Method for converting high-speed and spectrally efficient terahertz-wave signal into optical signal

Koichi Takiguchi

doi:10.1364/OE.27.006598

1. Introduction

Communications in the terahertz (THz) band are attractive because it can realize high-speed and short-reach wireless communication of more than 10 Gbit/s by utilizing its wide bandwidth. One of its application areas is to build-out fiber-to-THz radio bridges, namely, to provide a high-speed wireless link to connect fiber-optic links at a location where it is difficult to lay a fiber-optic cable (e.g. at an obstacle including a river or a canyon) [1,2]. For this application, the simple and seamless technology to connect the wireless and fiber-optic links is necessary. A signal in the THz band can be generated by mixing a delivered optical signal with a local continuous wave laser diode (LD) using a high-speed photo-mixer including a uni-traveling carrier photo-diode (UTC-PD) [3]. This THz-wave generation technology is well-established [1–3]. It is also important to develop a method, which easily and efficiently converts the THz-wave signal into the optical signal with a view to realizing the fiber-to-THz radio bridges.

In this paper, a method to convert a high-speed and spectrally efficient on-off keying (OOK) THz-wave signal into an optical signal without complicated processing is demonstrated. The method utilizes heterodyne detection and optical intensity modulation. The THz-wave signal is coherently detected with a local sinusoidal wave to generate a down-converted radio-frequency (RF) signal with a high signal-to-noise (S/N) ratio, which drives the optical intensity modulator after linear amplification. When the signal bandwidth is less than or equal to double the RF intermediate frequency (IF) and the intensity modulator bias is set to a null point, we can recover the original data in the optical domain by extracting one of the generated optical main sidebands at the modulator with an optical filter. After the operating principle of the conversion method is explained using calculation, some experimental results to verify the validity of the method are shown. Although the method was partly reported in [4], this paper provides substantial calculated and experimental results so as to explain the method and its validity in detail. A spectrally efficient 40 Gbit/s OOK signal in the THz band (300 GHz), which was generated from an optical signal shaped with a root Nyquist optical filter [5], was utilized in the experiments. It is also significant to investigate the use of spectrally efficient multiplexing schemes in the THz band for the future increase in data rate, and the spectrally efficient optical signal is tolerant to the chromatic and/or polarization-mode dispersion in the optical fiber [6]. The use of the spectrally efficient signal is also useful when considering the bandwidth limit of the RF components. Although the THz-wave communication using orthogonal frequency division multiplexing (OFDM) was already reported as the spectrally efficient multiplexing [7,8], the Nyquist pulse-based communication is adopted due to its implementation easiness in this investigation. Although some results relating to the fiber-to-radio bridges were already reported [9–11], the proposed method and target frequency band in this paper are different from those in [9–11]. In addition, the used symbol rate is much higher than those in [9–11], and offline digital signal processing is not utilized, which means that bit error rate (BER) measurement is carried out in real time. Although the atmospheric attenuation in the THz-waves increases with the increase of the frequency, the link budget is very close to a free-space path loss (FSPL) and is not degraded by the atmospheric contribution for up to kilometer-range systems in the 300 GHz band [2]. Therefore, the 300 GHz band communication targets hundreds of meters to kilometers transmission distance. As the 1 km-long THz system has to deal with 140 dB total loss at the carrier frequency of 300 GHz, high-gain antenna including phased array antennas must be realized to compensate for FSPL. Real-time and error-free 50 Gbit/s transmission over 100 meters was already realized in the laboratory by adopting 54 dBi gain antennas and coherent detection under the assistance of the forward error correction [12]. The performance progress on related devices including output power of the photo-mixer, the amplifier gain, and the antenna gain is indispensable with a view to realizing the kilometer-range communication in the 300 GHz band.

