Guided-Wave Intensity Modulators Using Amplitude-and-Phase Perturbations

A theoretical analysis of intensity modulation in coupled waveguides and Mach-Zehnder interferometers is reported. Simultaneous phase and amplitude perturbations A n + CA k are considered. Predictions are made about the performance of electrooptic GaAs and InP modulators controlled by the free-carrier effect ( A N ) or by the Franz-Keldysh effect ( A E ). The phase-dominant condition A n > 5A k is optimal. The predicted depth of modulation is greater than that of conventional loss-modulators over a range of A N or A E .


I. INTRODUCTION
ROUP IV and 111-V semiconductors exhibit carrier-G induced and field-induced electrooptic effects.The applied stimulus produces a simultaneous change in the semiconductor's optical attenuation and phase retardation.At certain wavelengths, the loss and phase components are comparable in size.These facts have been generally ignored in the design of optical intensity modulators.This paper explores the use of combined amplitude-and-phase modulation for enhanced intensity modulation.Coupled waveguides and Mach-Zehnder interferometers are examined.
In the past, guided-wave intensity modulation has been obtained with either the Pockels effect or the Franz-Keldysh effect.Pockels devices are usually operated at an optical wavelength X far from the fundamental absorption edge of the material X,.There, phase effects are strong and the associated loss is negligible.By contrast, Franz-Keldysh devices are operated quite near the edge.For those modulators, device engineers have relied solely on the loss component and have chosen to overlook the relatively weak phase retardation.This paper deals with an intermediate spectral region, further from the edge, where the phase-and-amplitude variations have similar magnitudes.Carrier-controlled and field-controlled devices are analyzed.We predict that the resulting modulators will have higher extinction ratios and lower insertion losses than conventional ''straight through" loss modulators.
Unlike conventional Franz-Keldysh modulators that have a background absorption of 25-50 cm-', the modulators proposed here have a static loss of less than 1 cm-' which should allow monolithic integration of our modulators with other guided-wave components (including laser diodes) on the same wafer.
Manuscript received March 11, 1987;revised August 12, 1987 11. BACKGROUND DISCUSSION Van Eck and coworkers [l] studied the Franz-Keldysh effect in bulk GaAs and InP.They suggested that the lossand-phase components could be combined in a bulk-optic Fabry-Perot resonator for improved modulation.We have applied their idea to two integrated-optic structures and have considered carrier control.
Previously, researchers have employed four types of guided-wave devices to convert phase variations into intensity modulation: 1) interferometers, 2) coupled waveguides, 3) mode extinction modulators, and 4) TE-to-TM mode converters.Here, we have generalized 1) and 2) to include optical "damping".Modulators 3) and 4) are not treated in this paper, but are promising candidates for future study.
In the analysis below, the complex mode-amplitude for the propagation-direction z is described by the expression If we include the effect of optical loss, then the complex wavenumber K is proportional to the complex index of refraction: K = 2n ( n + ik) /A, where the real part ( n ) is the conventional refractive index and the imaginary part ( k ) is the linear extinction coefficient.
We define the propagation coefficient as p = 2nn/X and the optical power absorption coefficient as CY = 4nk/X.
The units of both a and p are per centimeter.We are interested in electrooptic effects that produce a complex change in index: A n = A n + iAk.This produces a mode perturbation of the form exp i ( A 0 + iA CY/^ ) z , where The analysis below is quite simplified.For example, interfering modes are treated like plane waves.Also, we assume that the transverse index distribution A n (x, y ) is uniform and fills the optical waveguide.The response of coupled three-dimensional (3-D) channel waveguides is deduced from the behavior of coupled two-dimensional (2-D) slab waveguides.( 2 )

