate theproof of principle that not only the signal cancellation butalso spectral analysis across a wide bandwidth is attainableby optical means without significant DSP.

2. Photonic Processing andOptical Cancellation

The cancellation of signals common to two independentsignal sources, such as two antennas, can be implemented bymodulating the RF signal from each antenna onto an opticalphase modulator, each incorporated into one arm of a MachZehnder interferometer (MZI) and fed from a common laser.Conventional MZI modulators are widely available but areused for applications such as single sideband suppressionwhere only a single input signal is required and the outputis amplitude modulated. Using separate phase modulators ineach arm allows independent signals to be combined andindependent phase control is available for each signal, priorto coherent combination.

The simplest demonstration is where a phase shift of 𝜋is imposed upon one of the modulated laser fields by theapplication of a bias voltage and a photodiode detector canbe used to observe the resulting intensity after the two armsare recombined.This setup is shown schematically in Figure 1for the simplest case.

An electrooptic modulator subject to a sinusoidally oscil-lating RF electric field of modulation frequency 𝜔

𝑚gives rise

to an output field consisting of a series of sidebands centredaround the laser carrier frequency represented by (see e.g.,[16])

𝐸 (𝑡) = 𝐸0

{

∞

∑

𝑘=0

𝐽𝑘

(𝛿) cos (𝜔 + 𝑘𝜔𝑚

) 𝑡

+

∞

∑

𝑘=0

(−1)𝑘

𝐽𝑘

(𝛿) cos (𝜔 − 𝑘𝜔𝑚

) 𝑡 } ,

(1)

where 𝐽𝑘(𝛿) represents a 𝑘th order Bessel function and 𝛿 is

a modulator characteristic parameter. In the case above twomodulated fields 𝐸

1(𝑡) and 𝐸

2(𝑡) are produced in eachmodu-

lator, respectively, and then combined.Where onemodulator

Laser 2:2 fibre

RF source 2

RF source 1

Detector

DC voltage

splitter

Figure 1: A schematic diagram for observing common modecancellation in the simplest case.

has a 𝜋 phase change added to the carrier frequency 𝜔, thenall terms at frequency (𝜔+𝑘𝜔

𝑚) can be cancelled in principle.

In this arrangement all frequency components must be mea-sured through conventional sampling and spectral powersdetermined through the Fourier transform.

More generally the RF signals received at each modulatorwill have a phase difference, due, for example, to time of flightdifferences from source to antennas. The electric field exitingeach modulator can be represented in an ideal set up by

𝐸1

(𝑡) = 𝐸0cos (𝜔𝑡 + 𝛿 sin (𝜔

𝑚𝑡 + 𝜃)) , (2)

𝐸2

(𝑡) = 𝐸0cos (𝜔𝑡 + 𝜙 + 𝛿 sin (𝜔

𝑚𝑡)) , (3)

where 𝜃 is the signal phase offset between the received signals,𝜙 is the optical phase offset applied to the carrier by themodulator, and each modulator is assumed to receive thesame optical amplitude𝐸

0. After application of trigonometric

identities and ignoring harmonic terms above 𝑘 = 1 we canwrite for modulator (1):

𝐸1

(𝑡) = 𝐸0

[𝐽0

(𝛿) cos (𝜔𝑡) + 𝐽1

(𝛿) cos ((𝜔 − 𝜔𝑚

) 𝑡 − 𝜃)

−𝐽1

(𝛿) cos ((𝜔 + 𝜔𝑚

) 𝑡 + 𝜃)] .

(4)

Similarly from modulator (2),

𝐸2

(𝑡) = 𝐸0

[𝐽0

(𝛿) cos (𝜔𝑡 + 𝜙) + 𝐽1

(𝛿) cos ((𝜔 − 𝜔𝑚

) 𝑡 + 𝜙)

−𝐽1

(𝛿) cos ((𝜔 + 𝜔𝑚

) 𝑡 + 𝜙)] .

(5)

The amplitudes from each modulator are combined, withone arm experiencing a 𝜋 phase shift (due to being a MZI).

