Coherent ultrashort pulse generation from incoherent light by pulse trapping in birefringent fibers

doi:10.1364/OE.20.011073

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Coherent ultrashort pulse generation from incoherent light by pulse trapping in birefringent fibers

Eiji Shiraki and Norihiko Nishizawa »View Author Affiliations

Optics Express, Vol. 20, Issue 10, pp. 11073-11082 (2012)
http://dx.doi.org/10.1364/OE.20.011073

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Abstract

We investigated the nonlinear fiber phenomena of pulse trapping and amplification between incoherent light and an ultrashort soliton pulse in birefringent fibers both experimentally and numerically. Using the phenomena in a 1.4 km-long low-birefringence fiber, a coherent, nearly transform-limited, sech²-shaped, ultrashort pulse was generated from incoherent light from a super-luminescent diode. The average pulse energy and pulse width were 121 pJ and 640 fs, respectively. The estimated gain of this system was as large as 62 dB.

1. Introduction

Nonlinear phenomena in optical fibers are useful for mode-locking [1

I. N. Iii, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett. 16(8), 539–541 (1991). [CrossRef] [PubMed]

–3

G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).

], wavelength tuning [4

N. Nishizawa and T. Goto, “Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11(3), 325–327 (1999). [CrossRef]

N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009). [CrossRef]

], pulse shaping [6

T. Inoue, N. Kumano, M. Takahashi, T. Yagi, and M. Sakano, “Generation of 80-nm wavelength-tunable 100-fs pulse based on comblike profiled fiber comprised of HNLF and zero dispersion-slope NZDSF,” J. Lightwave Technol. 25(1), 165–169 (2007). [CrossRef]

N. Nishizawa, K. Takahashi, Y. Ozeki, and K. Itoh, “Wideband spectral compression of wavelength-tunable ultrashort soliton pulse using comb-profile fiber,” Opt. Express 18(11), 11700–11706 (2010). [CrossRef] [PubMed]

], and super-continuum generation [5

N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009). [CrossRef]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]

], etc. Since such fiber-based light sources are highly-functional, compact, and stable, they are effective in various fields, such as laser processing, metrology, spectroscopy, nonlinear microscopy, and ultrafast fiber-optic communications. Mode-locked fiber lasers in which ultrashort pulse trains can be generated from quantum noise and incoherent light originating from spontaneous emission have been developed using fiber-based [1

I. N. Iii, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett. 16(8), 539–541 (1991). [CrossRef] [PubMed]

–3

G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).

], semiconductor-based [9

U. Keller, D. A. B. Miller, G. D. Boyd, T. H. Chiu, J. F. Ferguson, and M. T. Asom, “Solid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry-Perot saturable absorber,” Opt. Lett. 17(7), 505–507 (1992). [CrossRef] [PubMed]

], and carbon-nanotube-based saturable absorbers [10

S. Yamashita, Y. Inoue, S. Maruyama, Y. Murakami, H. Yaguchi, M. Jablonski, and S. Y. Set, “Saturable absorbers incorporating carbon nanotubes directly synthesized onto substrates and fibers and their application to mode-locked fiber lasers,” Opt. Lett. 29(14), 1581–1583 (2004). [CrossRef] [PubMed]

], due to their intensity dependence. In addition, fiber Raman soliton lasers, where only intended light is amplified by a synchronous pump pulse through the Raman gain, also generate ultrashort pulses [11

J. D. Kafka and T. Baer, “Fiber Raman soliton laser pumped by a Nd:YAG laser,” Opt. Lett. 12(3), 181–183 (1987). [CrossRef] [PubMed]

,12

H. A. Haus and M. Nakazawa, “Theory of the fiber Raman soliton laser,” J. Opt. Soc. Am. B 4(5), 652–660 (1987). [CrossRef]

]; however, they require accurate adjustment of the components forming the cavity.

In the anomalous dispersion region of optical fibers, a scalar soliton is generated through the balance between the linear effect of group velocity dispersion (GVD) and the nonlinear effect of self-phase modulation (SPM) and it propagates along the fiber with the stable pulse shape. In 1989, Islam et al. discovered the phenomenon of soliton trapping in low birefringent optical fibers, in which two orthogonally polarized equal-intensity soliton pulses trap each other through cross-phase modulation (XPM). The twin pulses are temporally overlapped and they co-propagate along the fiber. To compensate the group velocity difference by the birefringence, the center wavelengths of the two solitons are shifted in opposite sides through SPM and XPM [13

M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett. 14(18), 1011–1013 (1989). [CrossRef] [PubMed]

]. Such a pair of two orthogonally polarized pulses is well known as a vector soliton and it propagates along a birefringent fiber without changing its shape [14

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

]. This soliton trapping phenomenon occurs in the picoseconds regime, where the effect of Raman scattering is negligible.