MODULATOR STRUCTURES
At zero perturbation, constructive interference occurs since the path length is the same in each arm.Then, the transmission is a maximum: 2Ai.Taking Pin = 2 A i , we obtain from ( 2 ) the throughput of the interferometer: ( 3 ) Analogous equations with A cy and A 0 can be developed for Fabry-Perot and Michelson interferometers.Consider now the Fig. l(c) device.We shall analyze the case in which an optical amplitude A. is launched into the "feed" waveguide, while an amplitude Bo is launched into the "branch" waveguide.Output amplitudes A and B from feed and branch, respectively, are calculated.One has the option of inserting the electrooptic perturbation in either the feed or branch.(The reason for not putting identical perturbations in feed and branch is given below).We shall label the inputs ports of the coupler as 1 and 2 , and designate the output ports as 3 and 4 .The normalized output powers are: p3/pI = IA/A~~~, P,/P, = ( B / A , ~~, P3/P2 = ) A / B O l 2 , and P4/P2 = IB/BoI2.The initial condition Bo = 0 is assumed below.
Coupled-mode equations for a uniform A 0-switch have been given in several textbooks such as Yariv and Yeh [ 2 ] .Those equations were derived under the assumptions of weak coupling, phase-matched guides, slab waveguides, and codirectional propagation.The uniform coupling coefficient is K per centimeter.
To handle the combined phase and amplitude shift, we where The justification for this procedure is given in the recent work of Thompson [3] who considered coupled guides that include gain or loss.In fact, Thompson's result [ 3 , eq. ( 7)] connects with our result if we interpret his static gain/ loss parameter 2K6 as our "dynamic" amplitude perturbation A a / 4 , and his phase shift 2KA 0 as our phase mismatch A 0 / 2 .
In ( 4 ) and (5) above, the plus sign in b denotes a perturbation in the feed, while the minus sign indicates a branch perturbation.Note that g is complex.For this modulator, we shall select a value of KL that gives either an initial crossover of light (the "cross" state, with KL = a / 2 , 3 n / 2 , 5 a / 2 , * * * ) or an initial straight-through condition (the "bar" state, with KL = a, 2 a , 3 a ,e ) .
A key parameter in the present theory is the ratio This p-parameter provides a measure of the relative strength of the phase versus the amplitude modulation at a given drive level.The A n / A k ratio is also useful in assessing the amount of chirp in the modulator [ 4 ] .The effect of p on Pout/Pi, is now determined.We have a choice of using either ACYL or A p L as the independent variable.To be specific, if we put ( 6 ) into ( 3 ) we find the response of the Mach-Zehnder ( M -Z ) is: where (gL? = ( 1 + i / p ? ( A @ L / 2 ?+ ( m a ? . Feed and branch perturbations produce the same result for P4/Pl, according to (10) and ( 12).It is possible to place a perturbation of length L in both guides in Fig. l(b) and l(c), which has been done in the past for Pockels-effect devices.Unlike push-pull Pockels devices that give + A 6 in one arm and -A @ in the other, the Franz-Keldysh and charge-controlled devices give the same sign of A p in both arms.Hence, the phase-velocity mismatch will vanish in the voltage-on state.This implies that the phase terms will cancel in the above equations and that only the loss terms will remain.Thus, we find that the modulator with two active arms has a throughput of P,,,/P,, = exp ( -A C Y L ) in Fig. 1(b) and (c).
In the sections below, we shall compare the complex modulators with both phase-sensitive and amplitude-sensitive devices.

