In principle, a wavelength shift in a FBG may be due to the changes in temperature, strain, pressure and/or other parameters. The shift in Bragg wavelength with strain and temperature can be expressed as [14]

where ε is the applied strain, Λ is the period of fiber, P_i,j are the Pockel’s (piezo) coefficients of the stress-optic tensor, and ν is the Poisson’s ratio. Note that n is the effective refractive index of the fiber core as defined in Equation (1), α is the thermal expansion coefficient of the silica fiber with a typical value of 0.015 nm/ºC, and ΔΤ is the temperature change in degree Celsius. The term (n²/2) [P₁₂－ν(P₁₁－P₁₂)] has a numerical value of 0.22. The strain can be measured under a constant temperature according to the following equation:

where λ_B is the Bragg wavelength, and this value gives a “rule-of-thumb” measurement of wavelength shift for a FBG with strain of 1 nm per 1000 με at 1.31 μm. To design a strain tunable FBG, firstly, it is embedded in a strip of composite thermal plastic material and then is attached to L-shaped holders at both ends. The FBG is then mounted on a precision translational stage with a high-resolution micrometer. By strained or compressed tuning of the precise screw of the micrometer, we can apply both directions in the transverse displacement for increasing the tuning range up to ±8 nm. Two steel rods are attached to the sides of the FBG composite strip to confine the applied strain or stress to the longitudinal direction only. The micrometer has a resolution of 0.5 mm /turn and a full range of 5.0 mm in translational distance, therefore up to ten turns can be applied to tune the FBG reflection wavelength.

The lasing wavelength as a function of turns of screw is shown in Figure 1(a), with a linear slope of 4.82 nm/ mm translational distance. Thus, Δλ_B＝0.00482 nm/μm × d, where d is the displacement of the translational stage in unit of micrometers. Another way is to embed the FBG in the outer laminar. The composite with the TFBG embedded within is attached to a 3-point tuning device by using instant adhesive glue. By tuning the precision screw of the 3-point bending device either by straining or compressing, we can apply transverse displacement in either direction to easily attain a tunable range of ±10 nm. This eliminates any use of complicated or bulky components to perform the tuning function.

Figure 1(b) shows the superimposed tuning spectra of two homemade tunable FBGs. The demonstrated tuning range of each FBG is approximately 15 nm with reflectance of 99.9%. Before tuning, FBG1 has a central reflection wavelength of 1540.5 nm while that of FBG2 is

1552.7 nm. Fine tune resolution as precise as 0.2 nm FBG can be realized.

The S-band tunable erbium-doped fiber lasers were achieved by connecting the active fiber to the thermooptic tunable SWPFs. The mechanism of the proposed SWPFs [12,13] is to interact with the guiding optical fields to cause fundamental mode loss at long-wavelength, and the cutoff wavelength can be tuned when the heating temperature applying on the filter changes. The dispersion engineering methods had been employed by controlling the propagation losses of lights at different wavelengths. Both the side-polishing and the fused-tapering techniques were adopted in our previous works [12,13]. When the SWPFs are temperature-tuned to attenuate the wavelengths longer than 1530 nm, the C + L band ASE is suppressed and the S-band gain is obtained. The commonly used S-band erbium-doped optical fiber amplifiers (EDFAs) employ erbium-doped fiber (EDF) with depressed inner cladding to achieve fundamental-mode cutoff at the longer wavelengths [15,16]. The cutoff wavelength and the mode field diameter can be adjusted through bending and local heating, but the fabrication, insertion loss, crosstalk and cost of the filters using dispersive fibers show great difficulties for practical use. Thus, an alternative way to obtain SWPFs is to interact with the light through the evanescent field that is spread out of the waveguide with wavelength-dependent properties. When the optical fiber is side-polished or tapered, the mode field is expanded out of the fiber cladding. Using dispersive liquids surrounding the side-polished fiber/taper fiber, the device can be a SWPF if the dispersion relations are properly designed. The tunable SWPF was achieved by tuning the temperature of the dispersive liquids to change the dispersive curves for obtaining different cutoff wavelengths [17,18].

