Abstract

We experimentally investigate fast wavelength-tuning characteristics of a polarization-maintaining Er fiber laser, which is mode-locked with a semiconductor saturable absorber mirror. Wavelength tuning was accomplished with an intracavity filter incorporating a galvanometer mirror and a diffraction grating. Within the tunability of 30 nm, we achieved a wavelength-tuning speed of <5 ms. We also show that the variation of repetition rates can be suppressed to <200 Hz by simply shifting the position of the grating. The presented scheme for generating wavelength-tunable pulses will be potentially useful for coherent Raman spectral imaging.

© 2015 Optical Society of America

1. Introduction

In the field of biological imaging, the development of practical and functional lasers is getting more important [1]. For example, two-color picosecond lasers are applied to coherent Raman scattering (CRS) microscopy, which is opening fruitful applications to label-free biomedical imaging [2, 3]. In particular, hyperspectral CRS imaging using wavelength-tunable two-color pulses is attracting much attention because it allows us to discriminate different constituents [411].

Nevertheless, there are stringent requirements for optical pulse sources for CRS microscopy such as (i) fast wavelength tunability within milliseconds for minimizing dead time in spectral imaging, (ii) picosecond durations for efficient signal generation without compromising spectral resolution, (iii) near-infrared wavelength regions at 0.8-1.5 µm, (iv) constant repetition rate for the ease of synchronization of two individual lasers, and (v) compactness from a practical point of view. So far, various techniques of generating wavelength-tunable optical pulses for CRS microscopy have been reported such as optical parametric oscillator with an electro-optic filter [4], Ti:sapphire oscillator with an acousto-optic filter [5], spectral filtering of broadband laser pulses or supercontinuum [613], and dispersion-tuning actively mode-locked fiber laser [14]. However, it seems still difficult to simultaneously meet all the above requirements.

For generating wavelength-tunable optical pulses, the use of Raman soliton self-frequency shift (SSFS) in optical fibers has been reported [1519]. However, in order to efficiently cause SSFS, we have to employ femtosecond pulses, which may lead to a reduced spectral resolution when applied to CRS microscopy. The spectral focusing technique [18, 19] has been employed to overcome this issue, but it is technically challenging to achieve with femtosecond pulses a high spectral resolution, which is comparable to that obtained with picosecond pulses (i.e., ~5 cm−1). Spectral compression of femtosecond pulses to picosecond regime using soliton effect is also reported [20]. However, this technique requires careful design of optical fibers, and therefore it seems difficult to apply to wavelength regions other than 1.5-1.8 µm. Spectral compression can also occur in second harmonic generation (SHG) process [21, 22]. However, fast wavelength tuning seems difficult therein because mechanical movement of SHG crystal is necessary.

Passively mode-locked fiber lasers (PMLFL’s) using saturable absorbers are regarded as compact and practical pulse sources, especially at 1.03-µm and 1.55-µm wavelength regions with ytterbium and erbium gain fibers, respectively. The mode-locking element includes semiconductor saturable absorber mirror (SESAM) [2325] and nanocarbon materials [12, 2629]. Generation of wavelength-tunable picosecond pulses is possible by using an intracavity bandpass filter such as a dielectric filter and a diffraction grating [23]. However, fast tuning of PMLFL has never been reported so far. Furthermore, PMLFL’s are susceptible to various imperfections in the cavity, and therefore careful design is necessary for stable operation especially when polarization maintaining (PM) fibers are used.

In addition, although the effect of group velocity dispersion (GVD) of cavity fibers on pulse shaping in picosecond regime is almost negligible, GVD may lead to wavelength-dependent repetition rates, which make it difficult to synchronize different lasers for generating two-color pulses.

In this paper, we demonstrate a PM-Er-PMFL with a pulse durations of ~10 ps and the tuning speed of milliseconds, based on the intracavity tunable bandpass filter comprised of a galvanometer scanner (GS) and a diffraction grating [6]. We investigate the wavelength tuning characteristics and show that this laser can simultaneously meet the above requirements.

2. Experiments

2.1 Laser setup

Figure 1 shows a schematic of the developed PMLFL. The laser is comprised of a PM-erbium doped fiber (EDF) (CorActive, SCF-ER30-5/125/25-PM) with a length of 1.08 m, a SESAM (BATOP GmbH, SAM-1550-30-2ps), a PM-wavelength division multiplexing (WDM) coupler (optizone, PMFWDM-5598), a 976-nm pump laser diode (3S Photonics, 1999CHP), a PM output coupler with a coupling ratio of 10% (optizone, PMFC-55-2-10-B), and a tunable filter. The output power of the LD was set to ~70 mW. The tunable filter consists of a PM collimator (optizone, PMC-55-S-1-C-1), GS (Thorlabs, GVSM001), a lens pair with focal lengths of f1 = 35 mm and f2 = 125 mm, and a diffraction grating with a groove density of 600 /mm (Thorlabs, GR25-0613). The total length of PM fibers including EDF is 2.4 m, and the repetition rate is 37.4 MHz. The focal lengths of the lenses were chosen so that the filter has a Gaussian-shape reflection spectrum with a full-bandwidth at half maximum (FWHM) of 1.7 nm. The reflection loss of the filter was measured to be ~4 dB including the diffraction loss of the grating of ~1.2 dB. By changing the direction of GS, we can control the incident angle on the grating so as to change the oscillation wavelength. Furthermore, by changing the separation (Xg) between the lens and the diffraction grating, the filter can introduce a delay that is dependent on the transmission wavelength. This compensates for the wavelength-dependent delay due to the GVD of the cavity fibers so as to minimize the repetition rate variation. Note that this filter does not introduce group delay dispersion (GDD) within the bandwidth of the filter. We have not optimized the output coupling ratio (i.e. 10%). There seems a room to increase it by reducing the reflection loss of the filter through the optimization of free-space optics.

