We present an optical delay line structure incorporating In_xGa_1-xAs quantum wells in the GaAs quarter-wave layers of a GaAs/AlAs distributed Bragg reflector (DBR). Applying an electric field across the quantum wells red shifts and broadens the e1-hh1 exciton peak via the quantum-confined Stark effect (QCSE). Resultant changes in the index of refraction thereby provide a means for altering the group delay of an incident laser pulse. Theoretical results predict tunable delays on the order of 50 fs for a 30-period structure incorporating 3 quantum wells per GaAs layer. Structure design, growth and fabrication are detailed. Preliminary group delay measurements on large-area samples with no applied bias are presented.
 
 

1. VCSEL arrays, optical beamforming, electrically tunable group delay, quantum-well devices, quantum-confined Stark effect.

1. Introduction

 

 
 
 
 
 
 
 
 

The construction of electrically tunable, multi-cycle optical delay lines (ODLs) would address the needs of several aerospace applications considered highly critical enabling technologies for future Air Force systems. One- or two-dimensional arrays of such delay lines can be employed to steer optical beams or to generate phased arrays of coherent emitters for use in laser radar systems. High-speed steering of optical beams has obvious beneficial implications for free-space optical interconnects and switching networks. Furthermore, arrays of delay lines could also be used to accomplish image correction to account for lens aberrations or adaptively correct for propagation of optical signals through turbulent media.
 
 

There exist several technological approaches for the generation of tunable optical delay lines and beam steering devices. Some of these approaches include microlens arrays, transmissive and reflective liquid crystal spatial light modulators¹, and piezo-electrically stretched optical fibers². There are several design considerations that must be addressed in the fabrication of ODLs: insertion losses; maximum achievable delay; drive currents or voltages; speed of operation; wavelength bandwidth; and ease of integration into a given system. Ultimately, the end application will determine which criteria are most critical for successful system performance, and hence which method will prove most appropriate.
 
 

We explore here an approach combining a distributed Bragg reflector (DBR) with electric-field-addressable multiple quantum wells (MQWs) to generate a tunable optical delay line. Such a device would have several key benefits compared to other approaches. First, the monolithic architecture makes for easy integration with an array of vertical-cavity surface-emitting lasers (VCSELs). No special alignment system is necessary, as the ODL may be grown on top of the VCSEL structure. Furthermore, III-V processing methods are very mature, making large-scale integration techniques readily achievable. Finally, the time scales inherent in this method are very short (~ 1 ps), such that switching speeds could be much faster than many current methods.
 
 

2. Group delay in distributed bragg reflectors

 

 
 
 
 
 
 
 
 

A typical DBR structure is a dielectric stack consisting of alternating layers of high refractive index and low refractive index materials. Constructive interference of multiple reflections generates very high reflectance, or, equivalently, very low transmittance over a range of wavelengths. This wavelength region is called the DBR transmission stopband. To either side of this region, interference produces a number of oscillations in the transmission spectra. The number of oscillations, their modulation depth, and the wavelength positions of the peaks and troughs are dependent upon the number of DBR layers, as well as the layer thicknesses and the dispersive indices of refraction of the constituent layers. Figure 1a shows a model transmission spectrum for a 20-period DBR comprised of alternating layers of GaAs (high index) and AlAs (low index) layers. Each layer has an optical path length that is one quarter of the stopband center design wavelength, which in this case was chosen to be 1150 nm (vertical dotted line). The first transmission peaks on either side of the DBR stopband, here located at 1081 nm and 1227 nm, are referred to as the short- and long-wavelength bandedge resonances, respectively. The vertical dashed lines give the theoretical wavelength positions of the bandedge resonances for an infinite-period DBR in the absence of dispersion.
 
 

Optical pulse delays in DBR structures were first considered by Dowling, Scalora and co-workers³. Theoretically, they predicted that pulses incident at the transmission bandedge resonances experience a group delay that is proportional to the square of the number of DBR periods. Their initial treatment was based on a transfer-matrix calculation of the complex transmission coefficient. They showed that the group velocity, v_groupº dw/dk, scales inversely with the derivative of the phase transmission, f, with respect to optical frequency, that is
 
 

(1)

 

Hence, in regions where the slope of the transmission phase is large, the group velocity for an incident pulse becomes very small, and the delay experienced by the pulse traveling through the structure is large; see Figure 1b. These findings were later verified experimentally⁴ at a wavelength of 1529 nm. Optical pulse delays of 0.27 ps were found for a 30-period GaAs/AlAs DBR, with negligible distortion of their 2-ps laser pulses. Good agreement to the measurements was obtained using both transfer-matrix (frequency domain) and pulse propagation (time domain) simulations^4,5.
 