In the simple example above involving Nyquist samplingof the detector signal, the amplitude at the modulationfrequency will be observed through the mixing within thedetector between the modulation signal and the unmodu-lated carrier. Whilst this provides coherent gain to increasethe signal amplitude, it prevents direct comparison of thesignal frequencies from each source and is prone to variationas the two carrier components being combined can becancelled independently from the modulation signals as thecarrier phase is varied. It is also possible that a single sourceof modulation in only one modulator can appear to becancelled solely through its phase difference with the carrier.To overcome this, the modulation components must be

Advances in Optical Technologies 3

DAQ

Optical

Fibre

RF source 2

RF source 1Phase modulators

Bias tee

RF splitter

Electrical connectionFibre optic connectionCoil of fibre

Offset voltage

Detector signal

DetectorData acquisition

Scanning etalon

splitter/combiner

Fibresplitter/combiner

isolator

and control system

Single frequencylaser 1550 nm

Etalon scancontroller

Experimental observations

Figure 2: System setup including a scanning Fabry Perot etalon.

separated from the carrier. Separating the carrier frequencyfrom the sidebands can in principle be achieved throughdispersion, such as using a diffraction grating. However, amodulation component of 10MHz has a frequency differenceof only 1 part in 107 from the unmodulated carrier and wouldthus require an impractical propagation distance before themodulation component could be spatially separated from thecarrier. Separation of the carrier andmodulation componentsis best achieved through filtering. The Fabry Perot etalon(FPE) is in optical terms (though not in RF terms) a highresolution tunable filter, formed of two reflective surfaces(mirrors) accurately separated by a known distance [17]. Thetransmission through the filter can be tuned by adjustingthe spacing between the mirrors and the filter bandwidthwhich is determined by the level of reflectivity of the mirrors.FPEs with a bandwidth of 10MHz are commercially availableand capable of discriminating between the laser carrier andmodulation sidebands. A photodiode detector placed afterthe FPE measures the intensity being transmitted and theparticular mirror separation during a scan determines thefrequency to which this intensity relates. Thus the spectralcharacteristics of the modulation are measured by scanningthe FPE filter not by rapid temporal sampling and processing.The spectral bandwidth limitations are those of the FPE andare determined by the free spectral range which can be 10sof GHz. It is also convenient to observe the intensity in boththe positive and negative sidebands if required.Thus spectralcharacteristics across an ultrawide bandwidth can be accessedwithout recourse to very high speed DSP.

After filtering with the FPE the observed intensity ineach sideband arises from the time average of the square ofthe total amplitude from both modulators. In the positive

sideband𝜔+𝜔𝑚, the observed time averaged intensity ismade

up of the positive sideband contributions in (4) and (5):

⟨𝐸 (𝜔 + 𝜔𝑚

)2

⟩ = ⟨𝐸2

0

(−𝐽1

(𝛿))2

× [cos ((𝜔 + 𝜔𝑚

) 𝑡 + 𝜃)

+ cos ((𝜔 + 𝜔𝑚

) 𝑡 + 𝜙 + 𝜋)]2

⟩

= 𝐸2

0

𝐽1

(𝛿)2

⟨1 − cos (𝜃 − 𝜙)⟩ .

(6)

Similarly for the negative sideband 𝜔 − 𝜔𝑚,

⟨𝐸 (𝜔 − 𝜔𝑚

)2

⟩ = 𝐸2

0

𝐽1

(𝛿)2

⟨1 − cos (𝜃 + 𝜙)⟩ . (7)

Thuswith a suitable choice of carrier phase offset𝜙, frequencycomponents common to both modulators can be minimisedin one or both of the sidebands. Hence the “processing”of cancellation and spectral transform are achieved throughonly optical means.

