Interval Adjustable Dual-Wavelength Erbium-Doped Fiber Laser Based on Cascaded Two Mach-Zehnder Interferometers

: An interference ﬁlter is designed by cascading two Mach-Zehnder interferometers (MZIs), which is then utilized in the construction of a wavelength interval adjustable dual-wavelength Erbium-doped ﬁber laser (EDFL). Each MZI consists of two 3 dB optical couplers (OCs) connected in series. The input light is split into two arms at the ﬁrst OC and recombined at the second OC. The ﬁrst MZI (MZI 1) has a smaller free spectral range (FSR) and is used for selecting the output wavelength of the laser. The second MZI (MZI 2) has a larger FSR and forms an envelope structure on the comb-like spectrum of MZI 1. By adjusting the optical path difference between the two arms of MZI 2, the FSR of the envelope can be changed, thereby altering the interval of the output wavelengths. The implemented ﬁlter is inserted into the EDFL to achieve stable dual-wavelength output. By stretching one arm of MZI 2, the interval of the dual-wavelength can be adjusted from 4.64 to 13.94 nm, with the side-mode suppression ratio of over 44 dB for all wavelengths.


Introduction
Multi-wavelength continuous wave fiber lasers offer advantages such as excellent heat dissipation, high beam quality, easy maintenance and low cost, making them widely used in various fields such as fiber sensing, fiber communication, biomedicine, and spectroscopy [1][2][3].However, due to mode competition in the gain fiber, it is challenging to achieve stable dual-wavelength output at room temperature.Inserting a filter into the Erbium-doped fiber laser (EDFL) is an effective approach to suppress mode competition.So far, various filters, such as fiber gratings and fiber interference filters have been used as wavelength-selective devices to achieve multi-wavelength output in fiber lasers.Additionally, to meet the demands of different fields, it is expected that multi-wavelength fiber lasers have flexibility in terms of the number and interval of wavelengths.The research on wavelength-interval adjustable multi-wavelength EDFL remains of great significance.
Various methods have been proposed to adjust the wavelength interval to enhance the versatility of multi-wavelength fiber lasers.Fiber gratings, such as fiber Bragg gratings [4] or sampled fiber Bragg gratings [5], are commonly used as wavelength-selective devices in fiber lasers.By adjusting the loss, polarization state, or sampling period and length of the fiber gratings, wavelength interval adjusting can be achieved.However, the fabrication of traditional fiber gratings requires phase masks and specific light sources, while femtosecond laser writing-based fiber gratings require expensive equipment.Lyot filters [6,7] and Sagnac filters [8] could be fabricated by incorporating polarization-maintaining fibers (PMFs) and polarization controllers (PCs), and various output states such as single-wavelength, multiwavelength, tunable or interval adjustable multi-wavelength have been realized.However, the excessive use of PCs and PMFs increases system complexity.
Fiber Mach-Zehnder interferometer (MZI) filters have also been used in fiber lasers to realize wavelength-interval adjustable outputs.Compared to fiber gratings and Lyot filters, MZI filters have a simple structure and are easier to implement.The principle of a MZI filter involves splitting the output light from the fiber into two arms, which then recombine after traveling different optical paths.Interference occurs due to the optical path difference (OPD) between the two arms.The two-part light may propagate within the same fiber or in two separate fibers.MZIs based on one single fiber typically involve fusion splicing a section of a photonic crystal fiber, multimode fiber or PMF between two sections of single-mode fibers.In 2012, B.K. Kim et al. [9] proposed a MZI filter using a twin-core photonic crystal fiber (TC-PCF), where two wavelength intervals were obtained by adjusting the polarization states.In 2019, Zhao et al. [10] designed a MZI composed of a segment of PMF and two segments of multimode fibers.By applying strain on the MZI filter, the wavelength interval of the dual-wavelength laser could be continuously tuned from 21.82 nm to 22.69 nm.In this type of MZI filters, the tuning range of the OPD between the two arms is relatively small, resulting in a limited range of wavelength interval variation in dual-wavelength fiber lasers.In MZI filters where the two-part light propagates in two independent fibers, it is more convenient to change the optical path of one arm without affecting the other one.In 2007, Chen et al. [11] introduced an optical variable delay line (OVDL) into one arm of the MZI, and the wavelength interval could be tuned from 0.1 nm to 100 nm.However, the delay time of the OVDL needs to be controlled by a computer, making it less convenient for manual operation.Another approach is to insert a segment of tapered fiber within one arm of the MZI filter, where the physical length of the tapered fiber could be adjusted by stretching [12,13]-thereby altering the OPD between the two arms and achieving variable intervals for multi-wavelength laser outputs.However, the mechanical strength of the tapered fiber is reduced, and additional losses could be introduced.Polarization beam splitter-based two-stage cascaded MZI has also been reported to implement a tunable and switchable all-fiber comb filter [14], where the dual-function of a channel-spacing tunable and wavelength-switchable filter is realized by adjusting the polarization state of the input light.Only two-channel spacing can be adjusted, and an OVDL is needed for a more flexible control of the channel spacing [14].Recently, the Vernier effect has been employed to fiber lasers for refractive index sensing [15] or single longitudinal-mode output [16,17].In 2023, a dual-wavelength erbium-doped fiber laser was reported with a parallel comb filter configuration based on the optical Vernier effect [15].Each branch of the filter is an in-line MZI filter.The interval of the two wavelengths can be adjusted by submerging the proposed filter in different sodium chloride/water mixtures.Even the sensitivity of the refractive index sensing is high; the tuning range is only about 4.3 nm.
In this article, an interval adjustable dual-wavelength fiber laser is demonstrated by cascading two MZI filters.Both MZI filters (MZI 1 and MZI 2) consist of two 3 dB optical couplers (OCs).The free spectral ranges (FSRs) of the two MZIs are 1.60 nm and 5.10 nm, respectively.Inserting the implemented filters into an EDFL, stable dual-wavelength outputs are obtained.By stretching one arm of the MZI 2, the dual-wavelength interval can be adjusted from 4.64 nm to 13.94 nm.Compared to an MZI based on OVDL, the filter proposed here offers a more straightforward operation, as it eliminates the need for the computer-controlled adjustment of the delay length.Additionally, compared to an MZI filter based on tapered fiber, the untapered fiber possesses a higher mechanical strength than tapered fiber.

