Low insertion loss optical pulse interleaving for ultra-low phase noise photonic microwave generation

Lingke Wang; Junchao Huang; Liang Liu; Tang Li

doi:10.1364/OE.25.012161

1. Introduction

Ultra-low phase noise and frequency-stable microwave signals based on photonics technology are required in a wide variety of applications, such as atomic frequency standards [1,2], high-performance radar systems, and precision measurements [3–5]. By using an optical frequency comb (OFC), the ultra-high spectral purity and frequency stability of a laser that has been stabilized to a reference cavity can be transferred to the microwave domain [6–8]. In comparison with conventional microwave oscillators, this method provides the lowest short-term instability. As a photonic approach, however, the phase noise of generated microwaves is limited by the thermal noise and shot noise of photodetection at frequencies far from the carrier. To circumvent this limit, it is important to keep the photodiode operating in an unsaturated condition. Once the photodiode is saturated, it is not possible to further increase the signal to noise ratio of photodetection by increasing the optical power. Either for commercial photodiodes [9] or custom-designed photodiodes [10, 11], saturation begins with an average power of only a few milliwatts for an Er:fiber femtosecond laser. To overcome this drawback, a feasible method is the multiplication of the femtosecond laser pulse repetition rate. Nowadays, two approaches are being used to achieve such multiplication. The first one utilizes a Fabry–Perot (FP) cavity as an optical spectrum filter [12]. This approach requires sophisticated optical collimation and a separate frequency-locking system but suffers an intrinsic optical power loss because of spectrum filtering. The second approach realizes multiplication by a Mach–Zehnder interferometer (MZI) [9, 13, 14]. This approach is more compact, robust, and has a lower insertion loss compared to the FP cavity method. Unfortunately, because of the output of the two ports, the MZI will inevitably exhibit half of the power loss. Recently, E. Portuondo-Campa et. al. suggested a fibered polarization-maintaining pulse interleaver that combines the two orthogonal-polarization outputs of the MZI into a single output [15]. They reported an estimated loss of 1–1.5 dB within the interleavers, which mainly originates from the 90° polarization-rotating splice and polarization beam combiner.

In this work, we demonstrate low insertion loss optical pulse interleaving by a cascaded fiber-ring interferometer. The optical power loss of a five-stage interleaver is approximately 0.5 dB, which is the lowest insertion loss for optical pulse interleaving to date. In addition, we propose a simple method to determine the delay error of the interleaver by measuring the power ratio between the harmonics of the generated microwaves. After precisely controlling the delay error of the interleaver, the phase noise reduction for the photodetection of a periodic train of ultra-short optical pulses is observed. Finally, by comparing the two multiplication systems, a phase noise level of −173 dBc/Hz for a single system at an offset frequency of 2 MHz is measured.

2. Optical pulse interleaver based on fiber-ring interferometer

Fiber-ring interferometers have already been successfully used in various fields such as optic gyroscopes [16–18], optical communications [19], and amplitude-modulated laser pulse rate multiplication [20, 21]. The interferometer is made of a 2 × 2 optical fiber coupler and one input port is connected to one output port to form a fiber loop. As illustrated in Fig. 1, port 1 is the input port and port 3 is the output port. An optical pulse train enters the interferometer at port 1 and is then split into two parts. One part passes through the coupler and directly outputs at port 3, while the other part is coupled to port 4 and travels back to port 2 through the fiber loop. The pulse train at port 2 continues to be split into two parts where one part proceeds to port 3 while the other part goes back to port 2 through the fiber loop. This process occurs continuously. Finally, the pulse train at port 3 is composed of two pulse trains, a synchronous part and a time-delayed part of the input pulse train. If the time delay of the fiber loop is exactly equal to an odd multiple of half the period of the input pulse train, the repetition rate of the output pulse train will be twice that of the input pulse train.

Fig. 1 Structure of fiber ring interferometer.

