Effective refractive indices at λ = 1550 nm.
Abstract
Tunable fibre lasers draw intensive attention because their emission wavelength can be systematically tuned within a certain spectral range, which allows using a single laser source instead of several sources. This is convenient and cost-effective for many applications in a range of fields, such as telecom, material processing, microscopy, medicine and imaging and so on. The laser wavelength can be tuned in a certain range of wavelength by inserting wavelength-selective elements into the laser’s optical cavity. This chapter describes the twin core fibre (TCF)-based filters, which work as the wavelength-selective element. They are introduced into the ring cavity to implement tunable single-, dual- and multi-wavelength fibre lasers. First, we deduced the coupled-mode theory of TCF-based filter. Second, we experimentally and numerically characterized the optical properties of TCF-based filters including free spectral range, polarization dependence, strain effect and bending effect. Finally, we investigated three tunable fibre lasers which operate at single-, dual- and multi-wavelengths, respectively. The operation mechanism of the fibre lasers mainly involved the elastic-optic effect, polarization hole burning effect and non-linear optical loop mirror. We emphasized the tuning mechanism and the tuning characteristics of the tunable fibre lasers.
Keywords
- Tunable fibre laser
- Twin core fibre
- Elastic-optic effect
- Polarization hole burning effect
- Non-linear optical loop mirror
1. Introduction
Tunable fibre lasers draw serious attention because their emission wavelength can be systematically tuned within a certain spectral range, which allows using a single laser source instead of several sources. This is convenient and cost-effective for many applications in a range of fields, such as telecom, material processing, microscopy, medicine and imaging and so on. Especially in a wavelength division multiplexing system, the tunable laser is recognized as a backup light source for fixed wavelength laser replacement, with the motivating factors being cost savings and potentially higher system reliability.
Tuning the laser wavelength across a certain wavelength range can be achieved by placing wavelength-selective elements into the laser’s optical cavity to provide a particular wavelength selection. Free space filters based on opto-VLSI processor [1] or two-dimensional (2D) dispersion arrangements [2] have been used as wavelength-selective elements for realizing tunable fibre lasers. These filters can provide relatively small tuning steps. However, these devices often suffer from high insertion loss which results in a low side-mode suppression ratio (SMSR). By contrast, in-line fibre filters have been widely used in the laser cavity due to the advantages of low insertion loss, compactness and integration in all fibre laser systems. Conventional Fibre Bragg gratings (FBGs) in single-mode fibres have been used for realizing tunable single-wavelength fibre lasers by highly stretching or bending the FBGs in the laser cavity [3, 4]. Various special fibre-grating structures have been designed to implement dual-wavelength fibre lasers, including a pair of identical FBGs [5], polarization maintained FBGs [6], multimode FBGs [7] and phase-shifted FBGs [8]. Besides the FBGs, a series of modal interferometers draws more attention on tunable single-wavelength fibre lasers due to their easy fabrication and low cost. These modal interferometers can be constructed by using fibre tips [9], two tapers [10, 11], and multimode fibres [12, 13]. High-birefringence Sagnac loop mirrors (HiBi-SLMs) [14, 15] and Lyot birefringence filters [16] were also employed to provide C- and L-band tunable fibre lasers. The modal interferometers and HiBi-SLMs usually lead to polarization hole burning effect which can weaken the homogeneous gain broadening of the erbium-doped fibre (EDF) and help to understand multi-wavelength fibre lasers. Generally, these lasers were switched to operate in dual-/three-wavelength oscillation by adjusting the polarization controllers (PCs). More effective mode suppression techniques have been exploited to obtain more wavelength emissions at room temperature, including phase modulation [17], four-wave mixing [18], Raman scattering [19], Brillouin scattering [20, 21] and a non-linear optical loop mirror (NOLM) [22, 23].
