Characterization of passive optical components with ultra-fast speed and high-resolution based on DD-OFDM

Banghong Guo; Tao Gui; Zhaohui Li; Yuan Bao; Xingwen Yi; Jianping Li; Xinhuan Feng; Songhao Liu

doi:10.1364/OE.20.022079

1. Introduction

Some special passive optical components with very fine structures in wavelength domain tend to be unstable due to the mechanical vibrations or thermal fluctuations. These passive optical components sensitive to the environment, such as Mach-zehnder interferometer or fiber Bragg gratings (FBGs), can be used for sensor application. But in some sensor application with the requirement on the speed and resolution, such as ultra-fast mechanical vibration or ultrasonic sensor, it is difficult to know the response if it is going to continue to change rapidly. Conventional measurement techniques with slow speed, e.g., optical spectrum analyzer (OSA) or a laser scanning system, cannot meet these demands [1–4]. Hence, it is very important to propose a characterization method with high-resolution and ultra-fast measurement speed. To achieve these requirements, we have recently demonstrated a method based on coherent detection technique and optical orthogonal frequency division multiplexing (OFDM) signal [5]. Unfortunately, coherent optical detection technique needs several expensive devices, including the narrow line-width laser sources and optical coherent receiver [6]. In contrast, direct-detection OFDM (DD-OFDM) signal can be detected without optical coherent receiver. In addition, for DD-OFDM signal, a low-cost electro-absorption modulated laser (EML) with several MHz line-width instead of the high-cost external cavity laser (ECL) is enough for the system requirement [7]. Therefore, the high-speed and high-resolution measurement technique using DD-OFDM signal can be implemented cost-effectively.

In this paper, we demonstrate an optical channel estimation technique using DD-OFDM signal to characterize the passive optical components. In experiment, by using FFT, EML and photo detector (PD), we can realize sub-MHz resolution with a measurement time bounded by the theoretical limit. In order to compare the measurement performance using DD-OFDM and CO-OFDM signals [5], we measure a fiber Bragg grating (FBG) and a home-built delay interferometer (DI) based on two techniques. The experimental results using DD-OFDM signal agree well with that using CO-OFDM signal.

2. Technical principle

In optical coherent detection system, the coherent optical receiver down-converts the whole optical signal modulated with RF signals linearly to an electrical signal by means of heterodyne or homodyne detection. The combination of coherent detection and digital signal processing techniques provide us the capability to obtain both the phase and intensity response of the passive optical components directly based on double sideband (DSB) or single sideband (SSB) modulated optical signal [8–10].

In contrast, for the DD-OFDM detection system, it is difficult to obtain the phase information from the passive optical components only based on DSB modulated optical signal directly, since the lower sideband and upper sideband optical signals after the direct detection at PD have the same amplitude but opposite phase and exactly cancel each other. Therefore, we adopt optical single-sideband (OSSB) modulation technique for DD-OFDM detection system, which can be described as “self-coherent” detection. With the help of self-coherent detection technique, the phase or delay information can also be recovered from OSSB modulated optical signal [11–13].

Therefore, we use the OSSB-DD-OFDM signal to measure the property of passive optical components. In general, the OSSB-DD-OFDM can be described as follows [14,15]:

s (t) = e^{j 2 π f_{0} t} + α \cdot e^{j 2 π (f_{0} + Δ f) t} \cdot s_{B} (t)

where s(t) is the optical OFDM signal, f₀ is the optical carrier frequency, Δf is the guard band between the optical carrier and the OFDM band, and α is the scaling coefficient indicating the relative amplitude between the OFDM signal and optical carrier. s_B(t) is the baseband OFDM signal given by Eq. (2):

s_{B} (t) = \sum_{k = - \frac{1}{2} N_{s c} + 1}^{\frac{1}{2} N_{s c}} c_{k} e^{j 2 π f_{k} t}

where c_k represents the mapped 4-QAM symbols on the kth subcarrier, f_k and N_sc represents the frequency of the kth subcarrier and the total number of subcarriers respectively. After the signal passing through the device under test (DUT), its impulse response function can be described as h(t) and thus the OFDM signal can be approximated as Eq. (3):

\begin{array}{l} r (t) = \int_{- \infty}^{\infty} s (t - τ) h (τ) d τ = \int_{- \infty}^{\infty} [e^{j 2 π f_{0} (t - τ)} + α \cdot e^{j 2 π (f_{0} + Δ f) (t - τ)} \cdot \sum_{k = - \frac{1}{2} N_{s c} + 1}^{\frac{1}{2} N_{s c}} c_{k} e^{j 2 π f_{k} (t - τ)}] \cdot h (τ) d τ \\ = e^{j 2 π f_{0} t} \cdot \int_{- \infty}^{\infty} h (τ) \cdot e^{- j 2 π f_{0} τ} d τ + α \cdot e^{j 2 π (f_{0} + Δ f) t} \cdot \sum_{k = - \frac{1}{2} N_{s c} + 1}^{\frac{1}{2} N_{s c}} c_{k} e^{j 2 π f_{k} t} \int_{- \infty}^{\infty} h (τ) e^{- j 2 π (f_{0} + Δ f + f_{k}) τ} d τ \end{array}

Since the channel response function H(f) represents the Fourier transform of the impulse response function, i.e.