The Principle and Structure of the Filter
The structure of the proposed filter is shown in Figure 1.Four 3 dB OCs were used to compose two MZIs (MZI 1, MZI 2) with different FSRs, and then the two MZI were connected in series to form the cascaded MZI filter.From Equation ( 2), the FSR of the oscillation curve is inversely proportional to ∆.Therefore, when we stretch one of the arms of the MZI filter, the ∆ will change and the FSR of the oscillation curve will change too.The characteristics of the implemented MZI filter were measured using a homemade amplified spontaneous emission (ASE) source, where a two meter-long erbium-doped fiber (EDF) was employed as the gain medium, as shown in Figure 2a.The light from the filter was collected using an optical spectrum analyzer (OSA, Yokogawa, Tokyo, Japan, AQ6370D), with a resolution of 0.1 nm.When the stretching amount was 0.00 mm, the transmission spectra of the MZI 1 and MZI 2 were as shown in Figure 2b,c, and the FSRs were around 1550 nm are 1.60 nm and 5.10 nm, respectively.According to Figure 2b,c and Equation (2), when  was set to be 1.46 [14], the initial values of ∆ for MZI 1 and MZI 2 were calculated to be 1.03 mm and 0.33 mm, respectively.One arm of the MZI 2 was fixed on two movable platforms equipped with a micrometer, and the stretching amount was determined based on the reading of the micrometer.The measurement accuracy of the micrometer was 0.01 mm, which can be estimated as reading 0.001 mm.The stretching characteristics of the individual MZI 2 were measured in the experiment, and the relationship between the FSR of the MZI 2 of around 1550 nm and the stretching amount is shown in Figure 2d.With increases in the stretching amount, the FSR increased.When the stretching amount was 0.31 mm, the FSR of the MZI 2 was measured to be 25.18 nm.Each MZI filter was implemented by connecting two 3 dB OCs in series.The incident light was divided into two arms through the first OC.The light in these two arms underwent different optical paths and was then coupled back into one fiber at the second OC.Due to the OPD between the two beams of light, a modulated interference spectrum was obtained.
The transmittance of a single MZI filter can be represented as [18]: The FSR of the oscillation curve can be represented as [18]: where n e f f represents the effective refractive index of the single-mode fiber.The pigtail fiber of the two arms used the same type of single-mode fiber with the same n e f f .∆L =|L1 − L2| represents the physical length difference between the two arms of the MZI and λ denotes the working wavelength.From Equation (2), the FSR of the oscillation curve is inversely proportional to ∆L.Therefore, when we stretch one of the arms of the MZI filter, the ∆L will change and the FSR of the oscillation curve will change too.
The characteristics of the implemented MZI filter were measured using a homemade amplified spontaneous emission (ASE) source, where a two meter-long erbium-doped fiber (EDF) was employed as the gain medium, as shown in Figure 2a.The light from the filter was collected using an optical spectrum analyzer (OSA, Yokogawa, Tokyo, Japan, AQ6370D), with a resolution of 0.1 nm.When the stretching amount was 0.00 mm, the transmission spectra of the MZI 1 and MZI 2 were as shown in Figure 2b,c, and the FSRs were around 1550 nm are 1.60 nm and 5.10 nm, respectively.According to Figure 2b,c and Equation (2), when n e f f was set to be 1.46 [14], the initial values of ∆L for MZI 1 and MZI 2 were calculated to be 1.03 mm and 0.33 mm, respectively.One arm of the MZI 2 was fixed on two movable platforms equipped with a micrometer, and the stretching amount was determined based on the reading of the micrometer.The measurement accuracy of the micrometer was 0.01 mm, which can be estimated as reading 0.001 mm.The stretching characteristics of the individual MZI 2 were measured in the experiment, and the relationship between the FSR of the MZI 2 of around 1550 nm and the stretching amount is shown in Figure 2d.With increases in the stretching amount, the FSR increased.When the stretching amount was 0.31 mm, the FSR of the MZI 2 was measured to be 25.18 nm.It is worth it to note that, to evaluate the stretchability of the fiber, we stretched a normal single−mode fiber as a test first.The maximum stretching limit of the fiber is related to the distance D between the two fixed points.When the distance was set to be 10.58 mm, the maximum stretching limit was approximately 2.0 mm−beyond which, the fiber would break.In the fiber laser experiment, the distance D was 11.5 mm and the corresponding maximum stretching limit was about 2.3 mm.The relationship between the