In this chapter, twin core fibre (TCF)-based filters acting as the wavelength-selective element are proposed to achieve tunable single-, dual- and multi-wavelength erbium-doped fibre lasers. This chapter is structured as follows: in Section 1, we will give an overview of the recent development in tunable fibre lasers; in Section 2, we will give the coupled-mode theory of TCF-based filter; in Section 3, we will characterize the optical properties of TCF-based filter, both experimentally and numerically; in Section 4, we will introduce three tunable fibre lasers which operate at single-, dual- and multi-wavelengths, respectively and the conclusion will be given in the fifth section.
2. Coupled-mode theory
The TCF used in our experiments was fabricated by means of the groove-stack-and-draw method. The TCF preform was first prepared by side grooving in a large-diameter pure silica rod; then the rectangular groove was filled with two small-diameter Ge-doped silica rods and some other small-diameter pure silica rods; finally the rods were fixed in a pure silica jacket tube. Figure 1(a), (b) and (c) illustrates the original preform, micrograph image of the TCF cross section and the magnified micrograph image of the core region, respectively. The diameters of the core and cladding are approximately 6.4 µm and 130 µm, respectively. The separation between the two core axes is 14.2 µm. The difference of the refractive index between the core and cladding is
In TCF, light couples back and forth between the two cores. Assuming that light launches into core 1, output amplitude of core 1 can be characterized by using the mode-coupled theory with symmetric and anti-symmetric mode [25]:
where
For a normalized incident light with a given state of polarization (SOP), the electric field can be given as 2D-column vector:
where
Therefore, the output field
Substituting Eq. (1) into Eq. (5), the output power in core 1 can be expressed as [26]
If two cores have identical refractive index and diameter, the two cores have the same propagation constants which result in
Here, the coupling coefficient
where
3. Characterization of TCF-based filter
The TCF-based filter is formed by splicing a section of TCF between two segments of SMFs as shown in Figure 2(a). The splicing between the TCF and the SMF is carried out by using an Ericsson fusion splicer (FSU 975) in manual operation mode. We used an active monitoring mode to make the SMF align to one core of the TCF. One end of the SMF was connected to a broadband light source, and one end of the TCF was connected to a power meter through a bare fibre adapter. The other ends of the SMF and TCF were placed in fibre holders of the splicer. We manually adjusted the position of the SMF and TCF by driving the motors in the splicer. When the output power reached the maximum value, we concluded that the SMF was aligned to one core of TCF. Then, we adopted a low-power arc to splice the SMF and TCF. Figure 2(b) shows the micrograph image of the splicing joint between TCF and SMF, which indicates that one core of TCF is precisely aligned to the core of SMF.
Theoretically, we used the finite element method to evaluate the optical properties of TCF. The TCF structure used for numerical calculation is the rebuilt geometry as shown in Figure 1(d). The refractive index of the cladding,
In the following Sections 3.1–3.4, we will investigate four optical properties of TCF-based filters, including free spectra range (FSR), polarization dependence, strain effect and bending effect. All the optical properties are closely related to the tunable fibre lasers discussed in Section 4. In short, the free spectra range mainly determines the tuning range of the fibre laser. The polarization dependence ensures stable dual-wavelength oscillations. The strain effect and bending effect help exactly reflect the tuning mechanism of the fibre lasers.
3.1. Free spectra range
In the TCF-based filter, the light from the SMF is launched into one core of the TCF at the first splicing point. Then, light couples back and forth between the two cores along the TCF. At the second splicing point, a comb-like spectrum was expected according to the coupled-mode theory in Section 2. The transmission dips and peaks occur when the following phase condition is satisfied:
where
which indicates that the FSR is inversely proportional to both the length of TCF and the derivative of the coupling coefficient with respect to wavelength.
