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We discuss experimental results that demonstrate all-optical switching and pulse-routing functionality, at 1.55 μm, of nonlinear multiple-quantum-well waveguides equipped with a Bragg grating. Basing on the nonlinear Time-Domain Beam Propagation Method, the switching behavior has been theoretically investigated using a model, developed as part of this work.
©1998 Optical Society of America
1. Introduction
Nonlinear media having a periodic modulation of the refractive index has been the subject of a considerable research effort over the last two decades. A large number of theoretical works, ranging from steady-state analysis to time-dependent treatments, investigated the nonlinear light propagation in this kind of structures [1–8] and demonstrated the possibility of obtaining several interesting effects such as optical bistability, soliton propagation and all-optical switching. Some of these effects were then experimentally observed in different periodic nonlinear materials and at different optical pumping energies [9–16] depending on the material optical nonlinearity and on the sample structure. Besides the fundamental interest raised by this subject, important applications are envisaged in the field of optical telecommunications. In particular, devices based on nonlinear periodic structures could be developed to achieve high-bit-rate all-optical switching and all-optical demultiplexing. To be useful for telecommunication applications, these devices should be operated at low-control energy, typically of order of 1 pJ/pulse, and should display a low-switching time, typically less then 10 ps. Furthermore, these devices could be advantageously integrated with other photonic devices, such as for example semiconductor optical amplifiers, in order to achieve more sophisticated functionality. In view of all these requirements, a convenient choice is using waveguiding structures, particularly channel waveguides that are basic components in integrated optics; although fiber gratings have proven very efficient when monolithic integration is not required [13–15]. Channel waveguides allow to reach high power densities with moderate optical power, and to obtain long interaction lengths, two factors that are crucial to the efficiency of the nonlinear process [17]. In the past there have been significant experimental achievements in this research field, although the goal of obtaining all-optical switching within all the constraints introduced in the above has not been fulfilled yet. In particular J. E. Ehrlich et al. reported all-optical tuning in planar waveguides exhibiting slow thermal nonlinearity [11]. N. D. Sankey et al. observed intensity-dependent transmission of a single beam tuned within the grating stop band in planar silicon waveguides, at pumping energy of 1-18 μJ/pulse [12]. Recently we observed all-optical switching and routing of weak signal pulses induced by low-energy control pulses (~ 1 pJ/pulse) in multiple-quantum well (MQW) ridge waveguides at 1.55 μm [16]. The switching-time was limited to about 600 ps by the material recovery time. This is the time in which the material recovers its linear optical properties after the control pulse. It has no direct relevance to the nonlinear process, but is rather the time in which the carrier pairs are eliminated from the structure after inducing the useful effect. It could be strongly reduced, without affecting the low-control energy required, if the carriers recombined non-radiatively [18].
Following our preliminary report [16], here we discuss in detail the experimental results and introduce a new numerical algorithm developed to model the nonlinear propagation of the optical pulses in our periodic waveguides. The numerical algorithm is based on a nonlinear Time-Domain Beam Propagation Method (TD-BPM) and includes the treatment of photogenerated-carrier nonlinearity in MQWs, which is substantially different from Kerr nonlinearity. The focus of this work is on convenience of using MQWs as nonlinear media, particularly in view of control-energy requirement, on advantages provided by the channel-waveguide geometry, and on the physical insight provided by the nonlinear TD-BPM.
The paper is structured as follows: In Section 2 the device structure and the fabrication details are addressed; further, the optical nonlinearities of MQWs and the features provided by the grating are discussed. In Section 3 the experimental results are described. In section 4 the nonlinear TD-BPM is introduced, and some numerical results are shown. Finally, Section 5 summarises the main conclusions of our work.
2. Device
The device structure we investigated is depicted in Fig. 1. Our device is a passive, single-mode ridge waveguide 2 μm wide and 300 μm long, with a grating etched onto the upper cladding layer to a depth of 0.15 μm and with a period of 0.24 μm. The grating causes a first-order coupling between forward and backward propagating fields at the Bragg wavelength, λB = 1.556μm. We chose counter-propagating coupling because it requires a short period grating, compatible with integrated-optics dimensions, and for the sake of simplicity, in fact it produces a transfer of energy between two opposite propagation directions of the same mode in the same single-mode waveguide.