In 2003, Nishizawa and Goto discovered interesting nonlinear fiber phenomena of pulse trapping and amplification in birefringent fibers: trapped pulse generation (amplification) [15

N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express 10(5), 256–261 (2002). [PubMed]

]. This trapping and amplification phenomena is observed in the femtoseconds regime, where stimulated Raman scattering (SRS) is effectively induced. When twin orthogonally polarized ultrashort pulses (signal and pump pulses) are aligned along the slow and fast axes of a birefringent fiber, and when the center wavelengths of the signal and pump pulses (λ_s and λ_p) are appropriately adjusted to longer- and shorter-wavelengths in the anomalous dispersion region, respectively, the twin pulses satisfy the group velocity matching condition,

v_{g f} (λ_{s}) = v_{g s} (λ_{p})

, where

v_{g f} (λ)

and

v_{g s} (λ)

are respectively the group velocities of pulses along the fast and slow axes of the birefringent fiber at wavelength λ. When the twin pulses are temporally overlapped, they are coupled through XPM in the same manner as that of a vector soliton and co-propagate at the same group velocity throughout the fiber even if they suffer soliton self-frequency shift (SSFS) originating from intra-pulse SRS.

In the case where the energy of the pump are distinctly larger than that of the signal pulse, the waveform of the pump pulse maintains an ultrashort sech²-shape due to the effects of GVD and SPM, while that of the signal pulse is formed into a nearly sech²-shaped, ultrashort pulse due to GVD and XPM induced by the sech²-shaped pump pulse. When the center wavelength of the pump pulse is shifted toward the longer wavelength side due to SSFS, the signal pulse is also red-shifted through XPM so that the group velocity matching condition between the twin pulses is always maintained. Thus, the large pump pulse can trap the small signal pulse through XPM.

In the propagation along the fiber, since the pulse energy is continuously transferred from the shorter-wavelength pulse to the longer-wavelength pulse due to SRS, the trapped signal pulse is greatly amplified by the pump pulse during propagation along the fiber (Raman amplification) [16

E. Shiraki, N. Nishizawa, and K. Itoh, “Ultrashort pulse generation from continuous wave by pulse trapping in birefringent fibers,” Opt. Express 18(22), 23070–23078 (2010). [CrossRef] [PubMed]

–19

E. Shiraki and N. Nishizawa, “Wideband amplification using orthogonally polarized pulse trapping in birefringent fibers,” Opt. Express 18(7), 7323–7330 (2010). [CrossRef] [PubMed]

]. When the energy of the trapped signal pulse becomes comparable with that of pump pulse as a result of the energy transfer, the twin pulses trap each other through XPM. The waveforms of the twin pulses maintain ultrashort sech²-shapes due to the balance among SPM, XPM, and GVD, and the pair is red-shifted due to SSFS.

In 2010, the trapping of a continuous-wave (cw) beam by an ultrashort pulse (pump pulse) was demonstrated [16

E. Shiraki, N. Nishizawa, and K. Itoh, “Ultrashort pulse generation from continuous wave by pulse trapping in birefringent fibers,” Opt. Express 18(22), 23070–23078 (2010). [CrossRef] [PubMed]

]. In this case, by appropriate adjustment of the wavelengths of the cw beam and the pump pulse (λ_cw and λ_p), the group velocity matching condition,

v_{g f} (λ_{c w}) = v_{g s} (λ_{p})

, is satisfied between the cw beam and the pump pulse along the fast and slow axes of the birefringent fiber, respectively, since a temporally overlapped part of the cw beam is modulated and trapped by the pump pulse, and a pulse is generated from the cw beam. Similarly to pulse trapping between two pulses, the pump pulse and the generated pulse trap each other and co-propagate along the fiber. In the propagation along the fiber, the generated pulse is formed into an ultrashort sech²-shape due to the soliton effect and is amplified by the pump pulse due to the Raman gain. Thus, a temporally overlapped part of coherent light with any temporal width, from femtosecond pulsed light to cw light, is trapped by an ultrashort pulse [15

N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express 10(5), 256–261 (2002). [PubMed]

–19

E. Shiraki and N. Nishizawa, “Wideband amplification using orthogonally polarized pulse trapping in birefringent fibers,” Opt. Express 18(7), 7323–7330 (2010). [CrossRef] [PubMed]

], and an ultrashort pulse is generated from the coherent light in a single path of a birefringent fiber using the pulse trapping and amplification phenomena.

Nonlinear fiber effects have been investigated for not only coherent light [14

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

] but also incoherent light [20

J. T. Manassah, “Self-phase modulation of incoherent light,” Opt. Lett. 15(6), 329–331 (1990). [CrossRef] [PubMed]

–27

K. Hammani, C. Finot, and G. Millot, “Emergence of extreme events in fiber-based parametric processes driven by a partially incoherent pump wave,” Opt. Lett. 34(8), 1138–1140 (2009). [CrossRef] [PubMed]

]. So far, nonlinear interactions through XPM [21

J. M. Hickmann, H. R. da Cruz, and A. S. Gouveia-Neto, “Cross-phase modulation of incoherent light in single-mode optical fibers,” Opt. Lett. 17(7), 478–480 (1992). [CrossRef] [PubMed]

], SRS [22

T. Zhang, X. Zhang, and G. Zhang, “Distributed fiber Raman amplifiers with incoherent pumping,” IEEE Photon. Technol. Lett. 17(6), 1175–1177 (2005). [CrossRef]

–24

K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express 16(21), 16467–16474 (2008). [CrossRef] [PubMed]

], and four-wave mixing [25

Y. S. Jang and Y. C. Chung, “Four-wave mixing of incoherent light in a dispersion-shifted fiber using a spectrum-sliced fiber amplifier light source,” IEEE Photon. Technol. Lett. 10(2), 218–220 (1998). [CrossRef]

–27

] have been demonstrated in the incoherent regime. However, pulse trapping between an ultrashort pulse and incoherent light has not been demonstrated yet. If a temporally overlapped part of the incoherent light could also be trapped by an ultrashort pulse, it would be possible to generate an ultrashort pulse from the incoherent light without using any cavity configuration.

