with M the avalanche photodiode (APD) multiplicationfactor, R the receiver responsivity, PLO the local oscillatorpower, Ps the received signal power, a\H the shot noisevariance, a\H the thermal noise variance and x the APDexcess noise factor (0 < x < 1). With the LO power split intotwo equal parts, the corresponding terms for a POLSKsystem are

LOPS) m0 = -

a, = G0 = lM2+xa2SH + 2a2

THy2

Ps)

(3)

After inserting the optimal M value for each modulationscheme, eqns. 1, 2 and 3 are combined to yield

yPOLSK

IASK_ cy\\/2 + x (4)

The above formula is valid for the case of M > 1. When usinga PIN photodiode (M = 1) under the condition that a\H >o\H, eqn. 4 simplifies to

TPOLSK

IASK(5)

Note that the SNR is proportional to the square root of thesignal Ps, and therefore a gain in receiver sensitivity of 2 to3 dB with respect to ASK can be achieved.

Experiment: The transmitter and LO are 1-3 fim BH lasers ina 3-cavity configuration.6 Fig. 1 shows the experimental set-up(Fig. la) and a sketch of the polarisation states involved (Fig.16). The light of the transmitter laser LT is coupled throughtwo isolators and input at an angle of 45° to the modulator(A). The LiNbO3 phase modulator produces a phase shift nbetween the TE and TM modes which rotates the polarisationby 90° (Fig. 16) (B). The orthogonal states are maintainedduring transmission in a fibre.3-4 In front of 3dB monomodefibre coupler (CO), the Babinet-Soleil compensators (BS)adjust the signal and LO light, so the desired linear polarisa-tion states are obtained at the Foster polarisation beam split-ter (FBS) (C).

The beat signals with an intermediate frequency (IF) of1-5 GHz for each Ge APD are amplified, filtered, envelope-detected and then subtracted.

Results: The 560Mbit/s transmission was performed with anIF linewidth of approximately 20 MHz. Fig. 2 shows parts ofthe signal processing stages in the system. In Fig. la the '1 'and '0' signals (D, E) behind the IF bandpass filter of the twobranches are shown. The corresponding baseband signals afterthe envelope detectors (F, G) and the resulting output signal(H) after subtraction are given in Fig. 26.

We compared the POLSK and ASK systems by measuringthe minimum peak signal power required for a bit error rateof 10"9. The LO power was measured to be — 8dBm. At firstASK transmission was accomplished by using only onebranch and feeding the total local oscillator power to thesame branch by simply rotating the linear state of polarisationof the local laser. A minimum peak power at the fibre end,before the polarisation beam splitter, of — 30-5 dBm was mea-

Fig. 2 Signal processing

a ASK signals:fIF= l-5GHz, 56OMbit/s: D -»'0' ;£ -» ' l '6 Signals behind envelope detectors: F-»'O', G-* inverted '1 '

sured. Both signal branches were then employed and the pol-arisation state of the local laser was properly aligned. Now aminimum power of —33 dBm was achieved. Hence oneobserves a 2-5 dB improvement.

Although it has been demonstrated that a POLSK systemoutperforms an ASK system, the receiver sensitivity is still farfrom the desired shot-noise limit of approximately — 50 dBm.The main cause of the system degradation results from a noisypreamplifier. With the given local oscillator power, a veryhigh APD multiplication factor is necessary to overcome thisnoise source. From the photodiode specifications and theAPD bias voltage we estimate M ^ 80. This high multiplica-tion factor results in a power penalty in the order of 10 to12 dB.7 The additional discrepancy from the shot-noise limitcan be attributed to the phase noise, intensity noise and lossesassociated with the polarisation splitter. Losses in the bulkset-up of the polarisation beam-splitter can be avoided whenfibre-type polarisation splitters are used.8

Conclusion: The experiment demonstrated that the POLSKmodulation method improves the effective receiver sensitivityby 2 to 3 dB, as predicted by theory.

Acknowledgment: The authors wish to thank E. Patzak and P.Meissner for helpful discussions. This work was supported bythe Bundesministerium fur Forschung und Technologie of theFederal Republic of Germany. The authors alone areresponsible for the content.