We fabricated seven TCF-based filters with different length
On the other hand, we calculated the coupling coefficient
3.2. Polarization dependence
To theoretically evaluate the polarization dependence of the TCF, we numerically calculated the ERIs of
In the experiment, we used a polarizer to obtain the linear polarized light from a broadband light source. A polarization controller was used to induce only rotation of this light. Figure 4(b) illustrates the evolution of transmission spectra of the TCF-based filter when the PCF was adjusted. It can be found that the maximum wavelength shift of the transmission peak is 1.2 nm, which is defined as the wavelength spacing between transmission peaks with
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1.444855015932922 1.444608454872977 1.444705605736814 1.444787015740477 |
1.444856531392316 1.444609352306018 1.444705931113986 1.444789030825202 |
3.3. Strain effect
As TCF-based filter is applied to axial strain, the refractive index of both core and cladding will decrease according to the photo-elastics [29]:
where
On the other hand, it is worth noting that the coupling coefficients also depend on the wavelength. As the wavelength is increased, the evanescent fields extend further away from the fibre core, the mode overlap increases and as well as the coupling coefficient. As discussed, when the TCF-based filter is stretched, the coupling coefficients would increase because of the elastic–optic effect. In order to keep the phase condition of the transmission peak unchanged in Eq. (10), the wavelength should shift to the short wavelength direction to give an opposite variation of coupling coefficient. Therefore, it is expected to find a ’blue’ shift of the transmission peak when the TCF-based filter is stretched.
To investigate the strain effect experimentally, the TCF-based filter with a TCF length of
3.4. Bending effect
Figure 6(a) shows that the TCF is bent with a curvature radius of
When the bending is applied to TCF, the part on outside of the bend (positive
where
When the TCF is straight, the two cores have identical refractive index, which results in the same propagation constant
According to Eq. (10), the phase condition of transmission dips is determined by both
Experimentally, we chose the TCF based-filter with a TCF length of
Initially, four resonance dips were found at 1461.82, 1510.38, 1558.58 and 1607.90 nm when the TCF-based filter was straight. Figure 7(a) illustrates the evolution of the transmission spectra of the TCF-based filter when its curvature was increased from 0 to 9.3 m−1 gradually. It can be found that the spectra shifted towards the shorter wavelength direction, which agrees with the theoretical prospect discussed earlier. Generally, if the curvature is large enough, the resonance dip would shift to the initial position of the adjacent dip, which makes it hard to distinguish the wavelength shift. Therefore, the FSR of the filter generally determines the maximum wavelength shift that can distinguished.
Figure 7(b) illustrates the wavelength shift of the four transmission dips; the curvature was increased from 0 to 9.3 m−1 gradually. The discrete experimental data can be fitted by a second-order polynomial with an
4. Tunable fibre lasers
The tunable fibre lasers were constructed by using a ring laser cavity as shown in Figure 8(a). A 980-nm diode laser is injected into the laser cavity through a wavelength division multiplexor (WDM) to pump the erbium-doped fibre. A polarization-dependent isolator (PDI) is used to ensure that the laser oscillates in a single direction around the ring. The polarization controller is used to adjust the SOP of the light. The laser output is monitored by the optical spectrum analyser (OSA, YOKOGAWA, AQ6370C) from the 5% port of a 95:5 fibre coupler. In the following three subsections, we will investigate three in-line filters to implement the tunable single-, dual- and multi-wavelength fibre lasers.
4.1. Dual-wavelength and single-polarized fibre laser
In this work, we proposed and experimentally demonstrated a tunable dual-wavelength and single-polarized fibre laser by use of a TCF-based filter [26]. Figure 8(b) illustrates the TCF-based filter with a TCF length,
In the dual-wavelength fibre laser, the TCF-based filter simultaneously works as the wavelength selector and the polarization-dependent element. The TCF-based filter gives rise to a comb transmission spectrum. The SOP of the wavelengths is adjusted by using the PC, and the wavelengths with particular SOPs could become transmission peaks according to Figure 4. The polarization dependence of the TCF is helpful for inducing the PHB effect and in turn simultaneously amplifying the particular transmission peaks and achieving stable dual-wavelength oscillation.