3. Experimental Observations

An experimental setup was constructed using commerciallyavailable optical fibre based components and is shown inFigure 2. A narrow linewidth laser (100KHz) operating at1550 nm with up to 40mW of power was split into two armsusing a 2 : 2 single mode fibre splitter, each of which wasconnected to a fibre coupled electrooptic phase modulator.The modulated outputs from the phase modulators wererecombined with the use of a 2 : 1 splitter/combiner. The out-put from the recombiner was collimated and then focussed

4 Advances in Optical TechnologiesPh

ase o

ffset

var

ying

with

tim

e

Carrierfrequency

+400 MHzcommon

signal

+500 MHzuniquesignal

−500 MHzuniquesignal

−400 MHzcommon

signal

Figure 3: A time evolving spectral plot (waterfall plot) showing pos-itive and negative sidebands around the central carrier frequency. A400MHz signal is common to both modulators whilst a 500MHzsignal is present in only one modulator and is unaffected by phasechanges.

into a scanning Fabry Perot etalon (FPE). The transmittedoutput intensity was measured with an amplified photodiodesampled with an ADC within a data acquisition unit (DAQ).Data was collected and processed using a LabView program.RF signals were supplied from a signal generator and directedto each modulator via a splitter. A DC voltage was controlledfrom the LabView program and applied to one modulatorvia a bias tee. The LabView program monitored the spectralamplitude at the signal frequency as the DC voltage wassystematically varied thereby varying the relative carrierphase between the two arms.

A scanning FPE with a free spectral range of 1.5 GHz anda finesse of 100 was incorporated into the system. This waschosen primarily to give a reasonable compromise betweenbandwidth (wide in RF terms), resolution (poor in RF terms),and physical size. Whilst significantly higher finesse etalonscould be used they are large and cumbersome devices notwellsuited to use outside of the laboratory.Thus for any system tobe widely useful in the real world, size matters. The etalonscan was set to cover a spectral range of 750MHz either sideof the laser carrier frequency so as to prevent confusion withsidebands from the neighbouring free spectral range; thus theeffective spectral range is 750MHz.The scan controller cycledthe etalon spacing at a rate of 100Hz and a detector followingthe etalon measured the spectral intensity in relation to thefilter position. The RF signal amplitude spectral componentsare related to the optical amplitude seen by the detector. Thefrequency is determined by the filter position and not byany temporal modulation; thus the spectrum can be obtainedwith a very low rate sampler, whilst covering a wide spectralrange

The detector was sampled at a rate of 10 kSps and relatedto the scan position using timing gates issued from theetalon scan controller. A time evolving spectral plot (waterfallplot) could be produced to examine the evolution of spectralamplitudes with time and hence with applied voltage (phase).

A common signal at 400MHz (5 dBm) was applied to bothmodulators via a set of splitters. Another “unique” signal at500MHz was applied to just one of the modulators. The plotof Figure 3 shows how the amplitudes of the two signals varywith time as phase changes. In this case a step change wasmade to the applied voltage and the system was then left tostabilise. The phase varied slowly with time due to thermaleffects and the common 400MHz signal is affected by thisin both sidebands. The carrier frequency amplitude is alsoaffected by this phase drift, but the unique 500MHz signalremains unaffected, thus demonstrating that signal present inonly one arm can be discriminated from pervasive commonsignals.

Some characteristics of this plot need explanation. Firstlythe upper and lower sidebands at 400MHz are out of phasein their response to the phase change. In this case this arisesfrom a difference in the length of the cables connecting thesignal generator to the modulators equivalent to a time offlight phase difference in the modulation signal. Secondlythe carrier power is cancelled at a different phase to thesidebands. This arises due to a lack of polarisation definitionbefore the laser light enters the modulators. Modulationoccurs predominantly for one polarisation state within themodulator and withoutmatching the input polarisation thereexist two “modes”—one modulated and one unmodulated—in the output field.The coherent addition of the unmodulatedcarrier mode and the modulated (𝐽

0(𝛿)) carrier mode results

in a carrier field with an offset phase relative to the sidebands.This situation will be rectified in future with the use ofmodulatorswith integral polarisation stages.Nevertheless theproposition that common mode signals can be cancelled isadequately shown here. During the course of these investi-gations it was observed that the phase applied to the carrierwas not linear with applied voltage. This was determined tobe due to ohmic heating in the modulator devices, whichare impedance matched for use at 10GHz.The thermal effectupon the refractive index of the modulator material results ina nonlinear phase response, as outlined in the appendix.