E. DIETRICH 15th December 1986B. ENNINGR. GROSSH. KNUPKE

Heinrich-Hertz-Institut far Nachrichtentechnik Berlin GmbHEinsteinufer 37D-1000 Berlin 10, W. Germany

References

1 DAKIN, j . p.: 'Improvements relating to optical fibre communica-tion systems'. UK patent GB 2153176A, Aug. 1985

2 DAKIN, j . p., and PRATT, D. J.: 'Improved noninvasive 'fibredyne'highway based on polarimetric detection of strain in polarisation-maintaining fibres', Electron. Lett., 1985, 21, pp. 1224-1225

3 JEUNHOMME, L. B.: 'Single-mode fiber optics' (Marcel Dekker Inc.,New York, 1983)

4 MACHIDA, s., SAKAI, j . , and KiMURA, T.: 'Polarisation conservationin single-mode fibres', Electron. Lett., 1981, 17, pp. 494-495

5 PERSONICK, s.: 'Receiver design for digital fiber optic communica-tion systems, Part I', Bell Syst. Tech. J., 1973, 52, pp. 843-874

6 WENKE, G., PATZAK, E., and MEISSNER, P.: 'Reliable laboratory trans-mitter with submegahertz linewidth', Electron. Lett., 1986, 22, pp.206-207

7 ALBRECHT, w., ELZE, G., and GROSSKOPF, G.: 'Optical detectors inoptical wideband transmission systems' in BAACK, C. (Ed.): (CRCPress, 1986), Chap. 6, pp. 73-85

8 YOKOHAMA, I., OKAMOTO, K., and NODA, j . : 'Analysis of fiber-opticpolarizing beam splitters consisting of fused-taper couplers', J.Lightwave Technol., 1986, LT-4, pp. 1352-1359

GENERALISED SUBCOMPLEMENTARYSETS OF SEQUENCES

Indexing terms: Codes, Complementary sequences

The generalisation of the constructive technique for gener-ating the subcomplementary sets of sequences, previouslyintroduced by Sivaswamy, is presented. In such a manner,still more efficient pulse compression and spread-spectrumwaveforms can be designed.

Introduction: Subcomplementary sets of sequences, as definedby Sivaswamy,1-2 comprise two or more finite sequences ofequal length (2*po)> such that the sum of their aperiodic auto-correlation functions is zero for all shifts p > p0, minimum forp0 > p > 0 and maximum for p = 0.

422 ELECTRONICS LETTERS 9th April 1987 Vol. 23 No. 8

Sivaswamy forms his subcomplementary sequences bycoherent signal repetition of some waveform of duration pQ inthe prescribed manner.2 This basic waveform can be anywaveform of duration p0, for example rectangular pulse, linearFM or Barker code.

Equivalently, we shall consider that Sivaswamy's sub-complementary sequences are formed by weighting eachelement of some corresponding discrete sequence with thesame basic waveform of duration p0.

Here we generalise the Sivaswamy method for generatingthe subcomplementary sets of sequences such that discreteelements of some sequence are weighted with different basicwaveforms, but the elements with the same ordering numberin all sequences from the set are weighted with the same basicwaveform.

Also, it will be shown that the lengths of sequences bothfrom generalised and Sivaswamy's subcomplementary sets arenot restricted only to 2kp0 in general.

Mathematically, we represent a generalised sub-complementary set of sequences as the product of twomatrices:

(1)

(2)

s =

s =

c

s

X

So

N-

w,0

1,0

... s0>

... s^_

M-

\,M

1

_

-

1

C =-0,0 C0,M-

C N - l , 0 • • • C N - l , A f - l

»/Lt ~ iPo) =vffl ipo<t<(

0 elsewhere

DPc

(3)

(4)

Rows of the matrix 5 are generalised subcomplementarysequences, rows of matrix C are some discrete sequences(which will be discussed later) and elements of matrix W aresome basic waveforms with duration p0.

When all basic waveforms are equal, the matrix S reducesto Sivaswamy's subcomplementary set.

Construction of generalised subcomplementary sets: We shallnow prove that the necessary and sufficient condition for thematrix S to be a generalised complementary set is that thematrix C has orthogonal columns. Otherwise, for Sivaswamy'ssubcomplementary sets it will be shown that it is necessaryand sufficient that the matrix C is some complementary set ofdiscrete sequences.

The generalised subcomplementary set S can also be rep-resented as

S=\S,{j,t)\ i = 0 , l , . .

M- 1

sjU,t)= l,ctJwjLt-jf7 = 0

(5)

The sum Zip) of the aperiodic autocorrelation functions R,{p)of all the sequences from the set is (for shifts 0 < p < Mp0)given by

Z{p) =

^ 0 - PN-i r

. = 0 Jtit + p) dt (6)

where '*' denotes conjugation (for generality, we assumedcomplex, i.e. polyphase sequences34). We shall consider onlypositive time shifts because Zi—p) = Z*ip).