2. Experimental set-up and operating principle of conversion method

Figure 1 shows an experimental set-up of the method, which converts a high-speed OOK THz-wave signal into an optical signal. The schematic spectrum diagrams were inset in the figure to clarify the spectra change. The lightwave from a laser diode (LD) 1 (wavelength: 1552.28 nm) was modulated with 40 Gbit/s non-return-to-zero (NRZ) OOK data, whose pseudo-random bit sequence (PRBS) was 2⁷-1. The spectrum of the produced data signal was shaped with a root raised-cosine Nyquist optical filter 1 consisting of a bulk grating, whose roll-off factor was 0.3. The filtered optical signal and lightwave from a local LD2 (wavelength: 1549.88 nm) were transmitted through an optical fiber 1, and were mixed at a UTC-PD-based photo-mixer [3] to generate a 40 Gbit/s THz-wave signal with high spectral efficiency. The phase between LDs 1 and 2 was not locked. Although the OOK modulation format was adopted in this investigation, the frequency fluctuation between the two LDs induces the carrier frequency fluctuation of the generated THz-wave signal and causes adverse effects on the coherent detection at the mixer after a horn antenna 2. The use of a mode-locked laser is necessary to avoid these problems. The fiber length was set to 100 m because this investigation was preliminary. The frequency difference between the optical signal and the local LD2 was 300 GHz, which corresponded to the carrier frequency of the generated THz-wave signal. The operable output frequency range of the used photo-mixer was 260 to 380 GHz (J-band). The intensity of the optical signal and the local LD2 into the photo-mixer was set to be equal (7.1 dBm) for the efficient operation of the photo-mixer, and the output power of the photo-mixer was −14.5 dBm. The generated THz-wave signal was radiated to a free-space link through a horn antenna 1. Then the signal received at the horn antenna 2 was mixed with a 270 GHz local sinusoidal wave, and was down-converted into a 40 Gbit/s RF signal, whose IF was 30 GHz. The wireless link length was set to 0.1 m with a view to carrying out preliminary experiments to verify the operational principle and obtain initial data. The gain of two antennas was 27 dBi, and the operational frequency range, bandwidth, and conversion loss of the mixer at the receiver were 220 to 330 GHz, 40 GHz, and 6.0 dB, respectively. The coherent detection was carried out with a view to obtaining the high S/N ratio for the following processing. Although the used mixer bandwidth is limited to 40 GHz, the whole bandwidth of 40 Gbit/s Nyquist pulse with the roll-off factor of 0.3 is 52 GHz [13]. Therefore, as the IF had to be set so as to keep the value low and accommodate the whole Nyquist pulse bandwidth, I adopted the 30 GHz IF. The linearly amplified RF signal was up-converted into an optical signal through an LN (LiNbO₃) optical intensity modulator 2 (IM2) (bandwidth: 36.9 GHz, half-wavelength voltage V_π: 2.1 V), which was connected to an LD3 (wavelength: 1546.94 nm). The bandwidth of the linear amplifier was 65 GHz. The bias of IM2 was set to a null point. This optimum bias condition is explained later. The spectrum of the IM2 output optical signal had two main sidebands in the null bias setting condition. One of the sidebands was extracted with a root raised-cosine Nyquist optical filter 2, whose configuration and characteristics were the same as the optical filter 1. Then the filtered optical signal was sent to the second optical fiber link (length: 100 m), and a BER of a received signal at the PD (bandwidth: 21.4 GHz) was evaluated in real time by using an error detector (ED). Each optical filter was set after each erbium-doped fiber amplifier (EDFA) to decrease the amplified spontaneous emission (ASE)-induced noise of the EDFA. The output power of EDFA2 was set so that the non-linear optical effect did not arise in the optical fiber 2. The BER changed depending on the signal power into the PD, which was controlled by a variable optical attenuator (VOA). It should be noted that, in the experiments, two root raised-cosine Nyquist optical filters were utilized, whose total filter characteristics were not optimized to receive the complete Nyquist pulse at the PD. This means that aperture distortion was not compensated for. We concentrated on investigating conditions to convert the THz-wave signal into the optical signal using the simple configuration as we tolerated intersymbol interference (ISI) at the PD to some extent.

Fig. 1 Experimental set-up for converting THz-wave signal into optical signal.