 

Fig. 1 Experimental setup. OSA: optical spectrum analyzer. AC: intensity autocorrelator. PD: photodetector. LD: 976-nm laser diode. GS: galvanometer scanner. L1-L4: lenses with focal lengths of f1 = 35 mm, f2 = 125 mm, f3 = –50 mm, and f4 = 11 mm, respectively. G: diffraction grating with a groove density of 600 /mm.

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For achieving mode-locking operation, we carefully adjusted the angle of PM axis of the collimator within ~2 degree so as to avoid unwanted crosstalk between slow and fast axes of PM fibers due to different diffraction efficiencies of p- and s-waves. Furthermore, it turned out that a key for realizing continuous wavelength tuning is fusion splice at the central point of PM-EDF, where the axes of the PM-EDFs are mutually different by 90 degree. This compensates for the polarization mode dispersion (PMD) of the PMF in the cavity. Otherwise, pulse splitting due to PMD and polarization-dependent loss given by the diffraction grating, which is equivalent to periodic optical filtering, competes with pulse shaping mechanism provided by SESAM. Indeed, when we did not introduce 90 degree splicing, the mode-locking operation failed at discrete wavelengths separated by ~5 nm (625 GHz), which roughly agreed with the inverse of the round-trip PMD (~1.6 ps) of PM fiber with a length of 2.4 m.

2.2 Generation of wavelength-tunable pulses

Figures 2(a) and 2(b) show the characteristics of the wavelength-tunable pulses measured with an intensity autocorrelator (Femtochrome, FR-103XL) and an optical spectrum analyzer (OSA) (ANDO, AQ6317B). We set the separation between the lens and the grating to be Xg = 25 mm, which is ~100 mm shorter than the focal length of the lens (i.e. f2), so as to compensate for anomalous dispersion of the cavity fibers. We can see that the wavelength was tunable from 1541 nm to 1574 nm. The pulse durations assuming Gaussian waveforms ranged from 9 to 15 ps, and the spectral widths ranged from 0.25 to 0.4 nm as shown in Fig. 2(c). The time-bandwidth product ranged from 0.49 to 0.54, which is only 10-25% larger than that of the Fourier transform limit (i.e. 0.44). Presumably the residual chirp arises from the intensity-dependent refractive index of SESAM. The optical power, measured with a power meter, ranged from 0.4 to 0.7 mW as shown in Fig. 2(d). In this way, wavelength-tunable picosecond pulses were successfully generated from the PMLFL.

 

Fig. 2 Measured characteristics of wavelength-tunable pulses. (a) Intensity autocorrelation traces. Red line: Gaussian fit. (b) Spectra. (c) Pulse width (left) and spectral width (right). (d) Time-bandwidth product (left) and optical power (right). (d) Repetition rate. Lines in (c) and (d) are for clarity.

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We also measured the repetition rate of the pulses using an RF spectrum analyzer (Agilent, E4411B). Figure 2(e) shows that the repetition rate variation was only ~180 Hz, which will be easily compensated for by attaching a piezoelectric actuator either on an optics element or a fiber. Note that, without dispersion compensation, the variation of repetition rates due to GVD is estimated to be 2DΔλfrep2~3.6 kHz, where D ~16 ps/nm/km is the GVD of fibers, Δλ = 34 nm is the tuning range, L = 2.4 m is the fiber length, and frep~37.4 MHz is the repetition rate. Therefore, we could reduce the variation of repetition rates by a factor of as much as 20.

2.3 Fast wavelength tuning

We investigated the speed of wavelength tuning. Figures 3(a) and 3(b) show the oscilloscope traces of optical pulses measured when the wavelength was changed (a) from 1565.4 nm to 1554.1 nm and (b) from 1554.1 nm to 1565.4 nm, respectively. We can see that the wavelength changed within ~0.7 ms, while mode-locking operation was maintained.

 

Fig. 3 Oscilloscope traces of optical pulses when the wavelength was changed (a) from 1565.4 nm to 1554.1 nm and (b) from 1554.1 nm to 1565.4 nm. Vertical axis: 400 µs/div. Horizontal axis: 20 mV/div.

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We found that the tuning range is dependent on the tuning speed and central wavelength. To investigate this point, GS was driven with a sinusoidal wave at various frequencies and amplitudes, while the optical spectra were measured with OSA in the peak-hold mode so that the failure in mode-locking operation could be detected. Figure 4 shows the measured spectra. When the driving frequency was 100 Hz (i.e., the wavelength was changed in 5 ms), the tuning range was as wide as 30 nm as shown with red line. When the driving frequency was increased to 500 Hz, the tuning range became as narrow as 12 nm, as shown by green line. This means that the wavelength tuning can be done in less than 1 ms within this wavelength range. This result is consistent with the results shown in Fig. 3. Furthermore, we can increase the wavelength range to ~18 nm by changing the central wavelength to 1561 nm, as shown by blue line. The mechanism behind such behavior is not clear at the moment. Presumably, pulse shaping and buildup dynamics are dependent on the wavelength.

 

Fig. 4 Optical spectra measured in the peak-hold mode when GS was driven with sinusoidal waves. Red: 100 Hz. Green and blue: 500 Hz.