In Figure 2(a), the blue and red curves are the dispersion curves of the Ge-doped core and the fused silica of SMF-28, and the black curve is the dispersion for Cargille index-matching liquids. The refractive index dispersion of the core and cladding intersect at a fundamental mode cutoff wavelength which divides the wavelengths into bound and refracting leaky modes, and the lights with wavelength longer than the cutoff wavelength can be highly attenuated due to the frustrated total internal reflection. In our measurement, a broadband white light source was launched into the fabricated SWPF, where the optical liquid surrounding the SWPF was heated by a thermoelectric cooler (TEC) to stabilize the temperature. Figure 2(b) depicts the experimental and simulated transmission spectra of a SWPF over the tuning temperature of 25ºC−27ºC, where the simulation results were performed by beam propagation method. The

experimental results agree well with the simulation ones. The results include tuning efficiency of 50 nm/°C, cut- off efficiency of −1.2 dB/nm, and rejection efficiency of 55 dB. Based on these experimental and simulated results, the mechanism of the SWPF is proved to be qualified for developing wavelength tunable S-band erbium- doped fiber lasers.

The proposed configuration of linear cavity for the tunable laser is shown in Figure 3. The linear cavity consists of a 3-port OC, two TFBGs, a segment of high-

concentration EDF, a 1480/1550 nm WDM coupler, and one 1480 nm pumping source. The 3-port OC here acts as a wavelength router by connecting port 3 with port 1. In this way, the residual pumping power travels back to the EDF for twice amplification to increase its pumping efficiency up to 2 dB difference in laser output power. A piece of EDF is inserted into the cavity to act as pump absorber. At the right hand side of this cavity, there is one 1 × 2 optical switch (OSW) and two TFBGs (i.e., TFBG1, TFBG2) connected to the two switched ports of OSW. The tuning range could cover the whole C-band by switching between the two OSW ports connected to individual TFBG. The original reflected wavelengths of TFBGs are 1540.5 and 1552.68 nm, respectively. Two variable optical attenuators (VOAs) are used in each port for the power equalization.

Figure 4(a) shows signal power versus 1480 nm pump power for various lengths of EDF. With the selected lasing signal at 1550 nm, the signal power is linearly proportional to the pumping power. The pumping efficiency increases from 3.7% to 40% as EDF length increases from 0.8 m to 5 m . Although the longer EDF length seems to have better conversion efficiency and to generate higher laser power, it also generates more ASE noise which results in lower signal-to-noise-ratio (SNR). As the EDF length increases, the extra gain provided by the pumping power is smaller than the loss attributed by the EDF. For this linear-cavity fiber laser, the parameters for achieving optimum performance are 1.9 m in length for EDF and 50% reflectance for the TFBGs.

Figure 4(b) shows the superimposed output spectra of the fiber laser. It is randomly tuned across the C-band with power equalization function. The power equalization can be realized by using VOAs independently. The power uniformity within ±0.1 dB over the tuning range has been achieved. No polarization mode competition effect is observed partially due to the narrow linewidth of TFBGs. The switching time for OSW is 10 ms in this case, which depends mainly on the specification of the mechanical OSW.

The proposed BFM-based liner-cavity tunable fiber laser in a backward pump scheme is shown schematically in Figure 5. The laser cavity consists of a BFM, a tunable FBG, and a piece of EDF. The BFM here acts as a broadband wavelength reflector integrated with a TFBG to form a laser cavity. It will lase as long as the reflected wavelength of TFBG is within the reflective range of the BFM. Also, a piece of EDF is inserted into the cavity to act as pump absorber.

Figure 6(a) shows the measured experimental results for the EDF length versus the output power at 1544.8 nm when Figure 5 has a constant pump power of 150 mW. We find that as the EDF length is increased from 0 to 4 m , the output lasing power is increased accordingly. If the EDF is longer than required, there is a region of the EDF where the pump power is relatively small, the signal has reached saturation intensity, and the gain is decreased according. The curves for various lengths of EDF with threshold power of 8 mW are shown in Figure

6(b). The transfer efficiency versus pump power for different lengths of EDF is shown in Figure 7(a). We find that the transfer efficiency is increased as the EDF length increases in the beginning. Then it reaches a constant value of 21.5% as the pump power is larger than 70 mW.

