**3. Broadband supercontinuum**

256

succeeding amplifier.

into NALM via CP1 with a splitting ratio of 45:55.

ically decreased to ~ms of magnitude.

net cavity dispersion. When the net dispersion was set to −0.115 ps<sup>2</sup>

time was observed. After optimizing the net dispersion to about −0.062 ps<sup>2</sup>

rate is lower than 10 MHz, a pulse picker has to be used between the laser oscillator and the

In this section, we introduce a PM figure-eight laser cavity which is the best option for oscillator operated at 10-MHz repetition rate. **Figure 4(a)** shows the experimental setup of the figureeight laser cavity. The linear loop comprises of a 980/1550 nm wavelength division multiplexer, a segment of Er-doped fiber (PM-ESF-7/125, Nufern), an isolator, a 2-nm bandpass filter at 1550 nm, and an output coupler CP2 with a splitting ratio of 20:80. The active gain applied in the linear loop is to compensate the cavity loses and facilitate self-started mode-locking. The band-pass filter is used to block longer wavelength (Raman self-frequency shift) and reduce the temporal width of the pulse to be self-consistent. Pulses from the linear loop are coupled

Over-pump with three LDs was applied to provide enough power for self-started modelocking. Interestingly, the buildup time of mode-locking was found to be closely related to the

Furthermore, we recorded the mode-locked pulse trains triggered by a square wave with 5- Hz modulation frequency which is simultaneously used to drive LD3. **Figure 4(c)** shows two

**Figure 4.** (a) Schematic of a polarization-maintaining figure-eight erbium-doped fiber laser. WDM1, WDM2, and WDM3: 980/1550 nm wavelength division multiplexers; ISO: isolator; EDF1 and EDF2: erbium-doped fiber; BP: 2-nm bandpass filter at 1550 nm; DCF: dispersion compensation fiber; CP1 and CP2: 1550 nm coupler with splitting ratio of 45:55 and 20:80. (b) The initial pulse that polarization-maintaining figure-eight erbium-doped fiber laser generated. (c) The buildup time measured by an oscilloscope. (d) The measurement of power stabilization once mode-locked.

, as long as 8-min buildup

, the time dramat‐

Recent years, supercontinuum generation (SC) has attracted much attention for its applications in optical coherence tomography, stimulated emission depletion microscopy, dense wave‐ length-division-multiplexing (DWDM) optical networks, and frequency comb generation [30– 33]. In this section, several nonlinear optical effects such as SPM, XPM, four-wave mixing (FWM), and stimulated Roman scattering (SRS) that facilitate SC generation would be firstly discussed. Secondly, spectral filtering method is demonstrated to be an effective way for broadband supercontinuum generation in picosecond region [34]. By spectral filtering, a linear-chirped picosecond pulse with a 1-nm bandwidth filter installed between two Yb-doped single-mode preamplifiers, pulse shortening, and high peak power is achieved, so that an octave-spanning SC with bandwidth of 650 nm from 750 to 1400 nm and 10-dB peak-to-peak flatness was obtained at an output average power of 190 mW. Thirdly, SC covering from 950 to 2200 nm is generated in a 20-cm-long PM HNLF by injecting 72-fs pulse with 150-mW average power and 60-MHz repetition rate at 1.56 μm. Furthermore, an inline f-2f interferom‐ eter, including a PPLN for frequency doubling and a PM-fiber delay line, is used to generate carrier-envelop offset signal (*f*ceo).

#### **3.1. Nonlinear effects in optical fibers**

Most of nonlinear effects in optical fibers attribute to nonlinear refraction, which refer to the intensity dependence of the refractive index. Especially, the lowest order nonlinear effects in optical fibers originate from the third-order susceptibility *χ*(3), which governs the four-wave mixing, Raman effect, third-harmonic generation, and polarization properties [24].