stretching amount and the output power of the single-mode fiber is shown in Figure 3.When the stretching amount was 2.0 mm, the loss was about 0.1 dB.In our experiment, the maximum stretching amount was 0.31 mm, which is far below the fiber breaking threshold.As shown in Figure 3, when the stretching amount was 0.31 mm, the loss of the fiber was about 0.02 dB-indicating that the loss of the proposed filter was very low.The MZI 1 and MZI 2 were connected in series to form the cascaded filter.The characteristics of the cascaded filter were measured using the setup shown in Figure 2a.Since the MZI 2 has a larger FSR than the MZI 1, when the two MZIs were cascaded, an interference pattern with an envelope was generated as shown in Figure 4.As shown in Figure 4a, the FSRs of the interference pattern and envelope around 1550 nm were 1.60 nm and 5.10 nm, respectively, agreeing with the values for the MZI 1 and MZI 2 shown in Figure 2. The FSR of the MZI 1 was fixed in the experiment to control the laser linewidth.When stretching the arm 2 of the MZI 2 along the horizontal direction, the FSR of the MZI 2 It is worth it to note that, to evaluate the stretchability of the fiber, we stretched a normal single−mode fiber as a test first.The maximum stretching limit of the fiber is related to the distance D between the two fixed points.When the distance was set to be 10.58 mm, the maximum stretching limit was approximately 2.0 mm−beyond which, the fiber would break.In the fiber laser experiment, the distance D was 11.5 mm and the corresponding maximum stretching limit was about 2.3 mm.The relationship between the stretching amount and the output power of the single-mode fiber is shown in Figure 3.When the stretching amount was 2.0 mm, the loss was about 0.1 dB.In our experiment, the maximum stretching amount was 0.31 mm, which is far below the fiber breaking threshold.As shown in Figure 3, when the stretching amount was 0.31 mm, the loss of the fiber was about 0.02 dB-indicating that the loss of the proposed filter was very low.It is worth it to note that, to evaluate the stretchability of the fiber, we stretched a normal single−mode fiber as a test first.The maximum stretching limit of the fiber is related to the distance D between the two fixed points.When the distance was set to be 10.58 mm, the maximum stretching limit was approximately 2.0 mm−beyond which, the fiber would break.In the fiber laser experiment, the distance D was 11.5 mm and the corresponding maximum stretching limit was about 2.3 mm.The relationship between the stretching amount and the output power of the single-mode fiber is shown in Figure 3.When the stretching amount was 2.0 mm, the loss was about 0.1 dB.In our experiment, the maximum stretching amount was 0.31 mm, which is far below the fiber breaking threshold.As shown in Figure 3, when the stretching amount was 0.31 mm, the loss of the fiber was about 0.02 dB-indicating that the loss of the proposed filter was very low.The MZI 1 and MZI 2 were connected in series to form the cascaded filter.The characteristics of the cascaded filter were measured using the setup shown in Figure 2a.Since the MZI 2 has a larger FSR than the MZI 1, when the two MZIs were cascaded, an interference pattern with an envelope was generated as shown in Figure 4.As shown in Figure 4a, the FSRs of the interference pattern and envelope around 1550 nm were 1.60 nm and 5.10 nm, respectively, agreeing with the values for the MZI 1 and MZI 2 shown in Figure 2. The FSR of the MZI 1 was fixed in the experiment to control the laser linewidth.When stretching the arm 2 of the MZI 2 along the horizontal direction, the FSR of the MZI 2 The MZI 1 and MZI 2 were connected in series to form the cascaded filter.The characteristics of the cascaded filter were measured using the setup shown in Figure 2a.Since the MZI 2 has a larger FSR than the MZI 1, when the two MZIs were cascaded, an interference pattern with an envelope was generated as shown in Figure 4.As shown in Figure 4a, the FSRs of the interference pattern and envelope around 1550 nm were 1.60 nm and 5.10 nm, respectively, agreeing with the values for the MZI 1 and MZI 2 shown in Figure 2. The FSR of the MZI 1 was fixed in the experiment to control the laser linewidth.When stretching the arm L2 of the MZI 2 along the horizontal direction, the FSR of the MZI 2 increased, and therefore, the FSR of the modulation envelope increased consequently.
Figure 4a-c depicts the transmission spectra of the cascaded filter when the stretching amounts were set to be 0.00 mm, 0.22 mm, and 0.30 mm, respectively.The interval between the two peak wavelengths near 1550 nm was about 4.56 nm, 12.84 nm, and 22.32 nm, respectively.Therefore, by stretching one arm of the MZI 2, it was possible to adjust the wavelength interval of the EDFL.
