## Abstract

In this work, a novel Single longitudinal mode (SLM) dual-wavelength random fiber laser (DW-RFL) with narrow line-width and tunable separation between the two modes in the range 1.5 – 25 nm (187 GHz – 3.12 THz) is presented. The laser is based on Rayleigh backscattering in a standard single mode fiber of 2 km length acting as distributed mirrors and a semiconductor optical amplifier (SOA) acting as the optical amplifier. Two optical band pass filters are used for the wavelength selection, and two Faraday Rotator mirrors are used to sustain the stability of the two lasing wavelengths against fiber random birefringence. The measured line-width of each mode of the laser varies from 3 to 11.5 kHz with lasing wavelengths and SOA pump currents. The power and the wavelength stabilities at the peak power of each mode were also investigated.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

Tunable multi-wavelength SLM lasers have a huge potential in many non-invasive sensing and telecommunication applications [1–3]. They can also be useful in microwave and terahertz (THz) generation, which is currently required in many biological sensing applications [4] where the simple and cost effective photoconductive mixing technique can be used to generate frequencies in this frequency band [5].

The formation of a dual wavelength laser source can be achieved using a Semiconductor Optical Amplifier (SOA) or an Erbium Doped Fiber Amplifier (EDFA) [3,6,7]. The SOA has many advantages as it can be easily modulated, and integrated with other semiconductor devices. It has also smaller size, and wider bandwidth than EDFA. In addition, the gain saturation is very fast in SOA due to the small carrier lifetime. Thus, it is very useful in high speed switching, and all optical signal processing applications compared to EDFA based sources.

In this work, we demonstrate a linear cavity configuration that allows the optical signal to travel through the gain medium twice per round trip compared with the ring configuration usually deployed [5]; thus reducing the number of SOAs utilized to only one, which leads to less complexity, power consumption and more cost effective. Two Fabry Perot optical filters are employed for the wavelength selection and tuning to allow easy and wide band tuning range compared with Bragg gratings commonly used. To the best of our knowledge, it is the first time to develop a theoretical model for simulating the laser built-up in random fiber laser either a single-wavelength or dual wavelength. The model is a time domain model that assumes homogeneous broadening in the neighbourhood of the lasing wavelength. The gain medium is thus presented by a specific saturation energy and carrier lifetime. The Rayleigh backscattering is represented by random scattering centers along the fiber length. The model allows predicting the output mode spectrum and its buildup evolution with time. The system is built experimentally in the laboratory and random laser oscillation of two single modes is demonstrated. The separation between the two lasing modes is tuned from 1.5 nm to 25 nm. A standard single mode fiber SMF-28e is used in the experiment.

In the following, the paper is structured as follows: section 2 describes the experimental setup of the dual-wavelength random fiber laser. Section 3 describes a simple theoretical model of the SOA time domain oscillation dynamics. Section 4 demonstrates the steady state analysis of the DW-RFL that gives an analytical equation of the output power and the threshold current. Section 5 presents the spectral model simulation of the single mode RFL, and DW-RFLs that shows the dynamics of the oscillation from noise to steady state. Section 6 illustrates the obtained experimental results. Finally, the paper is ended by the conclusion.

## 2. Experimental setup

The block diagram of the proposed dual-wavelength random laser is shown in Fig. 1. One SOA is used having wide bandwidth operation (150 nm) in wavelength range 1450–1600 nm. Two Fabry-Perot optical bandpass filters of bandwidth 0.3 nm were used: one is tunable (TOF) in C-band, and the other is fixed (OF).