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Provided that the optical field at port N of a 2 × 2 single-mode fiber coupler is E_N (N = 1, 2, 3, and 4), where E₁ represents the optical field at input and E₃ represents the optical field at output, the relation between the optical field at different ports can be defined as

(\begin{matrix} E_{3} \\ E_{4} \end{matrix}) = (\begin{matrix} \sqrt{α} & i \sqrt{β - α} \\ i \sqrt{β - α} & \sqrt{α} \end{matrix}) (\begin{matrix} E_{1} \\ E_{2} \end{matrix})

where

α

is the power coupling ratio of ports 1 to 3, and

β

represents the insertion loss of the coupler (

β = 1

means no insertion loss). With the complex envelope of an individual input pulse represented as

a_{0} (t)

, the periodic input pulse train at port 1 can be expressed as

a_{1} (t) = {| E_{1} |}^{2} = a_{0} (t) \otimes \sum_{n = - \infty}^{+ \infty} δ (t - n T)

where

\otimes

is the convolution operator and T is the repetition period.

Combining Eqs. (1) and (2), the output pulse train at port 3 can be expressed as

\begin{array}{l} a_{3} (t) = {| E_{3} |}^{2} = α [a_{0} (t) \otimes \sum_{n = - \infty}^{+ \infty} δ (t - n T)] + (β - α) (β - α) [a_{0} (t) \otimes \sum_{n = - \infty}^{+ \infty} δ (t - n T - t_{L})] \\ + (β - α) α (β - α) [a_{0} (t) \otimes \sum_{n = - \infty}^{+ \infty} δ (t - n T - 2 t_{L})] + .... \\ + {(β - α)}^{2} α^{m - 1} [a_{0} (t) \otimes \sum_{n = - \infty}^{+ \infty} δ (t - n T - m t_{L})] \\ = a_{0} (t) \otimes \sum_{n = - \infty}^{+ \infty} [α δ (t - n T) + \sum_{m = 1}^{\infty} {(β - α)}^{2} α^{m - 1} δ (t - n T - m t_{L})] \end{array}

where m represents the number of cycles of light in the fiber loop and

t_{L}

is the time delay of the fiber loop.

If the time delay $t_{L}$ of the fiber loop is equal to half the period of the input pulse train, that is, $t_{L} = T / 2$ , Eq. (3) becomes

a_{3} (t) = a_{0} (t) \otimes \sum_{n = - \infty}^{+ \infty} [(α + \sum_{q = 1}^{+ \infty} {(β - α)}^{2} α^{2 q - 1}) δ (t - n T) + \sum_{q = 0}^{+ \infty} {(β - α)}^{2} α^{2 q} δ (t - n T - \frac{T}{2})]

For generating a multiplied repetition rate pulse train with uniform amplitude, we have

\begin{array}{l} α + \sum_{q = 1}^{+ \infty} {(β - α)}^{2} α^{2 q - 1} = \sum_{q = 0}^{+ \infty} {(β - α)}^{2} α^{2 q} \\ \Rightarrow α = \frac{β^{2}}{1 + 2 β} \end{array}

Neglecting the insertion loss of the fiber coupler, $β = 1$ , we thus obtain the coupling ratio $α = 1 / 3$ . According to Eq. (3), in the frequency domain, the power of the n^th harmonic of the signal at port 3 can be presented as

\begin{array}{l} I_{n} (n f_{r r}) = A_{0} (n f_{r r}) \cdot [α \cdot e^{2 π i f_{r r} n t} + (^{β - α) 2} \cdot e^{2 π i f_{r r} n (t + t_{L})} + (^{β - α) 2} \cdot α \cdot e^{2 π i f_{r r} n (t + t_{L} \cdot 2)} + \\ ... + (^{β - α) 2} \cdot α^{m - 1} \cdot e^{2 π i f_{r r} n (t + t_{L} \cdot m)}] \\ = A_{0} (n f_{r r}) \cdot [α + {(β - α)}^{2} \cdot \sum_{m = 1}^{\infty} α^{m - 1} e^{2 π i f_{r r} n t_{L} m}] e^{2 π i f_{r r} n t} \\ with A_{0} (f) = F (a_{0} (t)) \end{array}