This section does not thoroughly focus on the discussion of theoretical issues. In simple, the refractive index of the optical fiber can be described by the following equation

$$n = n\_0 + n\_1 \left| E(t) \right|^2 \tag{1}$$

where *n*0 is the linear part and *n*1|*E*(*t*)|2 is the nonlinear part. An interesting phenomenon of the intensity dependence of the refractive index change in optical fiber occurs through SPM. When the input pulse is of low intensity, the corresponding refractive index remains a constant *n*0. As the input pulse increases, the corresponding refractive index becomes nonlinear change with power intensity *I*. Hence, an additional phase shift is produced:

$$
\delta\Phi(\mathbf{t}) \propto \left| E(t) \right|^2 \tag{2}
$$

This can be understood as an instantaneous optical frequency change from its central frequen‐ cy:

$$
\delta\mathfrak{\delta}\mathfrak{o}(\mathbf{t}) = -\frac{\partial}{\partial \mathbf{t}} \delta\mathfrak{\delta}\mathfrak{g}(\mathbf{t})\tag{3}
$$

Therefore, new spectral components are generated and time dependent frequency chirping is produced.

Another most widely studied nonlinear effect is XPM, which leads to asymmetric spectral and temporal changes for two co-propagating optical fields with different wavelength or orthog‐ onally polarization. The contribution of the nonlinear phase shift induced by XPM is twice that of SPM. Therefore, the nonlinear part Δ*n*<sup>j</sup> induced by the third-order nonlinear effects is given by (*j* = 1, 2)

$$
\Delta n\_{\cdot j} \approx n\_2 \left( \left| E\_{\cdot j} \right|^2 + 2 \left| E\_{\cdot - j} \right|^2 \right) \tag{4}
$$

Eq. (4) shows the refractive index of the optical media seen by an optical field inside a singlemode fiber depends not only on the intensity of that field but also on the intensity of the other co-propagating fields [35]. As the optical field propagates inside the fiber, an intensitydependent nonlinear phase shift shows up

$$\phi\_j^{\rm NL}\left(z\right) = n\_z \left(\alpha\_j \left/ \mathbf{c}\right) \left(\left|E\_j\right|^2 + 2\left|E\_{3-j}\right|^2\right) z\right.\tag{5}$$

The first term is related to SPM while the second term is related to XPM.

Stimulated Raman scattering (SRS) is an important nonlinear process that can produce redshifted spectral components. Once the spectrum of the input pulse is broad enough, the Raman gain can amplify the long-wavelength components of the pulse with the short-wavelength components acting as pumps, and the energy appears red-shifted. The longer the propagating fiber, the more red-shifted spectral components can be generated. The red-shifted components are called Stokes wave. The initial growth of the Stokes wave can be described by

$$\frac{dI\_s}{dz} = \mathbf{g}\_{\,\,R} I\_{\,\,\rho} I\_s \tag{6}$$

where *I*<sup>s</sup> is the Stokes wave intensity, *I*<sup>p</sup> is the pump-wave intensity, and *g*R is the Raman-gain coefficient, which is related to the cross section of spontaneous Raman scattering.

The Raman-gain coefficient *g*R (Ω) is the most important factor to describe SRS. *Ω* represents the frequency difference between the pump wave *ω*p and Stokes wave *ω*s. In the case of silica fibers, the Raman-gain spectrum is found to be very broad, extending up to approximately 40 THz. Assuming the pump wavelength is 1.5 μm and, peak gain is *g*R = 6 × 10−14 m/W, the frequency downshift can be calculated to be 13.2 THz.

When supercontinuum is generating in an optical fiber, the SPM, XPM, and SRS are always accompanied by FWM. In optical fibers, FWM transfers energy from pump wave (*ω*p) to two other waves in frequency domain, blue-shifted (anti-Stokes wave, *ω*as) and red-shifted (Stokes wave, *ω*s). Once the phase-matching condition Δ*k* = 2*k*(*ω*p) − *k*(*ω*s) − *k*(*ω*as) = 0 is satisfied, the Stokes and anti-Stokes waves can be amplified from noise or an incident signal at *ω*s or *ω*as, respectively [36, 37]. Therefore, FWM process is used to produce spectral sidebands for supercontinuum generation.

