Pulse repetition rate doubling in FM actively mode-locked fiber-optic parametric oscillator

Jianpeng Zhao; Bin Luo; Liyang Shao; Wei Pan; Lianshan Yan; Xihua Zou; Jia Ye; Hui Yang

doi:10.1364/OE.24.030079

1. Introduction

The generation of ultra-short pulses with high repetition rate has attracted considerable attention because of its potential applications in data storage, high-resolution spectroscopy, fast chemical detection and identification, studies of ultrafast processes, and laser metrology [1,2]. Mode locking of fiber-based laser represents a potential source of such pulses [1–3]. Among the various types of mode-locked fiber lasers, the mode-locked fiber-optic parametric oscillators (FOPOs) are especially attractive due to its obvious advantages, such as high gain, widely tunable wavelength, and high conversion efficiency [4–9]. Two techniques for mode-locking of a FOPO have been proposed to generate high repetition rate pulse. One efficient technique of that is demonstrated by using an external-cavity synchronous-pumping modulation [10–14]. The other technique is utilizing an intra-cavity time-varying perturbation to generate pulses, which is called actively mode-locked FOPO. In previous works [15–17], two kinds of active mode locking schemes have been demonstrated based on either amplitude modulation or frequency modulation, which are achieved by inserting an amplitude modulator (AM) or phase modulator (PM) in the cavity of FOPO pumped by continuous wave (CW), respectively. To our knowledge, all the previous reported actively mode-locked FOPOs produce pulses at a repetition rate which equals the frequency of the radio frequency (RF) signals applied to modulator. Therefore, the pulse repetition rate will be limited by the bandwidth of the intra-cavity modulator. Factually, according to the theory of frequency modulation (FM) laser oscillation, pulses can exist at either of the two phase positions which correspond to the maximum and the minimum point of the phase modulation [18–23], which can be controlled by varying the amplitude of RF signal applied to the intra-cavity modulator. This characteristic enables the multiplication of the pulse repetition rate in an FM laser [20,22]. Generally, due to the strong mode competition between the two groups of modes, only one mode-locked status pulse trains exist when the amplitude of RF signal is fixed in FM laser. However, two mode-locked states which correspond to two phase positions can be controlled by adjusting the state of polarization (SOP) of light which poured into the intra-cavity LiNbO₃ in FOPOs. This will result in a switching action between the two states. By properly adjusting the SOP of the optical wave, both of the two mode-locked states can be oscillated simultaneously when either one of mode-locked group of modes is insufficient to quench the other in the process of the fiber optical parametric amplification (FOPA). Therefore, the optical pulses with the pulse repetition frequency (PRF) that is twice of the RF drive frequency can be generated in FOPOs.

In this paper, a simple method to generate optical pulses at repetition rate which is two times of the RF drive frequency in FM actively mode-locked FOPO has been proposed and experimentally demonstrated. The switching of the two mode-locked states at different phase positions can be achieved by adjusting the SOP of the light which is poured into the intra-cavity LiNbO₃ PM. Moreover, the spectral and electrical characteristics of the generated pulses have been investigated. Furthermore, by continually adjusting the SOP of the incident light, both of two mode-locked states oscillate simultaneously in the process of FOPA, so that the pulses with PRF at twice that of the RF drive frequency are generated. In the experiment, we demonstrate the generation of optical pulses with PRF of ~8, 10, 12 and 14GHz when the frequencies of the RF signals applied to the PM are set as ~4, 5, 6 and 7GHz, respectively.

2. Principle

In a steady-state FM laser cavity, the laser oscillation signals have the general form as [18–20,23]:

ε (t) = E_{0} \exp [j 2 π f_{0} t + j Γ \sin (2 π f_{m} t)],

where

E_{0}

and

f_{0}

are the amplitude and frequency of the central mode, respectively. And the factor

Γ

is given by:

Γ = \frac{1}{π} \frac{Δ Ω}{Δ ν} δ,

where

δ

is the effective single-pass phase perturbation of the modulator.

