Generation of frequency-modulated sub-terahertz signal using microwave photonic technique

Ho-Jin Song; Kyoung-Hwan Oh; Naofumi Shimizu; Naoya Kukutsu; Yuichi Kado

doi:10.1364/OE.18.015936

1. Introduction

Terahertz science and technologies have been attracting great interest for various applications, such as material characterization, nondestructive testing, tomography imaging, chemical or biological sensing, and high-capacity wireless communications [1–5]. Terahertz waves can penetrate many dielectric materials and can therefore be used for non-destructive/noninvasive sensing and imaging of targets secured in non-metallic covers and containers or hidden by dust or smoke, which visible light cannot penetrate. Moreover, terahertz spectroscopic fingerprint patterns make it possible to distinguish one material from others [6].

In addition, radar technologies in a terahertz-wave imaging/sensing system would allow us to extract extra information, such as the distance between objects or an object’s thickness [7] and, ultimately, we could reconstruct a three-dimensional image of hidden objects or of the inside of objects [8,9]. The frequency modulation (FM) technique is one of the common ways to measure a distance. When we use the FM technique to detect range information, a wide swing span of the instantaneous frequency is preferred because it is inversely proportional to the range resolution; larger frequency deviation leads finer resolution. In general, FM in the microwave band is achieved with a voltage-controlled oscillator (VCO), which is usually fabricated with semiconductor devices, such as transistors, diodes, and variable capacitors. When control signal is fed to a VCO, the output frequency can be easily modulated, but there is a lack of devices for VCOs operating at frequencies higher than 100 GHz. For millimeter-wave and sub-terahertz regions, a frequency multiplication chain, which consists of several frequency multipliers and high-power amplifiers, is commonly used to generate a frequency-modulated sub-terahertz signal, but the operating frequency range and frequency tuning range are limited by the components of the chain.

In this paper, we present a new method for modulating the frequency of millimeter- and sub-terahertz-wave signal, with possible application to imaging systems and to sensing systems with range detection in the millimeter-wave and sub-terahertz regions. Since we use photonic technologies, the proposed scheme provides very low loss for handling or generating the signal, a high operating frequency, wide tunability of the center frequency, and large frequency deviation. We experimentally demonstrate a 350-GHz frequency-modulated sub-terahertz signal with a 6.7-GHz frequency deviation, and it should be possible to generate frequency-modulated signal of even over 1 THz with larger frequency deviation.

2. Principle

Mathematically, the frequency modulation of a sinusoidal signal can be implemented with phase modulation because a frequency can be represented by the differential of the phase with respect to the time and because the differential of a sinusoidal signal is also a sinusoidal signal at the same frequency. However, the FM index (m _FM) of the signal frequency modulated by using a phase modulation technique is very small, which is known as narrowband FM. This means that the instantaneous frequency of the FM signal is varied within a narrow frequency span compared to the center frequency, f _TH. However, if we phase modulate a signal at f ₀, where f ₀ >> f _TH, the absolute frequency deviation (Δf _m) will be wider than that of the signal phase modulated at f _TH directly because of the following relationship, though m _FM is still small due to the phase modulation.

Δ f_{m} = m_{F M} \times f_{0}

Therefore, we can generate a frequency-modulated terahertz wave signal with a wide frequency deviation by frequency down-converting the signal phase modulated at f ₀ to f _TH = f ₀ − f _LO. In this work, this idea was implemented with an optical phase modulator for 1550-nm telecommunications wavelength bands (cf. 193.548 THz for 1550-nm signal) and with a photomixer for frequency down-conversion to sub-terahertz wave bands.

Figure 1 schematically illustrates how the frequency-modulated sub-terahertz signal is generated. The details of the frequency-modulated signal generation are as follows. The optical signal from laser diode 1 (LD1) is given as

{\overset{⇀}{e}}_{1} (t) = E_{1} \times \exp {j (2 π ν_{1} t - θ_{1})}

where E ₁, ν ₁, and θ ₁ are the field intensity, optical frequency, and phase of the signal, respectively. The optical signal is phase-modulated with an optical phase modulator by an external control signal, k(t), and the output of the phase modulator is given as

{\overset{⇀}{e}}_{P M} (t) = {\overset{⇀}{e}}_{1} (t) \times L_{P M} \exp {j \frac{π}{V_{π}} k (t)}

where L _PM and V _π are the insertion loss and half-wave voltage of the phase modulator, respectively. Note that k(t) is assumed to be a narrowband signal at f _FM, so that V _π can be approximated as constant for the control signal, k(t).

Fig. 1 Schematic diagram of frequency-modulated sub-terahertz signal generation.