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The tuning speed is currently limited not only by the speed of GS but also by the pulse shaping dynamics. Indeed, in Fig. 4, we can see that the spectral intensity is dependent on the driving condition. This means that the effect of pulse shaping dynamics is present in the above experiments. When GS is driven fast, the pulses in the laser are deformed by the optical filter whose central wavelength is dynamically changing, while SESAM tries to maintain mode-locking. Nevertheless, we can tune the wavelength of the pulses within milliseconds, which will be useful for spectral imaging applications.

2.4 Compensation for the variation of repetition rates with the intracavity filter

We investigated how the position of the diffraction grating affects the dependence of repetition rates on the oscillation wavelength. The results are summarized in Fig. 5(a). We can see that the variation of frep can be controlled by changing the position of the grating. The slope of the curves are derived with linear least-square fit, and then plotted in Fig. 5(b). The slope is almost zero when Xg ~33 mm, which is inconsistent with the result shown in Fig. 2, where Xg was set to ~25 mm. We investigated this point, and noticed that not only the position of the grating but also the position of GS affects the amount of GDD compensation. This point will be discussed in Appendix 2. The dependence of the slope on the grating position was derived by linear least-square fit to be –1.68 Hz/nm/mm. This value is in good agreement with the theoretical value of –1.68 Hz/nm/mm, which will be derived in Appendix 1.

 

Fig. 5 Experimental results of the compensation of repetition frequency. (a) Variation of repetition rates with respect to that at 1556 nm. Lines are for clarity. (b) The slope of curves shown in (a) plotted as a function of the position of the grating.

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We also noticed that the curves in Fig. 5(a) are not perfectly linear; we can see that the repetition rate is higher than that interpolated at 1549 nm. Furthermore, the deviation from the linearity is not always identical for different grating positions. The reason of this point is not clear at the moment. Presumably, some imperfections in free-space optics may remain, leading to unwanted filtering characteristics. This may also explain the difference between the data in Fig. 2(e) and Fig. 5(a), which are taken on different days. Nevertheless, these small variations will be compensated for with an additional actuator as described above.

3. Conclusion

We have demonstrated a picosecond PM-PMLFL with an intracavity GS-driven filter using a diffraction grating, and investigated its fast wavelength-tuning characteristics. We confirmed a tunability of >30 nm, a tuning speed of <5 ms for entire tuning range and <1 ms for a tuning range of 18 nm. Furthermore, by shifting the position of the grating, the variation of repetition rates was suppressed to <200 Hz, which is easily compensated for by using additional element for controlling the repetition rate. This compact, narrowband, wavelength-tunable picosecond pulse source will be useful for synchronizing wavelength-tunable two-color lasers that may be applicable for hyperspectral CRS imaging. Although a grating was used for intracavity filtering, we could employ other types of optical filters such as dielectric filters. In that case, cavity dispersion should be adequately controlled so as to suppress the repetition rate variation. Currently, the wavelength tunability of >30 nm corresponds to the wavenumber tunability of ~130 cm−1, which may not be sufficient for CRS imaging, but will be doubled when second-harmonic generation was applied. Since the pulse shaping does not rely on intracavity dispersion, we expect that the same scheme will be applicable to Yb-MLFL, where we could further enlarge the wavenumber tunability to well beyond 300 cm−1, which can cover the whole CH-stretching region. Such a tunable Yb-MLFL synchronized to an Er-MLFL with SHG will be applicable to fiber-laser-based hyperspectral SRS microscopy [13] in a much simpler setup.

Appendix

A.1. Compensation of group delay by the position shift of the diffraction grating

We calculate the wavelength-dependent repetition rate introduced by shifting the position of the diffraction grating. The calculation here is based on our previous report on spectral filtering with wavelength-dependent group delay [13], but the notation is slightly modified here.

As shown in Fig. 6, we consider a 4-f geometry on a xy plane, where the origin O and R are conjugate points. Therefore, rays from R are imaged to O, and the optical path length from R to O is independent of the path. We assume that GS is positioned at R. The effect of the position shift of GS will be discussed in A.2.

 

Fig. 6 Geometric arrangement of the OBPF.

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To create wavelength-dependent group delay, we put a diffraction grating at (x0, 0). We denote the angle between the normal of the grating and the x axis as θ, and the angle between the ray on the grating and the x axis as φ. Suppose that the ray impinges on the grating at Q(x1, y1). The line OQ is given by

y=xtanφ,
and the grating plane is given by
(xx0)cosθ+ysinθ=0.
From Eqs. (1)-(2), we find
x1=x01+tanθtanφ,
y1=x0tanφ1+tanθtanφ.
When x0 > 0, the optical path length from GS to Q is shortened by
l(φ)=OQ¯=x12+y12=x0(1+tanθtanφ)cosφ.
This leads to
dldφ=x0(tanφtanθ)(1+tanθtanφ)2cosφ.
From the diffraction condition, we find
2dsin(θφ)=λ.
Differentiating Eq. (7) with λ leads to
dφdλ=12dcos(θφ).
From Eqs. (6) and (8), we obtain
dldλ=dldφdφdλ=x0(tanφtanθ)2d(1+tanθtanφ)2cosφcos(θφ).
Assuming φ ~0,

dldλ=x0sinθ2d(1sin2θ).

