spectral shape or the far-field characteristic of the emission have been presented. The only argument for lasing (in contrast to spontaneous emission) provided is the dependence of the far infrared output power on the injection current (Fig. 3 in [l]). It consists of very few data points which might also be interpreted as a superlinear increase in the emission (without threshold), as has been previously observed on different samples [5, 61. Finally, the supposed far infrared laser spectrum (inset of Fig. 3 in [l]) is extremely similar to spontaneous emission spectra (Fig. 3 in [2]) reported by the same authors. This close similarity is even more astonishing since the samples are equipped with different waveguide designs, which are supposed to influence the spectral shape of the emission, if it arises from the quantum dots. In conclusion, the existence of laser emission corresponding to transitions between discrete bound electron states could not be evidenced by the results presented in [l]. 0 IEE 2001 31 October 2000 Electronics Letters Online No: 20010055 DOI: 10.1049/el:20010055 A. Weber and M. Grundmann (Institut f u r Festkiirperphysik, Technische Universitut Berlin, Hardenbergstr. 36, 0-10623 Berlin, Germany) E-mail: aweber@physik.tu-berlin.de N.N. Ledentsov (A.F. Iofle Physical-Technical Institute, Politekhnicheskaya 26, 194021, St. Petershurg, Russiu) as described in our Letter [3]. This also addresses the transition linewidth issue. We also observed that, in our device, the interband lasing threshold current was a factor of 1.6 lower than the observed intersubband threshold current. The light-current characteristics of another device, showing a distinct threshold behaviour, which is different from the superlinear behaviour of LEDs observed by us [4] and Grundmann et al. [5], are shown in Fig. 1. Unfortunately, device heating prevents us from making measurements at higher injection currents. We have also measured the polarisation of the output and find it to be TE polarised as predicted by theory [2]. The output is broad and multimode as is characteristic of interband QD lasers at high injection levels. It may be noted that our waveguide design is not too different from that of an interband QD laser, for reasons mentioned in [3]. A distributed feedback (DFB) device should exhibit more single-mode behaviour. I .o M. Grundmann: Currently at: Universitat Leipzig, Institut fur Experimentelle Physik 11, Linntstrasse 5, D-043 17 Leipzig, Germany N.N. Ledentsov: Also with TU Berlin References 1 KRISHNA, S , BHATTACHARYA, P., MCCANN, P.J., and NAMJOU, K.: ‘Room-temperature long-wavelength (h = 1 3 . 3 ~ )unipolar quantum dot intersubband laser’, Electron. Lett., 2000, 36, pp. 1550-1551 2 KRISHNA, s., QASAIMEH, o., B H A ~ A C H A R Y A P., , MCCANN, P.J., and NAMJOU, K.: ‘Room-temperature far-infrared emission from a selforganized InGaAsiGaAs quantum-dot laser’, Appl. Phys. Lett., 2000, 76, pp. 3355-3357 3 STIER, o., GRUNDMANN, M., and BIMBERG, D.: ‘Electronic and optical properties of strained quantum dots modeled by 8-band k.p theory’, Phys. Rev. B, 1999, 59, pp. 5688-5701 4 SAUVAGE, S., BOUCAUD, P., GERARD, J.-M., and THIERRY-MIEG, V.: ‘Inplane polarized intraband absorption in InAsiGaAs self-assembled quantum dots’, Phys. Rev. B, 1998, 58, pp. 10562-10567 5 VOROB’EV, L E., FIRSOV, D.A., SHALYGIN, V.A., TULUPENKO, V.N., SHERNYAKOV, YU.M., LEDENTSOV, N.N., USTINOV, v.M., and ALFEROV, zH.1.: ‘Spontaneous far-IR emission accompanying transitions of charge carriers between levels of quantum dots’, J. Exp. Theor. Phys. Lett., 1998, 67, pp. 215-279 6 GRUNDMANN, M., WEBER, A., GOEDE, K., USTINOV, v.M., ZHUKOV, A.E., LEDENTSOV, N.N., KOP’EV, P.s., and ALFEROV, ZH.I.: ‘Midinfrared emission from near-infrared quantum-dot lasers’, Appl. Phys. Lett., 2000, 77, pp. 4-6 0.5 12.5 16.5 h, Ctm 1 0 0.5 ’ “ ” ‘ 1 1 ’ 1 .o injected current, A 1.5 Fig. 1 Light-current characteristics of quantum dot infrared emission The error bars in the measured data are also shown Inset: Polarisation dependence of output light TE _ - _ - TM T = 285K, I = 770mA, L = 0.8mm, ridge = SOP To summarise, we believe we observe intersubband gain and dominant stimulated emission in these devices with a distinct threshold. The output power is, of course, woefully low, since in the device we are converting a large population of interband photons to very few intersubband photons. 