Wideband tunable optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering

Huanfa Peng; Yongchi Xu; Xiaofeng Peng; Xiaoqi Zhu; Rui Guo; Feiya Chen; Huayang Du; Yuanxiang Chen; Cheng Zhang; Lixin Zhu; Weiwei Hu; Zhangyuan Chen

doi:10.1364/OE.25.010287

1. Introduction

Microwave or millimeter-wave signals are widely used in many applications. On the high end of applications, such as instrumentation, radar and communication, wideband tunability and low phase noise microwave or millimeter-wave sources are required. Conventionally, three ways are used to overcome the frequency tunability limitations in electronic-based oscillators. One is voltage-controlled oscillator (VCO) using varactors [1], another is yittrium iron garnet (YIG)-tuned oscillator (YTO) [1], and the other is based on frequency multiplication [2]. Usually, VCO is difficult to achieve tunable range more than an octave band at high frequency [1]. The phase noise performance of the YTO is degraded with the increasing of frequency [3]. For frequency multiplication method, power fading and phase noise degradation arise with the frequency. The phase noise of the frequency multiplication system generally increases quadratically with the frequency [2]. In the past few decades, microwave and millimeter-wave generation with photonic methods attract great attentions due to their large bandwidth, wideband tunability, low phase noise, and potential of chip-scale packaging integration [4–14]. Among various photonic methods, optoelectronic oscillator (OEO) has been demonstrated the ability to generate wideband tunable [11], ultra-low phase noise (−163 dBc/Hz at 6 kHz offset [4]) microwave or millimeter-wave signal. In OEO, a narrow-band electrical filter is needed to select the desired oscillation mode. To realize the frequency tunable OEO, usually two schemes are employed. One category uses a tunable narrow-band electrical filter or electrical filter bank [3], the other is based on the tunable single passband microwave photonic filter (MPF) [15], which can achieve ultra-wideband tunability [10–14]. Among all kinds of MPFs for tunable OEOs, phase-modulation-based single passband MPF attracts great attentions due to the advantage of no dc bias drift for the phase modulators (PMs) [10–12]. The phase-modulation-based single passband MPFs are realized by the conversion of phase-to-intensity modulation (PM-IM) by changing the phase or amplitude of the phase modulated sidebands. In [10], an optical notch filter formed by a reflective phase-shifted fiber Bragg grating (PS-FBG) is used to change the amplitude and phase of the phase modulated sidebands. The tuning range is limited by the total reflection bandwidth of the PS-FBG, and the 3-dB bandwidth of the MPF is not uniform over the tuning range. In [11], a tunable optical bandpass filter (OBPF) is placed after the PM to form a tunable single passband MPF by changing the bandwidth of the OBPF. The bandwidth of the MPF is defined by the frequency difference between the optical carrier and center of the OBPF. Due to the non-ideal roll-off characteristics of the OBPF, it is difficult to accurately control the bandwidth of MPF as small as tens of MHz, which results in mode hopping problem of the OEO. In [12], a whispering gallery mode resonator (WGMR) allows only one phase modulated sideband to pass, which realize a single passband MPF in the OEO. By changing the bias voltage applied on the WGMR, the frequency can be tuned. The key challenge for this type of OEO is the light coupling between the laser and WGMR, especially in a vibration environment.

Another approach to PM-IM conversion is based on the narrow-band optical filtering by stimulated Brillouin scattering (SBS) in a fiber [16]. SBS is a nonlinear process occurs by the interaction of two counter-propagating optical waves (a signal wave and a pump wave) through an acoustic mode [17], and can generate narrowband gain and loss spectral areas [18,19]. When one of the phase modulated first sidebands locates at either of two spectral areas, a single passband MPF is formed [20–22]. The SBS based MPF has the features of narrow-bandwidth, sharp roll-off passband, wideband tunability, and 3-dB bandwidth nearly independent of frequency. Furthermore, the SBS based MPF is easy to achieve due to the low threshold power of SBS in fiber [17]. In OEO, the fiber can serve as both the medium for the SBS and low-loss delay line, which makes the system cost-effective. In [23], tunable DC-60 GHz RF generation utilizing sideband amplification by SBS is reported. The same scheme is also demonstrated by a photonic chip [24]. Most of the components, including the photodiode, PM, and SBS gain medium have been demonstrated on photonic chip. The chip integration of optical circulator used in the OEO loop is challenging. However, some progress has been made in recent years [25,26]. The construction of a fully integrated SBS based OEO is feasible in the future. In SBS amplification based OEOs, amplified spontaneous emission noise (ASE) is a dominated phase noise floor [23].

In this paper, a wideband tunable OEO based on the deamplification of SBS is proposed and experimentally demonstrated. A single passband MPF with wideband tunability, sharp roll-off 3-dB bandwidth as small as tens of MHz realized by the sideband deamplification of SBS is employed in the proposed OEO. Compared with the MPF based on amplification of SBS, the ASE noise is avoided in this scheme. We will show the influence of chromatic dispersion and phase shift due to SBS on the out-of-band rejection in both MPF schemes based on amplification and deamplification of SBS. Among various sources of the phase noise in OEOs, the frequency noise of the laser can be converted to the phase noise through the chromatic dispersion [27], Rayleigh scattering [28–31] and facet reflections [32,33]. We will demonstrate theoretically and experimentally that in an OEO based on SBS, the laser frequency noise can also be converted to the phase noise via the phase shift induced by SBS and is the dominant source for close-in (< 1 MHz) phase noise. The conversion of laser frequency noise to the close-in phase noise is larger in the OEO based on SBS amplification than on SBS deamplification. A tunable 7 to 40 GHz OEO based on SBS deamplification is experimentally demonstrated. The phase noise is −128 dBc/Hz at 10 kHz offset for 10.30 GHz signal.