In this paper, we report the first demonstration of ultrashort pulse generation from incoherent light from a super-luminescent diode (SLD) using pulse trapping and amplification in a 1.4 km-long birefringent fiber. The mechanism and characteristics of pulse trapping between the incoherent light and ultrashort pulse were investigated both experimentally and numerically. The temporal coherence of the generated pulse was also examined.

2. Methods for experimental and numerical analysis

2.1 Experimental analysis

Figure 1 shows the experimental setup for pulse trapping between incoherent light and an ultrashort pulse in a low-birefringence polarization maintaining fiber (LB-PMF). An SLD with a center wavelength of 1650 nm was used as an incoherent light source. A wavelength-tunable ultrashort soliton pulse source was used as a pump pulse source [16

E. Shiraki, N. Nishizawa, and K. Itoh, “Ultrashort pulse generation from continuous wave by pulse trapping in birefringent fibers,” Opt. Express 18(22), 23070–23078 (2010). [CrossRef] [PubMed]

]. The temporal width of the pump pulse was ~130 fs full width at half maximum (FWHM), assuming a transform-limited (TL) sech²-shaped pulse. The incoherent light and pump pulse were coupled into the LB-PMF (Fujikura, SM15-PR-U25A-H) for pulse trapping. The fiber length was 1.4 km, the mode field diameter of the LB-PMF was 10.5 μm, the birefringence was 2.7 × 10⁻⁴, the second- and third-order dispersion parameters β₂ and β₃ were −22 ps²/km and 0.12 ps³/km, respectively, and the nonlinear coefficient γ was 1.4 W⁻¹km⁻¹. In order to satisfy the group velocity matching condition between the incoherent light and the pump pulse at the fiber input, their polarization directions were aligned along the fast and slow axes of the LB-PMF, respectively, and the wavelength of the input pump pulse was adjusted to 1600 nm, as shown in Figs. 6(a) and 6(c).

Fig. 1 Experimental setup for ultrashort pulse generation from incoherent light using pulse trapping and amplification in a low-birefringence polarization maintaining fiber (LB-PMF). SLD, super-luminescent diode; HWP, half-wave plate; QWP, quarter-wave plate; ISO, optical isolator; CP-EDFA, chirped-pulse Er-doped fiber amplifier; LMA-PCF, large-mode-area photonic crystal fiber; WC-PMF, wavelength-conversion polarization maintaining fiber; LPF; low-pass filter; PBS, polarizing beam splitter; POL, polarizer; PIN, p-i-n photodiode.

The average power, spectra, and auto-correlation traces were observed at the LB-PMF output. In addition, after splitting the two orthogonally polarized light components at a polarizing beam splitter, they were simultaneously observed by using two photo-detectors (biased InGaAs p-i-n photodiodes, cut-off frequency >2 GHz) and a digital oscilloscope (cut-off frequency >1.5 GHz) at 10 Gsample/s.

2.2 Numerical analysis

We also analyzed the phenomenon of pulse trapping between incoherent light and an ultrashort pulse numerically. Evolutions of the two light components along the PMF are represented by coupled nonlinear Schrödinger Eqs [14

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

,19

E. Shiraki and N. Nishizawa, “Wideband amplification using orthogonally polarized pulse trapping in birefringent fibers,” Opt. Express 18(7), 7323–7330 (2010). [CrossRef] [PubMed]

]. The fiber parameters were set to the same as those of the LB-PMF used in the experiment. The Raman gain coefficient, g_R, was 3 × 10⁻¹⁵ m/W. As the input pump pulse, a 130 fs, TL sech²-shaped, ultrashort pulse was used. As the incoherent light, noise having a Gaussian spectral shape was assumed. In order to obtain such noise, the amplitude and phase at each point in the temporal waveform were randomly varied, and in the Fourier domain, a Gaussian waveform whose spectral width was equal to that of the SLD light used in the experiment was multiplied by a random function. The pump pulse and noise had center wavelengths of 1600 nm and 1650 nm, respectively, and they were orthogonally polarized.

The coupled amplitude Eqs. can be analyzed with the split-step Fourier method [14

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

]. We analyzed the light propagation along the fiber for 1,300 events, in which the input waveforms of the noise were varied while keeping the average power constant.

3. Demonstration and characterization of ultrashort pulse generation from incoherent light

3.1 Analysis of mechanism

First, we numerically analyzed the mechanism of ultrashort pulse generation from incoherent light using pulse trapping in birefringent fibers. Figures 2 and 3 shows a representative numerical evolution of the light along the fast and slow axes in the propagation along the LB-PMF for 5.4 mW incoherent light and a 308 pJ pump pulse. The spectrograms shown in Figs. 2(a) and 2(b) were obtained using the Eq. for polarization-gate cross-correlation frequency resolved optical gating [16

E. Shiraki, N. Nishizawa, and K. Itoh, “Ultrashort pulse generation from continuous wave by pulse trapping in birefringent fibers,” Opt. Express 18(22), 23070–23078 (2010). [CrossRef] [PubMed]

], in which the reference pulse had a TL sech²-shape and a temporal width of 400 fs (FWHM).