 

It must be emphasized that a fixed DBR structure alone provides only a static group delay. To provide tunability, we must introduce a means of changing the optical path length (and hence the transmission phase) of the structure. Changing the angle of incidence provides one way to do this, and was demonstrated experimentally⁴. For fixed pulse propagation direction, however, this limits tunability to mechanical tilting of the DBR structure.
 
 

3. Electrically tunable delays using the quantum-confined stark effect

 

 
 
 
 
 
 
 
 

Mechanical adjustments for tunability are undesirable for space-based applications, where reaction forces can influence the alignment of an entire system. An electronic method of altering the refractive index of the structure is therefore preferred. This can be accomplished by growing one or more In_xGa_1-xAs quantum wells (QWs) in the GaAs layers of the DBR structure and applying an electric field perpendicular to the plane of the QWs. This causes the e1-hh1 exciton absorption peak to red shift, accompanied by a reduction in the peak absorption and a broadening of the absorption linewidth. This is the well-known quantum-confined Stark effect (QCSE)⁶. Previous research has indicated that the Stark shift of the absorption peak scales with the square of the applied field (DE µ F²)⁷. Furthermore, experiments on In_xGa_1-xAs QWs subjected to strong electric fields have indicated a 20 meV to 30 meV redshift for field strengths of 100 kV/cm, with peak absorption reduction and broadening factors near two⁸. Changes to the exciton absorption naturally give rise to changes in refractive index via the Kramers-Kronig relations⁹. The changes in refractive index are largest near the exciton peak, where absorption is also large. Theoretically, if the area under the exciton absorption resonance (i.e., the oscillator strength of the broadened e1-hh1 transition) is conserved, then far from the peak absorption wavelength, the refractive index falls off with decreasing energy as (DE)^-2, with DE = E_x - E, and E_x the exciton peak resonance energy. The absorption, however, in accordance with Urbach's rule, falls off exponentially as exp(-DE/E_x)⁷. Hence, there exists an inherent trade-off between maximizing refractive index changes and minimizing excitonic absorption losses in the design of the tunable DBR delay line.
 
 

A feasibility study was conducted to determine order-of-magnitude delay changes that could be expected from a tunable DBR/ODL. Quantum well absorption, Da_QW(l), was modeled using a Lorentzian lineshape fit to experimentally measured MQW absorption data in the vicinity of the exciton peak. The effects of an applied field of 100 kV/cm on the absorption spectrum were then simulated by (a) broadening the linewidth by a factor of 2, (b) decreasing the peak absorption by a factor of 2, and (c) red-shifting the peak absorption by 20 meV. The refractive index spectra of the In_xGa_1-xAs QWs were then generated by adding the Kramers-Kronig transformation of the Lorentzian absorption lines, yielding Dn_QW(l), to refractive index data of bulk GaAs, n_GaAs(l), as measured by in-house spectroscopic ellipsometry; i.e. n_QW(l) = n_GaAs(l) + Dn_QW(l). Treatments similar to this for modeling the optical constants of In_xGa_1-xAs QWs have been successful in describing so-called "motional narrowing" as well as nonlinear saturation of normal-mode coupling at low temperature^10,11 and for room-temperature light-matter interactions in GaAs/Al₂O₃ microcavities¹². Figure 2 graphically illustrates this approach for modeling 80-Å In_0.2Ga_0.8As QWs subjected to field strengths of 0 kV/cm (solid) and 100 kV/cm (dashed) field strengths.
 