_$F$is Fourier transformation operator and f_rr is pulse repetition rate. The term in bracket in line 3 of Eq. (6) represents the interference between the light coupled from port 1 to port 3 and the light circulating in the fiber loop. Under the conditions

α = 1 / 3

,

β = 1

and

t_{L} = T / 2 = 1 / (2 f_{r r})

, it is clearly to observe that the odd harmonics are destructive and the even harmonics are constructive.

The time-domain simulation of this multiplication process is presented in Fig. 2. Assuming that the individual input pulse has a Gaussian profile, the repetition rate is 250 MHz, $α = 1 / 3$ , and $β = 1$ .

Fig. 2 Optical pulse train (black) before multiplication and (red) after multiplication.

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Naturally, this configuration can realize a repetition rate multiplication of 2^N if an N-stage cascaded fiber-ring interferometer is constructed. In this work, we construct two five-stage interleavers to realize an OFC repetition rate multiplication of 32. For the OFC, we used a fiber optical frequency comb (FOFC) from Menlosystems Corporation (FC1500-250-WG) with a repetition rate of 250 MHz. After the five-stage interleaver, the repetition rate was multiplied to 8 GHz. Because the time delay of each stage can be chosen as an odd multiple of half the period of the input pulse train, the fiber length of each fiber loop is maintained to be larger than 50 cm for easier fiber splicing. For example, the length of the fiber loop for each stage interleaver is 122.514 cm, 61.257 cm, 51.048 cm, 86.781 cm and 84.228 cm respectively, which represents a time delay of 3(T/2), 3(T/4), 5(T/8), 17(T/16), and 33(T/32). In order to maintain a low insertion loss and amplitude mismatch of the interleavers, the optical fiber couplers we used were hand-selected and have a coupling ratio deviation of less than 1% and a low insertion loss (less than 0.1 dB). The total insertion loss of the two interleavers is approximately 0.5 and 0.7 dB, respectively. In the construction process of the interleaver, the most important point is to control the time delay errors of the fiber loops because they will not only degrade the signal to useless harmonics ratios but also cause excess phase noise during the photodetection process [22–24]. However, it is difficult to measure these errors with a resolution of less than 1 picosecond in the time domain unless one has an ultra-fast oscilloscope, which is very expensive. Here, we suggest a simple method of controlling the delay errors of the interleaver by measuring the power ratio between the harmonics of the microwave spectrum generated from a photodiode directly coupled to the output of the interleaver.

According to Eq. (6), under the condition $2 π f_{r r} n t_{L} \in [0, π]$ , the time delay $t_{L}$ can be uniquely determined. In other words, the time delay $t_{L}$ can be determined by measuring the power spectrum of the generated microwaves. In order to cancel the impact of the pulse envelope factor, the power of the n^th harmonic is divided by that of its adjacent harmonic. Moreover, this method can be used for the N-stage interleaver, the only difference is that the ordinal numbers of harmonics for the calculations should be multiplied by 2^N^–1.

We measured the power ratio of the 54^th and 53^rd harmonic of the repetition rate of 250 MHz using a first-stage interleaver with different delay errors. In our experiment, by slightly changing the repetition rate of the FOFC, the delay error of the first-stage interleaver can be precisely measured. The experimental results are presented in Fig. 3 and are observed to be consistent with the theoretical predictions that were simulated using the MATLAB software. Thus, this method provides a simple way to construct an optical pulse interleaver with an accurate time delay. In practice, the time delay of the interleaver is controlled by carefully polishing the fiber ends before splicing.

Fig. 3 Power ratio of 54^th and 53^rd harmonics of generated microwaves using a first-stage interleaver as a function of interleaver delay errors.