ELECTRONICS LETTERS 9th April 1987 Vol. 23 No. 8

For the exact evaluation of the above expression, we shallexpress the variable p through the variables p' and k such that

p = kpo + p' 0 < p' < p0 k = 0, 1, . . . , M - 1 (7)

Thus, substituting S,- from eqn. 5 and p from eqn. 7 into eqn. 6,we have

N - 1 M - l - *

= Z Z cuCTj,=0 j=0

o-

wf+kit)Wj(t + p') dt

0

N-l M-2-k

Z Z <jCUi=0 j=0

' } • wj+k+lit)wfit + p0 - p') dt

Interchanging summation and integration we have

Po-p'

Zip) = M Z I w*+kit)wM + p') dt7 = 0 J

0N - l

v V r r*ZJ i,j i.j + k

Z k7 = 0 J

(8)

M-2-k

+ Z h+*+i('KC + Po - P')+*+i(

AT— 1

X 2-i CtjCi,ji = 0

If the matrix C has orthogonal columns, i.e.

N - l

i = 0 '

(9)

(10)

it is obvious that Zip) equals zero for p > p0 (/c > 1).In the special case when all the basic waveforms are equal,

as is considered by Sivaswamy, Zip) can be expressed in theform

po-p'

Zip)= j w*it)wit + p') dt

0N-l M-l-k

X Z Z cuc*;+*;=0 j=0

\Mt)w*it + p0 - p') dt

0N-l M-2-k

x Z Z c*jciji = 0 / = 0

(11)

It is now easy to see that Zip) is zero for p > p0, if the matrixC represents some complementary set of N discrete sequences,i.e.

N - l M - 1 - *

Z Z> = o i=o

(12)

Of course, Zip) is also zero if C is a matrix with orthogonalcolumns. However, complementarity is a necessary and suffi-cient condition here, because any complementary set of dis-crete sequences has not to form a matrix with orthogonalcolumns, but the orthogonal set is always complementary.

Hence, we can deduce that Sivaswamy's subcomplementarypairs and sets can be generated by all known recursive andnonrecursive methods for the construction of complementarypairs and sets.3"6

423

Consequently, the length of sequences from Sivaswamy'ssubcomplementary sets is not restricted only to L = 2kp0. Inthe case when C represents a set of polyphase complementarysequences,34 or some binary complementary set,5 the lengthof sequences might be an arbitrary multiple of p0, while in thecase of binary complementary pairs L/p0 has to be even andexpressible as a sum of at most two squares.6

The length of generalised subcomplementary sequences canbe an arbitrary multiple of p0.

Finally, we wish to accentuate that, introducing multiplebasic waveforms in the generalised subcomplementarysequences, we have the possibility of minimising the combinedautocorrelation function Z{p) in the region 0 < p < p0. This isclear from the following expression for Z(p), which followsdirectly from eqn. 9 using condition expr. 10 and | citj | = 1:

Po-p

= NM'Z I wj(t)Wj(t + p) dtj=o J

0<p<Po(k = 0) (13)

If, for example, the basic waveforms wj(t), j = 0,1, ..., M — I,forms some (sub)complementary set of sequences of lengthL = Po = ^Poo> Z(P) is cancelled for all time shifts p > p00.Nevertheless, this will be also the case if the set of basic wave-forms consists only of two complementary basic waveformsthat are repeated an equal number of times.

The selection of the basic waveforms that are some ana-logue signals in general, for the minimisation of Z(p) in therange 0 < p < p0, has to be performed through computersimulation, because analogue complementary waveforms arenot known.1

Conclusion: In this letter generalised subcomplementary setsof sequences are introduced, and a general constructive tech-nique, based on orthogonal matrices, for generating such setsof sequences is presented. These sets, compared with Sivas-wamy's original subcomplementary sets, offer an additionalpossibility to reduce the autocorrelation and ambiguity func-tion sidelobes of waveforms for pulse compression radars andspread-spectrum systems.