IV. COMPARISON WITH A @ DEVICES
In the past, the coupler and the M-Z have been used with the Pockels effect, a "pure phase" perturbation.So, these structures can serve as phase-modulated references for the complex modulator in the limit of large p .As p is increased, the mixed modulator must blend continuously into the phase modulator.The "blending" is shown graphically below.In the following computations, we shall assume that p is a constant.Fig. 2 is a plot (per (8)) of the M-Z output as a function of A p L for p = 3, 10, and 5000 ( p -, 0 0 ) .The familiar raised cosine result at p -+ 00 with perfect nulls at odd multiples of a is seen.The complex modulator has nonzero minima and nonunity maxima because, with increasing A k, the amplitude imbalance between the two arms washes out the peaks and valleys of the interference ''pattern".However, the intensity minima and maxima of the complex device occur at the same values of T , 2 a , 37r, etc. (slightly left-shifted at low p ) .In the high-field limit (large A p L ) , the optical throughput of the mixed interferometer approaches the asymptote 1 / 4 .This is explained as follows.In the limit of large APL, assuming that A n and A k increase in unison, one arm of the interferometer becomes opaque, so half the power is lost.In addition, the large amplitude imbalance and phase imbalance of the optical signals entering the Y-combiner will cause half of the remaining power to be radiated into the substrate [5].Fig. 3 shows the responses P3/P, and P4/P1 of a 2 x 2 coupler switch (equations ( 1 1 ) and ( 12)) as a function of A p L for p = 5 , 15, and 5000 with an initial cross state, KL = a / 2 .For the upper drawing, the complex perturbation is in the feed.A companion plot, lower drawing, shows the effect of a branch perturbation.The p = 5000 device reaches the bar state at the well-known value A p L = &a.The quasibar state of the A n + iAk devices occurs at the same APL value, although the outputs differ from the ideal unity/zero values.
Next, we considered the initial bar state, KL = K .Fig. 4 presents results for P3,/PI and P4/Pl versus A p L for a feed perturbation (upper drawing) and for a branch perturbation (lower drawing).Again, we examined p = 5 (dotted line), 15 (dashed line), and 5000 (solid line).It is interesting that the p = 5000 device becomes a -3-dB coupler at APL = 2 a .Some insight into the mixed-modulator curves of Figs. 3 and 4 can be gained from a consideration of the phaseonly coupler.For example, if we plot P3/P, versus L for a phase-only coupler (as Thompson has done in [3, fig.5]), we find the usual raised cosine result at A b = 0, with perfect ones and zeros that represent the bar and cross states.For the mismatched condition, the L-dependent output power oscillates between -0.5 and unity when A -4 K .So, in the nonsynchronous condition, it is impossible to reach a perfect cross state, although any one of a series of bar states can be attained.We conclude that one can go from a perfect cross state at A @ = 0 to a perfect bar state at A @ # 0. But, a bar state at A @ = 0 will never lead to a perfect cross state at A @ # 0. Similar behavior holds for the phase-dominant mixed coupler shown in Figs. 3 and 4 .In addition, the loss component A a affects the coupled modes.One mode becomes more localized in the perturbed lossy guide, and its attenuation increases.The other mode becomes more localized in the transparent unperturbed guide, and its attenuation diminishes [3].In designing an intensity modulator, one selects the most highly damped output.That output is P 4 / P I in Fig. 3 (feed or branch perturbation) and P 3 / P 1 in Fig. 4 (feed perturbation).The collective action of A a and A is different in these two situations.In Fig. 3, increasing A p drives P 4 / P 1 "downwards" towards the bar state at 1 .7 3 ~.This tendency is reinforced by the increased damping A a which attenuates the cross coupled optical power.The situation is reversed in Fig. 4. Here, the phase component A p drives P , / P , to -0.5 as A p L approaches 2n.Then, P 3 / P 1 is driven "upwards" to unity at A p L = 3 .5 ~.But, the ACY component acts directly on P 3 / P l and drives that power towards zero, thereby opposing the AB effect.So, the Aa-effect is diluted.For these reasons, the intensity modulation is more effective in Fig. 3 7)) versus A a2 for p = 3, 5 , 7, 10, and 15 in a semilog plot.For com panson, the response of the exp ( -A a L ) modulator i: shown by the dashed line.Note that the horizontal scalc is not in units of R .The conclusion drawn from Fig. 5 i! that the interferometer gives better extinction than thc conventional device when A CY L is kept below 1.65 for I = 5 , below 1.30 for p = 7, 0.95 for p = 10, and 0.6: for p = 15.When A a L exceeds those critical values, thc M-Z has less depth-of-modulation than the in-line mod ulator.
Fig. 6 illustrates the coupler behavior.This figure rep resents the theoretical performance (equation ( 9) and (10) versus A a L for the case KL = n / 2 and p = 20.Thir mixed coupler is a 2 X 2 switch with unequal outputs ir the bar state.There is a deep minimum of P 4 / P l (bai state) at ACYL = 0.54 which is 2& a / p .Fig. 7 and 8 are semilog plots of one output (equations (10) and (9), respectively) as a function of ACYL.Result: for p = 2, 5, 10, 15, and 20 are shown.Fig. 7 presents P 4 / P I for KL = n / 2 (feed or branch perturbation), anc Fig. 8 shows P , / P , for KL = R (feed perturbation).Foi comparison, the response of the exp ( -A a L ) absorptior modulator is shown by the dashed line.For p > 5 in Fig 7, the curves are well below the dashed line, as desired We conclude from Fig. 7 that the phase-dominant condition A n > 5 A k is well suited for efficient intensity modulation.In Fig. 8, the output power oscillates about the dashed line and does not offer a significant improvemeni over the conventional loss modulator for reasons givep above.
We have examined the loss-dominant regime, p = 0.5.and have found that the p = 0.5 curves (not shown) are $ j J Y ?y , above the dashed line in Figs.7 and 8, so we concrude that the loss-dominant regime is not favorable in the coupler.A similar conclusion applies to the M-Z.