Both filters are used for the selection of the two lasing wavelengths. Both have a nominal value of an insertion loss of 3 dB. The central wavelength of the fixed filter is 1550 nm, while the central wavelength of the tunable filter varies through 1520–1570 nm. The source of Rayleigh backscattering is a standard single mode fiber (SMF-28e) of length 2 km. A variable optical attenuator (VOA) adjusts the gain condition for the dual-wavelengths. Therefore, more stability of the oscillating modes occurs [8]. Two Faraday rotator mirrors, of an insertion loss of 1 dB each, are used as feedback elements for lasing action to arise. Moreover, they can enhance the wavelength and power stability of the dual-wavelength laser against the random birefringence of the optical fiber. One 3-dB 2 × 2 directional coupler operating at 1550 nm is used for combining the light at the two wavelengths into the SOA in the forward direction. However, the directional coupler divides the power at both wavelengths almost equally into the two wavelength selective branches. Finally an optical isolator (ISO) is used at the output of the laser to eliminate back reflections. All fiber connections are performed using FC/APC connectors to highly reduce the Fresnel reflections.

## 3. Theoretical model

In this section we explain the model used for the simulation of the oscillation dynamics in the SOA-based random laser. The differential equation that governs the saturated amplification inside the SOA is given as [9,10]:

*h(t)*is the SOA integrated gain.

*g*is the SOA saturated gain coefficient;

*E*is the SOA saturation energy.

_{sat}*τ*is the carrier lifetime;

_{c}*P*is the SOA saturation power.

_{sat}*P*is the input power.

_{in}*L*is the SOA length. The output field from the SOA is defined as follows [10]: where

_{soa}*α*is Henry's line-width enhancement factor, which describes the coupling between the gain and the refractive index of the semiconductor material [10].

_{H}## 4. Steady state analysis

The SOA saturated gain is evaluated as $G = {e^{h(t )}}$ for each single SOA path. The steady state solution of Eq. (1a) gives:

We assume that SOA small signal gain*g*is varying linearly with the pumping DC current as reported in [9]. In this case the small signal gain can be expressed as: where a, and b are constants independent of the pump current.

_{o}The dual-wavelength RFL (DW-RFL) gain condition is: saturated G × *Loss* = 1, where *G = e ^{2h}* for each round trip, and the total cavity
loss is calculated based on the value of the Rayleigh backscattering power
reflection coefficient (

*R*), the coupling ratio of the 3-dB coupler (

*C*), and the insertion loss of the optical filter (

*IL*) and Faraday rotator mirrors (

_{fil}*IL*). The total cavity loss is given as:

_{FRM}*R*) is calculated from the following formula [11]: where

*L*is the single mode fiber (SMF) length in (km),

*r*is the Rayleigh backscattering coefficient that equals 2 × 10

^{−4}km

^{−1}for Silica SMF, and $\alpha $ is the SMF attenuation coefficient.

The DW-RFL output power is thus calculated as follows:

Substituting (3) and (4) in (7), the output power is expressed as: where: and then, the threshold current is given by: For the SOA parameters a and b, we characterized the small signal gain*g*, throughout the wavelength range of interest at different pump currents, using the following setup as depicted in Fig. 2.

_{o}The tunable optical filter is tuned to the same wavelength as the tunable laser to filter out the wide SOA-ASE spectrum. Although the ASE power at the selected wavelength is also measured, its power value is much lower than the output signal power. Therefore, it can be neglected without considerable degradation in the measurement accuracy.

By varying the SOA pump current, the SOA gain can be calculated as the
ratio between the output power, and the input power. A curve fitting
algorithm of the gain ratio (*G*) versus input
power measurements to the analytical expression in (3), was performed to
extract the values of the SOA small signal gain coefficient (*g _{o}*) at different pump currents.

*P*and

_{sat}*L*are chosen to 5 mW and 1.2 mm according to the SOA datasheet, respectively. The results are depicted in Fig. 3 at 1550 nm wavelength. It obeys a linear relationship. Thus a, and b are calculated based on curve fitting the data in Fig. 3 to (4).

_{soa}From the curve fitting performed at wavelength 1550 nm, we get (a = 25
m^{−1}/mA, b = 100 m^{−1}). The values of *I _{th}* for 1, and 2 km SMF from (8c), are
calculated to be 204, and 194 mA respectively. It is obvious that the
reduction of the SMF length will lead to decreasing the Rayleigh
coefficient (R), thus increasing the threshold current as the threshold
value of

*g*will be increased. Since the SOA used in experimental setup demonstrated in section 2 has limited pump current, the calculated values of I

_{o}_{th}guide us to use relatively long length of SMF (2 km) to have a stable oscillation at SOA pump current higher than I

_{th}.