Photonics 2023, 10, x FOR PEER REVIEW 5 of 12 increased, and therefore, the FSR of the modulation envelope increased consequently.Figure 4a-c depicts the transmission spectra of the cascaded filter when the stretching amounts were set to be 0.00 mm, 0.22 mm, and 0.30 mm, respectively.The interval between the two peak wavelengths near 1550 nm was about 4.56 nm, 12.84 nm, and 22.32 nm, respectively.Therefore, by stretching one arm of the MZI 2, it was possible to adjust the wavelength interval of the EDFL.The insertion loss of the cascaded filter was estimated to be about 2.39 dB.In Ref. [11], an OVDL was used in one arm of the MZI, and the insertion loss of the MZI was measured to be 1.3 dB.In Ref. [13], taper technology was used on one arm of the MZI to adjust the wavelength interval.With increases in the taper length, the loss of the filter increased from 4.6 dB to 7.5 dB.In Ref.
[19], a micro-air cavity (MAC) was designed to tune the wavelength interval, which was similar to a Fabry-Perot resonator; the reflectivity of the MAC was approximately 6.9% of the incident light power.The loss of the proposed filter here was higher than the result in Ref. [11] and lower than the loss of a MAC similar to a Fabry-Perot resonator or an MZI based on fused taper technology.Furthermore, the FSR of an MZI based on two discrete arms can be tuned continuously by stretching one arm, and a wide interval tuning range can be achieved.In a Sagnac loop filter based on PMF [8], the FSR of the filter is related to the length of the PMF.More than one segment of the PMF and PCs are needed to change the effective PMF length.It is worth it to note that the proposed filter is sensitive to ambient temperature, bending, pressure, and other mechanical perturbations.A sealed box may be useful for protecting the filter from the external environment.
We note that in the Vernier effect, the same modulated spectrum has been observed.The working principle of the cascaded filter presented here is a little different from the Vernier effect.For the traditional Vernier effect, the sensor consists of two cascaded twobeam interferometers, such as MZIs.The FSR difference between these two interferometers (FSR1, FSR2) must be small to employ the Vernier effect.The cascaded superimposed spectrum of the Vernier effect consists of a comb−like, fine spectrum and a large envelope.Furthermore, the time period of the envelop is given by [20]: The insertion loss of the cascaded filter was estimated to be about 2.39 dB.In Ref. [11], an OVDL was used in one arm of the MZI, and the insertion loss of the MZI was measured to be 1.3 dB.In Ref. [13], taper technology was used on one arm of the MZI to adjust the wavelength interval.With increases in the taper length, the loss of the filter increased from 4.6 dB to 7.5 dB.In Ref.
[19], a micro-air cavity (MAC) was designed to tune the wavelength interval, which was similar to a Fabry-Perot resonator; the reflectivity of the MAC was approximately 6.9% of the incident light power.The loss of the proposed filter here was higher than the result in Ref. [11] and lower than the loss of a MAC similar to a Fabry-Perot resonator or an MZI based on fused taper technology.Furthermore, the FSR of an MZI based on two discrete arms can be tuned continuously by stretching one arm, and a wide interval tuning range can be achieved.In a Sagnac loop filter based on PMF [8], the FSR of the filter is related to the length of the PMF.More than one segment of the PMF and PCs are needed to change the effective PMF length.It is worth it to note that the proposed filter is sensitive to ambient temperature, bending, pressure, and other mechanical perturbations.A sealed box may be useful for protecting the filter from the external environment.
We note that in the Vernier effect, the same modulated spectrum has been observed.The working principle of the cascaded filter presented here is a little different from the Vernier effect.For the traditional Vernier effect, the sensor consists of two cascaded twobeam interferometers, such as MZIs.The FSR difference between these two interferometers (FSR 1 , FSR 2 ) must be small to employ the Vernier effect.The cascaded superimposed spectrum of the Vernier effect consists of a comb−like, fine spectrum and a large envelope.Furthermore, the time period of the envelop is given by [20]: The FSR difference between the two cascading MZIs in the proposed filter was large (as shown in Figure 2), and the FSR of the envelope was determined by the larger one (such as the MZI 2, as shown in Figure 2c).