The waveguide was defined by optical lithography, while the grating was defined by electron-beam lithography. Both the waveguide and the grating were etched using reactive-ion etching (RIE). Waveguide facets were coated to avoid undesired Fabry-Perot effects. The core material is a stack of thirty InGaAs/InAlAs quantum wells sandwiched between InP cladding layers. The heterostructure used to fabricate our device was grown by chemical beam epitaxy on an InP: S substrate. The MQW structure was tailored to display useful nonlinear optical properties around 1.55 μm. The device has one input port and two output ports, see Fig. 1. One of them, the reflection port, physically coincides with the input port.
The nonlinear mechanism we exploit here consists in the modification of the optical properties of MQWs induced by a photogenerated carrier plasma: because of the rapid thermalization process, photogenerated electrons and holes are assumed to be in thermal equilibrium within the conduction and valence bands, respectively. The optical properties of MQWs strongly depend on the carrier density inside the structure, as it is shown in the curves of Fig. 2. This makes the optical properties implicitly intensity dependent, since under pumping at wavelength where the material is absorbing, carrier pairs are photogenerated and changes take place in the optical properties. In particular, clearly resolved absorption peaks arising from excitons do occur even at room temperature, and it is possible to quench these peaks at relatively low intensities. The quantitative description of this mechanism requires the solution of a many-body problem, and it can be addressed at different levels of approximation [19–21].
Fig. 2. Optical properties of the MQW material, calculated according to Ref. [21]: a) Linear spectrum of the real part of the refractive index. b) Linear spectrum of the imaginary part of the refractive index. c) Spectral changes of the real part of the refractive index at different carrier densities, ranging from 108 to 5×1011 cm-2. d) Same as c) but for the imaginary part of the refractive index. The orange dashed lines indicate the wavelength of the 1st exciton resonance, while the red dashed lines indicate the Bragg wavelength of the grating, around that the device is operated.
In particular, it has become possible to provide either a rigorous treatment, addressing purely 2D structures [19, 20] or an approximate treatment of the many-body effects on the optical properties, that take into account the finite well width [21]. The latter yields a close expression (in fact a generalized Elliott formula) for the, density dependent, complex refractive index n(A,N) = n(λ,N) = n(λ,N)+ik(λ,N) and it has been successfully used by us to interpret experiments on waveguided, nonlinear devices [10, 22]. In view of applications it is very important that a spectral domain there exist where the absorption is low enough to permit waveguide propagation, along optical paths of practical length, and yet strong enough to cause the photogeneration of a plasma of appreciable density and induce therefore sizeable nonlinearities. This spectral region occurs at wavelengths substantially longer, by tens of nm, than the first exciton resonance (e1-hh1 in the case addressed here). In particular in this region the refractive variations, Δn, are negative and strong enough to obtain all-optical switching, while the absorption variations, Δk, are positive and have a significant impact on the device operation.
MQW material is highly nonlinear thus requiring very low pumping energies to modify its optical properties; nevertheless, it needs a relatively long time to recover the linear optical properties after the pumping pulse, and this is due to the radiative recombination process, which lasts typically a few ns. The controlled introduction of defects in MQWs, causing non-radiative recombination processes, can significantly increase the elimination rate of carriers, without introducing detrimental effects on the linear and the nonlinear optical properties [18]. We succeeded in lowering the recovery time from the original 2.5 ns, in InGaAs/InP material, to 160 ps, in InGaAs/InAlAs material grown in As-rich conditions and having the wells 1 % compressively strained. A further reduction to 32 ps was obtained by lowering the growth temperature [18]. However at the moment we are limited by the etching process used to fabricate the device, CH4/H2 RIE, which causes an increase of the recovery time to about 600 ps, and we are currently working to find alternative etching processes which preserve the fast material characteristics.
