8 XIAN, Y. Y. : 'New proof of higher dimensional Hadamard matrices', J. Syst. Sci. & Math. Sci., 1987, 7, pp. 346-349 9 XIAN, Y. Y.: 'On the classification of 2 4 Hadamard matrices', ibid., 1987, 7, pp. 40-^6 10 XIAN, Y. Y.: 'The operations and applications about higher dimensional matrices', J. Chengdu Inst. Radio Eng., 1987, 16, pp. 191-199 11 XIAN, Y. Y.: 'On the numeration of 5-dimensional Hadamard matrices of order 2', J. Beijing Univ. Posts & Telecommun., 1987, 4 (2) If / = k + y/k for k > 1, then the equation group has no root. In fact, taking the product of the first 4/c ? 1 equations we have 4k-1 / 4k n 111 J=I bitbh, Appendix: Proof of theorem 2: 1 < �� Definition: Let B = (B^) be a two-dimensional matrix with elements 0, 1. If the equation W(Bn � Bn, ...,Bin@ Bjn) = \n holds for any i # 7 , where W(.) means the weight of the 0-1 vector and � means mod-2 sum, then the matrix B is called an H 0 -matrix. By this definition, theorem 2 is equivalent to the following theorem: Theorem 2': If k > 1, then there exists no H 0 -matrix with the form Bn= l "? T1 b3 ... bx T b2 v�i i.e. ...,bt4t_lb,l 14.*-1 Because 6, = 0 or 1, the length of every term bhbiv . � - A 1 + A2 +2, ???,&,玙,+4*-i is at least 4/c - 1, so ..., b b b h i 2, ???>bitk_lbil + 1 b i 2 + 2, ? ? ? , * > m - l + 4 k - i = 0 4k l i.e. (/c ? <Jk) ~ = 0. This is in contradiction with k > 1. (3) If / = k + y/k for k > 1, then the equation group 2 has no root. In fact, if blt b2,..., fe4k is a root of equation group 2, letting i-b2 l-by (i) ... ... i1- [l-b2 For the proof of theorem 2', we begin with two lemmas: Lemma 1: Let Bo be the above matrix, p = W(bt, . . . , 6 4k ); then p = k + I, W(bxbit b2 bj+ x , . . . , 6 4k 6 ; + 4 k _ t ) = /,; > 2. Proof: By the identical equations then Bo is a cyclic H 0 -matrix with lt = k ? y/k; this is in contradiction with step 2. According to the above three steps, we now know that the equation group 2 has no root. W(at + by, ..., an + bn) = W(au ..., an) + W(bu ..., bn) -2W(albl,...,anbn) and TWO-CHANNEL SYSTEM DEMONSTRATION OF DIFFERENTIAL FREQUENCY-DEVIATION MULTIPLEXING We have W(by, ..., bn)+W(bj, bj+y, ..., Indexing terms: Optical communications, Optical multi/ demultiplexers, Multiplexing bj+tk_y)- -2W(blbj,...,bAkb4k.1+j) = 2k i.e. 2p = 2k + 21. If the above Bo is existent, then by lemma 1 we know the following equation group has a root: A two-channel lightwave system using differential frequencydeviation multiplexing (DFDM) is presented. Both 90 Mbit/s channels are differentially detected using a fibre interferometer. The performance is independent of the absolute optical frequencies and received state of polarisation. Interchannel interference results in a 1 dB penalty for channel separations of 700 MHz. bxb2 + b2b3 + ... + bAtkbl = (2) b2bl b4k = k However, in the following lemma we prove that this equation group has no root, i.e. theorem 2' holds: Lemma 2: If k > 1 then the above equation group has no root. Proof: This is determined in three steps: (1) If the root is existent then / = k � Jk. In fact, if we add the first 4/c ? 1 equations in the equation group 1 together, we have bl(b2 + b3 + ... + 64t) + b2(b3 + 64 + ... + 6X) + ... + bAk{b, + b2 + ... + b^J = (4/c - 1)/ By this equation we obtain (k + l)(k + I - 1) = (4/c - 1)/, i.e. (k-l)3 1278 = k,l = k眣/k. A new multiplexing technique, called differential frequencydeviation multiplexing (DFDM), has recently been proposed. 1 In DFDM, information is transmitted as the relative optical frequency, or frequency deviation fd, between light pulses transmitted at successive time intervals. A fibre interferometer is used to superimpose light from the two time intervals, and the frequency difference is generated by a photodiode. Multiplexing is accomplished by assigning a unique fd to each channel. The microwave response bandwidth of each receiver can then be subdivided into independent narrowband channels. A desired channel can be received by detecting the microwave power through a bandpass filter centred on the appropriate frequency deviation. DFDM has several significant advantages over alternative multiplexing techniques. First, information is contained entirely within the relative frequency between two successive bit periods. Wavelength stabilisation is not required and pattern-dependent heating effects, which plague conventional coherent freuqency-shift-keyed (FSK) systems,2 are not a problem. Secondly, a DFDM receiver operates independently of the state of optical polarisation at the input to the interferometer. Finally, the electronic components at each transmitter ELECTRONICS LETTERS 19th November 1987 Vol. 23 No. 24 and receiver operate at speeds equal to the single-channel data rates. High-speed