Δ Ω

is the axial mode interval and

Δ ν

is the frequency difference between the axial mode interval and the driving frequency. The axial mode interval can be calculated by

Δ Ω = c / n L

, where c is the speed of light in vacuum, n denotes the equivalent refractive index of the ring, and L is the cavity length. According to Eq. (1), using the Bessel function of the first kind (Jacobi-Anger identity), the generated longitudinal modes are corresponding with Bessel function amplitudes and FM phases, and thereby comprise the sidebands of a frequency modulated light signal [18], as shown in Fig. 1(a). In the FM mode-locked laser, when the modulation frequency

f_{m}

equals approximately, but not exactly, axial mode interval, a periodic series of pulses can be generated at one or the other of the two extremums of the phase modulation cycles [18–24], as shown in Fig. 1(b).

Fig. 1 (a) Schematic of the perfect FM oscillation with the modulation depth of $Γ$ and with the center frequency at zeroth mode [18]. (b) The generated pulses in FM mode-locked laser [24].

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It can be seen from Eq. (1) that the frequency of the output signal from the FM laser appear to swing back and forth in sinusoidal shape at the modulation frequency $f_{m}$ . And then the peak-to-peak phase deviation and peak-to-peak frequency deviation of the FM laser signal are $2 Γ$ and $2 Γ f_{m}$ [24]. Consequently, the spectra of the FM output signals have two groups of modes, with the individual frequency components in each group uniformly separated by the modulation frequency $f_{m}$ . In general, only one group of modes exists in FM laser due to the strong mode competition between the two groups of modes in the gain medium. Actually, two groups of modes belonging to the two different states can be oscillated simultaneously in FOPO. When a LiNbO₃ crystal is used as a PM, the effective single-pass internal phase perturbation can be varied by adjusting the polarization of the optical wave which is poured into the crystal [25]. Consequently, the relative instantaneous phase deviation of two groups of modes can be varied by adjusting the SOP of light which poured into the LiNbO₃ crystal. This mainly results from the approximately identical gains of two envelops of modes are obtained in the process of FOPA. Therefore, both of the two groups of modes can be oscillated simultaneously in FOPO. This characteristic can make the PRF of generated pulse trains be two times of the RF drive frequency. However, it is difficult to obtain the exact quantitative relationship between the SOP of the incident light and the gains of two envelops of modes in the process of FOPA. Therefore, an exact quantitative relationship between the SOP of the incident light and the mode locked states is not attempted, but the qualitative relationship is observed in the experiment, as shown in Fig. 2.

Fig. 2 The experimental setup of the fiber optical parametric amplification (FOPA) based on the phase-modulated signal. TL: tunable laser. ASE: amplified spontaneous emission. PC: polarization controller. PM: phase modulator. EDFA: erbium-doped fiber amplifier. CIRC: circular. FBG: fiber Bragg grating. OC: optical coupler. HNLF: high nonlinear fiber. OSA: optical spectrum analyzer.

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The tunable laser (TL) is used as the pump source with the wavelength of 1559.63nm. In order to suppress the effects of the serious stimulated Brillouin scattering (SBS) in the high nonlinear fiber (HNLF), the CW light from TL is modulated by a PM (PM1) which is driven by RF signals with the frequency of 250MHz. The SOP of pump is aligned to the axis of the PM1 after the first PC (PC1) to maximize the suppression of SBS. Then the pump is amplified by an erbium-doped fiber amplifier (EDFA). The wavelength of the amplified spontaneous emission (ASE) spectrum is filtered out by a fiber Bragg grating (FBG) which reflects 90% of the light at 1551.77( ± 0.02)nm, with the full-width at half maximum (FWHM) of 0.2nm. PC2 is used to adjust the SOP of the signal wave poured into the LiNbO₃ PM (PM2). The pump and the phase-modulated signal are coupled into a piece of HNLF via a 3dB-optical coupler (OC1). In the experiment, the parameters of the HNLF are list below: the nominal zero-dispersion wavelength (ZDW) is 1556nm, the nonlinear coefficient is 30 $W^{-1} {km}^{-1}$ , the dispersion slope is 0.02 $ps \cdot {nm}^{- 2} {km}^{-1}$ and the length is 1000m. The spectrum of the signal is measured by an optical spectrum analyzer (OSA) with 0.05-nm resolution.