The remaining paper is organized as follows. In Section 2, the principle of the proposed OEO is given. The theoretical analysis of the frequency response of the MPF and phase noise performance of the proposed OEO are presented in Section 3. Based on the proposed scheme, experimental results of the frequency tunability, stability, and phase noise performance of the proposed OEO are shown in Section 4. Finally, a conclusion is drawn in Section 5.

2. Principle of the proposed OEO

Figure 1 shows the schematic diagram of the proposed OEO. One CW laser serves as the pump, the other narrow-linewidth tunable CW laser is employed as the signal. For the proposed OEO, the wavelength of the pump laser is larger than that of the signal laser by at least Brillouin frequency shift ν_B. A long none-zero dispersion shifted fiber (NZ-DSF) is introduced to the OEO loop to generate SBS and enhance the Q value of the OEO loop. The light from the signal laser is injected to the NZ-DSF after passing through the PM. The pump laser is sent into the NZ-DSF through an optical circulator. A polarization controller (PC) is used to control the polarization state of the pump wave. The output light from the port-3 of the optical circulator is separated to two fiber links (SMF1, SMF2) with different lengths to form a dual-loop OEO. The dual-loop architecture can suppress side-modes and improves frequency stability [34,35]. The outputs of the two PDs (PD1, PD2) are coupled together by a 3-dB electrical coupler (EC1) and amplified by a low noise amplifier (LNA) and a power amplifier (PA). The amplified electrical signal is fed back to drive the PM to form a closed loop.

Fig. 1 Left part: schematic diagram of the proposed OEO. PM: phase modulator; ISO: optical isolator; NZ-DSF: none-zero dispersion shifted fiber; OC: optical coupler; SMF1, SMF2: single-mode fibers; PD1, PD2: photodiodes; EC1, EC2: electrical couplers; LNA: low noise amplifier; ELPF: electrical lowpass filter; PA: power amplifier; PC: polarization controller; ESA: electrical spectrum analyzer. Right part: optical spectra of the nodes (A, B, and C). λ₀, λ_p: wavelength of the signal pump lasers; ν_B: Brillouin frequency shift.

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As shown in Fig. 1, the output light from the PM has two sidebands with symmetrical amplitudes and anti-phases between each other. With the pump light in the NZ-DSF, a narrow-band gain spectral area whose frequency is downshift by Brillouin frequency shift ν_B to the pump wave and a narrow-band loss spectral area whose frequency is by upshift Brillouin frequency shift ν_B to the pump wave are generated. If the phase modulated + 1st sideband falls on either of two areas, a RF signal is obtained at the output of PD. Two single passband responses exist by PM-IM. The center frequency of the passband induced by the gain spectral area is larger than that of the loss spectral with twice of Brillouin frequency shift. In this proposed OEO, the loss spectral area is used to form the single passband response. To realize single mode oscillation, the passband response induced by the gain spectral area should be suppressed, which can be realized by an electrical lowpass filter (ELPF) with high out-of-band suppression ratio. The center frequency of the single passband induced by the loss spectral area is the frequency difference between the signal and the center frequency of loss spectral area. The oscillation frequency of the OEO can be tuned by changing the wavelength of the signal laser. Compared with [22], in this scheme there is no OBPF. Due to the roll-off of the ELPF is sharper than that of the OBPF, the harmonics induced by the PM can be strongly reduced. The insertion loss of the ELPF is lower than that of the OBPF, which results in the power efficiency and phase noise performance of the proposed OEO can be greatly improved.

3. Theoretical analysis and simulations

In the following sections, the frequency response of the MPF utilizing the deamplification of SBS is theoretically analyzed by considering the chromatic dispersion, sideband amplitude attenuation and phase shift induced by the SBS. A model for the close-in (< 1 MHz) phase noise of the proposed OEO is also given.

3.1 Frequency response of the MPF

Figure 2(a) shows the scheme to measure the frequency response. A vector network analyzer (VNA) is used to drive the PM with a frequency sweep RF signal and receive the photo-detected RF power from the PD.

Fig. 2 (a) Setup for frequency response measurement of the MPF utilizing the sideband deamplification of SBS. (b) Schematic diagram of the amplitude and phase responses induced by the narrow-band optical gain and loss spectral areas of SBS to the + 1st phase modulated sideband.

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Under a RF signal modulation, the optical field at the output of the PM by only considering the ± 1st phase modulated sidebands and optical carrier can be described as

E (t) \approx \sqrt{P_{0}} e^{j 2 π f_{0} t} [J_{- 1} (β) e^{- j 2 π f_{m} t} + J_{0} (β) + J_{1} (β) e^{j 2 π f_{m} t}]

where

P_{0}

is the optical power of the signal laser,

β

is the modulation index of PM,

f_{0}

and

f_{m}

are the frequency of the signal laser and the modulation RF signal, respectively. The first component in Eq. (1) is the optical field of the + 1st sideband. After propagating through a fiber with length of

L

and chromatic dispersion coefficient of

D

, the output optical field is [17]

E^{'} (t) \approx \sqrt{P_{0}} e^{j (2 π f_{0} t - β_{0} L)} [α \cdot J_{- 1} (β) e^{- j 2 π f_{m} (t - \frac{n_{g} L}{c})} e^{j \frac{2 π D L λ_{0}^{2} f_{m}^{2}}{c}} e^{- j δ} + J_{0} (β) + J_{1} (β) e^{j 2 π f_{m} (t - \frac{n_{g} L}{c})} e^{j \frac{2 π D L λ_{0}^{2} f_{m}^{2}}{c}}]

where

β_{0}

is the propagation constant of the signal laser,

λ_{0}

is the wavelength of the signal laser,

n_{g}

is the group velocity of the modulation optical signal,

α

and

δ

are the sideband attenuation and phase shift induced by the deamplification of SBS to the + 1st sideband. The optical field of the + 1st sideband after SBS deamplification is described as [18]

