Frequency-division multiplexer and demultiplexer for terahertz wireless links

The development of components for terahertz wireless communications networks has become an active and growing research field. However, in most cases these components have been studied using a continuous or broadband-pulsed terahertz source, not using a modulated data stream. This limitation may mask important aspects of the performance of the device in a realistic system configuration. We report the characterization of one such device, a frequency multiplexer, using modulated data at rates up to 10 gigabits per second. We also demonstrate simultaneous error-free transmission of two signals at different carrier frequencies, with an aggregate data rate of 50 gigabits per second. We observe that the far-field spatial variation of the bit error rate is different from that of the emitted power, due to a small nonuniformity in the angular detection sensitivity. This is likely to be a common feature of any terahertz communication system in which signals propagate as diffracting beams not omnidirectional broadcasts.

where φ C is the angle at which the center of the receiver is located and where β is a scale parameter which determines the angular width of the detection. We choose the value of β such that the width of the function is equivalent to the angular acceptance aperture of the detector in our experiments. A value of β = 14.3 (for φ and φ C expressed in radians) gives an angular width of 2 1 0.53 radians. = β This filter function G(φ) is expressed in a linear (not dB) scale, so that the fraction of power at frequency f emitted by the demux and detected by the receiver is simply given by G(φ(f)). Of course, there is a one-to-one (but not linear) mapping between angle and frequency, as expressed by Eq. (3) in the text. At the center of the filter, G(φ C ) = 1 (i.e., the signal is not degraded at all by angular effects). For angles φ far from φ C , this analytic form for G(φ) becomes negative. For these values of φ, we assume that there is zero power detected (i.e., the signal simply misses the detector), and so we set G = 0.
We note that this is a rather flat filter, in the sense that G(φ) does not change very much in the range of angles that define the modulation bandwidth. For example, if the filter is centered at the angle corresponding to the carrier frequency f 0 , then sidebands located ±10 GHz away from the carrier frequency experience less than a 1% decrease in detection sensitivity (i.e., G ±10 GHz sideband ≈ 0.99).
For a given detector angle φ C , we can compute the value of G for the two lowest-order sidebands f 0 ± ∆f, located at angles φ + and φ − , respectively: φ , the two sidebands are detected asymmetrically. This asymmetric situation can be described as a superposition of amplitude modulation (for which the two sidebands are exactly in phase) and phase modulation (for which the two sidebands are π out of phase). This superposition is governed by a pair of linear equations, which describe the fact that: (a) for the larger of the two sidebands (say, G(φ + )), the amplitude and phase modulated signals coherently add; and (b) for the smaller of the two (say, G(φ − )), the amplitude and phase modulated signals coherently subtract. Thus, we have: and therefore the amplitude-modulated portion of the signal has a relative amplitude of 2

G G A
Our detector, which is insensitive to phase, detects only this amplitude-modulated fraction of the signal. Thus, an asymmetric detection leads to a degraded signal-to-noise. Assuming that the noise is independent of angle, we determine the change in the signal-to-noise induced by this angular filtering as the square of the AM-modulated fraction of the signal: We note that, due to the nonlinear mapping between angle and frequency, this change in the signal-to-noise does not vanish even if the detector is centered precisely at the angle corresponding to f 0 (i.e., since the filter is symmetric in angle, it is therefore not perfectly symmetric in frequency). However, for a reasonable filter width, this effect is quite small; even for a modulation rate of ∆f = 10 Gb/sec, it amounts to only about a 1% decrease in the value of A at f 0 . Thus we may ignore this effect in our analysis.
We must now convert this signal-to-noise degradation into a degradation in the BER. For incoherently detected ASK modulation, the BER is related to the energy/noise ratio by [1]: This represents the change in BER as a function of detector angle. However, this analysis ignores the fact that the BER depends on input power, even if the detector is positioned at the optimal angle. Since the BER depends on power level, it is necessary to normalize the minimum value of this function to the appropriate BER at the power level used in the measurements. This power dependence can be extracted from the data shown in Fig. 2. We note that, at a given input power, the log(BER) depends on the data rate (i.e., on ∆f), in a fashion which is approximately linear with data rate. Thus, we normalize the computed BER values according to: where N(∆f) is a normalization factor that varies linearly with ∆f. From Fig. 2 . Also, log(BER) min is the minimum value of the computed BER curve in the absence of normalization, given by: This data-rate-dependent normalization procedure is reasonable because in this analysis we are only interested in the change in BER due to a change in the angular position of the receiver, not in the absolute BER value at any given angle.
The result of this model calculation, a plot of log(BER) norm versus φ C for different values of ∆f, is shown in Fig. 1(d) with no fit parameters. This family of curves, plotted for the same four values of ∆f as used in the experiment (with the same color scheme), satisfactorily reproduces the measured angular width of the BER, as well as the weak dependence on data rate.