Experimental Results and Discussion
The implemented filter was inserted into the EDFL, and the experimental setup is shown in Figure 5.The gain medium is a two meter-long section of c-band EDF.A 974 nm pump laser was used as the pump source, and the pump light was coupled into the gain fiber through a 980/1550 nm wavelength division multiplexer (WDM).An optical isolator (ISO) was used to ensure unidirectional transmission of the light and to increase the stability of the laser.A 40/60 OC was used to couple 60% of the light out of the cavity.The spectrum of the laser was measured using an OSA with a resolution of 0.05 nm. Figure 5b gives the gain spectrum of the Er-doped fiber under 974 nm pumping.The gain peak was located at 1529.83 nm.
Photonics 2023, 10, x FOR PEER REVIEW 6 of 12 The FSR difference between the two cascading MZIs in the proposed filter was large (as shown in Figure 2), and the FSR of the envelope was determined by the larger one (such as the MZI 2, as shown in Figure 2c).

Experimental Results and Discussion
The implemented filter was inserted into the EDFL, and the experimental setup is shown in Figure 5.The gain medium is a two meter-long section of c-band EDF.A 974 nm pump laser was used as the pump source, and the pump light was coupled into the gain fiber through a 980/1550 nm wavelength division multiplexer (WDM).An optical isolator (ISO) was used to ensure unidirectional transmission of the light and to increase the stability of the laser.A 40/60 OC was used to couple 60% of the light out of the cavity.The spectrum of the laser was measured using an OSA with a resolution of 0.05 nm. Figure 5b gives the gain spectrum of the Er-doped fiber under 974 nm pumping.The gain peak was located at 1529.83 nm. Figure 6 gives the output characteristics of the laser when the filter was unstretched.The threshold pump power of the laser was about 13.4 mW.As shown in Figure 6a, the side-mode suppression ratio (SMSR) increased with increases in the pump power.When the pump power was set to be 47.2 mW, the SMSR was about 50 dB and the central wavelength was located at 1531.29 nm, resulting from the combined effect of the filter and the high gain at around 1529.83 nm.The corresponding output power was 6.8 mW.When the pump power was continuously increased to 53.2 mW, the laser was switched to a dual−wavelength operation, as shown in Figure 6b.The laser had two peak wavelengths at 1526.56 nm and 1531.24nm, with an interval of 4.68 nm.The SMSR of the two wavelengths were 44 dB and 51 dB, respectively.Compared with Figure 4a, the two peaks in Figure 6b are located at two adjacent envelopes.During the experiment, another dualwavelength state shown in Figure 6c was also observed.The two peak wavelengths were 1531.23 nm and 1532.83nm, respectively.The interval agreed with the FSR of MZI 1, indicating that the two wavelengths were located at one envelope.With further increases in the pump power, the peak at 1532.83 nm disappeared, and another peak at 1526.56 nm appeared.In addition, the polarization hole burning effect is usually introduced in multiwavelength fiber lasers [6].The polarization hole burning effect is related to the different polarization state of different wavelengths.No PC was used in the fiber laser shown in Figure 5.However, the polarization hole burning effect may be introduced by the tension resulting from fiber winding.Thus, the dual-wavelength shown in Figure 6b may be a result of the combined effect of gain, filtering, and the polarization hole burning effect.Figure 6 gives the output characteristics of the laser when the filter was unstretched.The threshold pump power of the laser was about 13.4 mW.As shown in Figure 6a, the side-mode suppression ratio (SMSR) increased with increases in the pump power.When the pump power was set to be 47.2 mW, the SMSR was about 50 dB and the central wavelength was located at 1531.29 nm, resulting from the combined effect of the filter and the high gain at around 1529.83 nm.The corresponding output power was 6.8 mW.When the pump power was continuously increased to 53.2 mW, the laser was switched to a dual−wavelength operation, as shown in Figure 6b.The laser had two peak wavelengths at 1526.56 nm and 1531.24nm, with an interval of 4.68 nm.The SMSR of the two wavelengths were 44 dB and 51 dB, respectively.Compared with Figure 4a, the two peaks in Figure 6b are located at two adjacent envelopes.During the experiment, another dual-wavelength state shown in Figure 6c was also observed.The two peak wavelengths were 1531.23 nm and 1532.83nm, respectively.The interval agreed with the FSR of MZI 1, indicating that the two wavelengths were located at one envelope.With further increases in the pump power, the peak at 1532.83 nm disappeared, and another peak at 1526.56 nm appeared.In addition, the polarization hole burning effect is usually introduced in multi-wavelength fiber lasers [6].The polarization hole burning effect is related to the different polarization state of different wavelengths.No PC was used in the fiber laser shown in Figure 5.However, the polarization hole burning effect may be introduced by the tension resulting from fiber winding.Thus, the dual-wavelength shown in Figure 6b may be a result of the combined effect of gain, filtering, and the polarization hole burning effect.By varying the pump power and the strain amount applied to the 2 arm of MZI 2, the interval between these two wavelengths was adjustable.Figure 7 shows the measured dual-wavelength spectra against the amount of stretching.From Figure 7, it can be ob- By varying the pump power and the strain amount applied to the L2 arm of MZI 2, the interval between these two wavelengths was adjustable.Figure 7 shows the measured dualwavelength spectra against the amount of stretching.From Figure 7, it can be observed that as the strain amount was increased from 0.00 to 0.25 mm, one wavelength was tuned from 1527.26 nm to 1524.18 nm while the other one was tuned from 1531.90 nm to 1538.12 nm, and the interval increased from 4.64 nm to 13.94 nm.Due