 

The design of a DBR/ODL is slightly more involved than the design of DBR mirrors or etalons. For mirrors or cavities, one simply chooses the stopband center design wavelength, l_{DES. Then, knowing the index of refraction of two materials at this wavelength, nHigh(}l_{DES) and nLow(}l_{DES), the appropriate physical thicknesses of each layer are then given by}
 
 
 

(2)

 
 

For a DBR/ODL, however, the goal is to design a heterostructure that places either the short- or long-wavelength bandedge resonance at a particular design wavelength. Complications arise because the wavelength positions of these resonances are not only functions of the refractive indices of the constituent DBR materials, but also depend upon the number of layers or periods in the heterostructure. This property is illustrated in Figure 3. Here, simulations were done for a DBR mirror with stopband center wavelength of 1150 nm. For a GaAs/AlAs DBR, this leads to quarter-wave thicknesses of 829 Å and 979 Å, respectively. One can see from the figure that as the number of periods increases, the transmission at the design wavelength decreases, the bandedge resonances become dramatically narrower, and they move in wavelength toward the aforementioned theoretical limiting wavelengths (dashed lines in Figure 3). Hence, it is necessary a priori to determine the number of periods in a particular DBR/ODL design for proper placement of a given bandedge resonance.
 
 

4. Theoretical results

 

 
 
 
 
 
 
 
 

The use of QWs and the QCSE to control the optical properties of a DBR structure is not a new concept. Blum et al.¹³ were interested in electrically tuning the Fabry-Pérot cavity resonance in a surface-emitting laser to the peak of the gain medium. They pointed out that this could be achieved by tuning the reflectance phase of one or both of the DBR mirrors comprising the resonator. To fashion a tunable mirror, InGaAs wells were grown in the layers of an InGaAs/InP DBR. With a reverse bias of 17 V applied to the mirror, they found differential transmission changes of 14% at 1570 nm in a 31-period structure containing eight QWs per period. In a later work, an interdigitated contact scheme was applied to the growth of a tunable GaAs/AlAs 30-period DBR mirror¹⁴. For that work, the mirror was designed with a stopband center wavelength of 1033 nm. Four InGaAs QWs per GaAs layer (peak absorption at 980 nm) were demonstrated to yield reflectivity changes as large as 12%. Due to the internal field charge from their interdigitated doping scheme, a forward bias of 1 V gave maximal reflectivity changes. In both of these studies, however, the design of the structure placed the QW e1-hh1 resonances at wavelengths less than the short-wavelength bandedge resonance. Furthermore, they did not investigate time delay or phase-shifting properties of their structures, other than indirectly through reflectivity and transmission measurements. On the other hand, Trezza and co-workers¹⁵ investigated asymmetric Fabry-Pérot microcavity modulators. Their devices used GaAs QWs in the cavity spacer of an AlGaAs/AlAs microcavity. They demonstrated the performance characteristics of these devices to modulate, emit, and detect light, so-called MED pixels. By flip-chip bonding a 256x256 MED pixel array to a CMOS driving chip, they showed both amplitude and phase modulation capabilities. Indeed, reflection phase changes near 2p were observed for applied reverse biases on the order of 10 V. They were also quick to point out, however, that the reflection amplitude characteristics of these Fabry-Pérot modulators are very sensitive functions of applied bias. In contrast to previous work, we seek to employ a design where the QW resonances are placed within the DBR stopband, and examine field-induced changes at the long-wavelength bandedge resonance.
 
 

Theoretical investigations are reported here for DBR/ODL structure designs that place the long-wavelength bandedge resonance at 1061 nm. Transfer-matrix simulations were carried out to model group velocity changes with and without applied field as a function of the number of periods. As previously mentioned, it was necessary to adjust the thicknesses of the constituent GaAs and AlAs layers to maintain the transmission peak near 1061 nm. The QWs, however, were always simulated as having a physical thickness of 80 Å, with peak absorption at 1011 nm. The resulting difference in refractive index for a single QW with and without applied field is then simulated to be Dn = 0.0041 at 1061 nm. The results of these simulations for one QW in each GaAs layer of the DBR stack are shown in Figure 4. The left axis tracks the FWHM of the 1061-nm transmission resonance as a function of the number of periods, N. This information is important when determining the spectral width of the incident pulse. Pulses that are too broad spectrally will experience distortion in propagating through the structure. The right axis gives a plot of the anticipated pulse delay, that is, the pulse propagation time with applied field minus the time without applied field. The change in delay shows a quadratic dependence on N, similar to the results obtained previously³.
 