Fig. 2 Numerical evolutions of ultrashort pump pulse and incoherent light in the propagation along the LB-PMF. Spectrograms for polarization directions aligned along the (a) fast and (b) slow axes of the fiber, respectively (Media 1).

Fig. 3 Numerical results of light evolution in the propagation along low-birefringence polarization maintaining fiber. (a) Temporal waveforms along the slow and fast axes of the fiber, respectively, and (b) the corresponding spectra. The right vertical axis of the graphs in (a) represents the phase of the light. Zero positions on the time scale are adjusted to the peak point of the pump pulse.

As shown in Fig. 2(a), the pump pulse maintained its ultrashort pulse shape in the propagation along the fiber due to the soliton effect. As shown in Fig. 2(b), part of the noise that had a wavelength of ~1650 nm (due to the group velocity matching condition) and that was temporally overlapped with the pump pulse was trapped by the pump pulse, and they co-propagated. At L = 80 m, a trapped component was observed along the fast axis.

In the time domain (Fig. 3(a)), along the fast axis, at the point where it temporally overlapped with the pump pulse, the phase of the noise was gradually flattened, and a pulse appeared due to pulse trapping. At the same time, the trapped component was amplified by the pump pulse due to the Raman gain, and it is formed into a sech²-shaped ultrashort pulse due to the soliton effect. Consequently, a high-power pulse along the fast axis was generated from the incoherent light. In the spectral domain (Fig. 3(b)), while the ultrashort pulse along the slow axis was red-shifted because of SSFS, the trapped pulse was also red-shifted through XPM so that the group velocity matching condition was maintained. The spectral waveform of the generated pulse became a sech²-shape at L = 800 m.

Since the amplitude and phase of the input noise randomly vary, the generated pulse energies depend on the input state of the noise. Figure 4 shows the evolutions of the generated pulse energy in the propagation along the fiber for two representative events where the large and small pulse energies were obtained at L = 1.4 km (events i and ii). As shown in the curve for event i, when the large component at the initial stage was trapped and amplified, a large pulse of 338 pJ was generated at L = 1.4 km. Then, in further propagation, the generated pulse energy was saturated because of the depletion of the pump pulse energy. In contrast, as shown in the curve for event ii, when the trapped component was small at the initial stage, it was embedded in the noise. Nevertheless, only the trapped component was amplified by the pump pulse in the propagation along the fiber, and a 10 pJ ultrashort pulse was generated at L = 1.4 km.

Fig. 4 Evolutions of generated pulse energy along low-birefringence polarization maintaining fiber. The solid lines are two representative events, events i and ii, when different incoherent light beams are trapped. The dotted lines are the cases where 3 fJ and 3 aJ sech²-shaped ultrashort pulses are trapped at the initial stage (events i' and ii'), respectively, the evolutions of which are in good agreement with the incoherent light cases.

In order to estimate the generated pulse energy in the propagation, we also analyzed the trapping of a 130 fs sech²-shaped ultrashort pulse (signal pulse) using the same pump pulse. Here we determined the input energies of the signal pulse so that the evolutions of the generated pulse energy matched those of the two cases where the large and small components of the incoherent light were trapped (curves i and ii). As shown in Fig. 4, when the trapped signal pulse energy was 3 fJ, the evolution of the pulse energy along the fiber (curve i') was comparable to that of the incoherent light case (curve i). Thus, it was estimated that the energy of the trapped incoherent light at the initial stage was 3 fJ for event i. In the same way, from the curve ii', the pulse energy at the initial stage was estimated to be 3 aJ for event ii. The amplification in pulse trapping using the 1.4 km-long LB-PMF was calculated to be 62 dB from the lower-energy case (curve ii') in Fig. 4, where the 3 aJ pulse was amplified to a 10 pJ pulse in the 1.4 km propagation. Generally speaking, the gain is much larger than that of conventional fiber amplifiers, such as rare-earth doped fiber amplifiers and Raman amplifiers pumped by cw lasers. The amplification by pulse trapping can be improved using a longer length of fiber, a pump pulse with higher energy, or higher-power incoherent light. In fact, a larger gain of 76 dB was obtained at L = 2.5 km numerically. Pulse propagation along the 2.5 km-long fiber is discussed in Section 4.

3.2 Demonstration of ultrashort pulse generation from incoherent light

Next, we experimentally examined pulse trains of generated pulses and pump pulses at the output of the 1.4 km-long LB-PMF. As shown in Figs. 5(a) and 5(b), when a 308 pJ pump pulse and 5.4 mW incoherent light were coupled into the fiber, in addition to the pump pulse along the slow axis, a pulse train was observed along the fast axis, which was the same polarization direction as that of the incoherent light. The interval of the fast-axis pulse train was 20 ns, which corresponds to a pump pulse repetition rate of 50 MHz. Because the pump pulse traps and amplifies the temporally overlapped component, as discussed in Section 3.1, we can say that the fast-axis pulse is a pulse generated from the incoherent light. Because of the trapping of the noisy light, the intensities of the two pulses fluctuated in distributions represented by the histograms shown in Figs. 5(c) and 5(d). The averages, μ, and the standard deviations, σ, were μ = 0.43 and σ = 0.19 for the generated pulse, and μ = 0.49 and σ = 0.21 for the pump pulse. Note that the sum of the intensities of the generated pulse and the pump pulse was almost constant (μ = 0.91, σ = 0.03) due to the energy transfer between the twin pulses though SRS.

