Photonic frequency-octupling scheme for stable microwave generation based on two incoherent optical sources

Hongyao Chen; Jianping Wang; Huimin Lu; Tigang Ning; Li Pei; Jing Li

doi:10.1364/OSAC.382199

1. Introduction

With the rapid development of broad-band mobile communication services and business, microwave wireless access becomes the most critical link of end users. However, there are many difficulties need to be conquered in the broad-band wireless systems. The notable problems lie in the higher air-link losses, the expensive broad-band circuits and difficulty in system design and implement [1,2]. Fiber-optical wireless radio over fiber (RoF) systems are currently considered as a likely candidate to solve these difficulties due to its numerous merits, such as low propagation loss and cost of deployment, small propagation delay and anti-electromagnetic interference [3–5].

In a RoF system, the high quality and cost-effective generation of microwave signals is a key technique, which needs to be further developed, especially for the signals with frequency over 30 GHz (millimeter-wave, MMW) [6,7]. All-electronic generation of MMW signals remains as a serious challenge because of restrictions on frequency responses of electronic devices. Thus, the microwave generation in optical domain has become extremely attractive, through which microwave signals with higher frequencies can be generated [8–13]. Usually, microwave signal can be generated by heterodyning two optical carriers and the frequency of the generated microwave signal is equal to the spectral spacing between the two wavelengths. Theoretically, high frequency signals can be obtained as long as the bandwidth of photoelectric detector (PD) is not a constraint. To acquire signal with stable frequency and high spectral purity, the phase fluctuations of the two lasers need to be correlated by optical phase-locked loop or optical injection locking as reported in [14–19]. Basically, these two methods require feedback control and the phase-lock process could be time consuming, which is not conducive to the real-time requirement of the signal generating system. As an alternative to the methods mentioned above, coherent beat signal is obtainable by deriving two laser beams from a same gain medium or a consistent integration environment. It provides an effective way for realizing system miniaturization, but requires high quality of optical apparatuses and strict integration process, which is not easy to be implemented by using commercial devices. In [20,21], a feed-forward modulation (FFM) technique has been demonstrated in high purity microwave signals generation with two commercial laser sources. FFM is intrinsically stable, wideband and easy to implement. Meanwhile, the technique has no requirement of phase-locked loop to realize phase coherence and has no demand on lasers’ characteristics. However, there are also drawbacks of such schemes, such as requirements of local oscillator (LO) in the receiving end and inability to realize frequency up-conversion.

In our previous work [22,23], we proposed an improved feed-forward modulation theory (IFFM) which provides an effective solution for the drawbacks of FFM schemes. Unfortunately, until now this theory is still in the theoretical stage, has not been demonstrated by experiments. In this work, the IFFM theory is proved in detail by experiments via a photonic frequency-octupling microwave generation scheme. Compared with our previous works, this scheme gets rid of the fixed modulation index and lower frequency multiplication factors, which makes the generator more cost-effective. Moreover, a signal enhancement method which can make full use of the generated coherent optical sidebands to enhance the quality of the target signal is proposed and discussed.

2. Principle and theoretical analysis

The schematic diagrams of the proposed generator and corresponding spectra are shown in Fig. 1(a) and Fig. 1(b). Two independent continuous-wave lasers (CW1and CW2) are employed as the optical sources with frequency deviation of f₂-f₁. The input optical field at point A in Fig. 1(b) can be defined as

(1)$${E_A}(t )= {E_0}\{{\exp [{j2\pi {f_1}t + j{\varphi_1}(t )} ]+ \exp [{j2\pi {f_2}t + j{\varphi_2}(t )} ]} \}.$$

where E₀ represents the amplitude of optical field, f₁ and f₂ denote the center frequency of CW1and CW2. φ₁(t) and φ₂(t) are considered as the phase noise of CW1and CW2. In order to distinguish the phase noise of different frequency components, we apply different color lines as shown in Fig. 1(b): φ₁(t), purple solid line; φ₂(t), green dotted line; neither φ₁(t) nor φ₂(t), black solid line. The radio frequency (RF) driving signal from a local oscillator (LO) is divided into two paths to drive two child Mach-Zehnder interferometers (MZI, MZ_a and MZ_b) of the DP-MZM. Respectively, they can be expressed as