#### **3.2. Supercontinuum generation**

258

shift is produced:

cy:

produced.

by (*j* = 1, 2)

of SPM. Therefore, the nonlinear part Δ*n*<sup>j</sup>

dependent nonlinear phase shift shows up

f

An interesting phenomenon of the intensity dependence of the refractive index change in optical fiber occurs through SPM. When the input pulse is of low intensity, the corresponding refractive index remains a constant *n*0. As the input pulse increases, the corresponding refractive index becomes nonlinear change with power intensity *I*. Hence, an additional phase

2

This can be understood as an instantaneous optical frequency change from its central frequen‐

Therefore, new spectral components are generated and time dependent frequency chirping is

Another most widely studied nonlinear effect is XPM, which leads to asymmetric spectral and temporal changes for two co-propagating optical fields with different wavelength or orthog‐ onally polarization. The contribution of the nonlinear phase shift induced by XPM is twice that

( ) 2 2

Eq. (4) shows the refractive index of the optical media seen by an optical field inside a singlemode fiber depends not only on the intensity of that field but also on the intensity of the other co-propagating fields [35]. As the optical field propagates inside the fiber, an intensity-

> ( ) ( )( ) 2 2 2 3 / 2 *NL j jj j*

Stimulated Raman scattering (SRS) is an important nonlinear process that can produce redshifted spectral components. Once the spectrum of the input pulse is broad enough, the Raman gain can amplify the long-wavelength components of the pulse with the short-wavelength components acting as pumps, and the energy appears red-shifted. The longer the propagating fiber, the more red-shifted spectral components can be generated. The red-shifted components

 w

The first term is related to SPM while the second term is related to XPM.

are called Stokes wave. The initial growth of the Stokes wave can be described by

δω(t) δφ(t) <sup>t</sup>

δφ(t) ( ) µ *E t* (2)

¶ = - ¶ (3)

induced by the third-order nonlinear effects is given

2 3 2 *jj j* D» + *n nE E* - (4)

*z n cE E z* = + - (5)

SC is a powerful laser sources for many applications, such as nonlinear microscopy, optical coherence tomography, and frequency metrology [38–40]. Nowadays, more than one octave SC can be easily generated with a length of PCF, and the average power can reach tens of Watts [41, 42]. When ultrashort optical pulses propagate through a PCF fiber, the combination of SPM, XPM, SRS, and FWM is responsible for the spectral broadening. Generally speaking, the feature of SC depends on whether the incident laser wavelength *λ* located is below, closed to, or above the Zero-dispersion wavelength *λ*D of the PCF. In the anomalous-dispersion regime (*λ* > *λ*D) where *β*2 < 0, soliton affects. If the *λ* nearly coincides with *λ*D, *β*2 ≈ 0, *β*3 dominant and the phase-matching condition of FWM are approximately satisfied. While in the normaldispersion regime, *β*2 > 0, GVD and SPM effects dominant SC generation. From the time domain of view, SPM and soliton effects dominant SC generation for femtosecond (typically <1 ps) pump pulses, while FWM and SRS contribute to spectral broadening for tens of picoseconds pulses.

#### *3.2.1. Spectrally filtered seed for broadband supercontinuum generation in single-mode fiber amplifiers*

There are several methods to extend the SC spectrum. Considerable spectral broadening could be observed with high-power incident laser. High-average/high-peak powers facilitate CW and pulse SC generation [43–45]. Besides, the SC bandwidth could also be increased by tapering PCFs. A flat (3 dB) spectrum from 395 to 850 nm was achieved in a tapered fiber with a continuously decreasing ZDW [46]. In this section, we demonstrate an effective method for broadband SC generation, which is valid in normal-dispersion fiber amplifiers. By spectral filtering of upchirped pulse at 1028 nm with 1-nm bandpass filter, as broad as 650-nm bandwidth from 750 to 1400 nm within 10-dB peak-to-peak flatness is obtained with an output power of 190 mW.

The experimental setup is shown in **Figure 5(a)**. The SC laser source is consisted of a picosecond mode-locked laser oscillator, a spectral filter, two-stage single-mode amplifiers, and 2-m-long PCF with ZDW at 1.02 μm. The laser oscillator operated in an all-normal-dispersion regime with repetition rate of 20 MHz. With 100 mW pumping power, 25 mW average output power laser is exported from the 30% port of the coupler. The pulse duration of highly up-chirped pulse was measured to be 10 ps.