Figure 3(a) shows the reflective spectrum of the ASE source through the FBG without pump power. When the power of input pump is 24.5dBm, the spectra of the signal in the FOPA process are observed in Fig. 3(b). The blue solid line represents the amplified spectrum of the CW signal wave and the parametric gain is about 16dB. The other lines show the spectra of modulated signal wave with different input polarizations when the RF signal with the power of 18dBm and the frequency of around 5GHz are applied to the PM2. As mentioned above, the spectrum of phase-modulated signal can be affected by the effective internal phase perturbation in the process of FOPA. It can been seen from Fig. 3(b) that the spectrum of modulated signal wave is no longer symmetric with rotating of the PC2 and the gains is smaller than that of the CW signal wave in the process of FOPA [15,16]. By adjusting the SOP of the light poured into the LiNbO₃ PM, either one or both of the two groups of modes which correspond to the peak upward or downward frequency deviation of the modulated signal can be amplified, as shown in Fig. 3(b). Furthermore, there occurs a smooth transition from one mode spectrum envelop to the other when the PC2 is continuously rotated.

Fig. 3 (a) The reflective spectrum of the ASE source through the FBG. (b) The spectra of the signal in the FOPA process under CW/mode-locked condition.

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3. Experimental results and discussion

The experimental setup of the proposed FM actively mode-locked FOPO is shown in Fig. 4. The parameters of pump are the same as those used in Fig. 2. The TL is used as the pump source at 1559.63nm. The CW light from TL is modulated by a PM (PM1) which is driven by the RF signal with the frequency of 250MHz to suppress the effects of the SBS in the HNLF. The SOP of pump is aligned to the axis of the PM1 by a PC (PC1) to maximize the suppression of SBS. Then the pump is amplified by an EDFA. The ring cavity of the FOPO is composed of a 3dB OC (OC1), a piece of 1-km HNLF, a CIRC, a PC (PC2), a PM (PM2) and a FBG which is used in Fig. 2. In the cavity, the feedback signal wave is modulated by a RF signal at PM2, and then the phase-modulated signal wave is coupled into the HNLF via OC1. PC2 is used to adjust the SOP of the feedback signal wave poured into the PM2. The output signal is then divided into two parts through a 1/99 OC (OC2). Note that the 1% port of OC2 is connected to an OSA for analysis. To make sure that only the desired wavelength enters the high-speed oscilloscope with 65-GHz optical bandwidth, a tunable filter with central wavelength at ~1551.77nm and 3-dB bandwidth of ~0.6nm is placed in the branch of the 99% output port of the OC2. In addition, in order to illustrate the generation of the mode-locked pulses, the filtered idler wave is detected by a photodetector with 3dB bandwidth of 15GHz and the RF spectrum of the generated pulses is measured by an electrical spectrum analyzer (ESA).

Fig. 4 The experimental setup of the proposed actively mode-locked FOPO. TF: tunable filter. PD: photodetector. ESA: electrical spectrum analyzer.