Next, let’s consider how the optical path length affects the repetition rate f, which is related to the cavity length L by

f=c2L,
where c is the speed of light. Since the optical path length is decreased by l, dl = –dL. Therefore,
dfdl=dfdL=c2L2=2f2c.
From Eqs. (10) and (12), the wavelength-dependent repetition rate introduced by the filter can be derived as
dfdλ=dfdldldλ=x0f2sinθcd(1sin2θ)=x0f2(λ/2d)cd[1(λ/2d)2]
Substituting f = 37.4 MHz, λ = 1.56 µm, d = 1/600 mm, and c = 3 × 108 m/s, and using the relationship x0 = f2Xg, we have

ddXgdfdλ=f2(λ/2d)cd[1(λ/2d)2]=1.68Hz/nm/mm.

A.2. The effect of the position shift of GS

In the above discussion, we assumed that GS is located at the focal plane of L1. Here let’s consider the case where the position of GS is shifted by Δx1 and located at R’, as shown in Fig. 6. The conjugate point of R’ is denoted by O’, which is shifted from O by Δx2. From the theory of geometrical optics, it is well known that

Δx2Δx1=(f2f1)2.
Considering that the optical path length from R’ to O’ is independent of optical path, the group delay dispersion introduced by the filter is zero when the grating is positioned at O’. Thus, the amount of repetition rate compensation is
1.68[Hz/nm/mm]×(f2XgΔx2)[mm],
while the repetition rate variation induced by the dispersion of the fiber is derived as
2DLfrep2=107Hz/nm.
From Eq. (16) and (17), we find Δx2 = 28 mm, which corresponds to Δx1 = 2.2 mm. Therefore, such small amount of misalignment of GS can account for the experimental data.

From the above discussion, we realize that it is much effective to shift the position of GS instead of shifting the position of the grating. Taking advantage of this, we can decrease the distance between the grating and lens for realizing a compact setup. This point will be especially useful for Yb fiber lasers, where the normal dispersion of optical fibers has to be compensated.

Acknowledgments

We’d like to thank Prof. N. Nishizawa of Nagoya Univ. and Dr. K. Sumimura of Kokyo Inc. for their fruitful comments. This work was supported by JSPS KAKENHI Grant Numbers 25702026 and 25600116, Advanced Photon Science Alliance, and Inamori Foundation.

References and links

1. C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7(11), 875–882 (2013). [CrossRef]   [PubMed]  

2. J.-X. Cheng and X. S. Xie, Coherent Raman Scattering Microscopy (CRC Press, 2013).

3. W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011). [CrossRef]   [PubMed]  

4. L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, and X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. 38(2), 145–147 (2013). [CrossRef]   [PubMed]  

5. H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013). [CrossRef]   [PubMed]  

6. Y. Ozeki, W. Umemura, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “Stimulated Raman hyperspectral imaging based on spectral filtering of broadband fiber laser pulses,” Opt. Lett. 37(3), 431–433 (2012). [CrossRef]   [PubMed]  

7. Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012). [CrossRef]  

8. D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013). [CrossRef]   [PubMed]  

9. D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013). [CrossRef]   [PubMed]  

10. S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014). [CrossRef]   [PubMed]  

11. Y. Otsuka, K. Makara, S. Satoh, H. Hashimoto, and Y. Ozeki, “On-line visualization of multicolor chemical images with stimulated Raman scattering spectral microscopy,” Analyst (Lond.) 140(9), 2984–2987 (2015). [CrossRef]   [PubMed]  

12. C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014). [CrossRef]   [PubMed]  

13. K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014). [CrossRef]  

14. S. Bégin, B. Burgoyne, V. Mercier, A. Villeneuve, R. Vallée, and D. Côté, “Coherent anti-Stokes Raman scattering hyperspectral tissue imaging with a wavelength-swept system,” Biomed. Opt. Express 2(5), 1296–1306 (2011). [CrossRef]   [PubMed]  

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22. A. Gambetta, V. Kumar, G. Grancini, D. Polli, R. Ramponi, G. Cerullo, and M. Marangoni, “Fiber-format stimulated-Raman-scattering microscopy from a single laser oscillator,” Opt. Lett. 35(2), 226–228 (2010). [CrossRef]   [PubMed]  

23. L. Hong, “Wavelength tunable, polarization stable mode-locked fiber laser,” US Patent, PCT/US2000/019170.

24. L. Lefort, J. H. V. Price, D. J. Richardson, G. J. Spüler, R. Paschotta, U. Keller, A. R. Fry, and J. Weston, “Practical low-noise stretched-pulse Yb3+-doped fiber laser,” Opt. Lett. 27(5), 291–293 (2002). [CrossRef]   [PubMed]  

25. O. G. Okhotnikov, T. Jouhti, J. Konttinen, S. Karirinne, and M. Pessa, “1.5-µm monolithic GaInNAs semiconductor saturable-absorber mode locking of an erbium fiber laser,” Opt. Lett. 28(5), 364–366 (2003). [CrossRef]   [PubMed]  

26. S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Ultrafast fiber pulsed lasers incorporating carbon nanotubes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 137–146 (2004). [CrossRef]  

27. Y.-W. Song, S. Yamashita, C. S. Goh, and S. Y. Set, “Carbon nanotube mode lockers with enhanced nonlinearity via evanescent field interaction in D-shaped fibers,” Opt. Lett. 32(2), 148–150 (2007). [CrossRef]   [PubMed]  

28. K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a fiber taper embedded in carbon nanotube/polymer composite,” Opt. Lett. 32(15), 2242–2244 (2007). [CrossRef]   [PubMed]  

29. N. Nishizawa, Y. Seno, K. Sumimura, Y. Sakakibara, E. Itoga, H. Kataura, and K. Itoh, “All-polarization-maintaining Er-doped ultrashort-pulse fiber laser using carbon nanotube saturable absorber,” Opt. Express 16(13), 9429–9435 (2008). [CrossRef]   [PubMed]  