to the limited gain bandwidth of the EDF, the dual-wavelength was only generated between 1520 nm and 1540 nm.By varying the pump power and the strain amount applied to the 2 arm of MZI 2, the interval between these two wavelengths was adjustable.Figure 7 shows the measured dual-wavelength spectra against the amount of stretching.From Figure 7, it can be observed that as the strain amount was increased from 0.00 to 0.25 mm, one wavelength was tuned from 1527.26 nm to 1524.18 nm while the other one was tuned from 1531.90 nm to 1538.12 nm, and the interval increased from 4.64 nm to 13.94 nm.Due to the limited gain bandwidth of the EDF, the dual-wavelength was only generated between 1520 nm and 1540 nm.In order to evaluate the stability of the proposed EDFL, the spectrum was scanned repeatedly when the 2 arm in MZI 2 was unstretched and stretched by 0.05 mm, respectively.During the measurement process, the spectra were recorded every 5 min, for a total monitoring duration of 60 min.Figure 8a,b shows the results when the fiber was unstretched, in which Figure 8a shows the recorded spectra and Figure 8b shows the central wavelength and output power.As shown in Figure 8b, the peak wavelength of the laser near 1527.21nm fluctuated from 1527.21 nm to 1527.26 nm, and the power varied between −4.141 dBm and −4.341 dBm.The wavelength variation range was less than 0.05 nm, and the power variation range was lower than 0.20 dB.The peak wavelength near 1531.85nm fluctuated from 1531.85 nm to 1531.92 nm and the power ranged from −7.071 dBm to −7.299 dBm.The central wavelength variation range was less than 0.07 nm, and the power variation range was lower than 0.249 dB.The results in Figure 8c,d were recorded when the stretching amount was 0.05 mm.The central wavelength variation range near 1527.12nm was less than 0.05 nm and the power variation range was less than 1.29 dB, while the central wavelength variation range near 1533.32 nm was less than 0.23 nm and the power variation range was lower than 1.25 dB. Figure 8e,f shows the results when the stretching amount was 0.25 mm.The central wavelength variation range near 1524.50nm was less In order to evaluate the stability of the proposed EDFL, the spectrum was scanned repeatedly when the L2 arm in MZI 2 was unstretched and stretched by 0.05 mm, respectively.During the measurement process, the spectra were recorded every 5 min, for a total monitoring duration of 60 min.Figure 8a,b shows the results when the fiber was unstretched, in which Figure 8a shows the recorded spectra and Figure 8b shows the central wavelength and output power.As shown in Figure 8b, the peak wavelength of the laser near 1527.21nm fluctuated from 1527.21 nm to 1527.26 nm, and the power varied between −4.141 dBm and −4.341 dBm.The wavelength variation range was less than 0.05 nm, and the power variation range was lower than 0.20 dB.The peak wavelength near 1531.85nm fluctuated from 1531.85 nm to 1531.92 nm and the power ranged from −7.071 dBm to −7.299 dBm.The central wavelength variation range was less than 0.07 nm, and the power variation range was lower than 0.249 dB.The results in Figure 8c,d were recorded when the stretching amount was 0.05 mm.The central wavelength variation range near 1527.12nm was less than 0.05 nm and the power variation range was less than 1.29 dB, while the central wavelength variation range near 1533.32 nm was less than 0.23 nm and the power variation range was lower than 1.25 dB. Figure 8e,f shows the results when the stretching amount was 0.25 mm.The central wavelength variation range near 1524.50nm was less than 0.02 nm and the power variation range was less than 0.67 dB, while the central wavelength variation range near 1538.49nm was less than 0.03 nm and the power variation range was lower than 0.91 dB.The laser exhibited excellent stability.In the experiment, the fiber was fixed on two movable platforms.The distance between the two fixed points was estimated to be 11.5 cm.This segment of fiber was suspended for easy stretching.The stretching process generates stress inside the optical fiber.The fluctuation of the power and variation in the central wavelength may come from changes in stress.than 0.02 nm and the power variation range was less than 0.67 dB, while the central wavelength variation range near 1538.49nm was less than 0.03 nm and the power variation range was lower than 0.91 dB.The laser exhibited excellent stability.In the experiment, the fiber was fixed on two movable platforms.The distance between the two fixed points was estimated to be 11.5 cm.This segment of fiber was suspended for easy stretching.The stretching process generates stress inside the optical fiber.The fluctuation of the power and variation in the central wavelength may come from changes in stress.In the cascaded interference filter proposed in this work, the two MZIs played different roles.MZI 1 had a smaller FSR and was used to select the operating wavelength of the laser.MZI 2 had a larger FSR and was used to modulate the comb filter effect of MZI 1. Figure 9 illustrates the changes in the filter transmission spectra when the OPD of one of the MZIs was changed.Figure 9a shows the simulated transmission spectrum of the cascaded MZIs. Figure 9b,c depicts the situations where MZI 1 remained unchanged, but the OPD of MZI 2 was modified.As can be seen from Figure 9a-c, when MZI 1 remained unchanged, the comb-like filtering structure remained the same, but the modulated envelope resulted from MZI 2 changing with changes in the OPD of MZI 2. In the simulation, the change in the OPD from 9a to 9b was set to be 43.8 µm.The transmission peaks of the filter shifted from A1 and B1 in Figure 9a, to A2 and B2 in Figure 9b, and then to A3 and B3 in Figure 9c.This situation is consistent with what we observed in our experiment.Comparing Figure 9a-c with Figure 4, the simulation results agreed with experimental results very well.Moreover, the step size of the wavelength interval was determined by the FSR of MZI 1.In the numerical simulation, the FSR of MZI 1 was 