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Thanks to the fiber optical parametric process, by increasing the total pump power into the 3dB coupler, the idler wave starts to oscillate when $G T = 1$ , where $G$ is the resulting gain and $T$ is the cavity loss of the FOPO [6–9]. In this configuration, the cavity round-trip loss is about 8.5dB, which is composed of the reflectivity the FBG and the losses of the OC1, HNLF, CIRC, PC2 and PM2. Consequently, the oscillation of the selected signal wave at low pump power can be achieved easily. At the same time, the idler wave with higher power can also be generated [6, 16]. We observe the pulses of idler wave with high-speed oscilloscope in time domain and the RF spectrum of the generated pulses with the ESA. Figures 5(a)-5(e) show the output pulse trains and the spectra of idler wave, depicting the effect of adjusting the SOP of incident light, when the pre-coupled pump power and the modulation frequency are 26dBm and ~5GHz, respectively. For a given modulation frequency, the pulses under different mode-locked conditions are generated by rotating the PC2 as shown in Figs. 5(a₁)-5(e₁). The upper trace represents the RF modulation signal with a frequency of 5.000037GHz and the power of 18dBm. From Fig. 5(a₁), compared to the reference RF signal, the pulses pass through the PM at peaks of RF signal. When the PC2 is rotated slightly, the pulses at the peaks of RF signal start to decrease while the pulses at the troughs of RF signal occur as shown in Fig. 5(b₁). To further rotate the PC2, both of the pulses at peaks and troughs point of the RF signal have approximately the same intensity. This indicates that a slight rotating of PC can lead to generate pulses with PRF which is twice of the RF drive frequency. By continuing to rotate the PC, the intensity of pulses at the troughs of RF signal is larger than that of pulses at the peaks of the RF signal. As further to rotate the PC2, the pulses at the troughs of the phase retardation have the maximum intensity while the pulses at the peaks of the phase retardation is vanished. As mentioned above, the generated pulses pass through the modulator consecutively at the extremum of the phase variation. However, it can be seen from Figs. 5(a₁)-5(e₁) that the series of generated pulses occurs earlier in time relative to the peaks or troughs of the modulation sinusoidal signal due to the detuning between the modulation frequency and the axial mode interval [18–21]. As shown in Figs. 5(a)-5(e), the pulse width of the pulse trains at the peaks of RF signal is around 51.11ps while that of the pulse trains at the troughs of RF signal is about 45.2ps. The output power of the different pulse trains under different mode-locked states is shown in Fig. 5(f). By adjusting the PC2, the output power of the pulses at the peaks of the RF signal decreased from ~4.654mW to ~0mW while that of the pulses at the troughs of the RF signal increased form ~0mW to ~4.866mW. It can be seen from Fig. 5(f) that different pulse trains have approximately the same output power by properly adjusting the SOP of the incident signal wave.

Fig. 5 (a)-(e) The output pulses and the spectra of the detected pulse trains at idler wavelength in different mode-locked status with adjusting the PC2. Upper trace in the left column: RF modulation signal when the modulation frequency is 5.000037GHz. (f) The output power of the different pulse trains by adjusting the PC2.

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Figures 5(a₂)-5(e₂) show the optical spectra of the generated pulse trains under different mode-locked statuses which correspond to Figs. 5(a₁)-5(e₁) respectively. Under mode-locked condition, the mode spectrum packet is shifted toward the low frequency side as shown in Fig. 5(a₂), while the mode spectrum packet is shifted toward the up frequency side as shown in Fig. 5(e₂), which agrees well with the observed results in Fig. 3(b). This is mainly due to the strong mode competition between the two groups of mode spectrum belonging to the two different mode-locked states [18–20]. If the PC2 is continuously adjusted, there occurs a smooth transition from one mode spectrum envelop to the other in the process of FOPA. At the same time, the corresponding time response also shows a switching action from one mode-locked pulse trains to the other mode-locked pulse trains. As mentioned above, when the phase retardation is varied with rotating PC2, one mode spectrum envelop with sufficient intensity of sidebands can quench the other mode spectrum. This will result the single generated pulse trains through at either of the extremum of the phase variation [21]. However, by continuously adjusting PC2 to obtain proper value of phase retardation, the intensity of either mode spectrum envelop is insufficient to quench the other as shown in Fig. 3(b), and thus both mode locked states can oscillate simultaneously to generate pulse trains at repetition rate which is two times of the RF drive frequency.