References

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  1. C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7(11), 875–882 (2013).
    [Crossref] [PubMed]
  2. J.-X. Cheng and X. S. Xie, Coherent Raman Scattering Microscopy (CRC Press, 2013).
  3. W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
    [Crossref] [PubMed]
  4. L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, and X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. 38(2), 145–147 (2013).
    [Crossref] [PubMed]
  5. H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013).
    [Crossref] [PubMed]
  6. Y. Ozeki, W. Umemura, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “Stimulated Raman hyperspectral imaging based on spectral filtering of broadband fiber laser pulses,” Opt. Lett. 37(3), 431–433 (2012).
    [Crossref] [PubMed]
  7. Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
    [Crossref]
  8. D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013).
    [Crossref] [PubMed]
  9. D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013).
    [Crossref] [PubMed]
  10. S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
    [Crossref] [PubMed]
  11. Y. Otsuka, K. Makara, S. Satoh, H. Hashimoto, and Y. Ozeki, “On-line visualization of multicolor chemical images with stimulated Raman scattering spectral microscopy,” Analyst (Lond.) 140(9), 2984–2987 (2015).
    [Crossref] [PubMed]
  12. C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014).
    [Crossref] [PubMed]
  13. K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
    [Crossref]
  14. S. Bégin, B. Burgoyne, V. Mercier, A. Villeneuve, R. Vallée, and D. Côté, “Coherent anti-Stokes Raman scattering hyperspectral tissue imaging with a wavelength-swept system,” Biomed. Opt. Express 2(5), 1296–1306 (2011).
    [Crossref] [PubMed]
  15. 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]
  16. H. Lim, J. Buckley, A. Chong, and F. W. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 µm,” Electron. Lett. 40(24), 1523–1525 (2004).
    [Crossref]
  17. J. Takayanagi, T. Sugiura, M. Yoshida, and N. Nishizawa, “1.0-1.7-µm wavelength-tunable ultrashort-pulse generation using femtosecond Yb-doped fiber laser and photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(21), 2284–2286 (2006).
    [Crossref]
  18. E. R. Andresen, C. K. Nielsen, J. Thøgersen, and S. R. Keiding, “Fiber laser-based light source for coherent anti-Stokes Raman scattering microspectroscopy,” Opt. Express 15(8), 4848–4856 (2007).
    [Crossref] [PubMed]
  19. E. R. Andresen, P. Berto, and H. Rigneault, “Stimulated Raman scattering microscopy by spectral focusing and fiber-generated soliton as Stokes pulse,” Opt. Lett. 36(13), 2387–2389 (2011).
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  20. 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).
    [PubMed]
  21. G. Krauss, T. Hanke, A. Sell, D. Träutlein, A. Leitenstorfer, R. Selm, M. Winterhalder, and A. Zumbusch, “Compact coherent anti-Stokes Raman scattering microscope based on a picosecond two-color Er:fiber laser system,” Opt. Lett. 34(18), 2847–2849 (2009).
    [Crossref] [PubMed]
  22. A. Gambetta, V. Kumar, G. Grancini, D. Polli, R. Ramponi, G. Cerullo, and M. Marangoni, “Fiber-format stimulated-Raman-scattering microscopy from a single laser oscillator,” Opt. Lett. 35(2), 226–228 (2010).
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  23. L. Hong, “Wavelength tunable, polarization stable mode-locked fiber laser,” US Patent, PCT/US2000/019170.
  24. L. Lefort, J. H. V. Price, D. J. Richardson, G. J. Spüler, R. Paschotta, U. Keller, A. R. Fry, and J. Weston, “Practical low-noise stretched-pulse Yb3+-doped fiber laser,” Opt. Lett. 27(5), 291–293 (2002).
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  25. O. G. Okhotnikov, T. Jouhti, J. Konttinen, S. Karirinne, and M. Pessa, “1.5-µm monolithic GaInNAs semiconductor saturable-absorber mode locking of an erbium fiber laser,” Opt. Lett. 28(5), 364–366 (2003).
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  26. S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Ultrafast fiber pulsed lasers incorporating carbon nanotubes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 137–146 (2004).
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  27. Y.-W. Song, S. Yamashita, C. S. Goh, and S. Y. Set, “Carbon nanotube mode lockers with enhanced nonlinearity via evanescent field interaction in D-shaped fibers,” Opt. Lett. 32(2), 148–150 (2007).
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  28. K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a fiber taper embedded in carbon nanotube/polymer composite,” Opt. Lett. 32(15), 2242–2244 (2007).
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  29. N. Nishizawa, Y. Seno, K. Sumimura, Y. Sakakibara, E. Itoga, H. Kataura, and K. Itoh, “All-polarization-maintaining Er-doped ultrashort-pulse fiber laser using carbon nanotube saturable absorber,” Opt. Express 16(13), 9429–9435 (2008).
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2015 (1)

Y. Otsuka, K. Makara, S. Satoh, H. Hashimoto, and Y. Ozeki, “On-line visualization of multicolor chemical images with stimulated Raman scattering spectral microscopy,” Analyst (Lond.) 140(9), 2984–2987 (2015).
[Crossref] [PubMed]

2014 (3)

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

2013 (5)

L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, and X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. 38(2), 145–147 (2013).
[Crossref] [PubMed]

H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013).
[Crossref] [PubMed]

C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7(11), 875–882 (2013).
[Crossref] [PubMed]

D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013).
[Crossref] [PubMed]

D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013).
[Crossref] [PubMed]

2012 (2)