At first, a single wavelength was obtained at
For fixed wavelength spacing, the simultaneous tuning characteristic of the dual-wavelength laser was investigated by stretching the TCF-based filter. As discussed in Section 3.3, the transmission spectrum of the TCF-based filter exhibited a ’blue shift’ when it was stretched. In contrast, the value of wavelength spacing remained unchanged because the birefringence of the TCF hardly changed. Therefore, we found that the two lasing wavelengths can be simultaneously tuned towards the shorter wavelength with fixed wavelength spacing. Dual-wavelength lasing with wavelength spacing of 0.4, 0.8 and 1.2 nm was linearly tuned over 1.7, 1.0 and 0.8 nm, respectively. Here, we give only the measured results of dual-wavelength lasing with wavelength spacing of 0.4 nm as shown in Figure 9(b). When the TCF was stretched by an increment length of
To study the SOPs of the dual-wavelength output, the laser output was connected to a polarization beam splitter (PBS) through a PC. The
4.2. Tunable single-wavelength fibre laser
In this work, we proposed and experimentally demonstrated a C-band tunable single-wavelength fibre laser by cascading two TCF-based filters [33]. Figure 8(c) illustrates the cascaded TCF-based filters with TCF lengths of 0.14 and 1.37 m. In this section, we discussed the tuning mechanism by characterizing the two TCF-based filters and investigated the tunable characteristics of the proposed tunable single-wavelength fibre laser by bending one TCF-based filter and stretching the other one.
4.2.1. Tunable mechanism
Figure 11 illustrates the tuning equipment of the cascading TCF-based filters, which consists of three transmission stages. Filter 1 was fixed by the left and middle stages with an initial distance of
We coarsely tuned the cascaded spectrum by bending TCF-based filter 1 and finely tuned the spectrum by stretching the TCF-based filter 2. Filter 1 is bent by moving the left stage towards the middle one. The moving distance of the left stage (
In order to realize a fine wavelength tuning, TCF-based filter 2 is stretched by moving the right stage away from the middle one. The moving distance of the right stage (
4.2.2. Characterization of tunable laser
The fibre laser was coarsely tuned by bending TCF-based filter 1 and finely tuned by stretching the TCF-based filter. Figure 13(a) illustrates the evolution of lasing spectra when we bent filter 1. It can be found that bending filter 1 makes the envelope shift towards shorter wavelengths and selects the transmission peak of filter 2 for lasing in a series of steps with a separation of 2.9 nm. Figure 13(b) illustrates the evolution of lasing spectra when we stretched filter 2. It was found that the lasing wavelength finely changed with a step of 0.22 nm. Figure 13(c) illustrates the whole tuning process. First, we obtained the initial single-wavelength lasing at 1565.00 nm. Second, we stretched filter 2 from
When we characterized the laser properties, we increased the pump power from 10 to 500 mW. The cavity loss was around 7 dB including the splicing loss (~4 dB) between the SMF and the TCF and the insertion loss of other optical devices. Such cavity loss gives rise to a threshold pump power of 20 mW. When the pump power was 500 mW, the lasing output saturated at 2.27 dB. Hence, we measured all 105 laser spectra at a pump power of 500 mW. For good visibility, only half of the lasing spectra are plotted in Figure 14. The SMSRs are 53 –58 dB, and the linewidth is ~0.05 nm. The intensity variation over the entire tuning range was less than ±0.1 dB.
4.3. Tunable multi-wavelength fibre laser
In this work, we proposed and experimentally demonstrated a tunable multi-wavelength fibre laser based on a non-linear optical loop mirror by using a compound filter [34]. Figure 8(d) illustrates the NOLM and the compound filter. The compound filter was formed by cascading a standard Mach–Zehnder interferometer (MZI) and a TCF-based filter. In this section, we first discussed the function of the NOLM as an amplitude equalizer. Second, we discussed the tuning mechanism by characterizing the transmission spectra of the standard MZI, the TCF-based filter and the compound filter. Third, we investigated the tunable characteristics of the proposed tunable multi-wavelength fibre laser by bending the TCF. Finally, we discussed the influence of the length of the TCF on the laser characteristic.