VI. ELECTROOPTIC EFFECTS
In a 111-V semiconductor, the Pockels, Franz-Keldysh, and free-carrier electrooptic effects coexist over a range of wavelengths.However, it is possible to isolate one effect, that is, to emphasize one and diminish the others.This can be done by choosing an appropriate crystallographic orientation, electrical contact structure, doping, wavelength, etc.In order to gauge the individual impact of each effect upon modulation, we shall examine the Franz-Keldysh and charge effects separately.
The optical influence of altered free-camer densities ( A N ) in Ge, Si, GaAs, InP, InAs, etc., has been discussed in the literature as the "plasma dispersion effect."The real and imaginary parts of this effect are called carrier refraction ( C R ) and carrier absorption ( C A ) , respectively.For GaAs, InP, and Si, some experimental and theoretical results on A a and A 0 as a function of AN have been plotted in [6, figs. 2 and 31.The combined CR and CA effects, designated here as C ( R + A ) are strongest away from the edge: X >> A,.
The ratio p for C ( R + A ) can be estimated using the simple Drude model cited in [7, eqs.( 4) and ( 5) ] .For one species of carrier, the model gives p = -2mm*p/eX, where m* is the conductivity effective mass, and p the carrier mobility.For most materials, experiments have verified a linear dependence of A 0 upon AN at "high" AN.However, Aa-measurements reveal that A a is a nonlinear function of AN, although the deviation from linearity is small.Thus, in practice, p is not independent of AN, but the variation of p with A N is smaller than the 1000-to-1 change of p with E in the Franz-Kelydsh effect.
In the C ( R + A ) effect, one has an opportunity to "tailor" p to a desired value by the proper choice of semiconductor material, alloy composition, optical wavelength, maximum AN, and species of carrier (electrons or holes).However, p is constrained by the dispersion relations [6].The C(R + A ) effect is polarization-independent.
To illustrate C ( R + A ) , the example of hole-injection into GaAs will be given.From room-temperature GaAs at the 1.15-pm wavelength, Carenco and Menigaux [8] cite experimental absorption work by Garmire and Merz, and theoretical refractive index work by Stem.For free holes, they find that A a ( c m -' ) and An = -9.9X 10-22ANh(~m-3), which implies that AP(cm-') = -5.4X 10-'7ANh(cm-3).These results are plotted in Fig. 9 as a function of injected hole density.It is seen that the ratio p is constant at 7.7, although other data on GaAs suggests that p tends to decrease with increasing AN.(For electrons in InP or GaAs, p is typically greater than 10 in the near infrared).Generally, as A N is increased from 10l6 to lOI9 c r K 3 in Si, Ge, GaAs, and InP, we expect p to decrease by a factor of five (approximately), tracking the decrease in mobility.
The real and imaginary parts of the Franz-Keldysh effect are called electrorefraction (ER) and electroabsorption (EA), respectively.These effects were examined theoretically for direct-gap 111-V materials by Bennett and Soref [9] and for an indirect-gap material (Si) in [7].In the transparent region X > A,, it is found that the phasepart increases approximately quadratically with the external electric field, A b = bE2 at low E, while the electroabsorption has a much stronger field-dependence: A a 0: E7 at low fields, changing to =E5 and a E 3 with increasing field.The E ( R + A ) effect peaks as the modulator wavelength X approaches the edge of the waveguide material A,, although one must not approach the edge too closely in order to minimize the zero-field extinction ko of the modulator.That loss arises from absorption-band tails.