E_{+ 1 s t} (L) = E_{+ 1 s t} (0) \exp (- g_{B} I_{p} L)

where

E_{+ 1 s t} (0)

and

E_{+ s t} (L)

are the optical fields of the + 1st sideband at the input and output of the fiber,

g_{B}

is the complex Brillouin gain coefficient,

I_{p} = P_{p} / A_{e f f}

is the power intensity of the pump laser,

P_{p}

is the pump power, and

A_{e f f}

is the effective mode area. The complex Brillouin gain coefficient is given by [18]

g_{B} = \frac{1}{2} \frac{g_{p}}{1 - 2 j (\frac{v - v_{B}}{Δ v_{B}})}

where

Δ v_{B}

is the loss bandwidth of SBS,

v_{B}

is the Brillouin frequency shift of SBS,

v

is the upshift frequency relative to the pump wave for the + 1st sideband,

g_{p}

is the line center Brillouin gain coefficient. By considering the amplitude attenuation and phase shift by the deamplification of SBS, the relation between the optical fields of the + 1st sideband at the input and output of fiber can also expressed as

E_{+ 1 s t} (L) = E_{+ 1 s t} (0) \cdot α \cdot e^{j δ}

When the + 1st sideband locates at the loss spectral area of SBS, as shown in Fig. 2(b), the following relation can be satisfied.

v - v_{B} = f_{o s c} - f_{m}

where

f_{o s c} = f_{0} - f_{p} - v_{B}

is the frequency difference between the signal wave and line center frequency of the loss spectrum. Compared with Eqs. (3) and (5), the sideband amplitude attenuation can be derived by using Eq. (6) as

α = \exp (Re (- g_{B} I_{p} L)) = \exp (- g_{p} I_{p} L \frac{1}{1 + 4 {(\frac{f_{o s c} - f_{m}}{Δ v_{B}})}^{2}})

Correspondingly, the phase shift induced by the deamplification of SBS is given by

δ = Im (- g_{B} I_{p} L) = g_{p} I_{p} L \frac{\frac{f_{m} - f_{o s c}}{Δ v_{B}}}{1 + 4 {(\frac{f_{m} - f_{o s c}}{Δ v_{B}})}^{2}}

After photo-detected by a PD, the generated photo-current is

I_{p h} \propto \sqrt{[1 + α^{2} - 2 α \cos (\frac{4 π D L λ_{0}^{2} f_{m}^{2}}{c} - δ)]} \cos (2 π f_{m} t + φ_{0})

where

φ_{0}

is a constant phase shift. Thus, the amplitude response of the MPF can be given by

| H (j f_{m}) | \propto \sqrt{[1 + α^{2} - 2 α \cos (\frac{4 π D L λ_{0}^{2} f_{m}^{2}}{c} - δ)]}

From Eq. (10), the frequency response of the MPF is determined by the + 1st sideband attenuation $α$ and phase shift difference between the + 1st sideband and −1st sideband due to the phase shift induced by chromatic dispersion and SBS.

Using the above model, the frequency response of the MPF based on SBS is simulated using the parameters in Table 1. Figure 3(a) shows the + 1st sideband amplitude response and the relative phase shift difference compared with −1st sideband induced by the chromatic dispersion, deamplification (red curves) and amplification (blue curves) of SBS. The frequency difference is 8 GHz between the signal and the center of loss spectral area of SBS, and 21.4 GHz between the center of gain and loss spectral areas. Figure 3(b) shows the frequency responses induced by the amplification (red curve) and deamplification (green curve) of SBS. Two passbands are expected, corresponding to the loss and gain spectral areas of SBS, respectively. There are three notches (orange circles) in the frequency response curves, corresponding to the zero points (1.57 GHz, 9.53 GHz, and 29.27 GHz) of the relative phase shift curves, where the phase shifts induced by chromatic dispersion and SBS cancel each other. The out-of-band rejection of the passbands is strongly influenced by the chromatic dispersion. The blue curve of Fig. 3(b) shows the response for the fiber with lower chromatic dispersion coefficient (2 ps/nm/km). By setting the variable of $f_{o s c}$ to be 8 GHz, 12 GHz, 16 GHz and 20 GHz, respectively, the roll-off characteristics of the proposed MPF at different central frequencies are obtained, as shown in Fig. 3(c). Figure 3(d) shows the tunable single passband frequency responses induced by the deamplification of SBS through changing the variable of $f_{o s c}$ from 7 GHz to 40 GHz with a step of 1 GHz.

Table 1. Simulation parameters for the response of MPF

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Fig. 3 Simulation results of the frequency response of the MPF. (a) The + 1st sideband amplitude response and phase shift difference compared with the −1st sideband induced by the chromatic dispersion and SBS. (b) Frequency responses of the MPF. (c) Comparison of passband responses with different center frequencies. (d) Calculated tunable single passband responses of the MPF.

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3.2 Phase noise performance of the proposed OEO

Figure 4(a) shows the phase noise model of the proposed OEO [23,36]. A NZ-DSF fiber is used as the SBS medium and delay line in the OEO loop. A narrow-band single passband MPF utilizing the deamplification of SBS is used to select the oscillation mode. Two SMFs are used to form a dual-loop of OEO. The oscillation loop is ruled by the Barkhausen in-phase condition, which can be expressed as

φ_{e} + φ_{o} = 2 k π \begin{matrix} (k = 0, \pm 1, \pm 2...) \end{matrix}

where

φ_{e}

and

φ_{o}

are the phase shifts of the electrical link and optical link of the OEO, respectively. Any fluctuations of phase shift in the loop will be converted to the additive phase noise of the OEO. In the proposed OEO, the + 1st sideband deamplification by SBS will introduce a phase shift, which is determined by the laser frequency, as shown in Eq. (8). The frequency fluctuations of the signal or pump lasers would contribute to the phase shift fluctuations of the + 1st sideband. After photo-detection, the phase fluctuations of the + 1st sideband is converted to the additive phase noise of the OEO.

Fig. 4 (a) Phase noise model of the proposed dual-loop OEO based on the deamplification of SBS. (b) Phasor representation of a noisy sinusoid RF carrier.