4.3.1. Non-linear optical loop mirror
An NOLM is formed by splicing together the output ports of a 70:30 coupler. A 2-km SMF is inserted inside the loop. The transmission of the NOLM is given as [23]:
where
According to Eq. (14), the transmission of NOLM is a cosine function of the total phase difference and varies with a change in
4.3.2. Tuning mechanism
The standard MZI is established by connecting two 50:50 filters between which the fibre path difference of two arms is
The compound filter was tuned by bending the TCF. The TCF-based filter was fixed by two fibre holders adhered onto two stages with an initial distance of 25 cm. The filter was bent by moving the right stage towards the left one. To quantify the bending of the filter, we recorded the displacement of the moving stage; the initial position of the moving stage is defined as the zero point
The principle of the proposed tunable multi-wavelength fibre laser can be expressed as follows. The ASE spectrum of the EDF is reshaped to a comb-like transmission spectrum by the standard MZI. The intensities of the transmission peaks are modified by the TCF-based filter. Because lasing is established once the cavity loss is smaller than the EDF gain, only the peaks with high transmissivity (low loss) can oscillate. The transmission peak of TCF-based filter has the lowest insertion loss; hence, only the near region of the transmission peak would be selected for lasing simultaneously, as shown in the blue region of Figure 15(b). The wavelength range of the blue region is determined by the balance between the EDF gain profile and the profile of the total cavity loss. The NOLM can work as an amplitude equalizer to enable the multiple transmission peaks to emit as lasing wavelengths. When the TCF is bent, the transmission band of the TCF-based filter shifts towards the short-wavelength direction to cover the different channels provided by the standard MZI. Thus, the corresponding multiple lasing lines shift towards the short-wavelength direction. As a result, a tunable multi-wavelength fibre laser is realized by bending the TCF.
4.3.3. Laser tunable characterization
To study the tuning characteristic, the moving stage was adjusted with a step of 0.05 mm. Figure 16(a) illustrates that the lasing wavebands can be continuously tuned to cover a range of 24 nm from 1542 to 1566 nm. The lasing spectra were measured when the TCF was bent with
When
In order to find out the relationship between the transmission spectrum of the TCF-based filter and multi-wavelength lasing spectrum, we plotted both the transmission peak of the TCF-based filter (blue pentagram symbols) and the centre of the lasing waveband (red circle symbols) as a function of
4.3.4. Influence of the TCF length on the tuning characteristic
In order to investigate the influence of the TCF length on the tuning characteristic, we fabricated two more filters with a TCF length of
We carried out a reverse experiment by using a large length of TCF with
5. Conclusion
In this chapter, we studied tunable single-, dual- and multi-wavelength fibre lasers by using TCF-based filters. First, we presented the coupled-mode theory of the TCF with symmetric and anti-symmetric mode and deduced the output of the TCF-based filter on the basis of the SOP of input light. Second, we experimentally and numerically characterized the optical properties of TCF-based filter including the free spectral range, polarization dependence, strain effect and bending effect. These optical properties are closely related to the tuning mechanism and tuning characteristics of the tunable fibre lasers. Third, we implemented three tunable fibre lasers which operate at single-, dual- and multi-wavelengths, respectively. In the case of a tunable single wavelength, the wavelength can be linearly tuned over 23.2 nm (from 1541.8 to 1564.0 nm), with a uniform step of ~0.22 nm. The total number of tunable wavelength is up to 105. In the case of a tunable dual-wavelength fibre laser, the single-polarized two wavelengths can be linearly tuned by stretching the TCF. The spacing of the two wavelengths can be tuned from 0.1 to 1.2 nm by adjusting the PC located before the TCF-based filter. In the case of a tunable multi-wavelength fibre laser, 19 wavelengths were tuned over 24 nm from 1542 to 1566 nm. After discussing the influence of the TCF length on the tunable multi-wavelength fibre laser, it is concluded that there is balance between the tuning range and the wavelength amount when we choose the length of the TCF.
Acknowledgments
This work was supported by National Natural Science Foundation of China (grant no. 61405128) and China Postdoctoral Science Foundation funded project (grant nos. 2014M552227 and 2015T80913).
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