(FWHM) of 0-8 nm was found. Assuming a triangular grating,these values correspond to an effective index modulation of3-3 x 10"3, which in turn can be related to an etching depthof 100 nm for the grating. This agrees with values measuredfrom SEM photographs.

-20

1486 1-488wave length, (jm 187 3 / 4

Fig. 4 Filter response of channel 1 for TE polarisation

Points: experimental data; line: coupled mode theory

Measurements of the propagation losses of the guides weremade on a sample without Bragg gratings. They indicatedlosses of the straight sections of about 6 dB/cm and additionalbending and branching losses of the Y-branch of 1 dB.

Conclusions: The authors have reported on the first demons-tration of an InGaAsP Y-branch grating demultiplexer. Thisdevice is suitable for further integration with photodiodes. ForTE polarisation, a crosstalk attenuation of more than 18 dBand a channel spacing of 13-5 nm was achieved.

Acknowledgment: The authors wish to thank V. Kulich fortechnical assistance and G. Gorges for the SEM photograph.This work has been supported by the Federal Ministry forResearch & Technology of the Federal Republic of Germanyunder grant no. TK 0273/3. The authors alone are responsiblefor the content.

C. CREMER 2nd February 1987G. HEISER. MARZH. RIECHERTM. SCHIENLE

Research Laboratories of Siemens AGOtto-Hahn-Ring 6D-8000 Mitnchen 83, W. Germany

References

1 WINZER, G.: 'Wavelength multiplexing components—a review ofsingle-mode devices and their applications', IEEE J. LightwaveTechnol., 1984, LT-2, pp. 369-378

2 SCHMIDT, R. V., FLANDERS, D. C , SHANK, C. V., a n d STANLEY, R. D. :

'Narrow-band grating filters for thin-film optical waveguides',Appl. Phys. Lett., 1974, 25, pp. 651-652

3 ALFERNESS, R. C , JOYNER, C. H., DIVINO, M. D., a n d BUHL, L. L.:

'InGaAsP/InP waveguide grating filters for A=l-5 / im\ ibid.,1984,45, pp. 1278-1280

4 YARIV, A. : 'Coupled-wave theory for guided wave optics', IEEE J.Quantum Electron., 1975, QE-9, pp. 919-933

SECOND-HARMONIC GENERATION IN ANOPTICAL FIBRE BY SELF-WRITTEN x(2)

GRATING

Indexing terms: Optical fibres, Harmonic generation

A mechanism for phase-matched generation of second-harmonic (SH) light in an optical fibre has been experimen-tally and theoretically studied. A weak non-phase-matchedSH signal, created via the quadrupole polarisation, initiatesthe self-writing of an axially periodic pattern of colourcentres which is postulated to lead to the growth of a x(2)

grating. The grating (at the phase-match period) gives rise toSH generation at efficiencies of 0-5%. The spectral band-width of this xi2) grating is 0-24 nm.

Introduction: Second-harmonic generation (SHG) by an elec-tric-dipole process is normally forbidden in a fused-silica fibrefor two reasons: (i) silica possesses a centrosymmetric struc-ture and (ii) it is difficult to achieve a phase-matching condi-tion. Despite this, however, SHG of an Nd : YAG laseroperating at 106/rni has been recently reported1 with effi-ciencies over 1%. The second-harmonic (SH) signal wasobserved to grow exponentially over a period of 8h. Wereport here similar efficiencies for SHG, together with experi-mental evidence that the effect is due to the existence of aspatially periodic 2nd-order nonlinear susceptibility / ( 2 ) in thefibre. Our hypotheses and experimental results are furthersupported by a coupled-wave theory in which it is shown thatthe phase-matching condition can be satisfied by the / ( 2 )

grating vector.

Physical mechanism: In silica optical fibres very weak SHGoccurs at high pump intensities owing to a nonlinear electricquadrupole susceptibility.2 For a pump wavelength kp of1 064/mi the coherence length Ac between the pump and theSH at 532 nm is approximately 30/mi as a result of bothmaterial and waveguide dispersion. This gives rise to a 30 /miperiodic intensity pattern of SHG (green) light along the fibreas energy is interchanged between pump and SH generatedlight.