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In the experiment, two highly linear PIN photodiodes with a bandwidth of 22 GHz (Discovery Semiconductors HLPD DSC30S) were used to detect the optical pulse signal. Both photodiodes were temperature-stabilized at 25 °C and voltage-biased at 9 V. Due to the limited bandwidth, the photodiodes output 8 GHz signal and its 2^nd harmonic signal. Figure 4 displays the output 8 GHz signal power of the photodiodes as a function of incident optical power. It is evident that the saturation limit of the photodiodes moves from 3 to 4 mW to about 35 mW when illuminated by the optical pulse from the five-stage interleaver. The maximum power of the 8 GHz signal is 8.5 dBm that is more than 24 dB larger than that of the 8 GHz signal generated by directly connecting the output of FOFC to the photodiode.

Fig. 4 Photodiode output microwave powers of 8 GHz signal as a function of input optical power.

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3. Microwave phase noise measurements

3.1 Phase noise reduction from continuous wave (CW) shot noise limit

In 2013, F. Quinlan et. al. showed that in the photodetection process of a periodic train of ultra-short optical pulses, correlations between the shot noise sidebands symmetric about harmonics of generated microwave signals reduce the impact of shot noise on the microwave phase stability [22]. The degree of this correlation is a function of the optical pulse width and time delay errors in the interleaver [23]. If the pulse width increases, the degree of correlation will decrease and finally disappear when illuminating the CW light to the photodiode. Therefore, CW here denotes that no correlations in the shot noise spectrum. In a subsequent experiment, the researchers demonstrated a phase noise reduction from the additive noise of optical amplification with different interleaver delay errors [24]. For the shot noise in the photodetection process, however, the relationship between phase noise reduction and interleaver delay errors has not been verified experimentally up until now. In this work, for the purpose of testing this relationship, we minimize the delay error of the former four-stage interleaver and measure the phase noise of the generated microwaves while varying the fiber length of the fifth-stage loop. The experimental setup is illustrated in Fig. 5.

Fig. 5 Experimental setup for measuring the residual phase noise of photodetection. OC: optical coupler, OA: optical attenuator, MI: microwave isolator, BPF: band-pass filter, MA: microwave amplifier, PS: phase shifter.

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The optical pulse train from the FOFC is sent to a five-stage interleaver and is then split into two parts by a 50/50 optical coupler to drive two separate HLPDs. The incident power on the photodiodes can be adjusted respectively by two optical attenuators. The generated microwave signals are band-pass filtered to isolate the 8 GHz signals, which are further amplified using ultra-low phase-noise amplifiers to feed a double balanced mixer for phase noise measurement. A phase shifter is inserted into one microwave path for phase quadrature adjustment. The delay error of the former four-stage interleaver is fine-tuned to 1.0, 0.4, 0.4, and 0.3 ps, respectively, using the above-mentioned method. Meanwhile, the delay error of the fifth-stage interleaver is set to 0.7, 7.5, 11, and 15 ps for the different phase noise measurements. In the experiment, the photocurrents of both HLPDs that are adjusted to about 12 mA yield a CW shot noise floor of −170.5 dBc/Hz that is calculated without considering shot noise correlations. The noise floor of the amplifiers and phase noise test set is −169.8 dBc/Hz. Therefore, the combination of the CW shot noise and test set noise floor results in the CW shot noise upper limit in this experiment. It should be noted that the incident optical power coupling to the photodiodes would be adjusted slightly to maintain the same CW shot noise floor level while changing the delay error of the fifth-stage interleaver. The experimental data are presented in Fig. 6.

Fig. 6 Measured phase noise of photodetection system with different interleaver delay errors.