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For steady-state oscillation, the oscillation frequency equals to the frequency difference between the signal and the central frequency of the loss spectral area, which is $f_{o s c}$ . By neglecting the constant phase shift $φ_{0}$ and using the relation of $f_{m} = f_{o s c}$ , the photo-current of Eq. (9) can be rewritten as

I_{p h}^{'} \propto [\cos (φ_{C D}) - α_{\min} \cdot \cos (φ_{C D} + δ)] \cos (2 π f_{o s c} t) - [\sin (φ_{C D}) + α_{_{\min}} \cdot \sin (φ_{C D} + δ)] \sin (2 π f_{o s c} t)

where

φ_{C D} = 2 π D L λ_{0}^{2} f_{o s c}^{2} / c

is the phase shift induced by the chromatic dispersion.

α_{\min} = \exp (- g_{p} I_{p} L)

is the amplitude attenuation coefficient of the + 1st sideband. At the oscillation frequency and with less chromatic dispersion, we have the conditions of

| φ_{C D} | < < 1

and

| δ | < < 1

. Equation (12) can be approximated as

I_{p h}^{'} \propto (1 - α_{\min}) \cos (2 π f_{o s c} t) + (φ_{C D} + α_{\min} \cdot φ_{C D} + α_{\min} \cdot δ) \sin (2 π f_{o s c} t)

The noised RF signal by the random phase shift induced by SBS can be described as

I_{p h_n o i s e d}^{'} \propto (1 - α_{\min}) \cos (2 π f_{o s c} t) + α_{\min} \cdot Δ δ \cdot \sin (2 π f_{o s c} t)

where

Δ δ

is the phase shift fluctuations induced by the deamplification of SBS and laser frequency noise. From Eq. (14) and Fig. 4(b), the quadrature components noise contributes to the additive phase noise of the RF carrier. Typically,

α_{\min}

~0.1 and

| Δ δ | < 0.001

. We have the condition of

| α_{\min} \cdot Δ δ | < 10^{- 4} r a d

, the random phase deviation of the RF carrier due to SBS deamplification can be derived as

Δ φ_{D} \approx \tan (Δ φ_{D}) = \frac{α_{\min}}{1 - α_{\min}} \cdot Δ δ

With the relation of $v_{B} = 2 n_{p} v_{A} f_{p} / c$ [17], the phase shift fluctuations induced by the close-in (< 1 MHz) laser frequency noise via SBS can be derived from Eq. (8) as

Δ δ \approx \frac{g_{p} I_{p} L}{Δ v_{B}} \cdot (Δ v_{l a s e r_s} - Δ v_{l a s e r_p} - \frac{2 n_{p} v_{A}}{c} Δ v_{l a s e r_p})

where

Δ v_{l a s e r_s}

and

Δ v_{l a s e r_p}

are the frequency fluctuations of the signal laser and pump laser. Since the acoustic velocity

v_{A}

is on the order of

10^{3} m / s

in standard single-mode fibers [17], the component of

2 n_{p} v_{A} / c

is on the order of

10^{- 5}

. The third component in Eq. (16) can be neglected. The frequency fluctuations of the signal laser and pump laser are independent. By substituting Eq. (16) into Eq. (15), we can get the power spectral density (PSD) of the additive phase noise as

S_{S B S_D} (f) = {[\frac{1}{\exp (g_{p} I_{p} L) - 1} \frac{g_{p} I_{p} L}{Δ v_{B}}]}^{2} \cdot [S_{v, l a s e r_s} (f) + S_{v, l a s e r_p} (f)]

where

S_{v, l a s e r_s} (f)

and

S_{v, l a s e r_p} (f)

are the PSD of optical frequency noise for the signal laser and pump laser, respectively. Similarly, by replacing

α_{\min}

with the peak gain of the amplification of SBS in Eq. (14). Typically, the peak gain of the amplification of SBS is on the order of ~10. We have the condition of

| G_{\max} \cdot Δ δ |

~

10^{- 2} r a d

. The random phase deviation of the RF carrier due to SBS amplification can be derived as

Δ φ_{A} \approx \tan (Δ φ_{A}) = \frac{G_{\max}}{1 - G_{\max}} \cdot Δ δ

where

G_{\max} = \exp (g_{p} I_{p} L)

is the peak gain of the amplification of SBS. By substituting Eq. (16) into Eq. (18), the close-in additive phase noise contributed by SBS in the OEO based on sideband amplification is derived as

S_{S B S_A} (f) = {[\frac{\exp (g_{p} I_{p} L)}{1 - \exp (g_{p} I_{p} L)} \frac{g_{p} I_{p} L}{Δ v_{B}}]}^{2} \cdot [S_{v, l a s e r_s} (f) + S_{v, l a s e r_p} (f)]

From Eq. (13), the chromatic dispersion can also convert the laser frequency fluctuations to the phase fluctuations of the RF signal. The additive phase noise induced by the combination of chromatic dispersion and laser frequency noise is expressed as [27,31]

S_{C D} (f) = \frac{1}{2} {(\frac{2 π f_{o s c} λ_{0}^{2} D L}{c})}^{2} \cdot S_{v, l a s e r_s} (f)

Laser frequency noise can be converted to the phase noise of the RF signal by the reflections of fiber connectors [32], PD faces [33]. Considering the optical interference by the double reflection process between the PD face and fiber connector of the PD, the additive phase noise contributed by the laser frequency noise via double reflection process can be expressed as [32]

S_{I n t e r f e r e n c e} (f) = 2 r_{c} \cdot r_{P D} \cdot \sin^{2} (2 π f_{o s c} τ_{d}) \frac{\sin^{2} (π f τ_{d})}{f^{2}} \cdot S_{v, l a s e r_s} (f)

where

r_{c}

and

r_{P D}

are the optical return loss (ORL) of the fiber connector and PD face,

τ_{d}

is the round trip time of the double reflection process.