In certain fibres with SiO2 cores doped with GeO2 andP 2 O 5 , semipermanent colour centres can be created by short-

322

wavelength radiation.3 These are known to form dipolecentres which we postulate give rise to enhanced second-ordernonlinear susceptibility. If this is the case, phase matching willbe automatically achieved because the colour centres whichenhance / ( 2 ) will be written periodically into the fibre atspatial locations where the green light intensity is highest, i.e.where the pump and second-harmonic signal are in phase. Atpoints where the pump and SH are out of phase few colourcentres are generated. This results in reduced %l2) and henceno destructive interference between existing generated greenlight and the second-order polarisation due to the nonlinearprocess.

The formation of colour centres is slow at 532 nm andincreases rapidly with intensity. Thus it takes time to createthe spatial grating in y}2) within the fibre, and this gives rise tothe observed rapid growth of SH light.

Coupled-wave analysis: We assume that the self-written x<2) issinusoidally modulated with distance x along the fibre at aperiod equal to the coherence length Ac of the SH polarisationat Xp = Xpo (the writing wavelength). This gives an electric pol-arisation

P = eo(EpXp + EsXs) + 60Z( 2 ) [ l

where

cos Kx]E2 (1)

(2)

K = 2n/A.c, M<2) is the modulation strength of the grating, xp

and xs are the susceptibilities at the pump (o>p) and SH (cos)frequencies, and Ep and Es are the corresponding electricfields. As we shall show, this x(2) grating automatically ensuresphase-matching (at kp = Ap0) between Ep and Es. The resultingtotal electric field is

E = Ap exp ( -j[kpx - wpt])

+ A_ls exp ( —j[ksX — <ost~\) + constant (3)

ks,are

For exact phase-matching between Ep and Es, K = 2kp

with kp = (2n/kp)Np and ks = (2n/As)Ns, where kp, ksp p p p

vacuum wavelengths and Nj,, Ns are the effective refractive

ELECTRONICS LETTERS 26th March 1987 Vol. 23 No. 7

indices. Putting eqn. 3 into the wave equation with P as pol-arisation, neglecting second-order spatial derivations of theamplitudes At and placing the coefficients of terms with identi-cal phase velocities to zero, leads to the following pair ofequations:

d^,

dx

da,

dx"

y = K(2){exp [ - / 0-5M(2) exp

(4)

(5)

where

a i =

v(2)

V9 =

K<2)

AJAJLO)

= ks — 2kp

(Aip/Apy2>

Ap(0)kpXl2)

N2

p

(6)

are, respectively, the field amplitudes normalised to the initialpump amplitude Ap(0), the SH dephasing parameter, thegrating dephasing parameter and the SH coupling constant.Power conversion is obeyed by solutions of eqns. 4 since onecan show that \as\

2 + 2\ap\2 is constant. The key to the very

large enhancement in SHG produced by a x(2) grating lies ineqn. 5. The first part of y yields the usual highly dephased (andhence very inefficient) SH coupling for constant x(2)- Thesecond part contributes SH coupling that is exactly phase-matched if vg = 0, i.e. if Ap = kpo. Neglecting therefore the firstterm in y, and solving first for zero pump depletion (da /dx =0):

\as\2 (x < L) = {K<2 )M( 2 )X}2 sine2 {v.x/2} (7)

where L is the total grating length. Hence for conversion effi-ciencies of less than about 5% the spectral bandwidth A/lpU/2)

of the SHG process is

V2)L (8)

In the presence of pump depletion and for vg = 0 an exactsolution exists:

I as |2 (x < L) = 2 tanh2 {K ( 2 ) M ( 2 ) X/V2} (9)

Thus peak conversion efficiency to the SH is approximatelyquadratic with x for JC(2)M(2)X <^ 1. However, much more sig-nificant is that the x(2) grating potentially yields efficienciesapproaching 100% for large enough L, as is commensuratewith phase-matching.