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The conditions, which are required for converting the THz-wave signal into the optical signal, are investigated in detail below. If we assume that the bandwidth and loss of the IM2 are infinite and negligible, respectively, the electric field signal E_ocn(t) (complex notation, t: time) at the IM2 output is calculated as

E_{o c n} (t) = \sqrt{2} E_{0} \exp {j (2 π f_{0} t - φ)} \cos \frac{ϕ (t)}{2},

where E₀, f₀, and φ are amplitude of an input lightwave into the modulator, a frequency of the input lightwave, and a lightwave phase shift through the IM2, respectively. ϕ(t) is a phase applied to the IM2 through the electrical driving signal, and is expressed by

ϕ (t) = ϕ_{0} + d (t) \sin (2 π f_{I F} t + θ),

where ϕ₀, d(t), f_IF, and θ are a bias phase for the IM2, an OOK signal in the RF domain expressed in radians, IF, and a phase of the IF signal. By substituting Eq. (2) in Eq. (1) and utilizing Jacobi-Anger expansion, E_ocn(t) is calculated as

\begin{array}{l} E_{o c n} (t) = \sqrt{2} E_{0} {\cos (2 π f_{0} t - φ) + j \sin (2 π f_{0} t - φ)} \\ \times [\cos \frac{ϕ_{0}}{2} {J_{0} (\frac{d (t)}{2}) + 2 \sum_{n = 1}^{\infty} J_{2 n} (\frac{d (t)}{2}) \cos 2 n (2 π f_{I F} t + θ)} \\ - 2 \sin \frac{ϕ_{0}}{2} \sum_{n = 1}^{\infty} J_{2 n - 1} (\frac{d (t)}{2}) \sin (2 n - 1) (2 π f_{I F} t + θ)], \end{array}

where J_k is a Bessel function of the first kind. Thus the IM2 output signal E_out(t) is derived as

\begin{array}{l} E_{o u t} (t) = Re {E_{o c n} (t)} = \sqrt{2} E_{0} \cos (2 π f_{0} t - φ) \\ \times [\cos \frac{ϕ_{0}}{2} {J_{0} (\frac{d (t)}{2}) + 2 \sum_{n = 1}^{\infty} J_{2 n} (\frac{d (t)}{2}) \cos 2 n (2 π f_{I F} t + θ)} \\ - 2 \sin \frac{ϕ_{0}}{2} \sum_{n = 1}^{\infty} J_{2 n - 1} (\frac{d (t)}{2}) \sin (2 n - 1) (2 π f_{I F} t + θ)] . \end{array}

From Eq. (4), E_out(t) is expressed by the following equations depending on the bias phase ϕ₀ setting conditions of IM2:

\begin{array}{l} E_{o u t} (t) = - 2 \sqrt{2} E_{0} \cos (2 π f_{0} t - φ) \sum_{n = 1}^{\infty} J_{2 n - 1} (\frac{d (t)}{2}) \sin (2 n - 1) (2 π f_{I F} t + θ) \\ (ϕ_{0} = π, null bias) . \end{array}

\begin{array}{l} E_{o u t} (t) = \sqrt{2} E_{0} \cos (2 π f_{0} t - φ) {J_{0} (\frac{d (t)}{2}) + 2 \sum_{n = 1}^{\infty} J_{2 n} (\frac{d (t)}{2}) \cos 2 n (2 π f_{I F} t + θ)} \\ (ϕ_{0} = 0, full bias) . \end{array}

\begin{array}{l} E_{o u t} (t) = E_{0} \cos (2 π f_{0} t - φ) {J_{0} (\frac{d (t)}{2}) + 2 \sum_{n = 1}^{\infty} J_{2 n} (\frac{d (t)}{2}) \cos 2 n (2 π f_{I F} t + θ) \\ ​ + 2 \sum_{n = 1}^{\infty} J_{2 n - 1} (\frac{d (t)}{2}) \sin (2 n - 1) (2 π f_{I F} t + θ)} \\ (ϕ_{0} = - π / 2, quadrature bias) . \end{array}