Based on the characterization results performed on the SOA at 1525, and 1550 nm and substituting in equations (8) b, and c, the values of the lasing threshold current and the slope efficiency for the dual-wavelength operation are found to be 200 mA, is 95 mW/A, respectively.

## 5. Spectral model

To study the oscillation dynamics inside the RFL, Fig. 4 illustrates the block diagram of the simulation model.

The Rayleigh backscattered reflected electric field can be modeled as the summation of backscattered light electric field in the SMF, and it can be written as [12]:

*n*is the refractive index of the fundamental mode in SMF.

*c*is the speed of light.

*v*is the light optical frequency, and

*T*is the total number of scattering centers in the SMF. The amplitude of the reflection coefficient of each scattering center is

*A*. It is assumed to be a Gaussian random variable with zero mean and a variance (

_{j}*rL/T*) [12]. The position of each scattering center (

*z*) follows a uniform random variable. The polarization effect is neglected in this model.

_{j}As shown in Fig. 4, ${H_r}(f )= \;
{E_R}/{E_{in}}$, represents the frequency domain transfer
function of the Rayleigh backscattering (RBS) as mentioned in Eq. (9), *H(f)* is the frequency domain transfer function of the optical
filter and is modeled as a Gaussian filter tuned at the wavelengths of
concern. It has single passband, or double passbands depending on whether
single lasing mode or dual-wavelength modes are considered. The saturated
gain of the SOA is represented in (1). Fast Fourier Transform FFT or
Inverse Fast Fourier Transform IFFT is applied to the electric field
before passing through the RBS or the optical filter transfer functions,
or the SOA saturated gain. The SOA amplified spontaneous emission noise is
added to the circulating electric field in the frequency domain. It is
described as [10,13,14]:

*N*and

_{1}*N*are two statistically independent identically distributed white Gaussian noise functions whose spectral density equal 0.5 each, and

_{2}*A*is related to the ASE power that is dependent on the pump current. The initial ASE power is calculated by integrating the measured ASE power spectral density under the simulation frequency span (330 GHz). Based on the experimental characterization performed on the SOA, the ASE value is highly reduced in the existence of signal power due to fast gain saturation and non-linear gain compression [15]. Therefore, we used this new value of the ASE power starting from the second round trip. We compute numerically and iteratively the oscillating electric field until a steady state regime is observed after hundreds of round trips.

In the simulation model, the values of the main parameters of the laser
cavity are chosen as follows: the length of the single mode fiber is 2 km,
and the number of scattering points (*T*) is
200. The 3-dB bandwidth of the optical filter is 0.3 nm, *g _{o}* is measured to be 6950 m

^{−1}, at pump current 300 mA. The evolution of the lasing spectrum with increasing the number of round trips is shown in Fig. 5. Initially, the output spectrum follows the filter transfer function. Throughout the first 50 round trips (

*RT*), the signal shows multimode operation. However, the power in the side modes begins to decrease as the number of round trips increases. This means that most of the power is transferred to the central mode. As the number of the round trip further increases, only single longitudinal mode operation dominates, and steady state regime is achieved.

Applying the same simulation process but with dual-wavelength optical
filter at 1525 and 1550 nm tuning wavelengths, and frequency span 20 THz .
Based on the characterization results performed on the SOA at 1525 nm, the
value of *g _{o}* at 1525 nm is
slightly modified to be 7000 m

^{−1}at the same pump current (300 mA). However, as shown in (1), the spectral dependence of

*g*values is not taken into consideration. Therefore, the average value of

_{o}*g*is used in simulating the spectral evolution of dual-wavelength random laser. By imposing an attenuation to one lasing frequency (e.g. f

_{o}_{2}) with respect to the other one (f

_{1}) to represent the VOA role to overcome the mode competition, and keep the power balance between the two modes, stable dual-wavelength oscillation is achieved after 150 round trips. Figure 6, illustrates the dual-wavelength simulation results with equal peak power of the two modes.