The transfer efficiency here is defined as

where η is the laser transfer efficiency, P_pⁱⁿ is the input pump power, and P_p^th is the threshold power. Figure 7(b) shows the superimposed output spectra of the tunable fiber laser using two TFBGs with original wavelength of 1539.13 and 1553.0 nm, respectively. High side mode suppression ratio (SMSR) of around 57 dB was obtained for the entire C-band.

In this section, a continuously tunable erbium-doped fiber laser is demonstrated by incorporating a tunable SWPF into ring resonator. The wideband tunable SWPF is based on dispersive evanescent tunneling from a side- polished single-mode fiber and a dispersive optical polymer overlay structure. In fabrication, a portion of the fiber jacket was stripped off and the section was then embedded and glued into the curved V-groove on a silicon substrate, as shown in Figure 8. The central cladding thickness after polishing was around 2.7 μm. Finally, the characteristics of the well-polished fibers were calibrated by liquid-drop experiments. The effective interaction length was estimated to be 11 mm at 1550 nm waveleng- th for side-polished SMF-28. In Figure 8, the tunable SWPF is incorporated into the resonant cavity to provide a wideband tunable transmission loss window. The dispersive optical polymer overlaying the side-polished fiber is OCK-433 (Nye Lubricants) with the thermo-optic coefficient dn_D/dT of −3.6 × 10⁻⁴/°C and is heated by a dual TEC. The refractive index of the OCK-433 decreases with increasing temperature. The tuning effici- ency is 7.65 nm/°C and the signal-to-ASE ratio is around 40 dB. The EDF used here has absorption coefficient of 12 and 30 dB/m for 1480 and 1530 nm wavelength, respectively, and is pumped by a 1480 nm pump laser diode (LD) in 250 mW launched power.

To investigate the influences of the sharpness of the spectral cutoff curve, the Cargille liquids were applied on SWPF. The spectral responses of the fiber laser are shown in Figure 9(a). When the refractive indices of 1.456 (n_D) and 1.458 (n_D) were used, the lasing wavelength moved to shorter wavelengths and the peak power decreased following the gain profile. Subsequently, the Cargille liquids were replaced by OCK-433 and the spe- ctral responses are shown in Figure 9(b). When the temperature cooled down, the lasing wavelengths were moved toward shorter wavelengths again. As the temperature was tuned to 39.6 ° C, the lasing wavelength was at 1569.8 nm. Thus, the tuning range of the fiber laser is 26 nm with temperature variation of 3.4 ° C, and typical signal-ASE-ratio is above 40 dB and the average FWHM is around 0.5 nm.

In this subsection, wideband tunable high cutoff-effici- ency SWPFs were discretely located in standard silica- based C-band EDF to filter out the C + L band ASE so that the optical gain for S-band could be acquired to realize fiber laser. To investigate the amplification characteristics in the S-band, a 980-nm pump laser with 135- mW output power was launched into EDF in a forward pumping scheme. The high-cutoff-efficiency short-pass filters in the 17.5-m-long EDF could discretely suppress the unwanted C + L band ASE and pass the S-band signal

and 980-nm pump light. Subsequently, an input power of −25 dBm was launched into the EDF from distributed feedback laser signals in the S-band. The input signal spectra and amplified output signal spectra in the S-band at 28.6°C are shown in Figure 10(a). In the S-band the net signal gain at 1486.9 nm was measured to be 18.92 dB.