To demonstrate that this cancellation can be carriedout across a wide instantaneous bandwidth a programmablesignal generator was used to repeatedly scan the commonmodulation frequency in steps of 20MHz between 100MHzand 600MHz, whilst a unique frequency of 500MHz wasmaintained in one of the modulators. The offset voltagewas then adjusted for maximum suppression of the com-mon signal. In this case the cable length connected to themodulators was matched so that no frequency dependentmodulation arising from the RF offset phase was present.The data showing the effect of common signal suppressionacross a 500MHz bandwidth is shown in Figure 4 where thecancellation level here is 11 dB across the entire frequencyrange simultaneously. In this case simultaneous cancellationoccurs due to zero relative phase (𝜃 = 0) of the signals ateach modulator; thus (6) and (7) are minimised for the samecarrier phase.

The amount of cancellation seen here is limited due toa number of contributions. In particular the central carrierfrequency is many orders of magnitude more intense thanthe sidebands and its tail adds noise to the sideband spectral

Advances in Optical Technologies 5

200 400 600

1

2

Frequency (MHz)

Phot

odio

de si

gnal

(V)

No cancellation

Tim

e (10

0 ms s

teps

)

0

2

4

6

(a)

200 400 600

1

2

Frequency (MHz)

Phot

odio

de si

gnal

(V)

With cancellation

Tim

e (10

0 ms s

teps

)

0

2

4

6

(b)

Figure 4: Data plots showing one sideband with a frequency scanning signal in both modulators and unique signal at 500MHz in only onemodulator (a). Simultaneous cancellation of common mode signals across a 500MHz bandwidth can be seen in the data on (b).

locations. Residual signal can be seen in the suppressed dataconfirming that cancellation is not complete. The lack ofpolarisation stage before the modulators leads to differencesin the amplitude of the modulated mode which will limit theamount of cancellation that is possible.This can be addressedsomewhat by variable attenuators placed after themodulatorsbut this leads to a reduction in overall signal. The isolationoffered by the FPE is also imperfect and this adds to thenoise level. Modelling has also exposed that the cancellationlevel is very sensitive to the precise amount of phase offsetapplied. In this particular case the voltage step resolutioncorresponded to a phase change of around 0.5∘ which wouldlimit the cancellation level to 30 dB and hence clearly othercontributions were the dominant limitation to the amountof cancellation achieved. Whilst the demonstrated level ofcancellation is a little disappointing it is valuable whenconsidering that this system has implemented the dual rolesof cancellation and spectral transform without any recourseto high speed sampling or DSP.The cancellation system setupapplies equally across a very wide bandwidth, limited here bythe free spectral range of the FPE, but in principle can operateacross the bandwidth of the modulator. Only an adjustmentofmodulator offset voltage is required to tune the cancellationfor any given frequency and offset signal phase. Cancellationacross a range 100–1500MHz is shown in Figure 5 wherehigher frequencies are seen entering from right to left andoriginate from a neighbouring spectral order. There is much

potential for improving the performance of this system insubsequent development.

4. Sideband Behaviour

Both upper and lower sidebands can be observed (as seenin Figure 3) and the behaviour of the spectral power in eachsideband is dependent upon the relative RF signal phasedifference in the two modulators and the carrier phase. Theunique signal is however unaffected by the carrier phase andtherefore cancellation of common signal can be observed inwhatever sideband is most beneficial.

If each modulator is subject to an RF signal obtained viaan antenna in a general setting, the distribution of sourcesin the local environment is likely to be uncontrollable. Thereceived signals will then be subject to a phase differencedependent upon the signal frequency and the spacing of thereceiving antennas. Thus cancellation will require a carrierphase setting specific for that source. It can be seen from (6)and (7) that, whatever the phase difference 𝜃 of the modula-tion signal, a value of carrier offset phase can be chosen thatwill result in cancellation of that modulation signal in eithersideband. This can be equivalently seen when a mismatchin cable lengths between signal generator and modulators isintroduced, which introduces a frequency dependent phaseshift. A cable of length 1m was introduced before one

6 Advances in Optical Technologies

Frequency (MHz) Frequency (MHz)

(a) (b)

With cancellationNo cancellation

0

2

1

0

2

1

600400200 600400200

Unique signal at 600 MHz

100–750 MHz 100–750 MHz

750–1500 MH

z

750–1500 M

Hz

Tim

e (10

0 ms s

teps

)

Tim

e (10

0 ms s

teps

)

Figure 5: A wideband frequency scanning signal into both modulators with a unique frequency at 500MHz. Time increases down thediagram and frequencies 100–750MHz proceed left to right, whilst 750–1500MHz from neighbouring spectral order proceed right to left.Cancellation is demonstrated in (b).