Fig. 5 Pulse trains at the output of the 1.4 km-long LB-PMF. Experimental waveforms of (a) the generated pulse and (b) the pump pulse, (c) and (d) experimental histograms of their pulse peaks for about 25,000 pulses, and (e) and (f) numerical histograms of pulse peaks of twin pulses for 1,300 events.

Also in the numerical results, the peak powers of the generated pulse and pump pulse at the 1.4 km point were different for each event, as shown in Figs. 5(e) and 5(f). This fact corresponds to the intensity fluctuation in the experiment. The average and standard deviation for the normalized peak powers were μ = 0.67 and σ = 0.22 for the generated pulse, and μ = 0.27 and σ = 0.20 for the pump pulse. The distributions of the peak powers in the numerical results are in good agreement with the experimental ones. The intensity variation led to wavelength variation due to the intensity dependence of SSFS. The range of the wavelength variation was ~14 nm at the 1.4 km point.

3.3 Characterization of generated pulse

Figure 6 shows the experimental spectra of the pulse generation from the incoherent light using the 1.4 km-long LB-PMF. The input spectra of the pump pulse and the incoherent light are shown in Fig. 6(a). First, for comparison, only the 308 pJ pump pulse was coupled into the fiber. As shown in Fig. 6(b), the pump pulse was red-shifted due to SSFS. Although a 2 pJ trapped pulse was observed along the fast axis at 1687 nm because of slight variations in the birefringence of the fiber and the polarization state of the pump pulse, we estimated that this trapped component was negligibly small at the initial stage compared with the incoherent light.

Fig. 6 Experimental results of spectra at (a) input and (b) output of LB-PMF. The red and blue lines represent the slow and fast axes of the fiber. The solid lines in (b) show the spectra when both incoherent light and a pump pulse were coupled, and the dotted ones show the spectra when only the pump pulse was present. (c) Group delay dispersion for the slow and fast axes (blue and red lines) of the LB-PMF. The group delays of each pulse composing the twin pulses were the same, which corresponds to the group velocity matching condition.

As shown in Fig. 6(b), when the 5.4 mW incoherent light was coupled into the fiber together with the same pump pulse, a pulse along the fast axis was observed at the longer wavelength side of 1681 nm, which satisfied the group velocity matching condition with the pump pulse along the slow axis at 1641 nm as shown in Fig. 6(c). Thus, we can say that the incoherent light was trapped and amplified by the pump pulse, and the pulse was generated from the incoherent light. Since intensity and wavelength fluctuations occurred, as mentioned in the above numerical and experimental analyses, because of the slow measurement speed of the spectrum analyzer, the quasi-broadened (averaged) spectra [28

K. Sumimura, T. Ohta, and N. Nishizawa, “Quasi-super-continuum generation using ultrahigh-speed wavelength-tunable soliton pulses,” Opt. Lett. 33(24), 2892–2894 (2008). [CrossRef] [PubMed]

] of the generated pulse and pump pulse were observed. The average energy of the generated pulse was 121 pJ, which means that 39% of the input pump pulse energy was transferred to the generated pulse.

Figures 7(a) and 7(b) show the autocorrelation traces of the pump pulse and generated pulse, respectively. Although the seed of the pulse generation was incoherent light, the autocorrelation traces were stably observed without any coherent spikes [29

R. K. Shelton, L. S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, “Phase-coherent optical pulse synthesis from separate femtosecond lasers,” Science 293(5533), 1286–1289 (2001). [CrossRef] [PubMed]

]. The temporal width, Δt, of the generated pulse was 640 fs (FWHM) from the auto-correlation trace under the assumption of a sech²-shape. The frequency bandwidth, Δf, was 0.74 THz from Fig. 6(b). It was confirmed that a chirp-free, sech²-shaped, ultrashort pulse was generated from the incoherent light in the numerical analysis (see Section 3.1). However, the time·frequency bandwidth product, Δt·Δf, was 0.47, which was not equal to the predicted value of 0.315 for a TL sech²-shaped pulse. The deterioration of Δt·Δf is mainly caused by the center wavelength variation in the pulse train, which leads to quasi-broadening of the spectrum, not a chirp in each pulse.

Fig. 7 Auto-correlation traces of (a) pump pulse alone, (b) generated pulse alone, and (c) the twin pulses (overlapped pump pulse and generated pulse) at the LB-PMF output. The solid and broken lines show the experimental and theoretical traces, respectively.