(2)$${V_{MZ\_\textrm{a}}}(t )= {V_0}\exp [{j2\pi {f_0}t} ].$$

and

(3)$${V_{MZ\_\textrm{b}}}(t )= {V_0}\exp [{j2\pi {f_0}t + {\pi \mathord{\left/ {\vphantom {\pi 2}} \right.} 2}} ].$$

The two MZI are biased at the maximum transmission point and the parent MZI of the DP-MZM (MZ_c) is biased at the minimum transmission point to provide an additional π phase shift between the output optical signals of the MZ_a and MZ_b. Therefore, the optical field at point B in Fig. 1(a) can be expressed as

(4)$${E_B} \propto {E_0}\sum\limits_{n = 1}^\infty {{J_{4n - 2}}(m )\left\{ \begin{array}{l} \exp [{j2\pi ({{f_1} - ({4n - 2} ){f_0}} )t + j{\varphi_1}(t )} ]\\ + \exp [{j2\pi ({{f_1} + ({4n - 2} ){f_0}} )t + j{\varphi_1}(t )} ]\\ + \exp [{j2\pi ({{f_2} - ({4n - 2} ){f_0}} )t + j{\varphi_2}(t )} ]\\ + \exp [{j2\pi ({{f_2} + ({4n - 2} ){f_0}} )t + j{\varphi_2}(t )} ]\end{array} \right\}} .$$

where J_n denotes the Bessel function of the first kind of order n. The modulation index (MI) m=π·V₀/2V_π is dependent on the magnitude of driving signal (V₀) and the half wave voltage of DP-MZM (V_π). At the output of DP-MZM, the optical carrier and odd-order optical sidebands are suppressed, only the even-order optical sidebands can be observed in the spectrum. In order to realize optical frequency quadrupling, only ±2^nd-order optical sidebands are desired, thus we need to calculate the optimization values of MI.

Fig. 1. (a) Schematic diagram of the frequency-octupling microwave generator and (b) corresponding spectra diagram (CW, continuous-wave laser; LO, local oscillator; DP-MZM, dual-parallel Mach-Zehnder modulator; C&G, Circulator and Grating; PD, photodiode; IM, intensity modulator).

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Here, we consider the MI should satisfy two conditions: 1) the normalized power of 2^nd-order optical sideband should be over −20dBm [as shown in Fig. 2(a)]; 2) the power ratio between 2^nd-order and 6^th-order optical sidebands should be more than 20dB [as shown in Fig. 2(b)]. To satisfy these two conditions, the modulation index m should be aligned within a proper range between 1.00 and 3.84 as present in Fig. 2(c). Within this range, it can be considered that only two 2^nd-order optical sidebands exist in the spectrum and the impact of high-order sidebands, such as 6^th-order, can be neglected. Thus, the optical field can be simplified to

(5)$${E_B} \propto {E_0}{J_2}(m )\left\{ \begin{array}{l} \exp [{j2\pi ({{f_1} - 2{f_0}} )t + j{\varphi_1}(t )} ]+ \exp [{j2\pi ({{f_1} + 2{f_0}} )t + j{\varphi_1}(t )} ]\\ + \exp [{j2\pi ({{f_2} - 2{f_0}} )t + j{\varphi_2}(t )} ]+ \exp [{j2\pi ({{f_2} + 2{f_0}} )t + j{\varphi_2}(t )} ]\end{array} \right\}.$$

Obviously, there are four frequency components, f₁-2f₀, f₁+2f₀, f₂-2f₀ and f₂+2f₀, exist in the spectrum, corresponding to sidebands 1, 2, 3 and 4 as shown in Fig. 1(b).

Fig. 2. (a) Normalized power curve of 2^nd-order optical sideband; (b) Power ratio curve between 2^nd-order and 6^th-order optical sidebands; (c) Relationship between the first-kind Bessel function J_n(m)² and modulation index m.