−0.5

0

0.5

1

1.5

2

−700 −500 −300 −100 100 300 500 700

Frequency (MHz)Measured sideband intensityPhase dependent envelope

Figure 6: Frequency dependent sideband intensity variations inupper and lower sidebands for a fixed path length difference en-route to the modulators.

modulator. The frequency dependent phase difference 𝜃(𝑓)is then

𝜃 (𝑓) =

𝑑𝜀𝑟

𝑓

𝑐

, (8)

where 𝑑 is the path difference and 𝜀𝑟is the relative permit-

tivity of the cable. Data was captured encompassing bothsidebands where a sequentially varying frequency input waspresented to the modulators. The strong, saturated centralcarrier component was removed from the data by fittinga Lorentzian lineshape (with a half-width of 1.9MHz andamplitude of 7592). Frequency calibration was carried outwith a linear fit to each sideband independently.The envelopeof the sideband data was then modelled using the expectedfrequency dependent phase and is shown in Figure 6. In thiscase the modelling revealed that the carrier offset phase wasset to 60∘, which could not be determined independently dueto the thermal effects upon the modulators.

5. Improvements and Extensions

Subsequent developments have shown that sharing the offsetvoltage across both modulators in a push-pull configura-tion improves stability significantly for two reasons. Firstlywhilst the electrooptic phase change is parity dependent, thethermal phase change is not; hence the thermal effects inboth modulators have a similar size and the differential effectupon the output phase from the pair of modulators is muchreduced. Also because the magnitude of the applied voltageto each modulator is half the required voltage, the powerdissipated in each modulator is reduced by a relative factorof 4. A relative test applying a 2V offset change (from 0V)was applied comparing application to a singlemodulator withapplication across the pair. This has seen the thermal phasedrift reduced from 4∘/s when applied to a single modulatorto 0.8∘/s in a push pull-configuration, with the settling timereduced from 200 s to 50 s.

In this paper the intended application has been thecomparison of signals from two separate antennas, withthe capability of removing signals common to both. Inother photonic cancellation work [12, 13] the usage has beenpredominantly removing a known transmission signal whichcan be easily obtained and used to provide the feedbackreference signal. Using 2 signals from spatially separatedantenna would clearly introduce a signal dependent phaseoffset which is related to the source location relative to theantenna and is the source of the 𝜃 term in (6) and (7).Therefore to observe cancellation effects for any particularsignal, the carrier phase offset must be adjusted and itis straightforward to conceive of capturing spectra whilstscanning the carrier phase. Indeed given the uncontrollablenature of source locations in the real world, it is necessaryto make measurements with at least 2 phase values in orderto observe changes in the amount of cancellation takingplace.These two measurements should differ by 180∘ to allowthe possibility of maximum and minimum cancellation to

Advances in Optical Technologies 7

be observed. Knowing the source frequency, the separationof the receiving antennas and relative phase obtained fromcomparing the sideband strengths allows two possibilitiesfor the angle of arrival to be determined and a measureof source location to be performed. Unambiguous sourcedirection finding would require 3 receivers. Preliminaryattempts have shown an angle-of-arrival influence upon thesideband strengths but this requires more investigation anddevelopment.