switching required for time-division multiplexing (TDM), or microwave modulators required for subcarrier multiplexing (SCM),3 are avoided. In this letter we present the results of an experiment in which two channels with data rates of 90 Mbit/s per channel are multiplexed using DFDM. A schematic diagram of the experimental system is shown in Fig. 1. Two single-frequency CH, modulating the current into the short cavity, whereas for the three-contact laser, fd up to at least 70 GHz can be obtained. The output from the parallel-resonant receiver is shown in Fig. 2, where LDX and LD2 are modulated with/d equal to 20 iiD data in 10 15 frequency, GHz Fig. 2 Output spectrum from parallel-resonant receiver and following amplifier with both channels operating L D t and LD 2 are modulated with/,,= 1-3 and 2 0 G H z , respectively. Thermal noise floor, obtained by blocking both beams, is shown by lower curve Fig. 1 Experimental two-channel DFDM system Outputs of two frequency-modulated C 3 lasers are combined in a 3 dB fibre coupler. Output from interferometer is coupled either to a parallel-resonant receiver or to a high-speed PIN. Desired channel is selected using a bandpass filter (BPF) and detected using a Schottky-diode detector (DET). The DET is followed by three DC-coupled amplifiers (A3) and a postdetection filter (PDF). Each laser is isolated from reflections using two isolators, for a total isolation of 60 dB cleaved-coupled-cavity (C3) lasers (LDt and LD2) are combined in a 3 dB fibre coupler. The fibre interferometer consists of two 3dB fibre couplers and has a delay time equal to 111ns, corresponding to a bit rate of 90 Mbit/s per channel. By adjusting the polarisation compensator (PC) within the interferometer such that the birefringence is equal in each arm, the polarisation states of the recombined optical signals are matched for any state of polarisation at the input to the interferometer. One of the output arms of the interferometer is coupled to a parallel-resonant PINFET receiver.4 This receiver uses a small inductance between the FET gate and ground to form a response resonance centred on 3-5 GHz. The lowfrequency components of the received photocurrent are shorted to ground. The response resonance is sufficiently broad that reasonable sensitivity is obtained from 1-5 to 6 GHz. A separate high-speed PIN followed by a DC-coupled, 7 GHz-bandwidth amplifier (A2) provides a frequencyindependent response for test purposes. The test channel is defined by the bandpass filter (BPF) which has a centre frequency of 20GHz and a 3dB bandwidth of 500MHz. Microwave power through this filter is detected using a low-barrier Schottky diode square-law detector and FET preamplifier. Pseudorandom data from two pattern generators are differentially encoded and used to frequency-modulate the lasers. Variable attenuators are used to adjust the magnitude of the current transitions to obtain the desired frequency deviations. The received decoded data from the test channel are compared to the transmitted data to obtain the error probability. LD t is a three-contact, two-cavity C3 laser that offers a considerable improvement in FM response characteristics over the conventional two-contact C3 laser LD2. The twocontact laser can be modulated with fd up to 2-5 GHz by ELECTRONICS LETTERS 19th November 1987 Vol. 23 and 1-3 GHz, respectively. Low-frequency components, including the / = 0 distributions from each channel, are shorted to ground by the inductor used to generate the receiver resonance. The upper trace shows the f=fd distributions from each channel. The lower trace, obtained by blocking both optical signals, is the thermal noise level from the receiver and amplifier. Although the average photocurrents received for each channel are equal, the microwave power contained in the distribution centred on fd = 20GHz is slightly higher. This is due to the frequency-dependent resonant response of the PINFET receiver. Fig. 3 shows the error probability Pe of the filtered and detected test channel (fd = 20GHz) as a function of the SNR EEH Fig. 3 Error probability Pe against signal/noise ratio (SNR) at output of bandpass filter LD 2 is blocked for trace (a). For traces (b) and (c), LD 2 is modulated such that the channel separations, or differences in frequency deviation, are 750 and 550 MHz, respectively No. 24 1279 signal/noise ratio (SNR) measured at the output of the bandpass filter (BPF). For the case where the signal from LD2 is blocked, an SNR of 12 dB, measured using a power meter at the output of the BPF, is sufficient for Pe= 10"9. This is obtained for an average received photocurrent of 7-5 fiA. The 12 dB SNR at the BPF output corresponds to a 20 dB SNR at the output of the postdetection