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Then the optical signal is coupled into a remodulation structure, which serves as a coherent sideband direct converter (CSDC) to achieve coherent sidebands generation and further enhance frequency multiplication factor of the proposed model. As inserted in Fig. 1(a), the remodulation structure consists of a circulator, a fiber Bragg grating (FBG), a photodiode (PD) and an intensity modulator (IM). The purpose of circulator and grating (C&G) is to separate two inner sidebands (2 and 3) form the two outer sidebands (1 and 4). According to the transmission function of the FBG, the optical field at points C and D in Fig. 1(a) can be expressed as

(6)$$\left\{ {\begin{array}{c} {{E_C} \propto {E_0}{J_2}(m )\left\{ \begin{array}{l} \exp [{j2\pi ({{f_1} - 2{f_0}} )t + j{\varphi_1}(t )} ]\\ + \exp [{j2\pi ({{f_2} + 2{f_0}} )t + j{\varphi_2}(t )} ]\end{array} \right\}}\\ {{E_D} \propto {E_0}{J_2}(m )\left\{ \begin{array}{l} \exp [{j2\pi ({{f_1} + 2{f_0}} )t + j{\varphi_1}(t )} ]\\ + \exp [{j2\pi ({{f_2} - 2{f_0}} )t + j{\varphi_2}(t )} ]\end{array} \right\}} \end{array}} \right..$$

A photodiode, PD1, is used to detect the two inner sidebands, the output photocurrent at points E in Fig. 1(a) can be expressed as

(7)$${i_E} \propto \cos [{2\pi ({{f_2} - {f_1} - 4{f_0}} )t + {\varphi_2}(t )- {\varphi_1}(t )} ].$$

It can be shown that the frequency of the photocurrent is f₂- f₁-4f₀, and it is affected by the phase noise φ₂(t) - φ₁(t). Subsequently, this RF signal acts as the driving signal of IM to complete the remodulation process. When the modulation index α of IM is adjusted to a proper value, optical sidebands higher than the 1^st-order can be neglected. The optical field at point F in Fig. 1(a) can be expressed as

(8)$${E_F} \propto {E_0}{J_2}(m )\left\{ \begin{array}{l} i{J_1}(\alpha )\exp [{j2\pi ({2{f_1} - {f_2} + 2{f_0}} )t + 2j{\varphi_1}(t )- j{\varphi_2}(t )} ]\\ + {J_0}(\alpha )\exp [{j2\pi ({{f_1} - 2{f_0}} )t + j{\varphi_1}(t )} ]\\ + i{J_1}(\alpha )\exp [{j2\pi ({{f_2} - 6{f_0}} )t + j{\varphi_2}(t )} ]\\ + i{J_1}(\alpha )\exp [{j2\pi ({{f_1} + 6{f_0}} )t + j{\varphi_1}(t )} ]\\ + {J_0}(\alpha )\exp [{j2\pi ({{f_2} + 2{f_0}} )t + j{\varphi_2}(t )} ]\\ + i{J_1}(\alpha )\exp [{j2\pi ({2{f_2} - {f_1} - 2{f_0}} )t + 2j{\varphi_2}(t )- j{\varphi_1}(t )} ]\end{array} \right\}.$$

There exist four new frequency components and two original frequency components optical sidebands, which are consistent with the sidebands 1(f₁-2f₀), 4(f₂+2f₀), 5(f₂-6f₀), 6(f₁+6f₀), 7(2f₁-f₂+2f₀) and 8(2f₂-f₁-2f₀) in point F in Fig. 1(b). As expressed in Eq. (8), the phase noise of sidebands 1 and 6 are φ₁(t) and that of sidebands 4 and 5 are φ₂(t). The corresponding frequency interval between the coherent lines can be calculated as 8f₀. The above calculation results indicate that by using the remodulation structure, two pairs of coherent optical sidebands with frequency interval of 8 times of the LO’s frequency can be generated, which can be used to generate stable microwave signals. After signal processing and photoelectric conversion with responsivity R, the photocurrent at point G in Fig. 1(a) can be expressed as

(9)$${i_G} \propto R{[{{E_0}{J_2}(m )} ]^2}{J_0}(\alpha ){J_1}(\alpha )\cos ({2\pi \cdot 8{f_0}t} ).$$

3. Experimental results and discussions

3.1 16 GHz microwave signal generation based on two incoherent CW lasers

To verify the mechanism of proposed scheme, experiments are conducted according to the setup as shown in Fig. 3. Two incoherent continuous-wave lasers CW1 and CW2 with wavelength of 1550.100nm and 1550.192nm are adopted. The wavelength spacing between the two lasers is 0.092nm (11.5GHz). The power of CW lasers is 0dBm. Considering the maximum response frequency of PD2 (KG-PD) is 20GHz, the LO (Hewlett 83711B) generates a 2GHz sinusoid signal to drive the DP-MZM (Fujitsu FTM7962EP). When the MI (m) of DP-MZM is applied around 3.5, frequency-quadrupling optical sidebands can be generated. The measured optical spectrum is shown in Fig. 4.