**Figure 5.** (a) Experimental setup for SC generation. Pump diode: 400 mW laser diode at 976 nm; WDM: 980/1040 nm wavelength division multiplexer; Yb-SMF: ytterbium-doped single-mode fiber; CP: 30:70 coupler; PC1 and PC2: polari‐ zation controller; PBS: polarization beam splitter; ISO: isolator; SMFA1 and SMFA2: single-mode fiber amplifiers; C1, C2, and C3: three collimators; SF: spectral filter; PCF: photonics crystal fiber. (b) The output spectrum of the laser oscil‐ lator. (c) SC with different filtering windows.

A bandpass spectral filter with 1-nm bandwidth at 1036 nm is installed between two singlemode fiber amplifiers. The transparent wavelength of the filter could be tuned from 1024 to 1036 nm by varying the incident deflection angle. For the large up-chirp with 10-nm spectral width (see **Figure 5(b)**) and 10-ps temporal duration, corresponding to a time-bandwidth product of 28.3, pulse can be greatly shortened by the filter. The shortest pulse duration of 2.9 ps was obtained with filtering window at 1028 nm. After the second-stage amplifier, the laser pulses could be amplified to an average power up to 190 mW with 400 mW pumping power.

A 2-m length of silica-based PCF with ZDW at 1024 nm is directly spliced to the fiber end of SMFA2. **Figure 5(c)** shows the output spectrum with different filtering window. The spectra keep unchanged when the filtering window is at the shoulder of the spectrum, shown as the red curve (1024.9 nm) and blue curve (1033.4 nm) in **Figure 5(c)**. When filtering window is located at the central wavelength of 1028 nm, the 10-dB bandwidth of SC is extended to 650 nm (from 750 to 1400 nm), shown as the pink curve in **Figure 5(c)**. Besides, filtering windows above or below the central wavelength produce a less broad SC.

#### *3.2.2. One octave supercontinuum for frequency comb generation*

260

power of 190 mW.

pulse was measured to be 10 ps.

lator. (c) SC with different filtering windows.

power.

bandwidth from 750 to 1400 nm within 10-dB peak-to-peak flatness is obtained with an output

The experimental setup is shown in **Figure 5(a)**. The SC laser source is consisted of a picosecond mode-locked laser oscillator, a spectral filter, two-stage single-mode amplifiers, and 2-m-long PCF with ZDW at 1.02 μm. The laser oscillator operated in an all-normal-dispersion regime with repetition rate of 20 MHz. With 100 mW pumping power, 25 mW average output power laser is exported from the 30% port of the coupler. The pulse duration of highly up-chirped

**Figure 5.** (a) Experimental setup for SC generation. Pump diode: 400 mW laser diode at 976 nm; WDM: 980/1040 nm wavelength division multiplexer; Yb-SMF: ytterbium-doped single-mode fiber; CP: 30:70 coupler; PC1 and PC2: polari‐ zation controller; PBS: polarization beam splitter; ISO: isolator; SMFA1 and SMFA2: single-mode fiber amplifiers; C1, C2, and C3: three collimators; SF: spectral filter; PCF: photonics crystal fiber. (b) The output spectrum of the laser oscil‐

A bandpass spectral filter with 1-nm bandwidth at 1036 nm is installed between two singlemode fiber amplifiers. The transparent wavelength of the filter could be tuned from 1024 to 1036 nm by varying the incident deflection angle. For the large up-chirp with 10-nm spectral width (see **Figure 5(b)**) and 10-ps temporal duration, corresponding to a time-bandwidth product of 28.3, pulse can be greatly shortened by the filter. The shortest pulse duration of 2.9 ps was obtained with filtering window at 1028 nm. After the second-stage amplifier, the laser pulses could be amplified to an average power up to 190 mW with 400 mW pumping

A 2-m length of silica-based PCF with ZDW at 1024 nm is directly spliced to the fiber end of SMFA2. **Figure 5(c)** shows the output spectrum with different filtering window. The spectra

Broadband supercontinuum of bandwidth up to 1250 nm can also be provided by HNLFs with spectral-tailored femtosecond pump pulses produced by erbium-doped power amplifiers. The schematic diagram of the experiment is shown in **Figure 6(a)**.