## 6. Experimental results

#### 6.1 Wavelength tuning and optical spectrum measurement

A unique feature of our laser structure is the ability to tune the separation between the two center wavelengths of both optical filters. The VOA was carefully adjusted to have a stable dual-wavelength laser with approximately the same output peak power. The laser spectra was measured by an optical spectrum analyzer (OSA) with a resolution bandwidth 0.07 nm. The lasing wavelengths are consistent with the peak wavelength of the two optical filters.

Figure 7 shows nine different dual-wavelength laser operation in the range from 1525 nm to 1560 nm at SOA bias current of 370 mA. The separation between the dual wavelength changes from 1.5 to 25 nm (187 GHz to 3.12 THz) beating signal. The lowest acceptable separation is limited to +/− 1.5 nm. The optical signal to noise ratio was measured for each lasing wavelength. It has a nominal value of 38 dB. As depicted in Fig. 7, the peak power of the different lasing modes changes in range −13.5 to −7 dBm due to the non-uniform gain spectrum of the SOA. Figure 8 shows dual-wavelength spectra of the random laser at 1535 and 1550 nm. When the SOA pump current increases from 350 to 370 mA, the output optical peak power increases from −8 dBm to −6.9 dBm, and the OSNR increases from 36.5 to 38 dB. This is because the small signal gain coefficient increases as the SOA pump current increases, which in turn leads to increasing the output optical power at each lasing wavelength according to (4) and (8).

As the SOA is practically considered as a nonhomogeneous broadening gain medium, each mode has its own carrier reservoir as long as the wavelength spacing between the two modes is higher than a specified limit depending on the SOA characteristics [16]. Thus mode competition effect is minimized. Furthermore, to guarantee a lower mode competition effect, the (VOA) is utilized to further minimize mode competition and keep the power balance between the two modes by carefully tuning the VOA. However, if the spacing between the two oscillating modes is get closer, as shown in Fig. 9 for 0.9 nm wavelength separation, inevitable mode competition reveals leading to a deterioration of the two spectra as clearly shown for the two closely spaced wavelengths.

For each oscillation wavelength mode, the random locations and values of the reflection coefficient of the scattering centers result in random longitudinal frequency modes within the optical filter bandwidth. The mode close to the center of the optical filter that satisfies the gain and phase conditions will have high possibility to sustain oscillation, while the other modes that have random amplitude, phase and frequency separation from the lasing mode will not sustain oscillation.

#### 6.2 Line width measurement

The RFL stability was investigated based on two criteria; the short term stability relies on lasing line-width measurement that represents an indication of the random temporal variation of the phase shift of the oscillating mode [11], and the long term stability that relies on recording the optical spectrum of the random fiber laser for a certain time period. In this sub-section, we will focus on the short-stability, while in subsection 6.3, we will illustrate the wavelength and power stability for a long time period.

The line-width of each lasing mode was measured at two SOA pump currents of 350 and 370 mA. Each one of the lasing wavelengths was selected by an optical tunable filter having 1 nm 3-dB bandwidth and then imported to the Self Delayed-Heterodyne technique [17,18], with a delay line of 68 km fiber length. For each lasing spectrum of the dual-wavelength, the RF beat signals are recorded. For example, the Self Delayed-heterodyne RF beat signals at 1551.5 nm and 1550 nm at two SOA pump currents (350 mA and 370 mA) are shown in Fig. 10. (a), and (b), respectively.

As depicted in Fig. 10, we do
not notice any side longitudinal mode at the whole tuning wavelength
range. If there were any spurious Fresnel reflections at the end of
the 2 km SMF, there would be multimode operation with free spectral
range *c/(2nL)* = 50 kHz. Therefore, each
lasing mode is a single longitudinal mode. Table 1 summarizes the whole results of the Self
Delayed-Heterodyne experimental set-up. The tunable filter wavelength
is denoted as λ_{TF} , while the fixed filter wavelength is
denoted as λ_{FF} .