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To down-convert the phase modulated optical signal to the sub-terahertz frequency region, we combine the phase-modulated optical signal with the other optical signal (e ₂(t)) from LD2, whose frequency is set to make |ν ₁ – ν ₂| = f _TH, and then mix them using the photomixer. The input (e _in(t)) and output (i _TH(t)) signals of the photomixer are written as

\begin{array}{l} {\overset{⇀}{e}}_{i n} (t) = {\overset{⇀}{e}}_{2} (t) + {\overset{⇀}{e}}_{1} (t) \times L_{P M} \exp {j \frac{π}{V_{π}} k (t)} \\ = {E_{1} L_{P M} \times \exp (j (2 π \frac{f_{T H}}{2} t + \frac{π}{V_{π}} k (t) + θ_{1})) + E_{2} \times \exp (j (- 2 π \frac{f_{T H}}{2} t + θ_{2}))} \exp (j 2 π ν_{c} t) \end{array}

\begin{array}{l} i_{T H} (t) = Re [ℜ \times {| {\overset{⇀}{e}}_{i n} (t) |}^{2}] \\ = ℜ \times ({| E_{1} L_{P M} |}^{2} + {| E_{2} |}^{2}) + ℜ \times 2 | E_{1} L_{P M} E_{_{2}}^{*} | \cos (2 π f_{T H} t + \frac{π}{V_{π}} k (t) + θ_{1} - θ_{2}) \end{array}

where ℜ is the responsivity of the photomixer and ν _c is (ν ₁ + ν ₂)/2. Note that though LD1 and LD2 are illustrated as free running in Fig. 1, it was assumed that e ₁(t) and e ₂(t) in Eq. (4) are coherent and phase-locked with each other to simplify the formulas.

In the second term on the left of Eq. (5), a signal phase-modulated by k(t) is equivalent to one frequency-modulated by the differential of k(t) because of the fundamental relationship between the frequency and phase. For example, when a sinusoidal signal is applied to the optical phase modulator as a control signal, k(t), the output signal is derived as

k (t) = k_{0} \sin (2 π f_{F M} t) = k_{0} \int \frac{\partial \sin (2 π f_{F M} t)}{\partial t} d t

i_{T H} (t) = I_{D C} + A_{T H} \cos [2 π \cdot \int (f_{T H} + \frac{π}{V_{π}} k_{0} f_{F M} \cos (2 π f_{F M} t)) d t + θ_{1} - θ_{2}]

where k ₀ and f _FM are the amplitude and the frequency of the control signal and I _DC and A _TH are the magnitude of the DC and sub-terahertz current components, respectively. As shown in Eq. (7), the frequency of the output signal is modulated by the cosine signal, the differential of the sine signal. The instantaneous frequency f(t) and frequency deviation Δf _m, defined as the maximum deviation of the instantaneous frequency from the center frequency, f _TH, can be written as

f (t) = f_{T H} + \frac{π}{V_{π}} k_{0} f_{F M} \cos (2 π f_{F M} t)

Δ f_{m} = \frac{π k_{0} f_{F M}}{V_{π}}

As shown in Eq. (9), the large modulating signal (k ₀), high modulating frequency (f _FM), and low half-wave voltage (V _π) of the optical phase modulator lead to a large frequency deviation. In the same manner, Eq. (7) can be generalized for any given control signal, k(t), and the result is derived as

i_{T H} (t) = I_{D C} + A_{T H} \cos [2 π \cdot \int_{0}^{t} (f_{T H} + \frac{1}{2 V_{π}} \frac{\partial k (τ)}{\partial τ}) d τ + θ_{1} - θ_{2}]

Finally, a signal frequency modulated by the control signal, k(t), is generated. As shown in Eq. (10), the instantaneous frequency of the signal is proportional to the differentials of the control signal applied to the optical phase modulator.

3. Experiment and results

Figure 2 shows the setup we used to experimentally demonstrate our concept for generating a frequency-modulated sub-terahertz signal. Two optical signals, e ₁(t) and e ₂(t), (Fig. 1) were prepared with an optical frequency comb generator (OFCG), which consists of a LD, a phase modulator, and nonlinear fiber. Since the comb signal used in this work is highly coherent, all modes are phase-locked with each other, as we assumed in Eq. (4) [10,11]. Two modes in the optical comb signal were extracted with a 25-GHz arrayed waveguide grating (AWG), and the frequency difference between the two modes was set to f _TH, which defines the center frequency of the frequency-modulated sub-terahertz signal after photomixing. One of the selected modes was phase-modulated by a single-frequency sinusoidal signal with an optical phase modulator at f _FM. The half-wave voltage of the phase modulator was measured as approximately 3.1 V at 1 GHz. Then, the phase-modulated optical signal was coupled with the other pre-selected mode again with an optical coupler and input to a J-band uni-travelling photodetector (UTC-PD) module. To analyze and characterize the frequency-modulated sub-terahertz signal after photomixing, the output signal was down-converted to the 14-GHz frequency band with a second-harmonic mixer based on a Schottky barrier diode and a multiplier chain for a local oscillator. During the experiment, the center frequency of the frequency-modulated signal was set to 350 GHz. The center frequency could be easily tuned even up to 1 THz by tuning the mode spacing of the optical comb signal.