 

The resultant tunable time delay shown in Figure 4a is relatively small for structures having less than 30 periods. To increase the amount of time delay we need to increase the changes in refractive index under an applied field. The most straightforward way to do this is to increase the number of quantum wells contained in each GaAs quarter-wave layer. Figure 4b compares the cases of one, two, and three QWs per GaAs layer. The time delay for any given number of periods is seen to be just less than doubled by placing twice the number of QWs in the structure, and less than tripled for three QWs per layer. The factors of less than two or three in tunable delay enhancement can be traced to a geometrical dependence of the overlap of the electric field of the propagating radiation with the location of the QWs in the DBR/ODL structure¹⁶. Furthermore, restrictions on the number of QWs that can be grown in a single GaAs quarter-wave layer introduce limitations on increasing the time delay change via this method. Using a minimum of 100 Å of GaAs barrier material on each side of a QW, we are then limited to a maximum of 3 QWs per GaAs layer. Further tunability must come from placing the exciton peak closer to the bandedge resonance.
 
 
 
 

5. DBR Optical delay lines: Growth and Processing

 

 
 
 
 
 
 
 
 

Three samples were grown by molecular beam epitaxy. The first sample was a calibration DBR sample consisting of 28-periods of GaAs and AlAs. The layers of this mirror were grown such that the long-wavelength bandedge resonance occurred at 1037 nm. Top and bottom GaAs cap layers were grown and doped with Be and Si for standard Ohmic metal contacts. The second sample consisted of twelve 80-Å In_0.2Ga_0.8As QWs separated by 1000 Å GaAs barriers. Again, top p-metal and bottom n-metal contacting layers were fashioned by doping appropriate GaAs layers with Be and Si. The third sample, the DBR/ODL structure, incorporated three QWs per GaAs quarter-wave layer. The design wavelength for the 30-period DBR/ODL structure was 1001 nm, chosen to put the long-wavelength bandedge resonance near 1064 nm. This is a wavelength of interest for both cw and pulsed laser investigations using Nd:YAG lasers. This DBR/ODL structure also includes a final period containing no QWs, but with a GaAs layer that was Be doped (p+ ~ 5e+18 cm^-3) for p-Ohmic contact. Likewise, a 1-m m thick Si doped (n+ ~ 1e+18 cm^-3) GaAs buffer layer provides an n-Ohmic contact layer. Reflectance and transmission spectra for this sample prior to device processing are shown in Figure 5.
 
 

Sample processing involved three steps: liftoff metallization for the top p-contact; electrical isolation via etching; and liftoff metallization for the bottom n-contact. Individual devices were designed to be cylindrical post structures 300 m m in diameter, and were formed into grids of 8x8 arrays of devices with 400 m m center-to-center spacing between devices. The top p-metal contact consists of an annulus 20 m m wide of 200 Å of evaporated titanium followed by 2500 Å of gold, all recessed from the edge of the mesa by 15 m m. A bonding pad of diameter 100 m m is also included in the p-metal liftoff, limiting the spot size for incident beams to diameters ~150 m m. The most important processing step for these devices was etching vertical post structures with smooth sidewalls to prevent reverse-bias breakdown. This was accomplished using an inductively coupled plasma reactive ion etching system. Etching the DBR/ODL structure required elevated substrate temperatures to aid in the removal of indium compounds from the sample surface. We used a substrate temperature setpoint of 60 ° C to accomplish this task. It must be emphasized that this was not the actual temperature of the GaAs substrate of our device because the processed samples, typically smaller than a quarter of a full 3-inch wafer, were mounted to 3-inch Pyrex mounting substrates for purposes of system loadlock transfer. A laser reflectance measurement system proved to be extremely beneficial for real-time monitoring of the etch process. The monitoring system consists of a diode laser (l = 760 nm) and a silicon photodetector connected to a pre-amplifier, the output of which is sent to a computer. The laser and detector are mounted to an aluminum housing which can be secured to the top viewport of the chamber of the reactive ion etching system. Collimating and focusing optics reduce the laser spot to a few millimeters in diameter at the sample surface. A removable plate beamsplitter and CCD camera are used to help align the laser spot to a clearfield pattern on the sample. Each oscillation in the time trace corresponds to the removal of a single DBR period. The system gave an average etch rate of 543 Å/s, with better than 5:1 selectivity for etching the sample compared to etching the AZ 1818 positive photoresist mask.
 