As shown in Table 1, it is observed that the values of the line-widths vary from 3 – 11.5 kHz. It is worth mentioning that the values of line-widths for every dual-wavelength are close to each other due to the proximity of the power of the two lasing modes and the similar bandwidth of the two optical filters.

As shown in Table 1, the laser linewidth shows a certain dependence on the dual modes wavelength separation. For the tunable wavelength, this is simply related to the SOA gain variation with the wavelength. For the fixed wavelength, this variation is due to the change of the VOA setting for each wavelength separation (and hence the SOA corresponding gain) to maintain the same level of power as the tunable wavelength output.

#### 6.3 Optical power and wavelength stability

We recorded the lasing wavelength and peak power every two seconds for a time period of 15 minutes utilizing the OSA with a resolution of 0.07 nm to figure out the temporal variation of the instantaneous wavelength and power with time, and hence, the stability of the proposed dual-wavelength RFL over this time span. The variation of the peak power and the peak wavelength with time are plotted in Fig. 11 at dual-wavelength, 1550–1551.5, nm and SOA pump current of 370 mA. We found that standard deviation of the lasing wavelengths was in the range of 0.01 nm (see Fig. 11(b)), which is lower than the bandwidth of the optical filter.

The peak powers of both wavelengths have fluctuations of 14%, which originates mainly from mode competition. It is worth mentioning that peak power values of both modes are close to each other. The measurements are repeated for five different wavelength separations, and similar results are observed. Stability measurements imply that the output wavelength and power at peak power are rather stable.

The terahertz beat signal of the dual-mode RFL having 1.5 nm separation is estimated from the subtraction of the two lasing frequencies, neglecting the effect of phase fluctuations between the two modes. The mean and the standard deviation for the generated terahertz are 0.186 THz and 1.89 GHz, respectively.

The beat frequency was calculated for five different wavelength separations (+/−1.5, 10, +/− 15 nm). The standard deviation of the beat frequency ranges from 1.77 to 2.45 GHz, at mean values of 0.185 and 1.89 THz, respectively, which indicates percentage error of 0.9% and 0.13%, respectively.

A comparison between our proposed laser and the one reported in [5] is presented in Table 2. Our laser has an advantage of having large tuning range at higher output power. One SOA was sufficient to deliver adequate gain to our laser, because the cavity is based on linear configuration rather than ring configuration. The values of the power fluctuation and the wavelength stability are close to the values reported in [5]. Our line-width is larger, because the SMF reported in [5] has longer length and higher Rayleigh backscattering coefficient than the SMF we used.

## 7. Summary

We have demonstrated a novel dual-wavelength random fiber laser with tunable separation range from 1.5–25 nm, based on an SOA and Rayleigh backscattering acting as the gain medium and the feedback mechanism, respectively. The proposed structure illustrates an outstanding characteristics and a rather simple design solution with an ultra-narrow line-width SLM dual modes of 3 – 11.5 kHz for the different wavelength separations, and with high power and wavelength stability. The wavelength and peak power stability measurement show little wavelength shift (0.01 nm) and power fluctuations (14%) over 15 min. time duration. The calculated terahertz beat frequency has good values of frequency fluctuations, which encourages us to have a simple solution to implement a tunable terahertz source. This demonstrated performance opens the door for a variety of applications in microwave photonic systems, optical communications, sensing, and DWDM systems.

## References

**1. **J. Chow, G. Town, B. Eggleton, M. Ibsen, K. Sugden, and I. Bennion, “Multiwavelength generation in
an erbium-doped fiber laser using in-fiber comb
filters,” IEEE Photon. Technol. Lett. **8**(1),
60–62 (1996). [CrossRef]

**2. **N. Park and P. F. Wysocki, “24-line multiwavelength
operation of erbium-doped fiber-ring laser,”
IEEE Photon. Technol. Lett. **8**(11),
1459–1461 (1996). [CrossRef]