1.5 nm, and the interval between A1 and B1, A2 and B2, and A3 and B3 were 13.5 nm, 18 nm, and 27 nm, respectively.The wavelength intervals were an integer multiple of the FSR of MZI 1.In the cascaded interference filter proposed in this work, the two MZIs played different roles.MZI 1 had a smaller FSR and was used to select the operating wavelength of the laser.MZI 2 had a larger FSR and was used to modulate the comb filter effect of MZI 1. Figure 9 illustrates the changes in the filter transmission spectra when the OPD of one of the MZIs was changed.Figure 9a shows the simulated transmission spectrum of the cascaded MZIs. Figure 9b,c depicts the situations where MZI 1 remained unchanged, but the OPD of MZI 2 was modified.As can be seen from Figure 9a-c, when MZI 1 remained unchanged, the comb-like filtering structure remained the same, but the modulated envelope resulted from MZI 2 changing with changes in the OPD of MZI 2. In the simulation, the change in the OPD from 9a to 9b was set to be 43.8 µm.The transmission peaks of the filter shifted from A1 and B1 in Figure 9a, to A2 and B2 in Figure 9b, and then to A3 and B3 in Figure 9c.This situation is consistent with what we observed in our experiment.Comparing Figure 9a-c with Figure 4, the simulation results agreed with experimental results very well.Moreover, the step size of the wavelength interval was determined by the FSR of MZI 1.In the numerical simulation, the FSR of MZI 1 was 1.5 nm, and the interval between A1 and B1, A2 and B2, and A3 and B3 were 13.5 nm, 18 nm, and 27 nm, respectively.The wavelength intervals were an integer multiple of the FSR of MZI 1. Figure 9d,e demonstrates the cases where MZI 2 remained unchanged, but the OPD in MZI 1 was varied.The change in the OPD from 9a to 9d was set to be 21.9 µm.Comparing Figure 9a with Figure 9d,e, it can be observed that the modulation envelope caused by MZI 2 remained unchanged.We specifically monitored the wavelengths marked as B1, D1, and E1, which were measured as 1550.43 nm, 1550.61nm, and 1550.77nm.In this case, the transmission peaks of the cascaded filter underwent slight displacements.In summary, in the cascaded fiber interference filter proposed in this paper, MZI 1 provided the comb filter spectrum-which limited the laser linewidth-and MZI 2 modulated the comb filter structure, which was capable of adjusting the interval of the transmitted wavelengths by varying the OPD of MZI 2.
MZI 2 remained unchanged.We specifically monitored the wavelengths marked as B1, D1, and E1, which were measured as 1550.43 nm, 1550.61nm, and 1550.77nm.In this case, the transmission peaks of the cascaded filter underwent slight displacements.In summary, in the cascaded fiber interference filter proposed in this paper, MZI 1 provided the comb filter spectrum-which limited the laser linewidth-and MZI 2 modulated the comb filter structure, which was capable of adjusting the interval of the transmitted wavelengths by varying the OPD of MZI 2. Table 1 lists the comparison of this work with reported results.In refs.[11][12][13], interval adjustable dual-wavelength fiber lasers have been reported based on MZI filters.In ref. [11], an OVDL was used to change the OPD, while in [12,13], stretching of a tapered fiber was employed to alter the OPD.All of these studies used only one MZI, which served the purpose of selecting the operating wavelength of the laser as well as adjusting the wavelength interval.It is mentioned in ref. [11] that the wavelength interval of the transmission curve of the filter could be tuned from 0.1 nm to 100 nm, but in the reported fiber laser, an interval tuning range of only 0.2 nm to 0.8 nm is presented.In ref. [12], the wavelength spacing of the comb filter could be changed from 0.2 nm to 3.0 nm.An erbiumdoped fiber laser based on parallel dual Lyot filters is demonstrated in ref. [6], and a wide tuning range of 3.03 nm to 17.15 nm was achieved.The fiber laser consisted of three PCs, two segments of PMF, and two 3 dB couplers.The excessive use of PCs and PMFs increases system complexity.In ref.
[19], an interval-adjustable multiwavelength erbiumytterbium doped fiber laser is proposed based on a micro-air cavity (MAC).By adjusting the MAC length from 0.1 nm to 2.4 nm, the wavelength interval could be continuously tuned from 8.61 nm to 0.47 nm.However, the reflectivity of the MAC was very low, resulting in a high loss in the cavity.Compared with the reported filters, the proposed filter Table 1 lists the comparison of this work with reported results.In refs.[11][12][13], interval adjustable dual-wavelength fiber lasers have been reported based on MZI filters.In ref. [11], an OVDL was used to change the OPD, while in [12,13], stretching of a tapered fiber was employed to alter the OPD.All of these studies used only one MZI, which served the purpose of selecting the operating wavelength of the laser as well as adjusting the wavelength interval.It is mentioned in ref. [11] that the wavelength interval of the transmission curve of the filter could be tuned from 0.1 nm to 100 nm, but in the reported fiber laser, an interval tuning range of only 0.2 nm to 0.8 nm is presented.In ref. [12], the wavelength spacing of the comb filter could be changed from 0.2 nm to 3.0 nm.An erbium-doped fiber laser based on parallel dual Lyot filters is demonstrated in ref. [6], and a wide tuning range of 3.03 nm to 17.15 nm was achieved.The fiber laser consisted of three PCs, two segments of PMF, and two 3 dB couplers.The excessive use of PCs and PMFs increases system complexity.In ref.
[19], an interval-adjustable multiwavelength erbium-ytterbium doped fiber laser is proposed based on a micro-air cavity (MAC).By adjusting the MAC length from 0.1 nm to 2.4 nm, the wavelength interval could be continuously tuned from 8.61 nm to 0.47 nm.However, the reflectivity of the MAC was very low, resulting in a high loss in the cavity.Compared with the reported filters, the proposed filter in this paper offers convenient adjustment and a larger range of wavelength interval variation.