The grating adds extremely important features to the waveguiding structure. For wavelengths located around the Bragg wavelength, the reflectance curve shows a pass-band while the transmittance curve shows a stop-band, see the solid-line blue curves in Fig. 3. The width and the depth of these bands is proportional to the coupling coefficient κ, which depends on the optical power fraction in the grating. The coupling coefficient can be adjusted by varying the distance between the grating and the core layer, the void fraction of the grating or its etching depth. In our structure the stop-band width is approximately 2 nm. When MQW core material is populated through the absorption of intense light pulses, its optical properties change and the device response is modified, see the dashed-line red curves in Fig. 3. In particular, as the real part of the refractive index is lowered, the grating spectral bands are shifted towards shorter wavelengths. The nonlinear absorption increase causes a reduction in the depth of these bands.
In our device, the switching from the linear to the nonlinear regime is achieved by injecting an intense control pulse, whose wavelength is strongly detuned from the Bragg wavelength. This control pulse propagates practically unimpeded by the grating; it is absorbed in the waveguide and creates the carrier population which in turn causes the changes of the optical properties. The operation of our device is based on the nonlinear displacement of the spectral bands induced by the control pulse. In particular a weak signal pulse whose wavelength λ1, lies within the (linear) grating stop-band can be either reflected in the linear regime or transmitted in the nonlinear regime. On the contrary, a weak signal pulse of wavelength λ2 slightly detuned toward shorter wavelengths from the (linear) grating stop-band, can be either transmitted in the linear regime or reflected in the nonlinear regime. In this way, the cross-bar switching functionality for wavelengths λ1 and λ2 can be achieved. The nonlinear mechanism is thus a cross interaction between a strong optical control pulse and a weak optical signal pulse. It is basically different from the self-interaction mechanism experienced by a single intense pulse tuned in proximity of the grating stop-band, which is at the basis of Bragg grating soliton generation [14, 15].
Fig. 3. Spectral features of the grating. a) Transmittance curve in the linear (blue solid line) and nonlinear (red dashed line) regime. b) Reflectance curve in the linear (blue solid line) and nonlinear (red dashed line) regime. These curves were calculated using the coupled-mode theory and taking into account the material dispersion. The nonlinear regime corresponds to a carrier density of 1011 cm-2. The black arrows indicate the position of the linear Bragg wavelength and the vertical black dashed lines indicate the width of the photonic band gap [8].
3. Experimental results
The experimental arrangement for the observation of the switching behavior consisted in a tunable, semiconductor cw laser, providing a TE-polarized probe, or signal, beam at low power (the typical coupled power was about 10 μW); further a NaCl:OH color-center laser, synchronously pumped at 76 MHz by a Nd:YAG mode-locked laser, was used as the (tunable) pump, or control, source [16]. The pump beam wavelength was detuned from the Bragg wavelength and held fixed at 1544 nm (not critical). The pump pulse width was about 10 ps, slightly in excess of the round-trip time of the waveguide. The outcoupled probe light was analyzed, either spectrally, or as a function of time using a fast, pigtailed photodetector and a 8 GHz digitising oscilloscope. Fig. 4 reports the results of the experiments in term of transmittance and reflectance variations.
Tuning the probe laser to the Bragg wavelength we observed inhibited reflection at the reflection port and induced transmission at the transmission port. While tuning the probe laser 5 nm below the Bragg wavelength we observed an opposite behavior, that is induced reflection at the reflection port and inhibited transmission at the transmission port, as expected from the nonlinear spectral-band displacement. The switching was obtained with coupled pump pulse energy of about 1 pJ. The recovery time was limited to about 600 ps by the slowing effect due to the etching process, discussed in the above.
Fig. 4. Transient changes of the cw probe beam induced by a 10-ps pump pulse tuned at 1544 nm. a) Transmittance variation observed at the transmission port, by tuning the probe beam either at the Bragg wavelength, λB, or 5 nm below λB. b) Reflectance variation observed at the reflection port , by tuning the probe beam either at the λB or 5 nm below λB. τ and E refer to the recovery time and to pump-pulse energy, respectively.