Figures 6(a)-6(e) show the fundamental and second-harmonic components of the RF spectra of the detected pulse trains at different mode-locked condition which correspond to Figs. 5(a)-5(e), respectively. In all the mode-locked condition, the fundamental and second-harmonic components of the detected pulses can be obtained simultaneously. The ESA displays the power of second-harmonic component is steady, but the power of fundamental component is unsteady and varies with rotating PC2. Form Figs. 5(a₁) and 5(a₂), the power of the fundamental component and second-harmonic component are about 0dBm and −14dBm, respectively. With rotating the PC2, the power of the fundamental component decreased to −16dBm when the two pulses occur simultaneously. After further adjusting PC2, the power of the fundamental component increases to ~0dBm again and the pulses transfer from one mode-locked state to the other. In general, when two signals with different frequencies are incident upon the PD, the output current is given by $I (t) \propto E_{n}^{2} + E_{n + 1}^{2} + 2 E_{n} E_{n + 1} \cos [(ω_{n + 1} - ω_{n}) t + θ]$ , where, $θ$ is the phase difference between the two signals and it is affected by the effective value of phase retardation. Therefore, when both states oscillate at the same time, the fundamental component would be diminished with rotating of PC while the second-harmonic component is almost constant.

Fig. 6 The RF spectra of the detected pulse trains under different mode-locked statuses. The upper and down figures represent the fundamental component and the second-harmonic components of the detected pulses, respectively.

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As mentioned above, the stable pulse trains at repetition rate which is two times of the RF drive frequency applied to PM can be generated by continually rotating the intra-cavity PC (PC2). Figures 7(a)-7(d) show the generated pulses with PRF of ~8, 10, 12 and 14GHz when the RF drive frequency applied to PM are around set to ~4, 5, 6 and 7GHz, respectively. It can be seen from Figs. 7(a)-7(d) that, compared to the modulation signal, these pulses pass through the crystal neither at the maximum nor at the minimum point of phase retardation. This is mainly due to the detuning between the modulation frequency and the mode spacing [18,19]. The output power of pulse keeps constant of 2.6mW with a small span at different modulation frequencies, as shown in Fig. 7(e). The results also demonstrate that the pulse width is decreased obviously when the modulation frequency is increased from 4GHz to 6GHz, which agrees well with the analysis in the Refs [16, 21].

Fig. 7 The optical pulse trains with PRF of ~8, 10, 12 and 14GHz in this proposed FM active mode-locked FOPO when the RF signal are set as (a) ~4GHz, (b) 5GHz, (c) 6GHz and (d) 7GHz. (e) The output power and pulse width of generated pulses at different modulation frequencies.

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4. Conclusion

In summary, we have demonstrated the generation of RF signals with the repetition rate that is two times of the driven RF signals in an FM actively mode-locked FOPO. In this scheme, by adjusting the SOP of the light which is poured into the LiNbO₃ PM, either one of two different mode-locked pulses could exist, or both might occur simultaneously when the modulation frequency is fixed. Moreover, by continually rotating the intro-cavity PC, the appropriate effective phase retardation can be obtained, and the spectra of the generated pulses have a smooth transition from one groups of modes to the other groups. At the same time, the switching of the mode-locked pulse trains is achievable. In addition, the optical pulses with PRF of around 8, 10, 12 and 14GHz have been experimentally obtained when the RF drive frequency applied to PM are chosen ~4, 5, 6 and 7GHz, respectively.

Funding

International Science and Technology Cooperation Program of China (2014DFA11170), National Natural Science Foundation of China (NSFC) (61505168, 61405165, 61335005).

References and links

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Pulse repetition rate doubling in FM actively mode-locked fiber-optic parametric oscillator

Abstract

1. Introduction

2. Principle

3. Experimental results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (7)

Equations (2)

Optics Express