The characteristics of the IM2 output OOK signal in the various bias setting conditions are obtained from Eqs. (5)-(7). Equation (5) indicates that E_out(t) has sidebands at f₀ ± (2m-1)f_IF (m: natural number) in the null bias condition. When marked d(t)/2 value and d(t) bandwidth are less than or equal to 0.87 rad and less than or equal to 2f_IF, respectively, we can mainly transfer the signal d(t) to the optical signals at f₀ ± f_IF sidebands with an accuracy of less than or equal to 10% and without spectral overlap. This accuracy can be obtained because J₁(x) is much more linear with respect to x than any other Bessel functions of the first kind when x is around zero. Thus we can extract one of the generated main sidebands with the optical filter 2 as the converted optical signal. While on the other hand, in the full bias setting condition, the converted optical sidebands appear at f₀ ± 2(m-1)f_IF. Also, in this case, the signal d(t) with the bandwidth of less than or equal to 2f_IF can be converted into the optical signals without spectral overlap. The converted optical signal at f₀ shows an inverted characteristic of d(t) owing to the properties of J₀, and can achieve zero amplitude level, namely, good extinction ratio only when the marked d(t)/2 value is 2.40 rad. This value means that precise amplitude voltage 1.53V_π (V_π: half-wavelength voltage of the IM2) is required with regard to d(t). It is generally difficult to produce this level of signal voltage with the bandwidth of around 50 GHz by using the amplifier, and the linearity of the converted optical signal is low. When the converted signals at f₀ ± 2mf_IF are utilized, both levels and linearity of the converted optical signals are low. In the calculation using Eq. (6), their peak intensity level is lower than the peak level of the f₀ signal by more than 20.5 dB when the marked d(t)/2 value is 0.82, which was used in the experiments. In the quadrature bias setting condition, the converted optical signals have components at f₀ ± (m-1)f_IF. Therefore, in this setting condition, just the signal d(t) with the bandwidth of less than or equal to f_IF can be converted into the optical signal without spectral overlap, and the maximum processable symbol rate falls to one-half compared to the null and full bias conditions. In addition, the highest level signal at f₀ faces the problems of low extinction ratio and linearity as it is for the full bias setting. The converted optical signals at f₀ ± (m + 1)f_IF show low levels and linearity. Thus the null bias setting is adequate for converting the high-speed and spectrally efficient RF OOK signal into the optical signal and extracting the desired frequency component with the optical filter.

3. Experimental results

Figure 2 shows measured spectra of the 40 Gbit/s optical signal and the local LD2 at a 3 dB coupler output for generating the THz-wave signal with the carrier frequency of 300 GHz. Figures 3(a) and 3(b) show optical eye diagrams of the original 40 Gbit/s NRZ OOK signal and shaped signal with the optical filter 1, respectively, at the BER of 10⁻¹². Figure 3(b) indicates that the ISI arose owing to the aperture distortion. Figure 4 shows a spectrum of the 40 Gbit/s RF signal with the IF of 30 GHz, which was down-converted from the 40 Gbit/s THz-wave signal. In Fig. 4, the lower-frequency component was maintained, but the higher-frequency component deteriorated due to the bandwidth limit of the RF components including the mixer and coaxial cables used for connection between the RF components. Figure 4 indicates that the photonics-based technology successfully produced the 40 Gbit/s THz-wave signal with high spectral efficiency.

Fig. 2 Spectra of 40 Gbit/s optical signal and local LD2 at 3 dB coupler output.

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Fig. 3 Optical eye diagrams of (a) original 40 Gbit/s NRZ OOK signal and (b) shaped signal with optical filter 1.

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Fig. 4 Spectrum of 40 Gbit/s RF signal with IF of 30 GHz.

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Figures 5(a)-(c) show measured optical spectra after the IM2 in the null, full, and quadrature bias setting conditions of IM2, respectively, when the marked d(t)/2 value was 0.82. The green signs indicate sidebands derived from Eqs. (5)-(7). While on the other hand, the red signs denote unanticipated sidebands that appeared because the IM2 bias could not be set to the precise points. In Fig. 5(b), the extinction ratios between peak intensity level of the carrier signal and sidebands exceeded 30 dB, which were larger than the calculated value of 20.5 dB. This was caused by the bandwidth limits of IM2 and RF components, which were not taken into account in the calculation. Figures 6(a) and 6(b) show optical spectra that were extracted from the spectra in Figs. 5(a) and 5(b), respectively, with the optical filter 2. The longer-wavelength main sideband at f₀-f_IF in Fig. 5(a) and the carrier frequency component at f₀ in Fig. 5(b) were filtered. When the bias setting condition of IM2 was quadrature, the effective signal spectrum could not be extracted from the IM2 output spectrum because the sidebands spectra overlapped each other in Fig. 5(c). Compared to the higher-frequency spectrum in Fig. 4, the longer-wavelength spectrum in Fig. 6(a) further deteriorated due to the bandwidth limit of IM2 and RF components.