H (f) = \int_{- \infty}^{\infty} h (τ) \cdot e^{- j 2 π f τ} d τ

Equation (3) can be simplified as

r (t) = H (f_{0}) e^{j 2 π f_{0} t} + α \cdot e^{j 2 π (f_{0} + Δ f) t} \cdot \sum_{k = - \frac{1}{2} N_{s c} + 1}^{\frac{1}{2} N_{s c}} H (f_{0} + Δ f + f_{k}) c_{k} e^{j 2 π f_{k} t}

At the receiver, the photo-detector can be modeled as the square law detector and the detected photocurrent is represented by Eq. (6):

\begin{matrix} I (t) \propto {| r (t) |}^{2} \\ = {| H (f_{0}) |}^{2} + 2 α Re {e^{j 2 π Δ f t} \sum_{k = - \frac{1}{2} N_{s c} + 1}^{\frac{1}{2} N_{s c}} \underset{received data}{\underset{︸}{[| H (f_{0} + Δ f + f_{k}) | e^{j ϕ (f_{k})} \cdot c_{k}]}} e^{j 2 π f_{k} t}} \\ + | α^{2} | \cdot \sum_{k_{1} = - \frac{1}{2} N_{s c} + 1}^{\frac{1}{2} N_{s c}} \sum_{k_{2} = - \frac{1}{2} N_{s c} + 1}^{\frac{1}{2} N_{s c}} c_{k_{2}}^{*} c_{k_{1}} e^{j (2 π (f_{k_{1}} - f_{k_{2}}) t)} H (f_{0} + Δ f + f_{k_{1}}) H {(f_{0} + Δ f + f_{k_{2}})}^{*} \end{matrix}

In Eq. (6), the first term is the DC component that can be filtered out. The second term consists of the recovered linear OFDM signal, which contains both the phase and intensity response information. So, the second term can be used for optical channel estimation. Let d_k represents the received data on the kth subcarrier, the complex channel response can be obtained by

H (f_{0} + Δ f + f_{k}) = d_{k} / c_{k}

. The intensity response is the absolute value of

H (f_{0} + Δ f + f_{k})

and the phase response is the angle value of

H (f_{0} + Δ f + f_{k})

. The third term is the intermodulation term in the low frequency, which should be removed [16]. We know that

α

is small, and

| α^{2} |

should be much smaller, so the power of the third term is much smaller than the second term, and can be ignored.

For optical channels estimation using DD-OFDM signal, there are some possible measurement error induced by the sensitivity of PD, noise of EDFA, non-ideal of IQ-mixer and intermodulation products (i.e. the third term of Eq. (6) etc.)

In order to minimize the effect of the noise from optical amplifiers and PD, averaging and low pass filtering techniques are necessary for the detected electric signals, which will influence the measurement speed. Even so, this method is still much faster than conventional methods, such as OSA or laser scanning technique.

Unlike the optical coherent detection, the direct detection is insensitive to polarization state of the optical signal. Polarization insensitivity is very important and convenient for the fast and fine measurement system since we need not to keep the polarization stability.

3. Experimental setup

Figure 1 shows the experimental setup of ultra-fast speed and high-resolution measurement system based on DD-OFDM signal. An OFDM baseband signal was generated in a computer and uploaded into a Tektronix AWG 7122B arbitrary waveform generator (AWG). The waveforms generated by AWG were continuously output at 8GS/s. 4-QAM signal was used to map the bit stream data to every OFDM sub-carrier. The measurement frequency resolution is determined by AWG sampling rate divided by FFT points. The longer of the OFDM symbol, which means the more points FFT, leads to a higher resolution. So a tunable frequency resolution can be achieved only by varying the length of the OFDM symbol. In the experiment, we use 2048 points FFT to achieve the frequency resolution about 3.9MHz. If using more points FFT, we can realize sub-MHz resolution with a measurement time bounded by the theoretical limit. However, too many points of FFT will increase the calculation complexity but also decrease the measurement speed. In addition, the signal will become more sensitive to the phase noise if the OFDM symbol is too long. Therefore, the length of OFDM symbol should be optimized for different applications.

Fig. 1 Experimental setup and DUT (device under test) (S/P: serial to parallel; P/S: parallel to serial; DDC: digital down-conversion; CP: cyclic prefix ratio; DUT: device under test.)