In the E ( R + A ) effect, the relative size of A b and A a can be adjusted by proper choice of: semiconductor material, X -X,, maximum E-field, crystallographic orientation, electrode placement, propagation direction, alloy composition, and layer thicknesses (in multiple-quantumwell samples).For the discussion below, we shall assume that the electrode placement and crystallographic orientation are chosen so that the Pockels effect is smaller than E ( R + A ) , although one can obtain comparable An-contributions from the linear and nonlinear electrooptic effects, if desired.The E ( R + A ) effect is polarizationdependent.l(c).Applying the carrier effect in GaAs to the coupled waveguides of Fig. 7, we note that p = 7.7 from Fig. 9. Then we select a practical value of A N , such as 5 X lOI7 cmP3, as a convenient starting point.Fig. 9 indicates that A a = 7.0 cm-' at this A N .Next, we note from the Fig. 7 result that the minimum value of P 4 / P I for p = 7.7 occurs at A CY L = 1.4 approximately.Thus, the required interaction length is 1.4/7.0,that is, L = 0.20 cm.It also follows that the coupling coefficient is 7r/2(0.2) or 7.9 cm-I.Next, we let A N vary from zero to 7 X 1017 cmP3 and determine the corresponding A a L values, which are inserted into (10) along with the fixed p value.This gives the modulation result shown in Fig. 12 as a function of the injected (or depleted) charge concentration.Also displayed on the graph, for comparison, is a dashed-line curve that illustrates the response of the conventional absorption modulator.
--- Turning to Fig. 1 1, we then find that p = 15 occurs at a field strength of 66 kV/cm, where A a = 3.0 cm-I also occurs.The required interaction length in this case is 0.7/3.0, that is, L = 0.233 cm.Hence, K = 6.7 cm-'.Now, we select an operating range of field values from zero to 100 kV/cm.At each E value, we determine from VIII.DISCUSSION AND SUMMARY The coupler and the M-Z will give effective intensity modulation when the complex electrooptic effect has a large phase component: A n > 5Ak.Fig. 13 shows that the intensity falls to 0.0055 at 66 kV/cm (22.6-dB extinction, compared to 1-dB extinction for the reference, and the modulation depth is far greater than that of the reference over the 0-to-90 kV/cm range.Similarly, Fig.
12 reveals higher extinction than the reference over the A N range from 0 to 7 X 1017 crnp3.In Fig. 14, the interferometer has better extinction than the reference modulator over the E-range from 0 to 76 kV/cm.The results of Figs.12-14 are based on approximations discussed earlier.The results give qualitative guidelines for device behavior.
The Franz-Keldysh intensity modulator has a lumpedelement equivalent electrical circuit, and driving the modulator is much like charging and discharging a capacitor.Modulation depth is governed by the electric field strength in the waveguide material, which in turn is proportional to the "capacitor voltage" (the reverse bias applied to the p-i-n waveguide diode structure).As shown in Figs.2-4, the same A p L is used in the on-state of phase-dominant and phase-only couplers (or interferometers).Thus, the switching power requirements are for mixed and pure-phase devices.tion in InP, GaAs, GaSb, InAs, and InSb," IEEE J .Quantum Electron., vol. QE-23, pp. 2159-2166, Dec. 1987. FL: Academic, 1985.the Same According to Fig. 10, the A n A k condition requires higher field strengths and more switching energy than does the phase-dominant A n L 5Ak condition.However, the absorption modulator could be operated at a wavelength closer to A, than the mixed modulator.In that case, the conventional modulator might gain an advantage.In [9, figs.8 and 91 it is shown that A n A k occurs at lower drive levels when X -A, shrinks.Hence, near A, , the switching power requirement of the absorption modulator might be one-half that of the mixed modulator, depending upon how small A -A, is.At the same time, however, the optical insertion loss of the absorption modulator would increase by several decibels because the background extinction coefficient goes up significantly as X -A, is reduced.
In summary, a theoretical analysis of intensity modulation is coupled waveguides and in Mach-Zehnder interferometers has been made.Simultaneous phase and amplitude perturbations A n + iAk were considered.
Performance predictions were made for electrooptic GaAs and InP modulators controlled by the free-carrier effect or by the Franz-Keldysh effect.The phase-dominant condition A n > 5Ak was optimal.The predicted depth of modulation was greater than that of conventional loss modulators over a prescribed range of charge densities or of field excursions.