Y. Ozeki, W. Umemura, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “Stimulated Raman hyperspectral imaging based on spectral filtering of broadband fiber laser pulses,” Opt. Lett. 37(3), 431–433 (2012).
[Crossref] [PubMed]

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[Crossref]

2011 (3)

2010 (2)

2009 (1)

2008 (1)

2007 (3)

2006 (1)

J. Takayanagi, T. Sugiura, M. Yoshida, and N. Nishizawa, “1.0-1.7-µm wavelength-tunable ultrashort-pulse generation using femtosecond Yb-doped fiber laser and photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(21), 2284–2286 (2006).
[Crossref]

2004 (2)

H. Lim, J. Buckley, A. Chong, and F. W. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 µm,” Electron. Lett. 40(24), 1523–1525 (2004).
[Crossref]

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Ultrafast fiber pulsed lasers incorporating carbon nanotubes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 137–146 (2004).
[Crossref]

2003 (1)

2002 (1)

1999 (1)

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]

Andresen, E. R.

Araki, T.

H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013).
[Crossref] [PubMed]

Bégin, S.

Ben-Amotz, D.

D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013).
[Crossref] [PubMed]

Berto, P.

Buckley, J.

H. Lim, J. Buckley, A. Chong, and F. W. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 µm,” Electron. Lett. 40(24), 1523–1525 (2004).
[Crossref]

Burgoyne, B.

Cahyadi, H.

H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013).
[Crossref] [PubMed]

Cerullo, G.

Cheng, J.-X.

D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013).
[Crossref] [PubMed]

D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013).
[Crossref] [PubMed]

Chong, A.

H. Lim, J. Buckley, A. Chong, and F. W. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 µm,” Electron. Lett. 40(24), 1523–1525 (2004).
[Crossref]

Côté, D.

Freudiger, C. W.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, and X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. 38(2), 145–147 (2013).
[Crossref] [PubMed]

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

Fry, A. R.

Fu, D.

Fukui, K.

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

Y. Ozeki, W. Umemura, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “Stimulated Raman hyperspectral imaging based on spectral filtering of broadband fiber laser pulses,” Opt. Lett. 37(3), 431–433 (2012).
[Crossref] [PubMed]

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[Crossref]

Gambetta, A.

Goh, C. S.

Goto, T.

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]

Grancini, G.

Hanke, T.

Hashiguchi, A.

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

Hashimoto, H.

Y. Otsuka, K. Makara, S. Satoh, H. Hashimoto, and Y. Ozeki, “On-line visualization of multicolor chemical images with stimulated Raman scattering spectral microscopy,” Analyst (Lond.) 140(9), 2984–2987 (2015).
[Crossref] [PubMed]

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[Crossref]

Hashimoto, M.

H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013).
[Crossref] [PubMed]

Holtom, G. R.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, and X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. 38(2), 145–147 (2013).
[Crossref] [PubMed]

Itoga, E.

Itoh, K.

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[Crossref]

Y. Ozeki, W. Umemura, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “Stimulated Raman hyperspectral imaging based on spectral filtering of broadband fiber laser pulses,” Opt. Lett. 37(3), 431–433 (2012).
[Crossref] [PubMed]

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).
[PubMed]

N. Nishizawa, Y. Seno, K. Sumimura, Y. Sakakibara, E. Itoga, H. Kataura, and K. Itoh, “All-polarization-maintaining Er-doped ultrashort-pulse fiber laser using carbon nanotube saturable absorber,” Opt. Express 16(13), 9429–9435 (2008).
[Crossref] [PubMed]

Iwatsuka, J.

H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013).
[Crossref] [PubMed]

Jablonski, M.

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Ultrafast fiber pulsed lasers incorporating carbon nanotubes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 137–146 (2004).
[Crossref]

Ji, M.

Jouhti, T.

Kanematsu, Y.

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

Karirinne, S.

Kataura, H.

Keiding, S. R.

Keller, U.

Kieu, K.

Kieu, K. Q.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

Kishi, T.

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

Kong, L.

Konttinen, J.

Krauss, G.

Kumar, V.

Leaird, D. E.

Lefort, L.

Leitenstorfer, A.

Lim, H.

H. Lim, J. Buckley, A. Chong, and F. W. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 µm,” Electron. Lett. 40(24), 1523–1525 (2004).
[Crossref]

Lu, S.

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

Makara, K.

Y. Otsuka, K. Makara, S. Satoh, H. Hashimoto, and Y. Ozeki, “On-line visualization of multicolor chemical images with stimulated Raman scattering spectral microscopy,” Analyst (Lond.) 140(9), 2984–2987 (2015).
[Crossref] [PubMed]

Mansuripur, M.

Marangoni, M.

Mercier, V.

Min, W.

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

Minamikawa, T.

H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013).
[Crossref] [PubMed]

Nielsen, C. K.

Niioka, H.

H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013).
[Crossref] [PubMed]

Nishizawa, N.

Y. Ozeki, W. Umemura, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “Stimulated Raman hyperspectral imaging based on spectral filtering of broadband fiber laser pulses,” Opt. Lett. 37(3), 431–433 (2012).
[Crossref] [PubMed]

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[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).
[PubMed]

N. Nishizawa, Y. Seno, K. Sumimura, Y. Sakakibara, E. Itoga, H. Kataura, and K. Itoh, “All-polarization-maintaining Er-doped ultrashort-pulse fiber laser using carbon nanotube saturable absorber,” Opt. Express 16(13), 9429–9435 (2008).
[Crossref] [PubMed]

J. Takayanagi, T. Sugiura, M. Yoshida, and N. Nishizawa, “1.0-1.7-µm wavelength-tunable ultrashort-pulse generation using femtosecond Yb-doped fiber laser and photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(21), 2284–2286 (2006).
[Crossref]

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]

Nose, K.