6. Conclusion

This work has demonstrated the basic principle that photonic(analog) processing can be used to implement widebandsignal cancellation between two signal sources modulatedonto coherent laser carriers using phase modulation. Furtherto this photonic processing can additionally be used to imple-ment frequency spectrum generation across an ultrawidebandwidth without recourse to high speed sampling, thusreplacing the digital signal processing required to performa Fourier transform. In the case given here filtering is usedto separate the sidebands from the carrier in order thatunambiguous cancellation effects can be observed, but thisis due in part to an inadequacy of the phase modulatorsused here. In principle significant carrier cancellation canalso take place which will help in reducing noise in the finalfiltered output by reducing the height of the Lorentzian tailof the residual carrier. These are improvements that can beincorporated in future developments, all of which shouldhelp to increase the level of cancellation observed at theoutput detector.The system is suitable for incorporation ontoan integrated waveguide system which would significantlyreduce the system size and complexity.The current limitationto the system performance is the Fabry Perot etalon wherethe finesse of 100 limits the isolation between carrier powerand sidebands, and the FSR is a limit to the unambiguousbandwidth that can be observed. Etalons with higher finesseand FSR are available but are large, bulky, and cumbersomeand hence not well suited to usage outside of laboratoryconditions. There are clearly a number of developments that,when implemented, could lead to significant improvementsin performance and would form part of a developmentprogramme. Nevertheless this is step towards analog signalprocessing for spectral analysis.

This proof of concept has shown that it is feasible toconsider the general case of common mode cancellationof signals across a very wide bandwidth, rather than justthe specific case of a cancellation of a single known signal.All that is required is the control of a single voltage levelapplied to a phase modulator enabling phase scanning andthe subsequent observation of the spectrum will reveal therelative phases of common signal components. Further tothis there is significance in the observation that signals thatare not common to both receivers are unaffected by thecancellation process. This, coupled with observations of thesideband intensities on the positive and negative sides, canreveal information about the spatial distribution of commonsources. Converting RF signals into the photonic domain can

therefore offer attractive benefits in terms of reducing DSPrequirements and acquiring signal source information.

Appendix

The phase offset Δ𝜙 from an electrooptic modulator has 2contributions, the electrooptic effect Δ𝜙EO and a thermaleffect Δ𝜙

𝑇:

Δ𝜙 = Δ𝜙EO + Δ𝜙𝑇 =2𝜋𝑓𝐿

𝑐

(Δ𝑛EO + Δ𝑛𝑇) , (A.1)

where Δ𝑛 is a change in refractive index, 𝑓 is the appliedfrequency, 𝐿 is the length of the modulator, and 𝑐 is the speedof light.

The electrooptic effect gives a refractive index change:

Δ𝑛EO =𝑛3

0

𝑟 𝑉 ⋅ 𝐿

2𝑑

, (A.2)

where 𝑟 is the electrooptic tensor value for the material, 𝑉 isthe applied voltage, 𝑑 is the electrode gap, and 𝐿 is the lengthof the crystal.

The change in temperature Δ𝑇 of the device is related tothe amount of energy 𝑄 deposited through the well-knownrelation:

𝑄 = 𝑚𝐶Δ𝑇, (A.3)

where 𝑚 is the mass of the device and 𝐶 is the specific heatcapacity.

The energy deposited is proportional to the square of theapplied voltage 𝑄 ∝ (𝑉2/𝑅) leading to

Δ𝑛𝑇

=

𝑑𝑛

𝑑𝑇

Δ𝑇 =

𝑑𝑛

𝑑𝑡

𝜅

𝑉2

𝑚𝐶𝑅

, (A.4)

where 𝜅 is a constant.Thus the phase change has the form

Δ𝜙 =

2𝜋𝑓𝐿

𝑐

(

𝑛3

0

𝑟33

𝑉 ⋅ 𝐿

2𝑑

+

𝑑𝑛

𝑑𝑡

𝜅

𝑉2

𝑚𝐶𝑅

) . (A.5)

For LiNbO3

𝑟33= 30 pm/V, 𝑑𝑛/𝑑𝑇 = 37 × 10−6/∘C.

This form will have the effect of reducing the spacingbetween consecutive voltages providing a 𝜋 phase offset. Theprecise device characteristics are not known and so accuratemodelling cannot be performed. However, estimating theelectrode gap to be of order 10 𝜇m, the EO component isof the order 𝑛3

0

× 10−7 which is similar in scale to 𝑑𝑛/𝑑𝑇.This broadly agrees with the voltage squared dependenceobserved, but the net result is that thermal effects causeslowly varying phase instability until thermal equilibrium isreached.

References

[1] A. J. Seeds, “Microwave photonics,” IEEETransactions onMicro-wave Theory and Techniques, vol. 50, no. 3, pp. 877–887, 2002.

8 Advances in Optical Technologies

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