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In the graph, it appears that the phase noise increases with the delay error of the interleaver. When the delay error is minimized to 0.7 ps, the phase noise floor reaches the level of −169 dBc/Hz, which is 2 dB lower than that of the combination of the CW shot noise and test set noise floor. In addition, a comparison of the measured and predicted phase noise deviation as a function of delay error is presented in Fig. 7. The calculation model is proposed by F. Quinlan et. al. [23]. The optical pulse width before coupling to the photodiodes is 5 ps, which is measured by an autocorrelator (APE PulseCheck SM1200). Here, the phase noise deviation is defined as the noise level compared to the CW shot noise floor. Despite a small offset, the measured data and theoretical phase noise level show reasonable agreement. The offset between the measured data and the theoretical predictions perhaps comes from the excess noise because of the impact of photocarrier scattering and distributed absorption [25], which is not included in our calculations.

Fig. 7 Calculated photodetection-limited phase noise deviation (red trace) and that with added noise floor of test set (black trace). The measured data are plotted as black points. The error bars result from the variance in the phase noise measurements.

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3.2 Phase noise of five-stage interleaver and photodetection system

In this measurement, we estimate the additive noise of the multiplication channel (five-stage interleaver + detection system) by comparing two identical system. The experimental setup is illustrated in Fig. 8, which is nearly identical to that of the above experiment. The only difference is that two identical five-stage interleavers are driven by the FOFC. The delay error of each stage of the second five-stage interleaver is fine-tuned to 0.1, 0.7, 0.2, 0.5, and 0.1 ps, respectively.

Fig. 8 Experimental setup for measuring the residual phase noise of multiplication channel.

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The measured data are presented in Fig. 9 (red trace). The green curve that is measured by using the experimental setup shown in Fig. 5 represents the noise floor of the detection system, while the black curve represents the noise floor of the test set. At frequencies close to the carrier, the measured phase noise is limited by the test set noise floor, meanwhile, the excess noise from 100 Hz to 100 kHz originates from the photodetection process. At frequencies higher than 100 kHz, the measured phase noise reaches a plateau of −167 dBc/Hz, which is also influenced by the test set noise floor. Because the measured noise floor of the test set is −169.8 dBc/Hz, a phase noise level of −170 dBc/Hz for two identical multiplication channel can be extracted. Therefore, for single multiplication channel, the phase noise is estimated to be −173 dBc/Hz at an offset frequency of 2 MHz. However, the excess noise between the measured data and noise floor of the photodetection system which perhaps originates from the photodetection process [25] should be further studied.

Fig. 9 Measured phase noise of multiplication channel (red trace) and the measured noise floor of photodetection system (green trace). The black trace corresponds to the noise floor of the test set.

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4. Conclusion and Outlook

A 32-times multiplication of optical pulse rate based on a cascaded optical fiber-ring interferometer with an insertion loss of only 0.5 dB for ultra-low noise photonic microwave generation has been demonstrated. This method avoids the excess optical power loss introduced by current pulse interleavers, such as MZI and polarizing beam combiner architectures. By measuring the power ratio of the different harmonics of the generated microwaves, the time delay errors of the pulse interleavers are precisely controlled and the relationship between the phase noise reduction from the CW shot noise limit and interleaver delay errors is verified experimentally for the first time. In addition to these, by comparing a pair of multiplication systems, the level of measured phase noise reaches −167 dBc/Hz at frequencies far from the carrier. This measurement is mainly limited by the noise floor of the test set; therefore, the heterodyne cross-correlation method [26] can be used for more precise phase noise measurements in the future. In addition, the construction of a second FOFC system for the characterization of full photonic microwave links and the use of high-power handling capacity photodiodes [27] are also planned.

Funding

National Natural Science Foundation of China (11034008, 11274324, 11604353); Key Research Program of the Chinese Academy of Sciences (KJZD-EW-W02).

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Low insertion loss optical pulse interleaving for ultra-low phase noise photonic microwave generation

Abstract

1. Introduction

2. Optical pulse interleaver based on fiber-ring interferometer

3. Microwave phase noise measurements

3.1 Phase noise reduction from continuous wave (CW) shot noise limit

3.2 Phase noise of five-stage interleaver and photodetection system

4. Conclusion and Outlook

Funding

References and links

Cited By

Figures (9)

Equations (6)

Optics Express