By considering the additive phase noise discussed above, the single-sideband (SSB) phase noise of the OEO based on the transfer function model [23,36] can be obtained as follows

ℒ (f) = (\frac{F k T + 2 q I_{p h} R + N_{r i n} I_{p h}^{2} R}{2 P_{R F}} + \frac{b_{- 1}}{f} + S_{S B S_D} (f) + S_{C D} (f) + S_{I n t e r f e r e n c e} (f)) \cdot | H_{d u a l - l o o p} (j f) |^{2}

where

F

is the noise figure of amplifier,

k

is the Boltzmann constant,

T

is the room temperature,

q

is the charge of an electron,

I_{p h}

is the photo-current at the output of PD,

R

is the load resistance of PD,

N_{r i n}

is the relative intensity noise (RIN) of signal laser,

P_{R F}

is the RF power at the output of PD,

b_{- 1}

is the flicker noise coefficient of amplifier,

H_{d u a l - l o o p} (j f)

is the transfer function of the dual-loop OEO.

Typically, the frequency noise of the laser is composed by the white frequency noise and flicker frequency noise components [32], which can be described as

S_{v, l a s e r} (f) = C_{1} + C_{2} / f

where

C_{1}

is the white frequency noise coefficient, and

C_{2}

is the flicker frequency noise coefficient. In the experiment and simulation, the frequency noise of the pump laser (as listed in Table 2) is far larger than that of the signal laser, so the pump laser dominates the laser frequency noise.

Table 2. Simulation parameters for the phase noise of the proposed OEO

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Using the parameters in Table 1 and Table 2, the phase noise performance of the proposed OEO is simulated based on the above models. Figure 5(a) shows the phase noises contributed by the laser frequency noise via SBS deamplification, chromatic dispersion of 1-km NZ-DSF, and optical interference due to facet reflection, flicker noise of amplifier, thermal noise, shot noise and RIN of the signal laser, respectively. It can be found that laser frequency noise to phase noise conversion through SBS deamplification is the dominant source for the close-in phase noise in the proposed OEO. Figure 5(b) shows the additive phase noise induced by the SBS amplification is beyond 20 dB larger than that of the SBS deamplification with a pump power of 10 dBm. The calculated additive phase noise induced by the ASE of SBS amplification using the model in [23] is also shown by the olive curve in Fig. 5(b). The ASE induced phase noise can be avoided in the proposed OEO. Figure 5(c) shows the simulated SSB phase noise of the dual-loop OEOs based on SBS amplification and deamplification with fiber lengths of 1.1 km and 1.2 km by using the phase noise model in Eq. (22). The phase noise performance of the OEO based on SBS deamplification is better than that of the OEO based on SBS amplification within the whole offset frequency range. As a comparison, a length of 1 km single-loop OEO based on the deamplification of SBS is also simulated, as shown by the olive curve in Fig. 5(c). The side-modes are strongly suppressed at integer multiples of 200 kHz offset by utilizing dual-loop configuration. The influence of the pump power on the phase noise performance of the OEOs based on SBS amplification and deamplification are also evaluated, as shown in Fig. 5(d). The pump power is changed from 5 dBm to 10 dBm with a step of 1 dB. The phase noise at 10 kHz offset of the OEO decreases with the pump power for the SBS deamplification scheme, while increases slightly with the pump power for the SBS amplification scheme.

Fig. 5 Simulation results of the phase noise performance for the proposed OEO. (a) A comparison of phase noise induced by different noise sources in the proposed OEO. (b) A comparison of additive phase noises contributed by the conversion of laser frequency noise via SBS deamplification and amplification. (c) Simulated SSB phase noise of the OEOs based on the deamplification and amplification of SBS. (d) A comparison of phase noise at 10 kHz offset between the OEOs based on the deamplification and amplification of SBS.

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4. Experimental results and discussions

In order to verify the above theoretical results, experiments based on the schemes shown in Figs. 1 and 2(a) are implemented. A wavelength tunable laser (NKT, E15) is used as the signal. It has a linewidth less than 100 Hz, power of 40 mW, and wavelength tuning range of 1 nm. The pump laser (TeraXion, NLL) has a fixed wavelength of 1549.92 nm, linewidth less than 5 kHz, and power of 80 mW. A 1.05 km NZ-DSF with chromatic dispersion coefficient of 5 ps/nm/km is used to generate the SBS effect. A 50-meter dispersion compensating fiber (DCF) is cascaded with the NZ-DSF to reduce the residual chromatic dispersion of the OEO loop. Two SMFs with lengths of 100-meter and 1-meter are used to form a dual-loop OEO. Low length difference between the two SMFs can achieve low residual chromatic dispersion of the both loops of the OEO. The 3-dB bandwidth of the phase modulator is 60 GHz. Two PDs with responsivity of 0.95 A/W, saturation power of 50 mW, 3-dB bandwidth of 20 GHz is used to convert the optical signal to electrical signal when the oscillation frequency is below 20 GHz. Another two PDs (u2t) with responsivity of 0.56 A/W, 3-dB bandwidth of 50 GHz are used when the OEO is operated above 20 GHz. Three low phase noise amplifiers with bandwidth of 6 to 12 GHz, gain of 15 dB, noise figure of 7 dB, saturation power of 17 dBm are cascaded to provide sufficient gain for the OEO when operated below 12 GHz. Two medium power amplifiers with bandwidth of 50 kHz to 40 GHz, gain of 25 dB, and a power amplifier with bandwidth of 26 to 40 GHz, gain of 30 dB are used when the oscillation frequency is above 12 GHz. An ELPF with cut-frequency about 20 GHz and an ELPF with cut-frequency of 37 GHz are used to suppress the passband induced by the amplification of SBS. An optical spectrum analyzer (OSA) and an electrical spectrum analyzer (ESA) are used to monitor the optical and electrical spectrum of the OEO. A signal source analyzer (Keysight, SSA E5052B + E5053A down-convertor) is used to measure the SSB phase noise and frequency stability of the OEO. A Keysight VNA (N5247A) is employed to measure the frequency response of the MPF.