Fig. 3. The experimental setup for frequency-octupling microwaves generation.

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Fig. 4. Optical spectrum at the output of the DP-MZM.

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Figure 4 shows the optical spectrum at the output of DP-MZM. There are two pairs of ±2^nd-order optical sidebands with 0.064nm wavelength spacing (8GHz) in the spectrum. There exists a good agreement between the measured optical spectrum and the calculated result in Eq. (5). The optical carrier suppression ratio (OCSR) of the generated signal is 17.8dB and the undesired mode suppression ratio (UMSR) of the output optical signal is 14.9dB. This generated frequency-quadrupling optical signal is used as the input light for the remodulation unit in the following processing. To provide a direct and precise description for phase noises of the generated optical sidebands, we analyze φ₁(t) and φ₂(t), corresponding to two different color backgrounds as shown in Fig. 4.

In remodulation unit, a chirp fiber Bragg grating (CFBG) is applied to separate optical sidebands by connection of a circulator. The transmission and reflection responses of CFBG are illustrated as grey dash lines in Fig. 5(a) and 5(b). As shown in the figure, the transmission depth of CBFG is around 6.3dB and the reflection depth of CBFG is around 6dB. The measured optical transmission and reflection spectra of CFBG are also given in Fig. 5. As in Fig. 5(a), the two inner optical sidebands are suppressed. Similarly, in Fig. 5(b), the two outer optical sidebands are also suppressed. The wavelength spacing between the two inner optical sidebands is 0.028nm (3.5GHz). To ensure the spectrum purity of the output signal of PD1, the cut-off frequency of PD1 used in the experiment is below 10GHz.

Fig. 5. Optical transmission spectrum and reflection spectrum of the CFBG (the responses of the CFBG are given by the dashed line)

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After detection, a 3.5GHz RF signal with signal-to-noise ratio (SNR) over 30dB can be obtained. Since the two inner optical sidebands are from two different lasers without phase fluctuation correlation, the spectral purity degrading and frequency instability will affect the quality of the generated signal. Figure 6(a) shows the scatter plot of the character of frequency jitter of the signal. From 0 to 600 seconds, signal’s frequency is variable within a range of ±0.1GHz from the center frequency of 3.5GHz. Therefore, the dependent frequency jitter scope (ΔR) of the output signal can be considered as 0.2GHz. Figure 6(b) plots the electrical spectrum of the generated RF signal of PD1 (KG-PD). Owing to the superposition effect of the spectrometer, spectrum of the generated signal presents as a rectangular spectral region with the width over 0.1GHz rather than a pure spectral line.

Fig. 6. Frequency characteristic and electrical spectrum of the generated signal of PD1.

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According to the foregoing, the remodulation is realized by using a driving signal of 3.5GHz as shown in in Fig. 5(a). Here, a commercial IM working in a state of weak modulation is used, of which the MI (α) is around 0.4. The measured optical spectrum is shown in Fig. 7. Obviously, a new optical sideband is excited on either side of the two outer optical sidebands, which agrees well with the theoretical result in Eq. (8). There are two pairs of optical sidebands with wavelength spacing of 0.128nm (16GHz) in the spectrum. Taking the two optical sidebands with power of P₁ and P₃ (corresponding to −20.2dBm and −26.5dBm) for example, they can be used to generate a 16GHz microwave signal by heterodyne detection. As there are two pairs of optical sidebands with wavelength interval of 16GHz, the generated microwave signal should be a superimposed microwave signal of 16GHz after detection. In the following discussion, we analyze the stability of the generated microwave signal and the coherence of the four optical sidebands.

Fig. 7. Optical spectrum after remodulation.