Fig. 5. Pulse routing experiment: a) Injected pump (control) pulses. b) Injected probe (signal) pulses. c) Transmitted probe (signal) pulses, having a wavelength detuned by 5 nm from the Bragg wavelength. d) Transmitted probe (signal) pulses, tuned to the Bragg wavelength.
In order to explore the pulse-routing capability of the device we turned to a pulsed pump-probe experiment [16]. Modulating the cw beam through an electro-optical modulator we generated probe pulses 300 ps long, with a period of less than 2 ns. The pump pulses and the detection scheme were the same as in the previous experiment. Fig. 5 reports the experimental outcomes in the form of transmitted power as a function of time. The first curve from top represents the injected pump (control) pulses, while the second curve represents the injected probe (signal) pulses. In the third curve we show the transmitted probe pulses tuned 5 nm below the Bragg wavelength. The probe pulse coinciding with the pump pulse is switched off, in fact this it is routed from the transmission port to the reflection port, while pulses injected at later time are transmitted. In the last black curve we report the transmitted probe pulses tuned at the Bragg wavelength. The behavior here is opposite: the probe pulse coinciding with the pump pulse is routed to the transmission port, while the others are reflected. Evaluating the ratio between linearly- and nonlinearly-transmitted pulses, we could measure an on-off ratio of 10 dB for inhibited transmission and 12 dB for induced transmission respectively, limited by the electrical noise level in detection.
4. Modelling
To study the pulse propagation within the nonlinear DFB MQW waveguide, we developed a model based on the TD-BPM. Our model can be schematised as follows: the optical pulse propagation is calculated using the slow-wave approximation of the wave equation, the carrier photogeneration is evaluated using the rate equation describing the absorption-recombination process, and finally the changes of the MQW optical properties are obtained by the model of our Ref. [21] which takes into account the many-body effects in the carrier plasma. All these three calculations are iterated jointly within a finite-difference scheme. The computational procedure allows the study of the propagation of intense pulses in nonlinear materials and waveguides, and takes into account the distributed reflections, which occur within a grating structure.
The propagation of a TE-polarized light pulse in a single-mode ridge waveguide can be described by the wave equation
where E is the transverse component of the electric field and no is the modal refractive index of the waveguide. Using the slow-wave approximation [23], which holds if the optical pulse contains more than a few optical cycles, and factoring a fast term, which oscillates with the angular frequency ω, equation (1) becomes
equation (2) is formally analogous to the well-known equation governing the (space-domain) Beam Propagation Method (BPM), a widespread numerical tool. Basing on this analogy, it is clear that BPM codes [24] can be applied to study the temporal evolution of optical pulses in waveguides. In particular we have solved the equation (2) using an implicit finite-difference scheme (Crank-Nicholson), frequently adopted in BPM codes [24]. The resulting Time-Domain Beam Propagation Method (TD-BPM) equation is
where the superscript * represents the complex conjugate, while the indexes j and k refer to the coordinate of the grid points zj, and tk , respectively. These define the computational window according to
The coefficients c1, c2, and c3, are
and λ is the wavelength in vacuum. The algebraic system (3) can be solved using a standard numerical method for tridiagonal matrix inversion [25].
In our simulations we adopted an input optical field expressed by the equation
which represents a gaussian pulse of width σt propagating in the forward direction.
The local photogenerated carrier density can be evaluated from a rate equation, which describes the process of creation and recombination of carriers
where N3D is the volume carrier density, p is the volume photon density and τ is the carrier recombination time. Equation (7) can be solved within a finite-difference approach adopting the same computational window of the TD-BPM. Following this approach, equation (7) becomes
where ħ is the reduced Planck constant, Jo is the pulse energy, σ is the waveguide-mode area, and Lw is the well width. The algebraic equation (8) has to be solved jointly with the TD-BPM equation (3). Using the model here described, we simulated the all-optical switching functionality of our structure.
Fig. 5. Propagation of the pump pulse calculated using the TD-BPM. The pump wavelength is detuned by 10 nm from the Bragg wavelength.