 

6. Characterization

 

 
 
 
 
 
 
 
 

After sample processing, the MQW and DBR/ODL structures were cleaved, mounted into transmissive testing packages, and wire-bonded for electrical characterization. DC testing of several devices on the MQW sample showed currents near 1 m A for an applied reverse-bias of 45 V, indicating the onset of breakdown. The DBR/ODL devices gave similar results for reverse-biases > 80 V. Optical absorption measurements on the MQW sample with varying applied biases are shown in Figure 6a. Here, absorption is defined through the relation aLº -ln[T], with a the absorption coefficient, L the sample thickness, and T the transmission through the sample. The inset of Figure 6a shows the energy shift of the exciton absorption peak in meV as a function of applied bias (bottom ordinate) or applied field (top ordinate). The low signal-to-noise ratios as well as the asymmetric lineshapes of these spectra prevent an accurate determination of the broadening of the e1-hh1 resonance under applied field. One does, however, see Stark shifts that vary in good agreement with previous findings^6-8, and the exciton appears nearly ionized at -20 V. Similar measurements were performed in reflectivity on the DBR/ODL structures. The relatively short penetration depth of incident light into the DBR's transmission stopband means that only the first few QWs are being probed, causing a further reduction in the reflectance signal. Naturally, as it is the electric field that generates the QCSE, larger reverse biases are required across the DBR/ODL structure to produce results similar to those in the MQW, due primarily to differences in sample thickness. Indeed, a reverse bias of 10 V across the MQW resulted in an energy shift of -8.8 meV, whereas -45 V was required across the DBR/ODL to generate a shift of -10.9 meV; see Figure 6b.
 
 

We performed group delay measurements on a 28-period DBR structure that had a long-wavelength photonic bandedge resonance near 1037 nm using the experimental arrangement shown in Figure 7. We divided theoutput pulse train from the RegA (250 kHz pulse train of ~100 fs at 810 nm) by a beam splitter into reference and probe pulse trains. A lens of focal length 75 mm focused the probe beam into a sapphire flat. This generated a white light continuum spanning a range of roughly 400-1170 nm. Subsequent filters spectrally narrowed this spectrum so as to span the region from 1000 nm to 1170 nm. Wavelengths shorter than 1000 nm were not needed and would have unnecessarily induced carriers in the sample. A turning mirror then directed the reference beam so that it propagated collinearly with the probe beam. A lens of focal length 75 mm focused the beams so they overlapped in a b-barium borate (BBO) crystal. The signal generated by the mixing process was spatially isolated and focused onto the entrance slit of a spectrometer. A precision controlled translation stage varied the group delay between the reference and the probe pulses over the temporal range of interest. This procedure mapped the temporal evolution of the spectrum in terms of 6.7 fs intervals (2 mm steps of the translation stage delay).
 
 

In this particular case the continuum probe consisted of a family of pulses of 100 fs duration having an approximately uniform distribution, aside from a slight chirp (Figure 8b), of wavelengths over the region from 1000 to 1070 nm. While a variety of probes could be used this particular probe was convenient given the 100 fs duration of the generating pulse. This family of pulses therefore provided information over three key resonances beyond the photonic bandedge. As a means of interpreting the data we have provided the data in a 2-dimensional plot and also provided simulations of the expected modification of this particular probe pulse on transmission through the sample.
 
 

The measurements show the group delay produced by the combined photonic band edge structure and the 520 mm thick GaAs substrate. The measurements span a spectral region including the first three transmission peaks of the photonic band edge. Although absorption by the GaAs substrate at these wavelengths is negligible, the proximity of the GaAs bandgap contributes significantly to group velocity dispersion of the transmitted pulses. Figure 8a shows the spectrum of the pulse passing through the sample, upconverted by mixing with the reference pulse. Figure 8b shows the similarly upconverted spectrum of the probe pulse not passing through the sample.
 