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Figure 8(a) presents the frequency characteristic of the generated microwave signal of PD2 (KG-PD). As shown in the figure, in the range of 0 to 600 seconds, the signal frequency keeps stable and no frequency jitter is observed. Thus, we can consider that the 16GHz microwave signal has the characteristic of high frequency stability. Meanwhile, in Fig. 8(b), (a) pure spectral line (Width<0.2MHz) of 16GHz instead of a rectangular spectral region is observed, which indicates that the generated signal is with low phase noise and it is not affected by incoherent phase noises from the two lasers. It is consistent with the theoretical result in Eq.9. Note that, the bandwidth of the signal is 0.2 MHz, because of using non-narrow linewidth lasers for making experiment phenomenon very obvious and experiment effect more perfect. According to these two points, we can consider that each pair of optical sidebands used in optical heterodyning are coherent and the coherent sidebands conversion can be realized by the proposed remodulation structure, which verifies the correctness of IFFM theory. To make sure it is not an accidental outcome, several cases with different driving frequencies are carried out, and the results are shown in Figs. 8(c∼f). In each figure, a pure spectral line with frequency eight times than that of LO frequency can be observed, which reinforces the universality of the IFFM theory and feasibility of the proposed scheme, note that the power difference in Figs. 8(c∼f) due to the influence of the insufficient bandwidth of the CFBG.

Fig. 8. Frequency characteristic and electrical spectra of the generated signals of PD2

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3.2 64 GHz MMW, 320 GHz Terahertz signals generation and discussions

Based on the above results, the frequency-octupling IFFM model has been proved to be feasible for stable microwave signal generation. However, the spectrum characteristics of the generated optical signals and the final signal are unsatisfactory. Therefore, further experiments are necessary to find the reason and overcome it. In the modulation, spectrum characteristic of output optical signal is determined by the frequency response of modulator. Meanwhile, the fabrication and performance of the grating will be affected by the filtering bandwidth of CFBG. In the following part, we elaborate the impact of these two aspects on the generated signals based on the proposed scheme.

The deduced formulas show that the frequency spacing of the two inner optical sidebands is depended on the wavelength spacing of the two independent optical sources, thus two CW lasers with wavelength spacing of 0.402nm (50.25GHz) are employed. The operating wavelengths of CW1 and CW2 are 1550.100nm and 1550.502nm. The power of each CW laser is 7dBm. Also, considering the frequency response of the DP-MZM and IM, a LO (Hewlett 83711B) is used to generate an 8GHz sinusoid driving signal. When the MI and bias points are set as that of the scheme in part 3.1, frequency-quadrupling modulation can be realized, and the measured optical spectrum at the output of the DP-MZM is as shown in Fig. 9(a). In the figure, the two optical carriers and the undesired harmonic sidebands are suppressed effectively, the OCSR of the signal is over 26.6dB and the UMSR of the signal is more than 24.8dB, which indicates that the spectrum characteristic of the output signal of the DP-MZM has been significantly improved. There are two pairs of ±2^nd-order optical sidebands with wavelength spacing of 0.256nm (32GHz) in the spectrum, and the frequency space of the two inner optical sidebands can be calculated as 18.25GHz. Another CFBG is made to separate the four optical sidebands, as expected, the grating performance is improved due to bandwidth enhancement. In Fig. 9(b) and 9(c), the transmission depth of the CFBG is about 33dB and the reflection depth of CFBG is over 15dB, which are high enough to satisfy our demand of completely separation of the four sidebands. After photoelectric detection of PD1 (KG-PD 20GHz), a driving signal with frequency of 18.25GHz is generated.

Fig. 9. Spectra of the output signals of the DP-MZM (a), C&G (b and c) and PD1 (d).

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The next step is to achieve the coherent optical sidebands generation with the IM. The IM is also operating at weak modulation state. The measured optical spectrum is shown in Fig. 10(a). Compared to the optical spectrum presented in Fig. 7, the spectrum here is optimized and improved obviously. The six optical sidebands are clearly visible and the harmonics interference is suppressed effectively. There are two pairs of optical sidebands with wavelength spacing of 0.512nm (64GHz), which can be used to generate millimeter-wave signal of 64GHz. Since the frequency is higher than the maximum frequency response of our PD, we complete the following work by importing the optical spectrum data into simulation software.