Experiment: Mode-locked, Q-switched pulses of <100psduration and peak powers of 10 kW from an Nd : YAG laserat 1-064/mi were launched into a variety of single-mode fibres.Very weak second- and third-harmonic generation wasobserved in several. To date, however, growth in SHG hasonly been observed in a silica fibre with the core and claddingdoped with < 1 % P 2 O 5 and the core doped with 15% GeO2.The SH signal grew with time from 100 pW to 50 W over aperiod of 10 h.

To confirm the establishment of a #<2) grating, the wave-length dependence of SHG was measured. Pulses from atunable Raman-shifted dye laser of 6 ns duration and peakpowers of 1 kW were launched into a fibre with a previouslyburnt-in y}2) grating. The pump was tuned over 4 nm, giving ameasured AAp(1/2) of 0-24 nm for the SH signal, as shown bythe experimental points in Fig. 1. The same behaviour resultedwhen the fibre was pumped from the other end. A best fit ofeqn. 4 to the experimental data occurs at an effective gratinglength L of 12 cm, with v(2) = 2;r/Ac = 0-207 /im"1. Side-scatter measurements nearer the input end of the gratingregion gave significantly broader linewidths, as one wouldexpect from eqn. 8.

Fig. 1 shows that the largest discrepancies between experi-ment and theory occur in the sidelobes. This is likely to belinked to nonuniformities in grating phase (and to a lesserextent M(2) and /(2)) along the fibre. Such variations are aninevitable consequence of the self-writing process, and a moreelaborate theory is at present being developed to deal withthese effects. Their presence is confirmed in Fig. 2, where aside-scatter measurement of the SH intensity is plotted as afunction of distance from the fibre end. The pump light waslaunched from the opposite end of the fibre. It can be appre-ciated that about 90% of the conversion occurs in the last15 cm, which agrees quite well with our best-fit value of 12 cm.

\-10 -05 0 0-5 10

n m [62 5/1|

Fig. 1 Wavelength dependence of SH conversion for deviations of pumpwavelength from 1064 nm

Circles are experimental points and solid curve a best theoretical fit

A variety of different phenomena are likely to contribute tothese axial nonuniformities in grating properties, such as themanifestly nonlinear x-dependence of the growing SH signal,group velocity walk-off between pump and SH, and pumpdepletion due to stimulated Raman or Brillouin scattering.The efficiency of SHG—as distinct from the writing process—will level off at very high pump powers owing to competingnonlinear processes such as the two just mentioned.

1000

100

10

a. (/)

•+•> 1

0110 20 30 40 50

distance from fibre end .cm60

[57T771

Fig. 2 Measured side-scattered SH intensity as a function of distancefrom fibre end

While the y}2) grating was written with pump light launched fromthe left, this measurement was made with pump light launchedfrom the opposite (RH) end

Finally, an estimate of the product y}2)M{2), the modulationdepth of x(2\ can be made if we take our result of 0-5%conversion efficiency at Xp = /po and compare it with the peakvalue given by eqn. 7. For the fibre spot-size diameter of 5 //m,Xpo = 1-064/mi and a peak pulse power of 10kW, 0-5% con-version occurs if x(2)Ml2) = 2-75 x 10~16m/V. From eqn. 9,60% conversion would be achieved if a grating of this strengthwere uniform over 1-7 m of fibre.

Conclusions: We have confirmed experimentally that 1% effi-cient second-harmonic generation is possible in an opticalfibre. We postulate that the mechanism is due to the gener-

ELECTRONICS LETTERS 26th March 1987 Vol. 23 No. 7 323

ation of a grating of colour centres which enhance the second-order susceptibility. The grating period is matched to thecoherence length between pump and SH waves. Confirmationof the grating model is provided by our measurements of theoperating bandwidth as 0-24 nm.

Acknowledgments: The authors are grateful to R. McGowanand R. Bailey for supplying the optical fibre. M. C. Farries issupported by the UK SERC under the JOERS scheme. D. N.Payne receives a Readership from Pirelli General.