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To realize the OSSB modulation and avoid the second-order intermodulation distortion (IMD) due to the square law detection at PD, the OFDM signal should be up-converted from the optical baseband onto the radio frequency (RF) signal [17]. In this experiment, an analog IQ-mixer with 5GHz bandwidth and 8-12GHz local oscillator frequency range is used to up-converted the OFDM signal from the baseband to a 8.5GHz RF signal. After amplified by the electric driver, OFDM signals are modulated to an optical signal through an EML. As shown in Fig. 1, OSSB OFDM signal is realized by using an optical filter to remove the lower sideband optical signal.

Figure 2(a) and Fig. 2(b) show the optical spectrum of DSB and SSB optical OFDM signal respectively. An erbium doped fiber amplifier (EDFA) is used to compensate for the loss of DUT. A FBG and a home-built delay interferometer with 3m long relative arm difference are used as DUT in the experiment.

Fig. 2 Optical OFDM spectrum after EAM modulation. (a) DSB modulated optical signal; (b) SSB modulated optical signal

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After passing through the DUT, OSSB OFDM signal is detected at PD. A real-time oscilloscope operated at 25GS/s is used to digitalize the detected electric OFDM signal. The OFDM symbols are converted to multiple subcarriers in frequency domain through FFT in computer. Digital signal processing techniques are used to estimate the phase and intensity response of the OFDM signal induced by passive optical components [18].

4. Experimental results and discussions

According to the above analysis, the frequency resolution is determined by FFT length. By setting the FFT length to 2,048 and the CP length to 128, measurement frequency resolution is approximately 3.9MHz theoretically. Obviously, it is difficult for OSA or a laser scanning system to achieve such a high resolution and fast measurement speed. The duration of each OFDM symbol is 0.272μs with the AWG sampling rate of 8GS/s. The effective bandwidth of the OFDM signal is about 6GHz.

We first measure the properties of DI using DD-OFDM and CO-OFDM signals and then compare the measurement results [5]. Figure 3(a) and Fig. 3(b) illustrates the measured transfer function by using the DD and CO-OFDM signal respectively. Figure 3(c) and Fig. 3(d) shows the measurement results in detail within 1GHz span. The experimental results are averaged by using 22 OFDM symbols. The measured extinction ratios of intensity response are larger than 20dB and the measured free spectral range (FSR) is 66.7-MHz.

Fig. 3 Measured transfer function of a DI with 66.7MHz FSR. The resolution is 3.9MHz. (a) DD-OFDM method within 6GHz span, (b) CO-OFDM method within 6GHz span, (c) DD-OFDM method within 1GHz span in detail, (d) CO-OFDM method within 1GHz span in detail.

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The discrete phase level with a difference of π and the periodic phase jumps demonstrate that we have accurately measured the phase response of the DI [19,20]. The experimental result based on DD-OFDM signal agree well with those measured using the CO-OFDM-based technique. Although there are some phase spikes using both techniques, they can be neglected since they only occurred at the edge of every phase jump.

We also characterize and compare the reflective and transmission spectrum of an FBG using the conventional OSA and DD-OFDM-based techniques. Figure 4 and Fig. 5 illustrate the reflective and transmission optical spectrum of FBG respectively based on two measurement techniques respectively. Figure 4(a) and Fig. 5(a) show the intensity response of FBG using OSA. Figure 4(b) and Fig. 5(b) show the measured relative intensity and phase response of FBG based on the DD-OFDM method. Here, we only show part of the measured intensity spectrum indicated by the red circle in Fig. 5(b). The measured intensity response has a good agreement with that measured by using OSA. However, optical channel estimation using DD-OFDM signal has a much better frequency resolution about 3.9MHz. In addition, our method can also obtain the phase response information shown by the pink line in Fig. 4(b) and Fig. 5(b), which cannot be obtained by using OSA.

Fig. 4 Reflective optical spectrum of FBG measurements by (a) Conventional laser scanning technique with 125MHz frequency resolution (b) DD-OFDM technique with 3.9 MHz frequency resolution of the red circle part.

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Fig. 5 Transmission optical spectrum of FBG measurements by (a) Conventional laser scanning technique with 125MHz frequency resolution (b) DD-OFDM technique with 3.9 MHz frequency resolution of the red circle part.

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Conclusion

We have demonstrated a novel optical channel estimation technique using DD-OFDM signal to characterize the passive optical components. By using optical DD-OFDM signal, the intensity and phase response of the passive optical components can be measured with a 3.9MHz frequency resolution. The experimental results indicate that the experimental result using DD-OFDM signal has a good agreement with those using CO-OFDM signal.

Acknowledgments

The authors would like to acknowledge the support from National High Technology Research and Development Program of China (863 Program) (No. 2012AA040210), Key Program of Natural Science Foundation of Guangdong Province, China (No. 10251063101000001), National Natural Science Foundation of China (No. 61071097, No. 61107060).

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Characterization of passive optical components with ultra-fast speed and high-resolution based on DD-OFDM

Abstract

1. Introduction

2. Technical principle

3. Experimental setup

4. Experimental results and discussions

Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Equations (6)

Optics Express