optical devices using semiconductor doped glasses (SDGs) have been demonstrated ... an increase in the. ELECTRONICS LETTERS 8th July 1993 Vol. 29 No.
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101 x 51 series terms. Only one curve is shown in Fig. 2 because the two results agree to within 0.1 R. This behaviour is not surprising, as it is qualitatively the same as that between two isolated perpendicular dipoles: the mutual reactance is zero only when the dipoles are symmetrically arranged. This case, and others not shown here, validate the new term for perpendicular dipoles in the infinite array environment.
Rotated dipoles: The Richmond code as modified was also used to provide data on a dipole that is rotated. In Fig. 1 the 'b' $lipole is allowed to rotate about its centre, with angle $ between the dipole and the x-axis. Fig. 3 gives the mutual resistance against angle, and it may be noted that this is roughly zero for perpendicular dipoles, probably because near-symmetric pairs of array dipoles have almost the same resistance, and these cancel. The mutual reactance is given as the solid line in Fig. 4, and as discussed above it is not zero at
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and BWLL, G.A. : 'Plane-wave expansions for arrays of arbitrarily oriented piecewise linear elements and its application in determining the impedance of a single linear antenna in a lossy half-space', IEEE Trans., 1979, AP-27, (3),pp. 331-343 LUEBBEXS, R. I., and MUNK, 8. A.: 'Mode matching analysis of biplanar slot arrays', IEEE Trons., 1979, AP-27, (3). pp. 44-443 MUNK, B. A., KORNBAU, I.w., and FULIYJN, R. D.: 'Scan independent phased arrays', Radio Science, 1979, 14, (6),pp. 979-990 SWUBERT,K. A., and m,B. A.: 'Matching properties of arbitrarily large dielectric covered phased arrays', IEEE Trans., 1983, AP-31, (1). pp. 54-59 LARS~N, c. I., and m,B. A.: 'The broad-band scattering response of periodic arrays', IEEE Trans., 1983, AP-31, (2), pp. 261-267 BALANIS, c. A.: 'Antenna theory-analysis and design' (Harper 81 Row Publishers,New York, 1982) MUNK, B. A., FULTON, R. D., and LUEBBFXS, R. I.: 'Plane wave expansion for arrays of dipoles or slots in presence of dielectric slabs'. Report No. AFAL-TR-76-53, Ohio State University ElectroScience Laboratory, Ohio, September 1976 RICHMOND, I. H., and GEARY, N. H.: 'Mutual impedance between coplanar-skew dipoles', I E E E Trans., 1970, AP-18, (3), pp. 414415
MUNK, B. A.,
MULTlKlLOHERTZ ALL-OPTICAL MODULATOR I N SEMICONDUCTOR DOPED GLASS CHANNEL WAVEGUtDE A. S. L. Gomes, C. B. d e Araujo, A. Miliou and R. Srivastava 0
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Indexing terms: Opticnl nodulation, Opticol waveguides
Fig. 3 Mutunl resistonce of rotated dipole to dipole arroy
A polarisation independent all-optical modulator is presented with 100% modulation depth at multikilohertz repetition rate in semiconductor doped glass channel waveguide. An interpretation of the modulation mechanism is given.
Introduction: Potentially useful picosecond/femtosecond alloptical devices using semiconductor doped glasses (SDGs) have been demonstrated in bulk and waveguide geometry [I-91. In this Letter, we describe the operational characteristics of an all-optical modulator in a channel SDG waveguide, whereby a CW signal beam is modulated by a pulsed beam of different wavelength. The modulator is polarisation insensitive, with 100% modulation depth and capability to operate at repetition rates up to lOkHz (2kHz was demonstrated), with relatively low driving powers. 0
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f Fig. 4 Mutunl renctnnce of rototed dipole to dipole nrroy __ spatial summation _ - - - PMM
$ = 90". The value there corresponds to a displacement of 0.15 in Fig. 2. The dashed line of Fig. 4 shows the reactance obtained from eqns. 1 and 2, with P, = [cos (akl, cos $) - cos
klJ(1 - a*) times the cos $ obliquity factor. Clearly this formulation is inadequate when $ > 10". The obvious combinations of $ = 0" and $ = 90" solutions have not proved suitable. The next step is to obtain a formulation that is correct for any value of rl.. When this is achieved, it is expected that the PMM can be easily modified, and used as in the past.