Conclusions
In conclusion, a cascaded filter composed of two MZIs is proposed and a dualwavelength EDFL with adjustable wavelength intervals is demonstrated in this paper.The FSR of the proposed MZI 1 was fixed, and the modulated envelop of the transmission spectrum of the filter was adjustable by stretching one arm of the MZI 2, inducing changes in the interval of the output dual-wavelength laser.When the stretching amount of one arm of the MZI 2 was increased from 0 to 0.25 mm, the dual-wavelength interval of the laser could be adjusted from 4.64 nm to 13.94 nm.The stability of the dual-wavelength laser was measured.When the MZI 2 arms were unstretched, the power fluctuation was less than 0.25 dB, and the wavelength variation range was less than 0.07 nm.When the stretching amount of one arm of the MZI 2 was 0.05 mm, the power fluctuation was less than 1.3 dB, and the range of wavelength variation was less than 0.23 nm.The proposed interval adjustable dual-wavelength EDFL has the advantages of a simple structure, good stability, and a wide tuning range, which make it highly promising for various fields.

Figure 1 .
Figure 1.Schematic diagram of a cascaded filter.

Figure 1 .
Figure 1.Schematic diagram of a cascaded filter.

Figure 3 .
Figure 3. Output power of single mode fiber as a function of stretching amount.

Figure 3 .
Figure 3. Output power of single mode fiber as a function of stretching amount.

Figure 3 .
Figure 3. Output power of single mode fiber as a function of stretching amount.

Figure 4 .
Figure 4. Transmission spectra of the cascaded filter when the stretching amounts were (a) 0.00 mm, (b) 0.22 mm, and (c) 0.30 mm.

Figure 4 .
Figure 4. Transmission spectra of the cascaded filter when the stretching amounts were (a) 0.00 mm, (b) 0.22 mm, and (c) 0.30 mm.

Figure 5 .
Figure 5. (a) Schematic diagram of the interval adjustable dual-wavelength EDFL.(b) The gain spectrum of the Er−doped fiber.

Figure 5 .
Figure 5. (a) Schematic diagram of the interval adjustable dual-wavelength EDFL.(b) The gain spectrum of the Er−doped fiber.

Figure 6 .
Figure 6.(a) The changes in the spectra with increases in pump power.(b) Output spectrum of the dual-wavelength fiber laser.(c) Output spectrum of another dual-wavelength state.

Figure 6 .
Figure 6.(a) The changes in the spectra with increases in pump power.(b) Output spectrum of the dual-wavelength fiber laser.(c) Output spectrum of another dual-wavelength state.

Figure 7 .
Figure 7. Output spectra of the dual-wavelength fiber laser with different intervals.

Figure 7 .
Figure 7. Output spectra of the dual-wavelength fiber laser with different intervals.

Figure 8 .
Figure 8.Output spectra scanned repeatedly within one hour when the stretching amount was (a) 0 mm, (c) 0.05 mm, and (e) 0.25 mm.Variations in central wavelength and output power within one hour when the stretching amount was (b) 0 mm, (d) 0.05 mm, and (f) 0.25 mm.
Figure 9d,e demonstrates the cases where MZI 2 remained unchanged, but the OPD in MZI 1 was varied.The change in the OPD from 9a to 9d was set to be 21.9 µm.Comparing

Figure 8 .
Figure 8.Output spectra scanned repeatedly within one hour when the stretching amount was (a) 0 mm, (c) 0.05 mm, and (e) 0.25 mm.Variations in central wavelength and output power within one hour when the stretching amount was (b) 0 mm, (d) 0.05 mm, and (f) 0.25 mm.

Figure 9 .
Figure 9. Simulation results of the changes in the filter transmission spectra when the OPD of MZI 2 (a-c) and MZI 1 (a,d,e) were changed.

Figure 9 .
Figure 9. Simulation results of the changes in the filter transmission spectra when the OPD of MZI 2 (a-c) and MZI 1 (a,d,e) were changed.

Table 1 .
Comparison of this work with literature data.