**Figure 6.** (a) Schematic diagram for SC generation. Pump diode: 400-mW pump at 976 nm; WDM/ISO/Coup: the de‐ vice combines wavelength division multiplexer, isolator, and coupler; EDF: erbium-doped fiber; EPC: electric polariza‐ tion controller; ISO: isolator; coupler: 30:70 polarization-maintaining coupler; PBS: polarization beam splitter; HNLF: high nonlinear fiber; LD1 and LD2: pumps at 976 nm; WDM1 and WDM2: 980/1550 nm wavelength division multi‐ plexer; FRM: Faraday rotation mirror. (b) Autocorrelation trace of chirped pulses poured into HNLFs. (c) SC generated by different kinds of HNLFs on logarithmic coordinate.

The laser system consisted of an erbium-doped mode-locking fiber oscillator, a single-mode fiber amplifier (SMFA), and 20-cm-long PM-HNLF. To improve the mode-locking stability, an electric polarization controller (EPC) is utilized to replace the conventional mechanical polarization controller such that automatic and active control of mode-locking is accessible. By applying the voltage on three axes (*x*, *y*, and *z*) of EPC, accurate control of the temporal duration, spectral shape, *f*rep, and *f*ceo can be achieved [47, 48].

With the help of a PBS and a FRM, a dual-pass single-mode fiber amplifier with bidirectional pump configuration was used to boost the laser average power to more than 150 mW average power and reduce the environmental disturbance on SMFA. The pulse duration at the output port was measured to be 2.84 ps. Additional PM-1550 fiber was used to dechirp the preamplified pulse to 72 fs (shown in **Figure 6(b)**). Therefore, considering a repetition rate of 60 MHz, the pulse peak power achieved as high as 34.7 kW. Three types of HNLFs, such as NL 1550-ZERO, PM-HNLF, and Zero-slope HNLF, were applied to generate the supercontin‐ uum by splicing the HNLFs to the dechirping fiber directly.

As shown in **Figure 6(c)**, 20-cm-long PM-HNLF with nonlinearity of 10.5 W−1 km−1 achieved the broadest spectrum, covering from 950 to 2200 nm, which is sufficient broad to produce *f*ceo signal. The HNLF type should be taken into consideration as it influences the SC generation. We used three kinds of HNLFs: 25-cm-long NL 1550-ZERO with nonlinear coefficient of 10.4- W−1 km−1 and effective mode area of 13-μm2 , 20-cm-long PM-HNLF with nonlinear coefficient of 10.5-W−1 km−1 and effective mode area of 12.7-μm2 , 25-cm-long Zero-slope HNLF with nonlinear coefficient of 10.8-W−1 km−1 and effective mode area of 12.4-μm2 , and the corre‐ sponding SC was depicted in **Figure 6(c)**. Obviously, PM-HNLF produces broader spectrum than other two HNLFs.

As shown in **Figure 7**, a collinear setup was established for the detection of *f*ceo signal. The SC generated by 20-cm-long PM-HNLF was coupled into free space via a lens (L1) with adjustable focal length. An inline f-2f interferometer, including a PPLN, several wave plates and lens, and a PM-fiber delay line, is used to produce the temporal overlapped components at 1.0 μm. The long-wavelength component of SC at 2092 nm was frequency doubled to match with the shortwavelength component at 1046 nm. After the PPLN, two lenses, L3 and L4, were used to couple the two components at 1046 nm back to PM-980 fiber. A half-wave plate, HWP2, is used to adjust the energy ratio on the fast and slow axes of PM-980 fiber. The pulse transmitted along the slow axis experiences a delay relative to the pulse on fast axis. With an optimized fiber length of 3.4 m, the differential delay between the fast and slow axes could be fully compen‐ sated [49]. Subsequently, a half-wave plate, HWP3, as well as a PBS were used to selected pulses to generate *f*ceo signal on APD. Finally, with 28-dB signal-to-noise ratio was generated by using this setup.

**Figure 7.** Setup for *f*ceo detection. Amp: fiber amplifier; L1, L4, and L5: optical lens with adjustable focal length; L2, L3, and L6: optical lens with focal length of 50 mm; HWP1, HWP2, and HWP3: half-wave plates; PPLN: periodically poled lithium niobate; PBS: polarization beam splitter; APD: avalanche photodiode.