28 November 2000 Electronics Letters Online No: 20010056 DOI: 10.IO49/el:200I0056 S. Krishna and P. Bhattacharya (Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, M I 481092122, USA) P.J. McCann and K. Namjou (Laboratory for Electronic Properties of Materials, Vniversity of Oklahoma, Norman, OK 73019-1023, USA) 0 IEE 2001 Reply to Comment on ‘Room-temperature long-wavelength (h= 13.3pm) unipolar quantum dot intersubband laser‘ S. Krishna, P. Bhattacharya, P.J. McCann a n d K. Namjou References The comments made by Weber et al. [l] are welcomed. Obviously, our Letter and the comment are in an important emerging area of application of self-organised quantum dots (QDs). Since our original report, we have carried out further work which makes us believe that we observe dominant stimulated emission and gain in these devices, with a distinct threshold and polarisation of the output. First, the emission at 1 3 . 3 p , in all probability, originates from electron transitions from higher quantum dot excited levels to the ground state, separated by -90-100meV. Theoretical calculations have confirmed the presence of these excited states [2]. The important point to note is that the carrier dynamics between the barrier/ wetting layer states and the ground state in these dots is the same WEBER, A., GRUNDMANN, M., and LEDENSTOV, N.N.: ‘C0n”nt: Room-temperature long-wavelength (h = 1 3 . 3 ~ )unipolar quantum dot intersubband laser’, Electron. Lett., 2001, 37, (2), pp. 96-97 2 JIANG, H.-T., and SINGH, J.: ‘Self-assembled semiconductor structures: electronic and optoelectronic properties’, IEEE J. Quant. Elect., 1998, 34, pp. 1188-1196 3 KRISHNA, s., BHATTACHARYA, P., MCCANN, P.J., and NAMJOU, K.: ‘Room-temperature long-wavelength (h = 1 3 . 3 ~ )unipolar quantum dot intersubband laser’, Electron. Lett., 2000, 36, pp. 1550-1 55 1 4 KRISHNA, s., QASAIMEH, o., BHATTACHARYA, P., MCCANN, P.J., and NAMJOU, K.: ‘Room-temperature far infrared emission from selforganized InGaAsiGaAs quantum dot laser’, Appl. Phys. Lett., 2000,76, pp. 3355-3357 ELECTRONICS LETTERS No. 2 18th January 2001 Vol. 37 1 97 5 GRUNDMANN, M., WEBER, A., GOEDE, K., ZHUKOV, A.E., LEDENSTOV, N.N., KOP’EV, P.S., and USTINOV, V M., ALFEROV, ZH.1.: ‘Mid-infrared emission from near-infrared quantum dot lasers’, =gk ’Yk Appl. Phys. Lett., 2000, 77, pp. 4 6 Cwkj.93 (g w+t j + w3o + wka) I C = 1,..., c CAD of rectangular-waveguideH-plane circuits by segmentation, finite elements and artificial neural networks J.M. Cid and J. Zapata where x,is the ith input, yk is the Mh output, gk(.) and g,{.) are activation functions (typically: sigmoid, tanh, ...), M is the number of neurons in the hidden layer and the IVS are adjustable parameters called weights. The use of the MLPs is based on the universal approximation theorem, using which it can be deduced that an MLP with only two layers of weights is capable of modelling virtually any real function to any desired degree of accuracy if the number of neurons in the hidden layer is large enough. Rectangular waveguide H-plane circuits are efficiently analysed by the segmentation finte element method. Artificial neural networks, the computation times of which are very fast, are used to generalise the responses to different configurations. The analytic model obtained in this way is used in optimisation programs for microwave circuit design. Application of the method to a three cavity fdter is presented. Introduction: In the last few years, the application of segmentation methods, as well as the growth in computer capability, have made the finite element method (FEM) faster and more flexible [l]. These advances suggest the introduction of the FEM in optimisation programs for microwave circuit design, which is the objective of this work. The design time is also reduced by applying artificial neural networks (ANNs) which model the response of the complete circuit starting from a small set of responses obtained by FEM. Theory: The optimisation of a microwave circuit is a problem where the differences between the circuit response and the desired response are minimised by adjusting the free parameters of the system. As a consequence, precise knowledge of the circuit response is needed to achieve a good design. Thus, the segmentation finite element (SFE) method presented in [l] is a powerful full-wave method of analysis which allows the response of arbitrarily shaped 3D microwave passive circuits to be obtained very efficiently. This method divides the circuit under study into small regions connected by waveguide segments of arbitrary cross-section, which are analysed separately. In each region, the generalised scattering matrix (GSM) is computed by FEM and the response of the complete circuit subsequently obtained by connecting all the GSMs through the respective waveguides. To apply this idea to H-plane rectangular waveguide circuits, a simplified version of the method in [l] is implemented by forcing the derivatives with respect to the waveguide height to be zero. This allows the problem to be solved in a 2D space. In general microwave circuit design, the cost function that must be minimised is extremely complex and has many local minima. The algorithms which manage this type of function are based on simulated annealing techniques or evolutionaq strategies, which solve a problem at the expense of calling the cost function excessively. The attainment of the circuit responses by means of a numeric method such as the SFE make the resolution of the problem too slow. To solve this matter, an analytic model based on ANNs is introduced. Using this model and maintaining high precision and flexibility, the circuit response is obtained much quicker than with SFE, and therefore the design time is reduced. In the analytic model proposed in this work, the segmentation concept is applied the complete circuit is divided (just as in the SFE method) and the behaviour of each section is modelled separately. In this way, the modelling of the circuit response is simplified drastically because the number of free parameters is less in a section than in the complete circuit, and the complexity of an approximating function increases exponentially with the dimension of the input space (the so-called curse of dimensionality). Moreover, the electromagnetic response of a small region is softer and thus easier to model. In each region of the microwave circuit, the GSM obtained starting from the analysis with the FEM is approximated applying multi-layer perceptrons (MLPs). An MLP is an ANN that can be seen as an application of RDin RC.The expression of an MLP with two layers of weights can be written [2]: 98 1377/11 Fig. 1 Geometry and segmentation of rectangular waveguide H-plane three-cavity filter Dimensions (in cm) are: A = 1.905; T = 0.2; R = 0.15 L I , L2, H I and H2 are free parameters of system 901 30 t 01 8 0.2 0.4 0.6 0.8 Hi, cm 1.0 1.2 ’ y-14 1-17 1.4 Fig. 2 Variation of iris response against H, at fixed frequency 0 computed by FEM computed by MLP I -60’ 1 1 .o 11.5 12.0 12.5 frequency, GHz 13.0 13.5 )377/31 Fig. 3 Filter response for optimised dimensions (in cm) of free parume- ters L1 = 1.0607; L2 = 1.1918; H I = 0.9168; H2 = 0.5910 computed by SFE method 0 computed by analytic model ELECTRONICS LETTERS 18th January 2001 Vol. 37 No. 2

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