filter. Fig. 3 also shows the effect of interchannel interference (ICI) when LD2 is modulated with fd= 1-25 and 1-45 GHz. This corresponds to channel separations of 750 and 550 MHz, for which the SNR required at the output of the BPF is increased by 1-3 and 3 0 dB, respectively. ICI is a significant limitation in this type of system. If interchannel separations must be 750 MHz to reduce the interference penalty to ldB, then the number of DFDM channels that can be located within reasonable receiver bandwidths is small. A significant reduction of the laser linewidth would result in a reduction of the minimum channel separation. In summary, a two-channel system that uses different frequency-deviation multiplexing (DFDM) has been evaluated, demonstrating the advantages and limitations of this technique. We have shown how multiplexing can be accomplished without optical frequency stabilisation or active polarisation control, without using time-division or subcarrier multiplexing, and using simple electronics at the transmitters and receivers. We thank A. R. Chraplyvy and R. W. Tkach for several helpful discussions. The C3 lasers were processed from wafers grown by D. P. Wilt. T. E. DARCIE C. A. BURRUS A. H. GNAUCK B. L. KASPER J. R. TALMAN letter we show that this is indeed the case, but the transistor continues to behave as an amplifying device with essentially unchanged current gain as the base-emitter junction is driven into reverse bias. In these circumstances, both emitter and collector behave as minority carrier extracting junctions which reduce the carrier concentrations in the base. The thermal generation of minority carriers within the base region is then seen to be equivalent to an offsetting base current bias. Experiment: The bipolar transistor is of the lateral array type described previously1 (Fig. 1). It consists of an array of circular 'loophole' diodes2~4 made of n-type annular regions in a 29th September 1987 ;base n-type AT&T Bell Laboratories Crawford Hill Laboratory Holmdel, NJ 07733, USA 111100 / References 1 2 DARCIE, T. E.: 'Differential frequency-deviation multiplexing for lightwave networks', J. Lightwave TechnoL, to be published JEROMIN, L. L., REIFFEN, B., and CHAN, v. w. s.: 'Minimum shift keying for frequency modulation of semiconductor lasers'. OFC conf. proc, 1985, p. 24 3 DARCIE, T. E.: 'Subcarrier multiplexing for multiple-access lightwave networks', J. Lightwave TechnoL, 1987, LT-5, pp. 1103-1110 4 DARCIE, T. E., KASPER, B. L., TALMAN, J. R., a n d BURRUS, C. A. I 'ReS- onant PIN-FET receivers for lightwave subcarrier systems', ibid., 1987, to be published NEAR-AMBIENT-TEMPERATURE BIPOLAR TRANSISTOR IN CADMIUM MERCURY TELLURIDE p-type CMT 7 sapphire 7 fi28/il Fig. 1 Schematic diagram of transistor, showing plan view and side elevation through centre of structure From Reference 1 p-type substrate. The central diode is chosen to be the emitter, with the nearest neighbour ring of diodes connected together and designated as the first collector (C^ and the next ring designated the second collector (C2). The junction diameters are 10 /mi and the diodes are on a pitch of 15/mi. The CMT composition is 30% mole CdTe with a detector cutoff wavelength of 4-3 /mi at 263 K. The electron diffusion length in the base region is 15 /mi. Common-emitter current/voltage characteristics are shown in Fig. 2 for C1 alone connected. Although the collector is not a continuous boundary, as would be the ideal case, the probability of emitted carriers escaping to the outer p-region is relatively low. It can seen that the characteristic for zero base base current 10uA Indexing terms: Semiconductor devices and materials, Transistors, Photodiodes We describe an npn cadmium mercury telluride transistor made from a close-packed array of lateral collection diodes. At 263 K and a collector current of 1 mA the hfe was ~ 20. A reverse base-emitter bias is required to turn off the collector current, owing to thermal generation of electrons in the base. Introduction: Ashley et al.1 recently described the use of an array of lateral collection photodiodes to demonstrate bipolar transistor action at low temperatures in the ternary alloy cadmium mercury telluride (CMT). At higher temperatures the properties of the transistor may be expected to be dominated by high base minority carrier generation rates, resulting in significant collector current at zero base current. In this 1280 0-1 02 03 0-4 collector-emitter voltage Vce 05 [128721 Fig. 2 Experimentally observed common-emitter transistor characteristics at 263 K for collector Clt with 10nA increments in base current ELECTRONICS LETTERS 19th November 1987 Vol. 23 No. 24

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