Fig. 5 Optical spectra after IM2 in (a) null, (b) full, and (c) quadrature bias setting conditions of IM2.

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Fig. 6 Optical spectra extracted from spectra in (a) Fig. 5(a) and (b) Fig. 5(b) with optical filter 2.

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Figures 7(a) and 7(b) show measured eye diagrams of the received optical signals at the final stage when the bias setting conditions of IM2 were null and full, respectively. The spectra of signals in Figs. 7(a) and 7(b) correspond to Figs. 6(a) and 6(b), respectively. As described in Section 2, unlike the eye diagram in Fig. 7(a), the eye in Fig. 7(b) showed small extinction ratio, and was not open due to the used d(t)/2 value of 0.82. Therefore, the BER at the final stage could not be measured in the full bias condition. The eye in Fig. 7(a) was measured when the obtained BER was the lowest (10⁻¹²). Figure 8 shows measured BERs of the 40 Gbit/s optical signals, which include the original NRZ OOK signal, the signal after the optical filter 1, and the signal received at the final stage when the bias setting condition of IM2 was null. The BERs measurement was carried out in real time by using ED. All the lowest BERs were 10⁻¹². The power penalty between the original NRZ and the filter 1 output signals was 2.0 dB at the BER of 10⁻⁹, which was mainly induced by ISI due to the aperture distortion. The penalty between the signals after the filter 1 and at the final stage was 0.6 dB at the BER of 10⁻⁹. This penalty was attributed to bias setting incompletion and the bandwidth limit of IM2 in addition to the bandwidth limit of used RF components.

Fig. 7 Eye diagrams of received optical signals at final stage when bias setting conditions of IM2 were (a) null and (b) full.

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Fig. 8 BERs of 40 Gbit/s optical signals including original NRZ OOK signal, signal after optical filter 1, and signal received at final stage when bias setting condition of IM2 was null.

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4. Conclusion

Seamless connection between high-speed THz-wave and optical signals with high spectral efficiency was demonstrated. A spectrally efficient 40 Gbit/s THz-wave OOK signal was generated by mixing a delivered 40 Gbit/s optical signal, which was shaped with a root Nyquist filter, with a local continuous wave lightwave using a high-speed photo-mixer. In this investigation, the used two root Nyquist optical filters were not optimized to produce the Nyquist pulse at the final stage, because we pursued highly spectrally efficient communication using the simple modulation format, multiplexing, and configuration as we tolerated ISI to some extent. The generated THz-wave signal was again transferred to an optical signal through heterodyne down-conversion and optical modulation. We confirmed that the optimum bias point of the optical modulator was null by carrying out calculation and some experiments. One of the main sidebands in the recovered optical signal was extracted with another root Nyquist optical filter, and was transmitted to a fiber-optic link. A measured BER of the received optical signal at the final stage became 10⁻¹², and the power penalty between the initially filtered and finally received optical signals was 0.6 dB when the BER was 10⁻⁹. I think that the demonstrated scheme is one of candidate technologies to realize seamless and flexible connection between the high-speed THz-wave and optical OOK signals with high spectral efficiency.

Funding

Ministry of Internal Affairs and Communications (MIC) SCOPE (185007006); SCAT Foundation.

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Method for converting high-speed and spectrally efficient terahertz-wave signal into optical signal

Abstract

1. Introduction

2. Experimental set-up and operating principle of conversion method

3. Experimental results

4. Conclusion

Funding

References

Cited By

Figures (8)

Equations (7)

Optics Express