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Suppression of Intermodulation Distortion in Phase-

Modulated Analog Photonic Links

Bryan Haas and Thomas E. Murphy

Laboratory for Physical Sciences and University of Maryland, College Park, Maryland USA,

20740. Tel: 301-935-3159, Email:bhaas@umd.edu

Abstract We describe and experimentally demonstratea technique to suppress the dominant in-band analogdistortion in an RF photonic link. The anisotropicelectrooptic coefficient of Lithium Niobate is exploited tomodulate orthogonally polarized fields. These fields arethen combined to null the third-order distortion. Thistechnique uses a single phase modulator, requiring noexternal bias or control, for a highly linear photonic

microwave relay. The link is limited by fifth-orderintermodulation distortion (IMD) instead of third-orderIMD. For many scenarios the added complexity ofheterodyne optical detection may be an appropriate cost togain simplicity at the remote end.

Index Terms distortion, heterodyning, intermodulationdistortion, phase modulation, polarization

I.INTRODUCTION

It has been shown that fiber optics can be an attractivetechnology for transmitting microwave signals in terms

of size, weight, power consumption, and power handlingcapability for relay links as short as fifty meters [1].Offsetting this potential is the third-orderintermodulation distortion (IMD) in a suboctave signal

created by the nonlinear modulation transfer functions indirect and external intensity-modulated schemes [1].Likewise, phase or frequency modulated links create

IMD similar to that of their intensity-modulated brethren[2] that is revealed when the signal is mixed with aphotonic local oscillator (LO) to produce an intensity

modulation that can be received by a photodetector.It follows that an optical transport link that can

minimize or eliminate or minimize IMD can be highly

advantageous over coaxial transmission. This has beenan area of research for over two decades, primarilyworking with more common intensity-modulated links.

There has been very little work with linearizing anglemodulated optical links reported in the literature. Oneadvantage of phase modulation is that the process ofheterodyne detection automatically downconverts thereceived signal to an intermediate frequency (IF) without

the need of an electrical mixer.Techniques for IMD suppression have included

cascading differently biased Mach-Zehnderinterferometric modulators in parallel or series to create

different transfer functions that cancel IMD in the third

order [3,4]. Similar efforts have used Y-branchmodulators [5], electrical predistortion [6], or even

combining direct and external modulation to suppressIMD [7]. A recent technique using phase modulationrelies on digital signal postprocessing to recover the

undistorted signal [8].The work of Johnson and Roussel [9,10] is particularly

germane to the technique used here. A single LithiumNiobate (LiNbO3) Mach-Zehnder modulator was

employed, but simultaneously using the differentmodulation efficiencies for TM and TE polarizationseffectively created two modulators with different transferfunctions that were set to oppose one another in third-order power.

II. IMD SUPPRESSION USING PHASE MODULATION

LiNbO3 exhibits an electrooptic coefficient r31 on theX (ordinary, or TE) axis which is approximately 1/3 ofthe r33 coefficient on the Z (extraordinary, or TM) axis.

Ultimately this means that a given electric field inducinga phase shift on light polarized along the Z axis willsimultaneously impart 1/3 of the phase shift on any light

polarized in the X-direction.

Fig. 1. Phase modulator showing orientation of polarizationangles at input and output.

Our method leverages this anisotropy in a phase

modulator. Given a sinusoidal input microwave signal,the modulator output for a linearly polarized inputoptical carrier (but not necessarily aligned with either theZ or X axes) for the setup in Fig. 1 can be represented as

(1)

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where is the polarization angle relative to the TM axis, is the electrooptic ratio (approximately 1/3), is theoptical carrier frequency, is the microwave frequency,

and m is the TM modulation depth defined as

(2)

This phase modulation results in an infinite number of

sidebands governed by a Bessel function expansion. Theelectrical signal is then mixed with a local oscillator(LO) that is tuned close to the upper sideband. The

electrical bandwidth of the detector limits detection tothe upper sideband. The relevant terms in the phasemodulated signal can then be described by

(3)

The nonlinear components of the modulated signal arerevealed mathematically by expanding the Besselfunctions to the third order:

(4)

After the microwave signal is modulated onto the twopolarizations, the TM and TE fields are combined at the

output with a linear polarizer, at an angle such that the

fields in the third order are of equal and oppositeamplitudes. This causes the third-order portion of thesignal to be cancelled while not completely cancellingthe linear signal . This polarizer is set at an angle tothe TM axis, resulting an a final output of

(5)One can see that the third order terms can be

eliminated when

(6)

Solving for and gives the polarization angle

settings with which third-order IMD can be suppressed.One reasonable solution for this is to maximize the linearsignal amplitude, resulting in the solution

(7)

Increased linearity comes at a cost of decreasedmodulation efficiency. Most of the optical field will

need to be inserted on the TE axis, which is modulated

only 1/3 as strongly as light on the TM axis. Choosingthe polarization angles in accordance with Eq. (7) causes

the linear signal amplitude to decrease by a factor of 2/7,

or a power reduction of approximately 11dB. As will beshown, this decrease is more than made up for by theresulting increase in dynamic range.