Fig. 1 Fig. 1 .
Fig.1illustrates the three single-mode channel waveguide structures that are analyzed here: in Fig.l(a)a straight segment of waveguide with variable attenuation, in 1 (b) a Mach-Zehnder interferometer made from Y-couplers, and in l(c) a pair of parallel coupled channels with uncoupled input and output lead-in channels.In all three devices, electrical control is imposed upon an interaction U.S. Government work not protected by U.S. copyright.

Fig. 2 .
Fig. 2 .Interferometer output as a function of electrooptic phase angle (real part of perturbation) for three values of A n / A k .

JnURNALFig. 3 .Fig. 4 .
Fig. 3 .Directional coupler output(s) as a function of electrooptic phase angle (real part of perturbation) for three values of A n / A k .The cross state is the initial condition.
Fig. 4. V. COMPARISON WITH A a DEVICES The straight-through attenuator of Fig. l(a) is now used as a reference for Fig. l(b) and (c).In practice, the straight

Fig. 6 .Fig. 7 .Fig. 8 .
Fig. 6 .Directional coupler output(s) as a function of electrooptic amplitude angle (imaginary part of perturbation) for A n = 20Ak.The cross state is the initial condition.

Fig. 9 .
Fig. 9. Carrier-induced optical phase shift and induced optical absorption in GaAs produced by a modulation AN of the free-hole concentration ( X = 1.15 pm and X, = 0.88 p n ) .

Fig. 10
Fig. 10 illustrates E ( R + A ) for room-temperature InP material at the 0.984-pm wavelength.The quantities A n and A k have been plotted as a function of applied field in Fig. 10 (a log-log plot) using the theoretical curves of [9].Here, the photon energy has been chosen to be 80 meV less than the bandgap energy.The 80-meV choice is advantageous because it reduces the background extinction at E = 0 to a low level: ko -3 x lop6.For use in numerical examples below, the ratio 2 A b / A a and the amplitude modulation A a are plotted versus E in the semilog plot of Fig. 11.VII.PREDICTED PERFORMANCE Three examples of intensity modulation are given here: E ( R + A ) in Fig. l(b) and (c), and C ( R + A ) in Fig.
Optical intensity modulation in coupled GaAs waveguides (per Fig.7) versus carrier injection/depletion, as produced by the Fig.9electrooptic effect.Here, K = 7.9 cm-' and L = 0.200 cm.The second coupled-waveguide example makes use of the field-controlled E ( R + A ) effect in InP at a photon energy 80 meV less than the bandgap energy, i.e., an operating wavelength of 0.984 pm.Again we take KL = n / 2 .It is estimated from Fig.7that when p = 15, the first minimum of P4/Pl occurs at A a L = 0.7.(The choice p = 15 is one of several practical alternatives).

Fig. 11 Fig. 13 .Fig. 14 .
Fig. 11 the corresponding p-value and the correspondingA a L value.The various p ( E ) and A a L ( E ) are then substituted into (10) for determination of the P4/P,-versus-E modulation characteristic.The result is presented in Fig.13.Again, for comparison, we show the throughput of the standard exp ( -A a L) modulator by the dashed curve.The final example includes the response of the Mach-Zehnder interferometer to the E ( R + A ) effect in InP at 0.984 pm.Here, we turn to the result of Fig.5and find that the ratio p = 15 gives a low value of Pout/Pin at a relatively low value of A a L , namely at A a L = 0.4.From the InP result of Fig.11, it is found that p = 15 corresponds to an electric field strength of 66 kV/cm.The absorption perturbation A a = 3.0 cm-' corresponds to that field.The interaction length needed is 0.4/3.0, or L = 0.133 cm.Now we allow E to range from zero to 100 kV/cm.At each E-value, we find from Fig.11the corresponding p value and the A a L value.Those numbers are substituted into (7) to give the optical throughput of the interfering guides.The result is presented as a function of E in Fig.14.As before, we compare the result with the transmission of a conventional loss modulator (dashed curve).Estimates of the optical insertion loss in each of the above three examples will now be made.The zero-field loss in decibels of the mixed modulator, either coupler or M-Z, is given approximately by -10 log [exp (-4rkoL/X)].Taking ko = 3 X lop6 for InP at 0.984 pm and ko I 1 x for GaAs at 1.15 pm, (extrapolated values from [lo]) together with the 0.200, 0.233-, and 0.133-cm interaction lengths, we find that the inser- [IO] E. D. Palik, Ed.Handbook of Optical Constants of Solids.Orlando, Ordinary absorption modulators (Fig. l(a)) tend to be operated in the loss-dominant regime where A n z A k .
. The authors are with the Rome Air Development Center, Solid-state IEEE Log Number 87 18499.Sciences Directorate, Hanscom AFB, MA 01731.