24th February 1987B. M. POPOVICS. Z. BUDlSlNInstitute of Applied PhysicsBulevar Lenjina 165 b11070 Novi Beograd, Yugoslavia

References

1 SIVASWAMY, R.: 'Digital and analog subcomplementary sequencesfor pulse compression', IEEE Trans., 1978, AES-14, pp. 343-350

2 SIVASWAMY, R.: 'Self-clutter cancellation and ambiguity propertiesof subcomplementary sequences', ibid., 1982, AES-18, pp. 163-181

3 SIVASWAMY, R.: 'Multiphase complementary codes', ibid., 1978,IT-5, pp. 546-552

4 SARWATE, D. v.: 'Sets of complementary sequences', Electron. Lett.,1983,19, pp.711-712

5 TSENG, c. c , and LIU, C. L.: 'Complementary sets of sequences',IEEE Trans., 1972, IT-18, pp. 644-652

6 GOLAY, M. j . E.: 'Complementary series', IRE Trans., 1961, IT-7,pp. 82-87

ELECTRO-OPTIC EFFECT INHe+-IMPLANTED OPTICAL WAVEGUIDESIN LiNbO3

Indexing terms: Integrated optics, Electro-optics, Opticalwaveguides

The electro-optic coefficient r13 of LiNbO3 has been mea-sured at DC, using a phase modulator fabricated using He+

ion implantation, and has produced a mean value for r13 of(813 ± 0-4) x KT^mV"1, which is ~20% lower than pre-viously reported values measured using modulators fabri-cated using other waveguide technologies.

Introduction: In recent years interest has grown in integrated-optical devices for applications in signal processing and com-munications.1"3 Modulators use the electro-optic effect toproduce phase modulation in the arms of an interferometer tomodulate the intensity of the output beam.

It has been suggested previously4 that the electro-opticeffect is reduced by up to 70% in ion-implanted waveguides,since the fabrication process produces damage which destroysthe crystal lattice of the material. This diminished electro-optic effect has reduced the interest shown in ion-implantedoptical waveguides in LiNbO3 and therefore the progress ofthis promising technology.

In this letter we report the first measurements of the electro-optic effect in He+-implanted stripe optical waveguides, whichshow that the electro-optic coefficient r13 is only reduced by~20% for applied DC voltages, as compared to the pre-viously reported figure of Destefanis et ai*

Experimental method: The waveguides used in these experi-ments were fabricated in Y-cut ^-propagating LiNbO3. A1-2 MeV implant was used to form a single-mode planarwaveguide (at X = 0-6328 nm). Subsequently, a thick gold ionimplantation mask was formed on the sample surface toprotect the guiding region during the subsequent implantationat 0-5 MeV, which was used to produce the waveguide sidewalls. The gold implantation mask was then removed and thesample was annealed in flowing oxygen at 200°C for 30 min toreduce the damage in the guiding region produced by theplanar implantation, and thus reduce the insertion loss of thedevice. The end faces of the sample were polished to allowendfire coupling. Finally, aluminium electrodes were producedon either side of the waveguide using photolithography andchemical etching. Further details of the waveguide fabricationprocess can be found in Reference 5.

The experimental configuration used to measure theelectro-optic coefficient consisted of a Mach-Zehnder interfer-ometer with the phase modulator in one arm, and an outputlens to expand the output beam on to a vidicon TV camera. Adirect voltage was applied to the electrodes of the phasemodulator, and the output beam was found, when observed onthe video monitor, to comprise a series of fringes which wereshifted laterally as the voltage was increased. By measuringthe voltage required to move the fringes by one completefringe spacing, Vn was determined.

Discussion of results: The phase modulators were studied hereusing TM polarised light at a wavelength of 0-6328 /im. Therelationship between Vn and the electro-optic coefficient r13 isgiven by6

V.L =

where L is the electrode length (which ranged from 0-5 to1-12 cm), G = 42 /zm is the electrode gap, A is the optical wave-length and F is the overlap integral between the electrical andoptical fields.

The above overlap integral was calculated using theapproximations of Marcuse,7-8 which assume an optical modeprofile which is Gaussian in width and Hermite-Gaussian indepth.

The variation of Vn with 1/L is given in Fig. 1 for a series ofL values. A mean value of 813 ± 0-4 x 10" ̂ m V " 1 for theelectro-optic coefficient r13 is seen to compare favourably withthe previously reported value of 9-6 x 10"1 2mV~1 for DCand audio signals,9 and values of 11 x 10" ̂ m V " 1 (forundoped LiNbO3),10 10-7 x 10" ̂ m V " 1 (for Ti-indiffusedLiNbO3)10 and 10 x 10" ̂ m V " 1 for single-crystal LiNbO3

at 100°C.n In these experiments the waveguide was fabricatedusing a mask with 5 /im-wide stripes and an electrode spacingof 42 fim. A value for VK of 38 V is rather high for deviceapplications, but Vn could be significantly reduced by opti-mising the waveguide width and the electrode spacing. Thevalue of 42 jzm for the electrode gap was used because a suit-able mask with this dimension was available; it was not spe-cifically designed for this use.

The results presented here differ significantly from those of

424 ELECTRONICS LETTERS 9th April 1987 Vol. 23 No. 8