4.1 Frequency response of the MPF utilizing deamplification of SBS

Figure 6(a) shows the frequency responses from 10 MHz to 50 GHz of the MPF. Two narrow-band passbands with a spacing of 21.4 GHz, just twice of Brillouin frequency shift, are observed without ELPF, as shown by the green curve in Fig. 6(a). The lower frequency passband at 8 GHz is induced by the deamplification of SBS. The higher frequency passband is induced by SBS amplification, which can be suppressed by an ELPF. The out-of-band rejection is influenced by the chromatic dispersion of the fiber. A DCF with length of 50-meter is used to compensate the chromatic dispersion of the fiber link. Without fiber dispersion compensation, the minimum out-of-band rejection is measured to be 19.5 dB with a frequency range from 10 MHz to 20 GHz. By utilizing the DCF, the minimum out-of-band rejection is improved to 31.76 dB, as shown in the blue curve in Fig. 6(a). By tuning the wavelength of the signal laser, the frequency difference between the signal laser and the central of SBS loss spectral area is changed from 8 GHz to 20 GHz with a step of 4 GHz, and the frequency responses of the single passband at different center frequencies are shown in Fig. 6(b). The 3-dB bandwidth of the MPF is measured to be 45.6 MHz at center passband frequency of 8 GHz. The 3-dB bandwidth of MPF at different frequencies are nearly unchanged. There are some small peak responses due to more than one acoustic modes are exited in the fiber [37].

Fig. 6 Measured frequency response of the MPF. (a) Frequency responses induced by the sideband deamplification and amplification of SBS. (b) Comparison of frequency responses at different passband frequencies.

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Figure 7 shows the measured frequency responses of the tunable MPF by tuning the frequency difference between the signal laser and the central of SBS loss spectral area from 7 GHz to 36 GHz with a step of 1 GHz. Two ELPFs with cut frequencies of 20 GHz and 37 GHz are used to suppress the passband response induced by the sideband amplification of SBS, as shown in Figs. 7(a) and 7(b). The 3-dB bandwidth of the MPF is nearly constant for the whole tuning range. The chromatic dispersion degraded the out-of-band rejection performance of the MPF with the increasing of frequency. Especially, the OEO may not oscillate due to the poor frequency selective performance of the MPF at higher frequency. Thus, lower residual chromatic dispersion is important to extend the frequency tunable range of the OEO.

Fig. 7 Measured frequency responses of the tunable single passband MPF by changing the wavelength of the signal laser. (a) Passband responses with center frequency tuned from 7 GHz to 20 GHz. (b) Passband responses with center frequency tuned from 21 GHz to 36 GHz.

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4.2 Frequency tunability, stability and phase noise of the OEO

The optical and electrical spectra of the generated 10.30 GHz signal by the proposed OEO are shown in Fig. 8. The + 1st sideband is significantly attenuated due to the deamplification of SBS, as shown in Fig. 8(a). The suppression of the + 1st sideband can be improved by increasing the pump power, using a longer fiber or a fiber with larger SBS gain parameter. The corresponding electrical spectrum is shown in Fig. 8(b) with an observation span of 1 MHz and resolution bandwidth (RBW) of 9.1 kHz.

Fig. 8 Optical and electrical spectra of the generated 10.3 GHz signal. (a) Optical spectrum. (b) Electrical spectrum.

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By changing the wavelength of the signal laser, tunable microwave and millimeter-wave signals from 7 to 40 GHz are generated. The tunable electrical spectra are divided into four diagrams due to the utilizing of electrical amplifiers and ELPFs with different frequency response ranges, as shown in Fig. 9. The tuning range is limited by the bandwidth of the PM, electrical amplifiers, PDs, and the residual chromatic dispersion of the fiber link. The frequency tuning resolution of the proposed OEO is determined by the minimum wavelength tuning step of the signal laser, which is 1 pm within the whole tuning range of 1 nm. This corresponds to a 125 MHz frequency tuning resolution for the proposed OEO within the whole tuning range of 7-40 GHz. Some weak harmonics and spurs exist due to the harmonic components generated by the PM and the beat notes between the phase modulated sidebands and the reflection of the pump wave by the fiber connectors.

Fig. 9 (a) Electrical spectra for the tunable range from 7 to 12 GHz. (b) Electrical spectra for the tunable range from 13 to 20 GHz. (c) Electrical spectra for the tunable range from 21 to 28 GHz. (d) Electrical spectra for the tunable range from 29 to 40 GHz.

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Figure 10(a) shows the SSB phase noises of the generated 8.28 GHz with dual-loop configurations of 1.1 km-1.2 km and 2.1 km-2.2 km, respectively. A SSB phase noise of −130 dBc/Hz at 10 kHz offset is obtained. The phase noise performance is better with longer fiber used. There are some spurs at approximate integer multiples of 100 kHz or 200 kHz, which corresponding to the side-modes defined by the fiber loop length around 1 km or 2 km.

Fig. 10 Measured SSB phase noises of the microwave signals generated by the proposed OEO. (a) SSB phase noises of the generated 8.28 GHz with dual-loop fiber lengths of 1.1 km-1.2 km and 2.1 km-2.2 km. (b) Measured SSB phase noise of the generated signal with different oscillation frequencies and dual-loop fiber lengths of 2.1 km-2.2 km.

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Figure 10(b) shows the SSB phase noise for the generated signal with different oscillation frequencies. Due to the bandwidth limitation of the SSA, only the oscillation signal with frequency below 26.5 GHz can be measured. The SSB phase noise performance at 10 kHz offset are all below −120 dBc/Hz for the generated signal with different oscillation frequencies. As a comparison, the phase noise of the wideband tunable electronic oscillator based on YIG at 10 GHz is on the order of −100 dBc/Hz at 10 kHz offset [3,38].