0IEE 1993 5th M o y 1993 R. C. Hansen (Consulting Engineer, PO Box 570215, Tarrann, CA, 91356, USA) References 1 LUEBBERS, R. I., and MUNK, B. A.: 'Some effects of dielectric loading on periodic slot arrays', IEEE Trans., 1978, AP-26, (4). pp. 536-
542 1 246
Experimental details and discussion: The signal beam to be modulated was provided by a CW laser diode operating at 670nm and delivering a maximum average power of 800pW. The pump beam was the second harmonic of a CW Qswitched/modelockedNd :YAG laser, delivering a pulse train with 20 pulses of loops duration separated by the 1011s roundtrip time. Only a few milliwatts (a few kilowatts) average (peak) power was necessary to modulate the signal beam. Both beams were spatially overlapped through a beam splitter, into a channel waveguide using a x 10 microscope objective. A combination of Glan-Thompson polarisers and half-wave plates were used to control the power and the polarisation of the beams. A x40 microscope objective was used to collect the spectrally filtered output beam. The singlemode channel waveguides were fabricated by Kf-Na+ exchange in a specially prepared Schott OG 515 glass (-10% sodium content). This substrate was the same as used in the work of Reference 4, and was l m m thick with 85% transmission at 5 3 2 ~ 1 , which corresponds to an absorption coefficient tl = 1,2cn-'. Channel waveguides 2cm long were fabricated onto the substrate using the method described in Reference 4, with a depth of 3 pm and variable width (several waveguides with widths variable from 0.5 to 10pm in steps of 0.5 pm were constructed). Typically, a waveguide with 5pm width was employed. After the ion exchange process, an increase in the
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ELECTRONICS LETTERS 8th July 1993 Vol. 29 No. 14
index of refraction of the waveguide, A = 0.007, was measured with respect to the index of refraction of the substrate. As the modulation depth is a function of both Intensity and incidence angle, qualitative studies of the input angle were performed (due to the low accuracy of the mechanical support) while quantitative studies based on intensity and polarisation dependence were carried out. With the signal beam optimised for coupling, the required modulation intensity would change according to the incidence angle. Typically, 2-3 pW throughput power at the modulation beam (12-18MW/cm2) was enough to provide 100% modulation. A ‘threshold’ behaviour was observed at -0.4pW transmitted pump power. Fig. 1 shows a representative trace of the modulated CW beam, showing 100% modulation depth at 2kHz, limited by the laser repetition rate. By changing the
modulation time (FWHM) was 50p in this case. At even higher power (3.1 pW, Fig. 2c) the 100% modulation depth is
-0 2 p-s
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Fig. 1 Modulated signal beam intensity showing .. 100% modulation depth at 2 kHz Modulation beam throughput average power: 2.2pW
repetition rate from 2kHz to 100Hz, while keeping all other parameters constant, no change was observed in the modulation depth. As for the polarisation studies, for both pump and signal parallel (either launched in TE or TM mode) 100% modulation depth was obtained at typical transmitted powers of 2-3pW. For the signal launched in TM and pump in TE mode, similar results were obtained. For the signal launched in the TE mode and the pump in the TM mode, while maintaining the same power, the modulation depth would decrease to 50%. However, by increasing the power by roughly 50% the modulation depth was recovered to 100%. We now briefly discuss the modulation mechanism and the origin of the nonlinearity. The two main contributions to the nonlinearity arise from electronic and thermal effects. As shown previously [l], for laser frequencies below the SDG frequency gap the sign of the electronic contribution to n2 is negative. Furthermore, it has been shown [4] that dn/dT < 0 for this particular substrate (sodium rich glass matrix), which implies a negative thermal nonlinearity. SDG waveguides with negative thermal nonlinearities have already been described by Patela et al. [2]. Therefore, both electronic and thermal nonlinearities contribute to reducing the total index of refraction of the waveguide. We believe that the main effect which contributes to the modulation process is the inhibition of total internal reflection at the interface between the waveguide and the substrate [IO, 111, which is accomplished through the medium nonlinearity. A related interpretation in terms of guided modes was given in Reference 5 for the observed switching in SDG planar waveguide with a CW laser. Basically, in the expression for the index of refraction of the waveguide n = no + A n , l , the last two terms cancel out, inhibiting the guiding of the signal beam. At 100% modulation depth, and in order that n2 I compensate for A = 0.007, we calculate n,(eff) = -6 x 10-10cm2/W, where n,(eff) is mainly thermal in origin. This thermal nonlinearity is further evidenced by looking at the time evolution of the modulation process. We first notice that no modulation was observed (using an ultrafast detector) at the subnanosecond/picosecond time scale. Fig. 2- show the observed time evolution. At low intensities (