The experimental set-up of the tunable EDF ring laser is shown in Figure 11, where the tunable fused-tapered SWPF with the use of Cargille index liquid (n_D = 1.456) can provide a sharp filter skirt and a deep stop band rejection efficiency (> 50 dB). However, a single local SWPF is inefficient for the standard EDF to be operated at the shorter wavelengths (S-band) of the gain bandwidth. Consequently, we employ four-stage in-line tunable fused-tapered fiber SWPFs discretely located in the standard silica-based EDF to achieve the tunable S-band fiber laser. When the SWPF is turned on, the C + L-band ASE is suppressed to obtain the gain for S-band lasing. The four filters are discretely located in a 16-m-long stan-

dard silica-based C-band EDF to substantially suppress the ASE at the wavelengths longer than the lasing wavelength which can be tuned by varying the applied temperature on SWPFs. When a 980-nm laser with pump power of 208 mW launches into the EDF, the laser spectra at different temperatures are shown in Figure 10(b). When the applied temperature slightly decreases, the lasing wavelength moves to shorter wavelength. The average η for the tunable laser is measured to be as high as 57.3 nm/°C from 1545.2 to 1451.9 nm ascribing to the wideband tunable high-cutoff-efficiency SWPFs. The average FWHM is 0.53 nm and the signal-to-ASE ratio is above 40 dB.

A versatile and cost-effective laser source should have the ability to allow the user to choose which wavelength is needed or the desired scanning range. The wavelength tunable FBG-based lasers we presented here can satisfy such requirement. It is well known that the cavity of a fiber laser may be designed based on a pair of FBGs that work as its end mirrors and determine the resonant wavelength. When one of the resonant wavelengths of the FBGs is changed slightly by tension or heating, the reflection power by the FBG pair at a new laser wavelength will decrease due to wavelength misalignment between them, thus it is difficult to fine-tune the FBG pair back to the same wavelength. Nevertheless, either the OC-based or BFM-based laser configuration could overcome such a problem because one FBG only is used to tune the lasing wavelength. Other advantages of FBG- based tunable fiber lasers are: 1) Narrow laser linewidth and near polarization-independent; 2) both the OC- based and BFM-based tunable fiber lasers improve the pumping efficiency by recycling the residual pump power back to the gain medium using backward pumping; 3) the TFBG could be used to tune the desired wavelength precisely and quickly; 4) the proposed FBG-based tunable fiber lasers may use one OSW pair and a plurality of tunable FBGs to expand the output wavelength range; 5) they are simpler and potentially less expensive than other commercial products; and 6) the sizes are compact and the weights are light.

It is advantageous to explore a widely tuning fiber laser with lasing wavelength down to S-band at a high tuning speed. Conventionally, the silica-based EDF at room temperature can only emit fluorescence at wavelengths longer than 1490 nm. Thus, achieving high-performance S-band lasers critically depends on the SWPFs. The side- polished SWPFs were adopted because they are mecha- nically strong, and the polishing depth and interaction length can be precisely determined. From a different point of view, SWPFs using the fused-tapering technique are easy, fast, and cost-effective fabrication processes. An optimized side-polishing/tapered fiber filter structure can attain high-cutoff efficiency and wide tuning range. Based on the proposed SWPFs, widely tunable, single- frequency rare-earth-doped fiber lasers can be achieved. Besides, the SWPF-based tunable fiber lasers have other advantages such as: 1) wide tuning range covering the S- and C-bands, 2) high power and low noise, 3) simplicity and cost-effectiveness, and 4) high index sensitivity up to 1 ´ 10⁻⁵ with high Q resonator.

To design a single-frequency tunable fiber laser, various kinds of methods such as multiple ring cavities, FBGs, microrings, spatial hole burning in unpumped EDF, and nonlinear loop mirror were proposed. Also, a short cavity length is usually required to enlarge the mode spacing. For the linear-cavity fiber lasers as mentioned, a simpler way to achieve single-longitudinal-mode (SLM) operation is to put a piece of EDF as pump absorber between the WDM coupler and 1 × 2 OSW for the OC-based linear-cavity tunable fiber laser as shown in Figure 3; and between the 1480/1550 nm WDM and TFBG for the BFM-based linear-cavity tunable fiber laser as shown in Figure 5, individually. On the other hand, the SWPF in tunable fiber lasers is naturally a broadband filter that is obviously difficult for single-longitudinal mode laser operation. However, a SWPF made of a highly dispersive waveguide structure can introduce high chromatic dispersion inside the laser cavity to significantly reduce the cavity modes into one. One suggestion is to concatenate the SWPF and an additional ultra-narrowband filter inside the cavity to attain SLM operation.