Fig. 10. Measured optical spectrum (a) and corresponding simulation results (b and c).

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Before optical heterodyning, optical filters with the selection of frequency band are commonly used to filter harmonic and inhibit the stray. Here, we use dispersion effect to realize signal superposition, after which MMW signal with higher spectrum purity is achieved. As is well known, the phase change of optical signal can be caused by dispersion effect. Indeed, we have two pairs of coherent optical sidebands and thus it is feasible to use the dispersion effect to control the signals superposition process. The dispersion difference-output power curves are shown in Fig. 10(b). The result shows that the power of signal is greatly influenced by dispersion and changes periodically. Compared with using general filter, the peak power of output signal of PD2 can be increased by more than 10dB. Although signal power fluctuation brings extra power penalty in transmission process, its impact on data transmission is far less than that of power enhancement at the receiving end, which can be seen from eye diagrams insert in Fig. 10(b). Figure 10(c) shows the spectrum of the generated 64GHz MMW signal. In Fig. 10(c), a pure spectral line (Width<0.2MHz) of 64GHz exists in the spectrum, which is in accordance with the case of 16GHz microwave signal in Fig. 8, the difference is that the electrical spurious suppression ratio (ESSR) for the MMW signal is over 26dB. This confirms that the spectrum characteristics of the generated microwave signal is irrelevant with the proposed scheme and the IFFM theory, it is cause by the inherent characteristics of system components or installations.

Following the same steps as it did in experiment, the THz signal generation and transmission are also studied. The results are shown in Fig. 11. As shown in Fig. 11(a), the spectrum of the generated 320GHz signal is pure and stable. The ESSR is over 28dB and the width is lower than 0.2MHz, which indicates that the scheme and the IFFM theory are suitable to RF signal generation in different bands. Moreover, by using the method of signal superposition, the THz signal has good transmission characteristics in the 40.5km fiber link. The bit error rate (BER) performance and eye diagram are almost as good as that of using filter and amplifier with gain of 10dB. Note that, the length of fiber link is concerned with the dispersion management, which can be estimated by the target gain and dispersion. In Fig. 11(b), the BER curves of the two signals of same frequency can both reach 10⁻⁹ and the receiving sensitivity difference is only 0.5dB. The eye diagrams are widely open, compared with that of the signal generated by direct heterodyning of the two sources, the phase noise performance improves remarkably.

Fig. 11. Measured THz spectrum (a) and corresponding transmission results (b).

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4. Conclusion

This study has experimentally demonstrated the IFFM theory via a photonic frequency-octupling microwave generation scheme. It has three advantages: 1) this scheme can realize stable microwave, MMW or THz signal generation without supporting of phase-locked loop and complete the phase transformation and frequency up-conversion at the same time; 2) this scheme needs no special or fixed modulation index, the MI can be aligned within a proper range (from 1.00 to 3.84), such a property is beneficial in realizing a low-cost and easy-implementation system; 3) this scheme can generate two pairs of coherent optical sidebands concurrently, combined with the dispersion effect, the signals superposition can enhance the generated signal’s spectrum purity significantly. Experiments are carried out to generate a 16GHz microwave signal and a 64GHz optical millimeter wave signal. According to the setup as in experiments, a purity 320GHz terahertz wave signal is also obtained by simulation. Based on the achieved experimental and simulative results, we believe that the IFFM technology and the proposed scheme are attractive for future stable RF signals generation and cost-effective RoF system.

Funding

Fundamental Research Funds for the Central Universities (FRF-TP-18-059A1); China Postdoctoral Science Foundation (2019M660461).

Acknowledgments

We thank the Key Lab of All Optical Network & Advanced Telecommunication Network of EMC for the use of their equipment.

Disclosures

The authors declare no conflicts of interest.

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Photonic frequency-octupling scheme for stable microwave generation based on two incoherent optical sources

Abstract

1. Introduction

2. Principle and theoretical analysis

3. Experimental results and discussions

3.1 16 GHz microwave signal generation based on two incoherent CW lasers

3.2 64 GHz MMW, 320 GHz Terahertz signals generation and discussions

4. Conclusion

Funding

Acknowledgments

Disclosures

References

Cited By

Figures (11)

Equations (9)

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