As shown in Fig. 7(c), the autocorrelation trace of the overlapped twin pulses was also observed stably without any spikes. The trace forms a narrower temporal waveform with a few peaks [29

], which is caused by interference between the temporally overlapped, two-color twin pulses (coherent overlapping). The experimental trace was in good agreement with the theoretical one, in which completely temporally overlapped, two-color, twin pulses were assumed. Thus, we confirmed that the generated pulse and pump pulse were temporally overlapped stably. These stable observations of clear autocorrelation and coherent overlapping also indicate that the generated pulse had temporal coherence. We consider that the coherent ultrashort pulse was generated from the incoherent light since only a part of the incoherent light was converted into an ultrashort pulse and was amplified by a temporally overlapped, coherent ultrashort pulse through SRS. Unlike fiber Raman soliton lasers [11

J. D. Kafka and T. Baer, “Fiber Raman soliton laser pumped by a Nd:YAG laser,” Opt. Lett. 12(3), 181–183 (1987). [CrossRef] [PubMed]

,12

H. A. Haus and M. Nakazawa, “Theory of the fiber Raman soliton laser,” J. Opt. Soc. Am. B 4(5), 652–660 (1987). [CrossRef]

], where a pulse is synchronously amplified through SRS in a similar manner, our method does not require any cavity for the coherent pulse generation.

As mentioned above, the ultrashort pulse generation from the incoherent light is based on pulse trapping and amplification. Pulse trapping is also induced between an ultrashort pulse and coherent light of any temporal width, for example, from an ultrashort pulse to a cw beam [15

N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express 10(5), 256–261 (2002). [PubMed]

–19

E. Shiraki and N. Nishizawa, “Wideband amplification using orthogonally polarized pulse trapping in birefringent fibers,” Opt. Express 18(7), 7323–7330 (2010). [CrossRef] [PubMed]

]. Thus, we can say that the ultrashort pulse traps any type of light regardless of the coherence and the temporal width of the trapped light. A key point for pulse trapping is the presence of overlapped light at the same time and with the same group velocity as that of the pump pulse.

4. Suppression of intensity fluctuation in generated pulse train

Most ultrashort pulse applications require a stable pulse train with the same intensity and pulse width for all pulses. Figure 4 also shows numerical results of the evolutions of the generated pulse energy in further propagation along the LB-PMF. The energy difference between the events gradually decreased due to the output saturation. At the 2.5 km point, since most of the pump pulse energy was transferred into the generated pulse, the generated pulse energies became almost the same in most events. The maximum gain was as large as 76 dB. The temporal waveform of the generated pulse also became almost the same as a sech²-shaped ultrashort pulse, the average temporal width of which was 729 fs. This is because the generated pulses experience the soliton effect. The average peak power was 193 W, and the average and standard deviation for the normalized peak power were μ = 0.98 and σ = 0.008, respectively. These numerical results show that the intensity variation can be suppressed using gain saturation in pulse trapping. Thus, we expect that a stable pulse train with an ultrashort sech²-shape can be generated from incoherent light using a 2.5 km-long LB-PMF.

5. Conclusion

In this paper, we demonstrated and investigated ultrashort pulse generation from incoherent light from a super-luminescent diode by an ultrashort pulse using the nonlinear fiber phenomena of pulse trapping and amplification in a birefringent fiber. Since a trapped part of the incoherent light experiences the Raman gain and soliton effect induced by the ultrashort pulse along the 1.4 km-long low-birefringence polarization maintaining fiber, an ultrashort pulse is generated from the incoherent light. The obtained pulse energy was 121 pJ (average), and the gain was as large as 62 dB. Intensity and center wavelength fluctuations were observed because of the trapping of noisy light. Although the pulse was generated from the incoherent light in propagation along a single path in a birefringent fiber, the generated pulse was coherent light. Thus, we can generate a coherent ultrashort pulse without using any resonators. From the numerical results, it was confirmed that a pulse train with a stable intensity is obtainable from the incoherent light by using a longer fiber of 2.5 km in length due to the output saturation and soliton effect, where the maximum gain was as large as 76 dB.

We also confirmed that the incoherent light was trapped by the ultrashort pulse. From the fact that an ultrashort pulse also traps coherent light of a cw beam and an ultrashort pulse, as well as incoherent light, we can say that it is possible to trap any type of light by pulse trapping merely by satisfying the group velocity matching condition and temporal overlapping.

Acknowledgment

Part of this work was supported by the KDDI Foundation.