The frequency and power fluctuations of the OEO are also measured by the SSA. The measurement time interval between two adjacent samples is set to 1 second. The total measurement sample points is 1000. Figure 11 shows the measured frequency and power fluctuations of the generated 10.69 GHz signal. Maximum frequency and power drifts are 5.7 kHz and 1.4 dB, respectively. The frequency stability is calculated to within 1 ppm. The frequency stability of the proposed OEO are influenced by the frequency fluctuations of the signal and pump lasers and the temperature drift. The frequency fluctuation of signal and pump lasers introduces a phase deviation $Δ φ_{D}$ to the oscillation signal, which results in a frequency drift of the oscillation signal. It can be characterized by [36]

\frac{Δ f_{o s c}}{f_{o s c}} = \frac{Δ φ_{D}}{2 Q}

where

Δ f_{o s c}

is the frequency drift of the oscillation frequency,

Q = π f_{o s c} \cdot τ_{d}

is the quality value of the OEO loop,

τ_{d}

is the time delay of the OEO loop. According to the datasheets of the signal and pump lasers, the optical frequency Allan deviations of both the signal and pump lasers are below 10⁻⁸ at average time of 100 seconds, corresponding to a maximum optical frequency fluctuation below 2 MHz. The approximation of

Δ φ_{D}

in Eq. (15) is effective with this laser frequency fluctuation. In our experiment, we have the conditions of

α_{\min}

~0.2,

Δ v_{B}

~

50 M H z

,

τ_{d}

~

5 μ s

,

f_{o s c}

~

10 G H z

, and

g_{p} I_{p} L

~2.6. Thus, the frequency stability in Eq. (24) is calculated to be 0.17 ppm during 100 seconds. High Q value of the OEO loop can significantly reduce the sensitivity of the frequency fluctuation of the OEO to the frequency drifts of the signal and pump lasers. For comparison, the influence of temperature drift on the frequency stability of a 10 GHz fiber based OEO is expected to be 8 ppm/°C [39]. The frequency stability of the proposed OEO can be improved by phase-locked to an ultra-stable reference [35].

Fig. 11 Measured frequency and power fluctuations of the proposed OEO. (a), (b): Frequency and power fluctuations of the generated 10.69 GHz signal, respectively.

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As a comparison, the maximum frequency drift of a free running 10 GHz OEO is measured to be 10 kHz during 10 minutes [40]. Typically, the frequency stability of an electronic oscillator based on dielectric resonator is below 10 ppm/°C [39].

4.3 Effects of laser frequency noise on the phase noise of the proposed OEO

To investigate the additive phase noise of the proposed OEO converted by the laser frequency noise via phase shift of SBS deamplification, three different lasers (Santec-TSL210H, Teraxion-TNL, NKT-E15) are tested as the signal laser. The NLL laser (Teraxion Inc.) is used as the pump laser. The frequency noises of the lasers are measured by the optical noise analyzer (SYCATUS, A0040A), as shown in Fig. 12(a). The frequency noise of NKT-E15 is approximated from the datasheet of NKT Inc [41], as shown by the orange curve in Fig. 12(a).

Fig. 12 Experimental measurements for the tested laser frequency noises and the corresponding SSB phase noises of the OEOs. (a) Measured frequency noises of the lasers. (b) A comparison between the calculated and measured SSB phase noises. The olive curve (1), blue curve (3), and red curve (5) stand for the measured SSB phase noises. The wine curve (2), magenta curve (4), and purple curve (6) stand for the calculated SSB phase noises through model in Eq. (17), but multiplied the transfer function of the dual-loop OEO. Dark yellow curve (7) stands for the phase noise induced by the flicker phase noise of the cascaded amplifiers.

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By substituting the measured laser frequency noise into Eq. (17), and multiplying the transfer function of the dual-loop OEO, we can get the calculated SSB phase noise, as shown in Fig. 12(b). For comparison, the measured SSB phase noise of the OEOs using different lasers are also shown in Fig. 12(b). The thermal noise floor (−157 dBc/Hz), shot noise floor (−165 dBc/Hz), and phase noise floor determined by the flicker phase noise of the cascaded amplifiers (Dark yellow curve 7) are also given. The additive phase noise of the cascaded amplifiers is measured by the SSA (Rohde & Schwarz, FSWP). The curves nearly coincided at close-in offset (below 1 MHz) frequency. Even the spurs of the frequency noise coincided with the measured phase noise spurs below 1 MHz. The differences at below 500 Hz are caused by the utilizing of dual-loop configuration. A dual-loop OEO is also a self-injection locking oscillator, which can reduce the phase noise at smaller offset frequency [35]. Lasers with better frequency noise performance should preferably be used to improve the close-in phase noise performance of the proposed OEO.

4.4 Comparison of phase noise between OEOs based on amplification and deamplification of SBS

Figure 13 compares the phase noise of the OEOs based on amplification and deamplification of SBS at 10.30 GHz. The signal laser is a Teraxion TNL laser. With the same pump power of 14 dBm, the SSB phase noise at 10 kHz offset for the proposed OEO is beyond 20 dB lower than that of the OEO based on SBS amplification, as shown in Fig. 13(a).

Fig. 13 (a) Comparison of SSB phase noise of the OEOs based on SBS amplification and deamplification. (b) Comparison of phase noise at 10 kHz offset for the two OEOs.

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The difference of the phase noise at 10 kHz offset between the two kinds of OEOs versus pump power is illustrated in Fig. 13(b). The results coincided with the theoretical trend as shown in Fig. 5(d). With phase modulation, the laser frequency noise equally distributes to the symmetrical ± 1st sidebands with anti-phases, and will cancel each other at PD. If the + 1st sideband is amplified or attenuated by the SBS, the phase shift fluctuations induced by SBS is imposed to the + 1st sideband. The phase between the two sidebands are not correlated. The phase fluctuations induced by SBS cannot cancel out, which convert the laser frequency noise to the additive phase noise of the OEO. From Eqs. (15) and (18), $Δ φ_{D} \approx α_{\min} \cdot Δ δ$ for SBS deamplification when $α_{\min} \leq 0.1$ , while $Δ φ_{A} \approx - Δ δ$ for SBS amplification when $G_{\max} \geq 10$ . The phase noise performance for the OEO based on sideband deamplification is much better than that of the OEO based on sideband amplification. Furthermore, from the red curve in Fig. 13(b), with larger pump power, the better close-in phase noise for the OEO based on sideband deamplification is obtained due to a larger loss to the + 1st sideband via SBS deamplification. Thus, a higher pump power can achieve a lower close-in phase noise of the proposed OEO.