M. C. FARRIES 20th January 1987P. ST. J. RUSSELLM. E. FERMANND. N. PAYNEOptical Fibre GroupDepartment of Electronics & Computer ScienceUniversity of SouthamptonSouthampton SO9 5NH, United Kingdom

References

1 OSTERBERG, u., and MARGUUS, w.: 'Dye laser pumped byNd : YAG laser pulses frequency doubled in a glass optical fibre',Opt. Lett., 1986,11, pp. 516-518

2 BETHUME, D. s.: 'Quadrupole second-harmonic generation for afocused beam of arbitrary transverse structure and polarisation',ibid., 1981,6, pp. 287-289

3 GREAVES, G. N. : 'Intrinsic and modified defect states in silica', J.Non-Cryst. Solids, 1979, 32, pp. 295-311

INDIUM PHOSPHIDE AND QUATERNARYDOPING SUPERLATTICES GROWN BYLIQUID-PHASE EPITAXY

Indexing term: Semiconductor devices and materials

Stacks containing from 20 to 100 alternating n- and p-layers,each less than lOOnm thick, have been produced by liquid-phase epitaxy in both InP and in the quaternary alloyInj.^Ga^As^Pj.j,. Increasing the excitation intensity shiftsthe photoluminescence (PL) towards shorter wavelengths bythe expected magnitude. Hetero-m>/ quaternary structuresdisplaying two PL peaks have also been grown. The relativeintensities of the two peaks depend strongly on the excitationintensity.

Doping superlattices are semiconductor structures comprisingmultiple layers alternately doped with acceptors and donors.The theory of such structures and their realisation in GaAs byMBE growth have been described by Dohler and Ploog.1"3

Doping superlattices in GaAs have also been produced byLPE4 and by MOCVD.5 Analogous InP structures have beenproduced by hydride VPE6 and by MOCVD.7 All these struc-tures display a photoluminescence peak at a longer wave-length than that corresponding to the simple direct gaptransition, with a decrease in the wavelength as the excitationintensity is increased. Konig and Jorke8 used LPE to produceperiodic doping variations in Ino.53GaO47As on InP, but thethicknesses and dopant concentrations were not appropriatefor doping superlattice characteristics.

We now report the growth of InP and lattice-matched quat-ernary npnp superlattices by LPE at 600°C in an automatic-ally operated furnace incorporating a graphite boat with alinear slider. Layers as thin as 50 nm were grown alternatelyfrom two solutions with identical compositions apart fromdoping with Te or Zn at concentrations giving n orp = I x 1018cm~3 in thick layers.

Photoluminescence spectra were obtained using 514nmargon laser radiation at powers from about 1 mW to 1Wfocused and unfocused. The npnp samples were held at 80 K ina flow cryostat; the PL was analysed using a i m spectrometerand an ADC cooled Ge PIN detector. The spectra shown in

Fig. 1 demonstrate the peak shift with excitation power whichis characteristic of a doping superlattice. The peak wavelengthis plotted against the logarithm of excitation power in Fig. 2(peaks A and B). It shows the expected linear behaviour,except at very high and very low excitation power densities.

The slope of 30 meV/decade obtained here for the quatern-ary superlattice is similar to that previously reported4"9 forother semiconductor doping superlattices with doping in the

hetero-nipi

1W

10 12wavelength, (jm |897/i|

Fig. 1 Luminescence spectra of quaternary (Q, peak A) and InP dopingsuperlattices (peak B), and of a quaternary hetero-nipi structure showingpeaks Cl and C2

Excitation powers are marked on the curves. Spectra are offsetvertically for clarity

130

1 20

110

1 00

FA510

FA510

Q multiple n-p

UJT- 10" 1OH 10 10relative excitation power density |897/2|

Fig. 2 Excitation power density dependence of peaks seen in spectra ofFig. 1

Since varying degrees of focus are used for excitation laser beam,power density is not standardised and curves are not directly com-parable on this axis

324 ELECTRONICS LETTERS 26th March 1987 Vol. 23 No. 7