Fig. 2 Experiment setup for generating frequency-modulated sub-terahertz signal.

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Measured time-domain traces and frequency-domain spectra of the frequency-modulated sub-terahertz signal for several modulation indices are shown in Fig. 3 . First, unmodulated 350-GHz signal was generated and measured with a sampling oscilloscope and an electrical spectrum analyzer after the frequency down-conversion to 14 GHz. As can be seen in Fig. 3(a), the signal shows only a single frequency component. To modulate the frequency of the 350-GHz signal, we applied 1-GHz sinusoidal signal to the phase modulator located on one of the optical branches after the AWG as shown in Fig. 2. The peak voltage of the modulating signal was around 3.42 V (equivalent to radio frequency (RF) power of 20 dBm). From Eq. (9), the frequency deviation is expected to be around 3.36 GHz, which means that the instantaneous frequency of the sub-terahertz signal would vary from 350 – 3.36 GHz to 350 + 3.36 GHz within a 6.72-GHz frequency span. As shown in Fig. 3(b), the time period of the frequency change is consistent with that of the 1-GHz modulating signal, and the measured spectrum nearly fits the theoretical calculation in Eq. (7) for signal frequency modulated by a 1-GHz signal with 3.36-GHz frequency deviation. When we increased the peak voltage of the modulating signal to 6.83 V (equivalent to RF power of around 26.3 dBm), as can be seen in Fig. 3(c), the frequency deviation and the occupied bandwidth of the signal increased to approximately 6.7 and 15 GHz, respectively. In the time-trace of Fig. 3(c), a larger frequency change is also observed, but the envelop of the signal is no longer flat. This must be due to the limited performance of the experiment setup, which may arise from the relative large loss of the interconnection between harmonic mixer and the spectrum analyzer in the IF bands or from the limited IF/RF bandwidths of the harmonic mixer. This effect is also observed in Fig. 3(c) as an intensity difference at over 20 GHz between the measured and calculated frequency spectra of the down-converted signal.

Fig. 3 Measured time-traces (left) and spectra (right) for several modulation indices. Red dotted lines in the spectra are spectral envelopes calculated using Eq. (7)

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According to radar theory [7], the range resolution with linearly modulated a FM signal is given by Δr = c/2ΔF, where Δr is the resolution and c is the speed of light in air. ΔF is the chirp radar bandwidth and equal to the swing span of the instantaneous frequency, 2Δf _m in this case. Therefore the FM signal with a 6.7-GHz frequency deviation described here can theoretically provide depth resolution of around 1.12 cm. In this work, the maximum RF power was limited to around 27 dBm (approximately 500 mW) because of the power limitation of the driver amplifier. However, since the phase modulator used in this experiment can handle high power of up to 1 W, 13-GHz frequency deviation would be easily possible, leading to 0.58-cm range resolution. A larger frequency deviation would also be possible with a high-power external 50-ohm termination for the phase modulator. In terms of frequency deviation or signal bandwidth, the performance with this photonic frequency down-conversion of the phase-modulated optical signal is comparable with that of the conventional methods for sub-terahertz applications with electrical frequency multipliers [8]. However, unlike the conventional methods, the photonic techniques allow us to tune the center frequency easily while maintaining the frequency deviation or other parameters and to handle or deliver the frequency-modulated photonic sub-terahertz signal with low loss using optic-fiber cables. The optical comb signal in this work occupies the over-1-THz frequency span [9]; therefore, generating FM signal at higher frequencies could be easily accomplished by simply selecting higher optical modes or tuning the mode spacing of the optical comb signal.

4. Conclusion

A frequency-modulated sub-terahertz signal was successfully generated with a photonic technique based on a high coherent optical comb signal, optical phase modulator, and photomixer. In this work, peak frequency deviation of up to 6.7 GHz at 350 GHz was experimentally demonstrated and thus, theatrically, we should be able to distinguish objects with 1.12-cm depth difference using this scheme. The frequency deviation could be further increased by increasing the modulating frequency or applying a higher voltage to the phase modulator, depending on application. In addition, photonic techniques make this scheme provide wide and high operating frequencies of up to 1 THz. The results show the potential of using millimeter and terahertz frequencies for imaging or non-destructive sensing applications.

Acknowledgment

The authors thank Prof. Nagatsuma for his encouragement and discussions, and Drs. A. Wakatsuki, T. Furuta and N. Shigekawa for providing UTC-PDs. This work was supported in part by the National Institute of Information and Communications Technology, Japan.

References and links

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Generation of frequency-modulated sub-terahertz signal using microwave photonic technique

Abstract

1. Introduction

2. Principle

3. Experiment and results

4. Conclusion

Acknowledgment

References and links

Cited By

Figures (3)

Equations (10)

Optics Express