In Fig. 5 we show the results of a simulated propagation of the pump pulse in our device. On the left the pump intensity is shown in a color representation as a function of propagation coordinate and time. The grating waveguide is located within the white dashed lines. We see that the pump pulse is strongly absorbed and marginally reflected. On the right the carrier density photogenerated within the device is shown as a function of space and time. The pump pulse reaches the device after about 10 ps and then populates the MQW material changing its optical properties. In this simulation the pump pulse energy was 5 pJ and its width was 5 ps.
Fig. 6. Propagation of the probe pulse, tuned within the grating stop-band (λ=λB+1nm), calculated using the TD-BPM. a) Linear (without pump). b) Nonlinear (with pump).
Fig. 6 depicts the calculated propagation of a probe pulse whose wavelength is 1 nm longer than the Bragg wavelength, thus lying within the grating stop-band. On the left the linear propagation is shown. In this case the probe pulse is strongly reflected. On the right the probe-pulse propagation is shown in a structure whose optical properties were modified by the absorption of the pump pulse. In this case the probe pulse is mainly transmitted and partly absorbed due to the previously discussed nonlinear absorption increase. These two graphs represent the two states of the switching device for a signal wavelength lying within the grating stop-band. The relevant contrasts are about 12 dB. Opposite behaviours were found for probe wavelength slightly detuned from the grating stop-band, as it is shown in Fig. 7.
Fig. 7. Propagation of the probe pulse, tuned at one edge of the grating stop-band (λ=λB-2nm), calculated using the TD-BPM. a) Linear (without pump). b) Nonlinear (with pump).
5. Conclusions
We have presented an analysis of an all-optical switching element based on a DFB MQW waveguide. Its functionality is due to the nonlinearity in the MQW waveguide core, which causes an intensity-dependent modification of the spectral properties induced by the grating. The device can be operated in both reflection and transmission and can handle two optical signals at two different wavelengths λ1 and λ2, accomplishing a cross-bar switching functionality on these two wavelengths: from reflect λ1/transmit λ2 in the absence of the control pulse to transmit /λ1/reflect λ2 in the presence of the control pulse. The on-off contrast ratio here reported is 10 dB or slightly more. This figure can be improved by increasing the coupling coefficient, and by improving the quality of the grating lithography process. One advantage of using passive nonlinear devices, over their active counterparts, is that electrical wiring and contact pads are eliminated, making the operation of the former class of devices intrinsically reliable. In addition, passive devices are more readily and easily integrated within monolithic or hybrid optical circuitry, making it possible to achieve more sophisticated functionality.
Acknowledgements
We are grateful to our colleagues that contributed to the realization and characterization of the device investigated here: L. Gastaldi, G. Meneghini, D. Re, R. De Franceschi, D. Soldani, and M. C. Bossi.
References and links
1. H. G. Winful, J. H. Marburger, and E. Garmire, “Theory of bistability in nonlinear distributed feedback structures,” Appl. Phys. Lett. 35, 379–381 (1979). [CrossRef]
2. W. Chen and D. L. Mills, “Gap solitons and the nonlinear optical response of superlattices,” Phys. Rev. Lett. 58, 160–163 (1987). [CrossRef] [PubMed]
3. G. Assanto and G. I. Stegeman, “Optical bistability in nonlocally nonlinear periodic structures,” Appl. Phys. Lett. 56, 2285–2287 (1990). [CrossRef]
4. C. M. de Sterke and J. E. Sipe, “Switching dynamics of finite periodic nonlinear media: A numerical study,” Phys. Rev. A 42, 2858–2869 (1990). [CrossRef] [PubMed]
5. H. G. Winful, R. Zamir, and S. Feldman, “Modulation instability in nonlinear periodic structures: Implications for ‘gap solitons’,” Appl. Phys. Lett. 58, 1001–1003 (1991). [CrossRef]
6. J. He and M. Cada, “Optical bistability in semiconductor periodic structures,” IEEE J. Quantum Electron. 27, 1182–1188 (1991). [CrossRef]
7. G. P. Bava, F. Castelli, P. Debernardi, and L. A. Lugiato, “Optical bistability in a multiple quantum well structure with Fabry-Perot and distributed feedback resonators,” Phys. Rev. A 45, 5180–5192 (1992). [CrossRef] [PubMed]
8. C. M. de Sterke and J. E. Sipe, “Gap solitons” in Progress in Optics XXXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Chap. III.