5. Conclusions

A wideband tunable OEO based on the deamplification of SBS is proposed and experimentally demonstrated. This work suggests that less residual chromatic dispersion of the fiber loop is needed to extend the frequency tunable range of the OEO. Signal and pump lasers with lower frequency noise, higher pump power should preferably be used to improve the close-in (< 1 MHz) phase noise performance of the proposed OEO. The conversion of the laser frequency noise to the close-in phase noise of the proposed OEO via phase shit of SBS deamplification is theoretically and experimentally demonstrated to be lower than that of the OEO based on amplification by SBS. Compared with the OEO based on amplification by SBS, the proposed OEO in this work can achieve more than 20 dB phase noise performance improvement. A tunable 7 to 40 GHz OEO is experimentally demonstrated. The SSB phase noise is −128 dBc/Hz at 10 kHz offset for 10.30 GHz signal. The experimental results agree well with the theory. Furthermore, most of the components in the proposed OEO are feasible to be integrated on a photonic chip, which can effectively reduce the size, weight and power consumption of the system in the future.

Funding

National Natural Science foundation of China (Grant No. 61690194, Grant No. 61401005, and No. 61505002).

Acknowledgments

The authors would like to thank SYCAUTS for offering the optical noise analyzer (A0040A) and Rohde & Schwarz for offering the signal source analyzer (FSWP).

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Name	Symbol	Value
Fiber length	$L$	$1 k m$
Dispersion coefficient	$D$	$5 p s / (n m \cdot k m)$
Effective mode area	$A_{e f f}$	$63.6 μ m^{2}$
Line center Brillouin gain coefficient	$g_{p}$	$2 \times 10^{- 11} m / W$
Loss bandwidth of SBS	$Δ v_{B}$	$50 M H z$
Wavelength of signal laser	$λ_{0}$	$1550 n m$
Pump power	$P_{p}$	$11.7 m W$
Brillouin frequency shift	$v_{B}$	$10.7 G H z$

Name	Symbol	Value
Oscillation frequency	$f_{o s c}$	$10 G H z$
ORL of fiber connector	$r_{c}$	$- 50 d B$
ORL of PD	$r_{P D}$	$- 30 d B$
Round trip time of double reflection process	$τ_{d}$	$1 μ s$
White frequency noise coefficient of pump	$C_{1}$	$1.0 \times 10^{3} H z^{2} / H z$
Flicker frequency noise coefficient of pump	$C_{2}$	$1.0 \times 10^{8} H z^{3} / H z$
Noise figure of amplifier	$F$	$7 d B$
Room temperature	$T$	$300 K$
Photo-current at the output of PD	$I_{p h}$	$4 m A$
Load resistance of PD	$R$	$50 Ω$
Relative intensity noise of signal laser	$N_{r i n}$	$- 158 d B / H z$
Flicker noise of the amplifier	$b_{- 1}$	$- 120 d B \cdot r a d^{2} / H z$
RF power from PD	$P_{R F}$	$400 μ W$

Name	Symbol	Value
Fiber length	$L$	$1 k m$
Dispersion coefficient	$D$	$5 p s / (n m \cdot k m)$
Effective mode area	$A_{e f f}$	$63.6 μ m^{2}$
Line center Brillouin gain coefficient	$g_{p}$	$2 \times 10^{- 11} m / W$
Loss bandwidth of SBS	$Δ v_{B}$	$50 M H z$
Wavelength of signal laser	$λ_{0}$	$1550 n m$
Pump power	$P_{p}$	$11.7 m W$
Brillouin frequency shift	$v_{B}$	$10.7 G H z$

Name	Symbol	Value
Oscillation frequency	$f_{o s c}$	$10 G H z$
ORL of fiber connector	$r_{c}$	$- 50 d B$
ORL of PD	$r_{P D}$	$- 30 d B$
Round trip time of double reflection process	$τ_{d}$	$1 μ s$
White frequency noise coefficient of pump	$C_{1}$	$1.0 \times 10^{3} H z^{2} / H z$
Flicker frequency noise coefficient of pump	$C_{2}$	$1.0 \times 10^{8} H z^{3} / H z$
Noise figure of amplifier	$F$	$7 d B$
Room temperature	$T$	$300 K$
Photo-current at the output of PD	$I_{p h}$	$4 m A$
Load resistance of PD	$R$	$50 Ω$
Relative intensity noise of signal laser	$N_{r i n}$	$- 158 d B / H z$
Flicker noise of the amplifier	$b_{- 1}$	$- 120 d B \cdot r a d^{2} / H z$
RF power from PD	$P_{R F}$	$400 μ W$

Wideband tunable optoelectronic oscillator based on the deamplification of stimulated Brillouin scattering

Abstract

1. Introduction

2. Principle of the proposed OEO

3. Theoretical analysis and simulations

3.1 Frequency response of the MPF

3.2 Phase noise performance of the proposed OEO

4. Experimental results and discussions

4.1 Frequency response of the MPF utilizing deamplification of SBS

4.2 Frequency tunability, stability and phase noise of the OEO

4.3 Effects of laser frequency noise on the phase noise of the proposed OEO

4.4 Comparison of phase noise between OEOs based on amplification and deamplification of SBS

5. Conclusions

Funding

Acknowledgments

References and links

Cited By

Figures (13)

Tables (2)

Equations (24)

Optics Express