**3. **M. A. Ummy, N. Madamopoulos, M. Razani, A. Hossain, and R. Dorsinville, “Switchable dual-wavelength
SOA-based fiber laser with continuous tunability over the C-band at
room-temperature,” Opt. Express **20**(21),
23367–23373 (2012). [CrossRef]

**4. **H. Ahmad, F. D. Muhammad, C. H. Pua, and K. Thambiratnam, “Dual-Wavelength Fiber Lasers
for the Optical Generation of Microwave and Terahertz
Radiation,” IEEE J. Sel. Top. Quantum
Electron. **20**(5),
166–173 (2014). [CrossRef]

**5. **Y. Xu, L. Zhang, L. Chen, and X. Bao, “Single-mode SOA-based
1kHz-linewidth dual-wavelength random fiber laser,”
Opt. Express **25**(14),
15828–15837 (2017). [CrossRef]

**6. **H. Omran, H. E. Kotb, and D. Khalil, “Dual wavelength SOA based
fiber ring laser,” Proc. SPIE **10083**, 1008322
(2017). [CrossRef]

**7. **H. A. Shawki, H. E. Kotb, and D. Khalil, “Narrow Line Width Dual
Wavelength EDFA based Random Fiber Laser,” in
35th National Radio Science Conference, (NRSC
2018), March 20–22,
2018.

**8. **T. Zhu, B. Zhang, L. Shi, S. Huang, M. Deng, J. Liu, and X. Li, “Tunable dual-wavelength fiber
laser with ultranarrow linewidth based on Rayleigh
backscattering,” Opt. Express **24**(2),
1324–1330 (2016). [CrossRef]

**9. **G. P. Agrawal and A. Olsson, “Self Phase Modulation and
Spectral Broadening of Optical Pulses in Semiconductor Laser
Amplifiers,” IEEE J. Quantum
Electron. **25**(11),
2297–2306 (1989). [CrossRef]

**10. **S. L. Girard, M. Piche, H. Chen, G. W. Schinn, W. Y. Oh, and B. E. Bouma, “SOA Fiber Ring Lasers: Single-
Versus Multiple- Mode Oscillation,” IEEE J.
Sel. Top. Quantum Electron. **17**(6),
1513–1520 (2011). [CrossRef]

**11. **H. A. Shawki, H. E. Kotb, and D. Khalil, “Single-longitudinal-mode
broadband tunable random laser,” Opt.
Lett. **42**(16),
3247–3250 (2017). [CrossRef]

**12. **M. Pang, X. Bao, L. Chen, Z. Qin, Y. Lu, and P. Lu, “Frequency stabilized coherent
Brillouin random fiber laser: theory and experiments,”
Opt. Express **21**(22),
27155–27168 (2013). [CrossRef]

**13. **A. Bilenca, S. H. Yun, G. J. Tearney, and B. E. Bouma, “Numerical study of
wavelength-swept semiconductor ring lasers: the role of refractive
index nonlinearities in semiconductor optical amplifiers and
implications for biomedical imaging applications,”
Opt. Lett. **31**(6),
760–762 (2006). [CrossRef]

**14. **M. Shatif and G. Eisenstein, “Noise Characteristics of
Nonlinear Semiconductor Optical Amplifiers in the Gaussian
Limit,” IEEE J. Quantum Electron. **32**(10),
1801–1809 (1996). [CrossRef]

**15. **M. J. Connelly, “Wideband Semiconductor Optical
Amplifier Steady-State Numerical Model,” IEEE
J. Quantum Electron. **37**(3),
439–447 (2001). [CrossRef]

**16. **H. Dery and G. Eisenstein, “The Impact of Energy Band
Diagram and Inhomogeneous Broadening on the Optical Differential Gain
in Nanostructure Lasers,” IEEE J. Quantum
Electron. **41**(1),
26–35 (2005). [CrossRef]

**17. **T. Okoshi, K. Kikuchi, and A. Nakayama, “Novel method for high
resolution measurement of laser output spectrum,”
Electron. Lett. **16**(16), 630
(1980). [CrossRef]

**18. **A. Yariv, * Optical
Electronics in Modern Communications*
(Oxford University Press,
1997).