References and links

1.	I. N. Iii, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett. 16(8), 539–541 (1991). [CrossRef] [PubMed]
2.	M. E. Fermann, M. J. Andrejco, Y. Silberberg, and M. L. Stock, “Passive mode locking by using nonlinear polarization evolution in a polarization-maintaining erbium-doped fiber,” Opt. Lett. 18(11), 894–896 (1993). [CrossRef] [PubMed]
3.	G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).
4.	N. Nishizawa and T. Goto, “Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11(3), 325–327 (1999). [CrossRef]
5.	N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009). [CrossRef]
6.	T. Inoue, N. Kumano, M. Takahashi, T. Yagi, and M. Sakano, “Generation of 80-nm wavelength-tunable 100-fs pulse based on comblike profiled fiber comprised of HNLF and zero dispersion-slope NZDSF,” J. Lightwave Technol. 25(1), 165–169 (2007). [CrossRef]
7.	N. Nishizawa, K. Takahashi, Y. Ozeki, and K. Itoh, “Wideband spectral compression of wavelength-tunable ultrashort soliton pulse using comb-profile fiber,” Opt. Express 18(11), 11700–11706 (2010). [CrossRef] [PubMed]
8.	J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
9.	U. Keller, D. A. B. Miller, G. D. Boyd, T. H. Chiu, J. F. Ferguson, and M. T. Asom, “Solid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry-Perot saturable absorber,” Opt. Lett. 17(7), 505–507 (1992). [CrossRef] [PubMed]
10.	S. Yamashita, Y. Inoue, S. Maruyama, Y. Murakami, H. Yaguchi, M. Jablonski, and S. Y. Set, “Saturable absorbers incorporating carbon nanotubes directly synthesized onto substrates and fibers and their application to mode-locked fiber lasers,” Opt. Lett. 29(14), 1581–1583 (2004). [CrossRef] [PubMed]
11.	J. D. Kafka and T. Baer, “Fiber Raman soliton laser pumped by a Nd:YAG laser,” Opt. Lett. 12(3), 181–183 (1987). [CrossRef] [PubMed]
12.	H. A. Haus and M. Nakazawa, “Theory of the fiber Raman soliton laser,” J. Opt. Soc. Am. B 4(5), 652–660 (1987). [CrossRef]
13.	M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett. 14(18), 1011–1013 (1989). [CrossRef] [PubMed]
14.	G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).
15.	N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express 10(5), 256–261 (2002). [PubMed]
16.	E. Shiraki, N. Nishizawa, and K. Itoh, “Ultrashort pulse generation from continuous wave by pulse trapping in birefringent fibers,” Opt. Express 18(22), 23070–23078 (2010). [CrossRef] [PubMed]
17.	E. Shiraki, N. Nishizawa, and K. Itoh, “Ultrafast all-optical signal regenerator using pulse trapping in birefringent fibers,” J. Opt. Soc. Am. B 28(11), 2643–2649 (2011). [CrossRef]
18.	N. Nishizawa, Y. Ukai, and T. Goto, “Ultrafast all optical switching using pulse trapping in birefringent fibers,” Opt. Express 13(20), 8128–8135 (2005). [CrossRef] [PubMed]
19.	E. Shiraki and N. Nishizawa, “Wideband amplification using orthogonally polarized pulse trapping in birefringent fibers,” Opt. Express 18(7), 7323–7330 (2010). [CrossRef] [PubMed]
20.	J. T. Manassah, “Self-phase modulation of incoherent light,” Opt. Lett. 15(6), 329–331 (1990). [CrossRef] [PubMed]
21.	J. M. Hickmann, H. R. da Cruz, and A. S. Gouveia-Neto, “Cross-phase modulation of incoherent light in single-mode optical fibers,” Opt. Lett. 17(7), 478–480 (1992). [CrossRef] [PubMed]
22.	T. Zhang, X. Zhang, and G. Zhang, “Distributed fiber Raman amplifiers with incoherent pumping,” IEEE Photon. Technol. Lett. 17(6), 1175–1177 (2005). [CrossRef]
23.	A. M. Rocha, B. Neto, M. Facão, and P. S. André, “Study of Raman amplification with low cost incoherent pumps,” Microw. Opt. Technol. Lett. 50(2), 301–303 (2008). [CrossRef]
24.	K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express 16(21), 16467–16474 (2008). [CrossRef] [PubMed]
25.	Y. S. Jang and Y. C. Chung, “Four-wave mixing of incoherent light in a dispersion-shifted fiber using a spectrum-sliced fiber amplifier light source,” IEEE Photon. Technol. Lett. 10(2), 218–220 (1998). [CrossRef]
26.	Y. Yan and C. Yang, “Four-wave mixing between coherent signal and incoherent pump light in nonlinear fiber,” J. Lightwave Technol. 27(22), 4954–4959 (2009). [CrossRef]
27.	K. Hammani, C. Finot, and G. Millot, “Emergence of extreme events in fiber-based parametric processes driven by a partially incoherent pump wave,” Opt. Lett. 34(8), 1138–1140 (2009). [CrossRef] [PubMed]
28.	K. Sumimura, T. Ohta, and N. Nishizawa, “Quasi-super-continuum generation using ultrahigh-speed wavelength-tunable soliton pulses,” Opt. Lett. 33(24), 2892–2894 (2008). [CrossRef] [PubMed]
29.	R. K. Shelton, L. S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, “Phase-coherent optical pulse synthesis from separate femtosecond lasers,” Science 293(5533), 1286–1289 (2001). [CrossRef] [PubMed]

OCIS Codes
(060.7140) Fiber optics and optical communications : Ultrafast processes in fibers
(190.4370) Nonlinear optics : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: December 13, 2011
Revised Manuscript: March 16, 2012
Manuscript Accepted: April 26, 2012
Published: April 30, 2012

Citation
Eiji Shiraki and Norihiko Nishizawa, "Coherent ultrashort pulse generation from incoherent light by pulse trapping in birefringent fibers," Opt. Express 20, 11073-11082 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-10-11073