 

Figure 9 shows a simulation of the measured results. The simulation was performed by using the transfer matrix approach³ to propagate the probe pulse through the structure and the substrate. Convolving this result with a 9-nm FWHM reference pulse at 810 nm via
 
 
 

, (3)

 
 

with E_p the probe pulse, E_r the reference pulse, and t the relative time delay between the two, then constructed the time axis¹⁷. All pulses were assumed to be transform limited. As the spectral region of interest is close to the band edge of the GaAs substrate, significant group velocity dispersion is added to the effects of the structure. The simulation in Figure 10a shows the effect of the DBR structure without a substrate, while Figure 10b illustrates the simulated effect of the substrate with no DBR structure.
 
 
 
 
 
 

7. Conclusions

 

 
 
 
 
 
 
 
 

We have demonstrated the design, growth, and fabrication of a proposed voltage-tunable optical delay line by using multiple InGaAs quantum wells in the GaAs layers of a GaAs/AlAs distributed Bragg reflector. Initial transfer-matrix simulations using a Lorentzian model for the dispersive quantum well refractive index indicate the potential for nearly 50 fs of tunable delay time for pulses incident at the long-wavelength bandedge resonance. Furthermore, these pulses will experience negligible distortion provided their spectral bandwidth is small compared to the bandwidth of the long-wavelength bandedge resonance. Measurements of the quantum-confined Stark effect in a multiple quantum well sample showed results in accord with previously published works.
 
 

The preliminary group delay measurements show a basic agreement with the expected group delay caused by the photonic band edge structure. The substrate, however, contributes large group velocity dispersion. Thinning or removing the substrate could reduce this. The consistency of the measurements with the predicted influence of the sample provides a basis for designs that depend on the knowledge of the influence of a photonic band edge that includes multiple resonances on short optical pulses. A wide variety of other measurements are, of course, possible using either shorter or longer duration optical continuum pulses.
 
 

8. acknowledgments

 

 
 
 
 
 
 
 
 

T.R. Nelson, Jr., would like to thank S.A. Feld (Wright State University), W.J. Siskaninetz (Wright State University), and R.E. Sherriff (AFRL/MLPA, Wright-Patterson AFB) for their aid and expertise in processing and characterizing the samples. Support is gratefully acknowledged from the AFOSR via the Entrepreneurial Research fund for Defense Research Sciences.

The University of Alabama in Huntsville Laser Science & Engineering group thanks the AFOSR for funding through grants F49620-96-1-0206 and F49620-93-1-0410, NASA for funding through grant NGT8-52812, NSF for funding under grants IFCA-UAH1 and GER-9553475, and also Jon Dowling, Mike Scalora, Mark Bloemer, and Charles Bowden for discussions of the photonic bandedge structure during early stages of the work.
 
 