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

Okhotnikov, O. G.

Otsuka, Y.

Y. Otsuka, K. Makara, S. Satoh, H. Hashimoto, and Y. Ozeki, “On-line visualization of multicolor chemical images with stimulated Raman scattering spectral microscopy,” Analyst (Lond.) 140(9), 2984–2987 (2015).
[Crossref] [PubMed]

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[Crossref]

Ozeki, Y.

Y. Otsuka, K. Makara, S. Satoh, H. Hashimoto, and Y. Ozeki, “On-line visualization of multicolor chemical images with stimulated Raman scattering spectral microscopy,” Analyst (Lond.) 140(9), 2984–2987 (2015).
[Crossref] [PubMed]

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[Crossref]

Y. Ozeki, W. Umemura, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “Stimulated Raman hyperspectral imaging based on spectral filtering of broadband fiber laser pulses,” Opt. Lett. 37(3), 431–433 (2012).
[Crossref] [PubMed]

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).
[PubMed]

Paschotta, R.

Pessa, M.

Peyghambarian, N.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

Polli, D.

Price, J. H. V.

Ramponi, R.

Richardson, D. J.

Rigneault, H.

Sakakibara, Y.

Sakamoto, M.

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

Satoh, S.

Y. Otsuka, K. Makara, S. Satoh, H. Hashimoto, and Y. Ozeki, “On-line visualization of multicolor chemical images with stimulated Raman scattering spectral microscopy,” Analyst (Lond.) 140(9), 2984–2987 (2015).
[Crossref] [PubMed]

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[Crossref]

Sell, A.

Selm, R.

Seno, Y.

Set, S. Y.

Y.-W. Song, S. Yamashita, C. S. Goh, and S. Y. Set, “Carbon nanotube mode lockers with enhanced nonlinearity via evanescent field interaction in D-shaped fibers,” Opt. Lett. 32(2), 148–150 (2007).
[Crossref] [PubMed]

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Ultrafast fiber pulsed lasers incorporating carbon nanotubes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 137–146 (2004).
[Crossref]

Slipchenko, M. N.

D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013).
[Crossref] [PubMed]

D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013).
[Crossref] [PubMed]

Song, Y.-W.

Spüler, G. J.

Sugiura, T.

J. Takayanagi, T. Sugiura, M. Yoshida, and N. Nishizawa, “1.0-1.7-µm wavelength-tunable ultrashort-pulse generation using femtosecond Yb-doped fiber laser and photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(21), 2284–2286 (2006).
[Crossref]

Sumimura, K.

Takahashi, K.

Takai, Y.

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

Takata, H.

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

Takayanagi, J.

J. Takayanagi, T. Sugiura, M. Yoshida, and N. Nishizawa, “1.0-1.7-µm wavelength-tunable ultrashort-pulse generation using femtosecond Yb-doped fiber laser and photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(21), 2284–2286 (2006).
[Crossref]

Tanaka, Y.

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Ultrafast fiber pulsed lasers incorporating carbon nanotubes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 137–146 (2004).
[Crossref]

Thøgersen, J.

Träutlein, D.

Umemura, W.

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[Crossref]

Y. Ozeki, W. Umemura, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “Stimulated Raman hyperspectral imaging based on spectral filtering of broadband fiber laser pulses,” Opt. Lett. 37(3), 431–433 (2012).
[Crossref] [PubMed]

Vallée, R.

Villeneuve, A.

Wang, P.

D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013).
[Crossref] [PubMed]

Weiner, A. M.

D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013).
[Crossref] [PubMed]

D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013).
[Crossref] [PubMed]

Weston, J.

Winterhalder, M.

Wise, F. W.

C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7(11), 875–882 (2013).
[Crossref] [PubMed]

H. Lim, J. Buckley, A. Chong, and F. W. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 µm,” Electron. Lett. 40(24), 1523–1525 (2004).
[Crossref]

Xie, X. S.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, and X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. 38(2), 145–147 (2013).
[Crossref] [PubMed]

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

Xu, C.

C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7(11), 875–882 (2013).
[Crossref] [PubMed]

Yaguchi, H.

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Ultrafast fiber pulsed lasers incorporating carbon nanotubes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 137–146 (2004).
[Crossref]

Yamashita, S.

Yamazaki, K.

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

Yang, W.

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

Yoshida, M.

J. Takayanagi, T. Sugiura, M. Yoshida, and N. Nishizawa, “1.0-1.7-µm wavelength-tunable ultrashort-pulse generation using femtosecond Yb-doped fiber laser and photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(21), 2284–2286 (2006).
[Crossref]

Zhang, D.

D. Zhang, M. N. Slipchenko, D. E. Leaird, A. M. Weiner, and J.-X. Cheng, “Spectrally modulated stimulated Raman scattering imaging with an angle-to-wavelength pulse shaper,” Opt. Express 21(11), 13864–13874 (2013).
[Crossref] [PubMed]

D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013).
[Crossref] [PubMed]

Zumbusch, A.