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References

I. N. Iii, “All-fiber ring soliton laser mode locked with a nonlinear mirror,” Opt. Lett.16(8), 539–541 (1991). [CrossRef] [PubMed]
M. E. Fermann, M. J. Andrejco, Y. Silberberg, and M. L. Stock, “Passive mode locking by using nonlinear polarization evolution in a polarization-maintaining erbium-doped fiber,” Opt. Lett.18(11), 894–896 (1993). [CrossRef] [PubMed]
G. P. Agrawal, Applications of Nonlinear Fiber Optics, 2nd ed. (Academic Press, 2008).
N. Nishizawa and T. Goto, “Compact system of wavelength-tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett.11(3), 325–327 (1999). [CrossRef]
N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron.45(11), 1446–1455 (2009). [CrossRef]
T. Inoue, N. Kumano, M. Takahashi, T. Yagi, and M. Sakano, “Generation of 80-nm wavelength-tunable 100-fs pulse based on comblike profiled fiber comprised of HNLF and zero dispersion-slope NZDSF,” J. Lightwave Technol.25(1), 165–169 (2007). [CrossRef]
N. Nishizawa, K. Takahashi, Y. Ozeki, and K. Itoh, “Wideband spectral compression of wavelength-tunable ultrashort soliton pulse using comb-profile fiber,” Opt. Express18(11), 11700–11706 (2010). [CrossRef] [PubMed]
J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys.78(4), 1135–1184 (2006). [CrossRef]
U. Keller, D. A. B. Miller, G. D. Boyd, T. H. Chiu, J. F. Ferguson, and M. T. Asom, “Solid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry-Perot saturable absorber,” Opt. Lett.17(7), 505–507 (1992). [CrossRef] [PubMed]
S. Yamashita, Y. Inoue, S. Maruyama, Y. Murakami, H. Yaguchi, M. Jablonski, and S. Y. Set, “Saturable absorbers incorporating carbon nanotubes directly synthesized onto substrates and fibers and their application to mode-locked fiber lasers,” Opt. Lett.29(14), 1581–1583 (2004). [CrossRef] [PubMed]
J. D. Kafka and T. Baer, “Fiber Raman soliton laser pumped by a Nd:YAG laser,” Opt. Lett.12(3), 181–183 (1987). [CrossRef] [PubMed]
H. A. Haus and M. Nakazawa, “Theory of the fiber Raman soliton laser,” J. Opt. Soc. Am. B4(5), 652–660 (1987). [CrossRef]
M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett.14(18), 1011–1013 (1989). [CrossRef] [PubMed]
G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).
N. Nishizawa and T. Goto, “Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers,” Opt. Express10(5), 256–261 (2002). [PubMed]
E. Shiraki, N. Nishizawa, and K. Itoh, “Ultrashort pulse generation from continuous wave by pulse trapping in birefringent fibers,” Opt. Express18(22), 23070–23078 (2010). [CrossRef] [PubMed]
E. Shiraki, N. Nishizawa, and K. Itoh, “Ultrafast all-optical signal regenerator using pulse trapping in birefringent fibers,” J. Opt. Soc. Am. B28(11), 2643–2649 (2011). [CrossRef]
N. Nishizawa, Y. Ukai, and T. Goto, “Ultrafast all optical switching using pulse trapping in birefringent fibers,” Opt. Express13(20), 8128–8135 (2005). [CrossRef] [PubMed]
E. Shiraki and N. Nishizawa, “Wideband amplification using orthogonally polarized pulse trapping in birefringent fibers,” Opt. Express18(7), 7323–7330 (2010). [CrossRef] [PubMed]
J. T. Manassah, “Self-phase modulation of incoherent light,” Opt. Lett.15(6), 329–331 (1990). [CrossRef] [PubMed]
J. M. Hickmann, H. R. da Cruz, and A. S. Gouveia-Neto, “Cross-phase modulation of incoherent light in single-mode optical fibers,” Opt. Lett.17(7), 478–480 (1992). [CrossRef] [PubMed]
T. Zhang, X. Zhang, and G. Zhang, “Distributed fiber Raman amplifiers with incoherent pumping,” IEEE Photon. Technol. Lett.17(6), 1175–1177 (2005). [CrossRef]
A. M. Rocha, B. Neto, M. Facão, and P. S. André, “Study of Raman amplification with low cost incoherent pumps,” Microw. Opt. Technol. Lett.50(2), 301–303 (2008). [CrossRef]
K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express16(21), 16467–16474 (2008). [CrossRef] [PubMed]
Y. S. Jang and Y. C. Chung, “Four-wave mixing of incoherent light in a dispersion-shifted fiber using a spectrum-sliced fiber amplifier light source,” IEEE Photon. Technol. Lett.10(2), 218–220 (1998). [CrossRef]
Y. Yan and C. Yang, “Four-wave mixing between coherent signal and incoherent pump light in nonlinear fiber,” J. Lightwave Technol.27(22), 4954–4959 (2009). [CrossRef]
K. Hammani, C. Finot, and G. Millot, “Emergence of extreme events in fiber-based parametric processes driven by a partially incoherent pump wave,” Opt. Lett.34(8), 1138–1140 (2009). [CrossRef] [PubMed]
K. Sumimura, T. Ohta, and N. Nishizawa, “Quasi-super-continuum generation using ultrahigh-speed wavelength-tunable soliton pulses,” Opt. Lett.33(24), 2892–2894 (2008). [CrossRef] [PubMed]
R. K. Shelton, L. S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye, “Phase-coherent optical pulse synthesis from separate femtosecond lasers,” Science293(5533), 1286–1289 (2001). [CrossRef] [PubMed]

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