9. references

1. P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D.P. Resler, R.C. Sharp, and E.A. Watson, "Optical phased array technology," Proc. of the IEEE, vol. 84(2), pp. 268-298, 1996.
2. W.M. Neubert, K.H. Kudielka, W.R. Leeb, and A.L. Scholtz, "Experimental demonstration of an optical phased array antenna for laser space communications," Applied Optics 33(8), pp. 3820-3830, 1994.
3. J.M. Bendickson, J.P. Dowling, and M. Scalora, "Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures," Phys. Rev. E 53(4), pp. 4107-4121, 1996.
4. M. Scalora, R.J. Flynn, S.B. Reinhardt, R.L. Fork, M.J. Bloemer, M.D. Tocci, C.M. Bowden, H.S. Ledbetter, J.M. Bendickson, J.P. Dowling, and R.P. Leavitt, "Ultrashort pulse propagation at the photonic band edge: Large tunable group delay with minimal distortion and loss," Phys. Rev. E54(2), pp. R1078-R1081, 1996.
5. M. Scalora and M.E. Crenshaw, "A beam propagation method that handles reflections," Opt. Commun 108, pp. 191-196, 1994.
6. D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard, W. Wiegmann, T.H. Wood, and C.A. Burrus, "Electric field dependence of optical absorption near the band gap of quantum-well structures," Phys. Rev. B32, pp.1043-1060, 1985.
7. J.S. Weiner, D.A.B. Miller, and D.S. Chemla, "Quadratic electro-optic effect due to the quantum-confined Stark effect in quantum wells," Appl Phys. Lett. 50(13), pp. 842-844, 1987.
8. J. Kavaliauskas, G. Krivaite, A. Galickas, I. Šimkiene, U. Olin, and M. Ottosson, "Quantum confined Stark effect in InGaAs/GaAs quantum wells under high electric fields," Phys. Stat. Sol. (B)191, pp. 155-159, 1995.
9. see, for example, J.D. Jackson, Classical Electrodynamics, Second edition, Chapt. 7, John Wiley & Sons, New York, 1975.
10. C. Ell, J. Prineas, T.R. Nelson, Jr., S. Park, H.M. Gibbs, G. Khitrova, S.W. Koch, and R. Houdré, "Influence of structural disorder and light coupling on the excitonic response of semiconductor microcavities," Phys. Rev. Lett. 80(21), pp. 4795-4798, 1998.
11. G. Khitrova, D.V. Wick, J.D. Berger, C. Ell, J.P. Prineas, T.R. Nelson, Jr., O. Lyngnes, H.M. Gibbs, M. Kira, F. Jahnke, S.W. Koch, W. Rühle, and S. Hallstein, "Excitonic effects, luminescence, and lasing in semiconductor microcavities," Phys. Stat. Sol. (B)206, pp. 3-17.
12. T. R. Nelson, Jr., J.P. Prineas, G. Khitrova, H.M. Gibbs, J.D. Berger, J.-H. Shin, H.-E. Shin, Y.-H. Lee, P. Tayebati, and L. Jauniskis, "Room-temperature normal-mode coupling in a semiconductor microcavity utilizing native-oxide AlAs/GaAs mirrors," Appl. Phys. Lett. 69(11), pp. 3031-3033, 1996.
13. O. Blum, J.E. Zucker, T. H. Chiu, M.D. Divino, K.L. Jones, S.N.G. Chu, and T.K. Gustafson, "InGaAs/InP multiple quantum well tunable Bragg reflector," Appl. Phys. Lett 59(23), pp. 2971-2973, 1991.
14. O. Blum, J.E. Zucker, X. Wu, K.H. Gulder, H. Sohn, T.K. Gustafson, and J.S. Smith, "Low-voltage-tunable distributed Bragg reflector using InGaAs/GaAs quantum wells," IEEE Photon. Tech. Lett. 5(6), pp. 695-697.
15. J.A. Trezza, K. Kang, J.S. Powell, C.G. Garvin, and R.D. Stack, "High-speed electrically controlled GaAs quantum well spatial light modulators: device creation and applications," Proc. SPIE 3292, pp. 94-102, 1998.
16. M.D. Tocci, M.J. Bloemer, M. Scalora, C.M. Bowden, and J.P. Dowling, "Spontaneous emission and nonlinear effects in photonic band gap materials," appearing in Microcavities and Photonic Bandgaps: Physics and Applications, J. Rarity and C. Weisbuch, eds., pp. 237-248, Kluwer Academic Publishers, Boston, 1996.
17. J.-P. Foing, J.-P. Likforman, M. Joffre, and A. Migus, "Femtosecond pulse phase measurement by spectrally resolved up-conversion: Application to continuum compression," IEEE J. Quant. Electron 28(10), pp. 2285-2290, 1992.

1. Figures

Figure 1. (a) Simulated transmission spectra of a 20-period GaAs/AlAs DBR; (b) Transmission phase for the same structure.

The vertical dotted line represents the design wavelength (1150 nm), while the two vertical dashed lines give theoretical

positions of the bandedge resonances for an infinite-period structure.

Figure 2. Lorentzian oscillator model of the (a) the absorption coefficient and (b) refractive index of an 80-Å

In(0.2)Ga(0.8)As quantum well. To simulate the effects of an applied field of strength F = 100 kV/cm (dotted lines),

we assume a red shift of 20 meV, as well as broaden the absorption line and reduce it's peak absorption.

Figure 3. Simulated transmission of three DBRs with design wavelength 1150 nm. This figure

illustrates the influence of the number of periods in a DBR structure on the wavelength locations

and spectral widths of the bandedge resonances. The vertical lines again give design wavelength (dotted)

and the bandedge resonance wavelengths in the infinite-period limit.
 
 
 
 

Figure 4. (a) Simulation results showing increasing time delay (time with applied bias - time without bias)

and decreasing transmission FWHM with increasing number of DBR periods. (b) Simulation results showing

increasing tunable time delay by increasing the number of quantum wells (QWs) in each GaAs layer of the DBR.