III. THEORETICAL RESULTS

Fig. 2 plots the calculated output RF power versusinput RF power for the linear and largest IMD signals ina two-tone IMD test. The dashed lines are the expectedresult for conventional TM-polarized input and outputwhereas the solid lines are the expected result using thetechnique described above. Note that the linear signal

using this technique is decreased in power but thelimiting distortion is now a fifth-order product,increasing the overall range and useable modulation

power.

Fig. 2. Calculated two-tone IMD for conventional TMpolarized input and the linearized technique propsed here.

IV. EXPERIMENTAL SETUP

To access both the TM and TE axes of a singlemodulator, the modulator must be able to guide bothpolarizations. This requires a Titanium-indiffused

wavguide; Proton-exchanged waveguides do not guideTE light and cannot be used in this application.

An adjustable linear polarizer was placed at the inputof the modulator to vary the input optical field ratiobetween the axes. Another adjustable linear polarizerwas placed at the modulator output to recombine the two

separately modulated polarizations.The modulator itself was a standard Ti-indiffused Z-

cut LiNbO3 phase modulator designed for digital

operation up to 12.5 Gb/s. This was opened to exposethe crystal facets and enable freespace optical couplinginto and out of the waveguide. The measured V of the

modulator at 1GHz was approximately 4.25 and 13.0volts for TM and TE polarizations, respectively. The ratio was just under 1/3 and optimum polarization input

and output angles of approximately +/-78 degrees from

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the TM axis were calculated from Eq. 7. Sinusoidal

tones of 979.5 and 980.5 MHz were combined and inputto the modulator electrodes.

The output of this polarizer was heterodyne detected

using a LO that was frequency shifted from the signalcarrier by 1GHz. In this experiment the source laser

power was split to form the signal and LO paths, with theLO frequency generated by an acousto-optic shifter.This provided sufficient phase coherency withoutnecessitating the use of a true optical local oscillator.

V. EXPERIMENTAL RESULTS

Fig. 3 shows measured tone and IMD power forincreasing input powers for both the TM and mixedpolarization cases. For the TM case, IMD power rises

3dB for every 1dB increase in tone power, indicating that3

rdorder IMD is the limiting distortion product. The

mixed polarization case described here shows an increase

of 5dB IMD power for every 1dB increase in tone power.This reveals that 3

rd-order IMD is being suppressed and

that 5th-order IMD is now the limiting product.

Fig. 3. Received versus input RF power for both TM(dashed) and mixed (solid) polarizations. The upper pointswith slope = 1 are the linear signal powers while the lowerpoints are 3

rd- and 5

th-order IMD powers, respectively.

In order to clearly display IMD suppression in Fig. 4and 5, different input RF powers were used to keep theoutput tone power constant. The calculated difference inreceived tone and IMD power for the TM case in Fig. 4

was 38dB, matched by the actual results as shown in thespectrum analyzer trace in the figure. For the mixed-polarization technique in Fig. 5, the IMD products werenot detectable above the noise floor even when input RFpower was increased to match the original (TM case)tone power. Even though the system is being driven with

almost 10dB more input power, this result showsapproximately 10dB improvement in dynamic range forthis particular case.

Fig. 4. Experimental result for two-tone IMD test withstandard TM polarization. Tone-IMD delta is approximately -38dB.

Fig. 5. Experimental result for two-tone IMD test withmixed polarization technique. Input power is increased 10dB tokeep the fundamental tones at the same level, and IMDproducts have been suppressed to the noise floor.

The input polarizer angle, as predicted, wasapproximately 78 degrees. However, optimal IMDsuppression was obtained when the output polarizer

angle was very close to the TE axis, or almost a full 90degrees off the TM axis. Any of several factors maycontribute to this unexpected discrepancy. These can

include unexpected polarization-dependent loss (PDL) orcompensation for birefringent phase mismatch betweenTM and TE polarizations. This will be explored in

further experimentation.

VI.CONCLUSION

We have developed the concept and experimentallyshown that a single phase modulator can, with judicious

choice of input and output polarizations, suppress third-order IMD. This is done by canceling the modulatedthird-order fields, leaving fifth-order distortion as thedominant IMD product. Advantages to this technique

include a very simple and compact modulator with no

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requirement for external bias or any sort of processing or

control at a remote end.

ACKNOWLEDGEMENT

The authors wish to thank Dr. Timothy Horton of the

Laboratory for Physical Sciences for his help in theexperimental setup and insightful discussions.

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