9. B. Acklin, M. Cada, J. He, and M. -A. Dupertuis, “Bistable switching in a nonlinear Bragg reflector,” Appl. Phys. Lett. 63, 2177–2179 (1993). [CrossRef]
10. C. Coriasso, D. Campi, C. Cacciatore, L. Faustini, C. Rigo, and A. Stano, “Butterfly bistability in an InGaAs/InP multiple-quantum well waveguide with distributed feedback,” Appl. Phys. Lett. 67, 585–587 (1995). [CrossRef]
11. J. E. Ehrlich, G. Assanto, and G. I. Stegeman, “All-optical tuning of waveguide nonlinear distributed feedback gratings,” Appl. Phys. Lett. 56, 602–604 (1990). [CrossRef]
12. N. D. Sankey, D. F. Prelewitz, and T. G. Brown, “All-optical switching in a nonlinear periodic-waveguide structure,” Appl. Phys. Lett. 60, 1427–1429 (1992). [CrossRef]
13. S. La Rochelle, Y. Hibino, V. Mizrahi, and G. I. Stegeman, “All-optical switching of grating transmission using cross-phase modulation in optical fibers,” Electron Lett. 26, 1459–1460 (1990). [CrossRef]
14. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, “Bragg grating solitons,” Phys. Rev. Lett. 76, 1627–1630 (1996). [CrossRef] [PubMed]
15. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, “Nonlinear pulse propagation in Bragg gratings,” J. Opt. Soc. Am. B. 14, 2980–2993 (1998). [CrossRef]
16. C. Coriasso, D. Campi, C. Cacciatore, L. Faustini, C. Rigo, and A. Stano, “All-optical switching and pulse routing in a distributed-feedback waveguide device”, Opt. Lett. 23, 183–185 (1998). [CrossRef]
17. G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, and C. T. Seaton, “Third order nonlinear integrated optics,” J. Lightwave Technol. 6, 953–970 (1988). [CrossRef]
18. C. Rigo, L. Gastaldi, D. Campi, L. Faustini, C. Coriasso, C. Cacciatore, and D. Soldani, “Multiple quantum well compressive strained heterostructures for low driving power all-optical waveguide devices,” J. Crystal Growth 188, 317–322 (1998). [CrossRef]
19. D. Campi and G. Colì, “Green’s-function approach to the optical nonlinearities in semiconductors and quantum-confined structures,” Phys. Rev. B 54, R8365–R8368 (1996). [CrossRef]
20. D. Campi, G. Colì, and M. Vallone, “Formulation of the optical response in semiconductors and quantum-confined structures,” Phys. Rev. B 57, 4681–4686 (1998). [CrossRef]
21. D. Campi and C. Coriasso, “Optical nonlinearities in multiple-quantum wells: Generalized Elliott formula,” Phys. Rev. B 51, 10719–10728 (1995). [CrossRef]
22. C. Cacciatore, L. Faustini, G. Leo, C. Coriasso, D. Campi, A. Stano, and C. Rigo, “Dynamics of nonlinear optical properties in InxGa1-xAs/InP quantum-well waveguides,” Phys Rev. B 55, R4883–R4886 (1997). [CrossRef]
23. P. -L Liu, Q. Zhao, and F. -S. Choa, “Slow-Wave Finite-Difference Beam Propagation Method,” IEEE Photon. Technol. Lett. 7, 890–892 (1995). [CrossRef]
24. Y. Chung and N. Dagli, “An assessment of Finite Difference Beam Propagation Method,” IEEE J. Quantum Electron. 26, 1335–1339 (1990). [CrossRef]
25. W. H. Press, B. P. Flannery, S. A. Teucolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing. (Cambridge Univ., New York, 1986), pp. 40–41.