Anal. Chem. (1)

D. Zhang, P. Wang, M. N. Slipchenko, D. Ben-Amotz, A. M. Weiner, and J.-X. Cheng, “Quantitative vibrational imaging by hyperspectral stimulated Raman scattering microscopy and multivariate curve resolution analysis,” Anal. Chem. 85(1), 98–106 (2013).
[Crossref] [PubMed]

Analyst (Lond.) (1)

Y. Otsuka, K. Makara, S. Satoh, H. Hashimoto, and Y. Ozeki, “On-line visualization of multicolor chemical images with stimulated Raman scattering spectral microscopy,” Analyst (Lond.) 140(9), 2984–2987 (2015).
[Crossref] [PubMed]

Annu. Rev. Phys. Chem. (1)

W. Min, C. W. Freudiger, S. Lu, and X. S. Xie, “Coherent nonlinear optical imaging: beyond fluorescence microscopy,” Annu. Rev. Phys. Chem. 62(1), 507–530 (2011).
[Crossref] [PubMed]

Biomed. Opt. Express (1)

Electron. Lett. (1)

H. Lim, J. Buckley, A. Chong, and F. W. Wise, “Fibre-based source of femtosecond pulses tunable from 1.0 to 1.3 µm,” Electron. Lett. 40(24), 1523–1525 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Ultrafast fiber pulsed lasers incorporating carbon nanotubes,” IEEE J. Sel. Top. Quantum Electron. 10(1), 137–146 (2004).
[Crossref]

IEEE Photon. Technol. Lett. (2)

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]

J. Takayanagi, T. Sugiura, M. Yoshida, and N. Nishizawa, “1.0-1.7-µm wavelength-tunable ultrashort-pulse generation using femtosecond Yb-doped fiber laser and photonic crystal fiber,” IEEE Photon. Technol. Lett. 18(21), 2284–2286 (2006).
[Crossref]

J. Biomed. Opt. (1)

H. Cahyadi, J. Iwatsuka, T. Minamikawa, H. Niioka, T. Araki, and M. Hashimoto, “Fast spectral coherent anti-Stokes Raman scattering microscopy with high-speed tunable picosecond laser,” J. Biomed. Opt. 18(9), 096009 (2013).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. (1)

K. Nose, T. Kishi, Y. Ozeki, Y. Kanematsu, H. Takata, K. Fukui, Y. Takai, and K. Itoh, “Stimulated Raman spectral microscope using synchronized Er- and Yb-fiber lasers,” Jpn. J. Appl. Phys. 53(5), 052401 (2014).
[Crossref]

Nat. Photonics (3)

Y. Ozeki, W. Umemura, Y. Otsuka, S. Satoh, H. Hashimoto, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “High-speed molecular spectral imaging of tissue with stimulated Raman scattering,” Nat. Photonics 6(12), 845–851 (2012).
[Crossref]

C. W. Freudiger, W. Yang, G. R. Holtom, N. Peyghambarian, X. S. Xie, and K. Q. Kieu, “Stimulated Raman scattering microscopy with a robust fibre laser source,” Nat. Photonics 8(2), 153–159 (2014).
[Crossref] [PubMed]

C. Xu and F. W. Wise, “Recent advances in fibre lasers for nonlinear microscopy,” Nat. Photonics 7(11), 875–882 (2013).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (9)

Y.-W. Song, S. Yamashita, C. S. Goh, and S. Y. Set, “Carbon nanotube mode lockers with enhanced nonlinearity via evanescent field interaction in D-shaped fibers,” Opt. Lett. 32(2), 148–150 (2007).
[Crossref] [PubMed]

K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a fiber taper embedded in carbon nanotube/polymer composite,” Opt. Lett. 32(15), 2242–2244 (2007).
[Crossref] [PubMed]

G. Krauss, T. Hanke, A. Sell, D. Träutlein, A. Leitenstorfer, R. Selm, M. Winterhalder, and A. Zumbusch, “Compact coherent anti-Stokes Raman scattering microscope based on a picosecond two-color Er:fiber laser system,” Opt. Lett. 34(18), 2847–2849 (2009).
[Crossref] [PubMed]

A. Gambetta, V. Kumar, G. Grancini, D. Polli, R. Ramponi, G. Cerullo, and M. Marangoni, “Fiber-format stimulated-Raman-scattering microscopy from a single laser oscillator,” Opt. Lett. 35(2), 226–228 (2010).
[Crossref] [PubMed]

L. Lefort, J. H. V. Price, D. J. Richardson, G. J. Spüler, R. Paschotta, U. Keller, A. R. Fry, and J. Weston, “Practical low-noise stretched-pulse Yb3+-doped fiber laser,” Opt. Lett. 27(5), 291–293 (2002).
[Crossref] [PubMed]

O. G. Okhotnikov, T. Jouhti, J. Konttinen, S. Karirinne, and M. Pessa, “1.5-µm monolithic GaInNAs semiconductor saturable-absorber mode locking of an erbium fiber laser,” Opt. Lett. 28(5), 364–366 (2003).
[Crossref] [PubMed]

E. R. Andresen, P. Berto, and H. Rigneault, “Stimulated Raman scattering microscopy by spectral focusing and fiber-generated soliton as Stokes pulse,” Opt. Lett. 36(13), 2387–2389 (2011).
[Crossref] [PubMed]

Y. Ozeki, W. Umemura, K. Sumimura, N. Nishizawa, K. Fukui, and K. Itoh, “Stimulated Raman hyperspectral imaging based on spectral filtering of broadband fiber laser pulses,” Opt. Lett. 37(3), 431–433 (2012).
[Crossref] [PubMed]

L. Kong, M. Ji, G. R. Holtom, D. Fu, C. W. Freudiger, and X. S. Xie, “Multicolor stimulated Raman scattering microscopy with a rapidly tunable optical parametric oscillator,” Opt. Lett. 38(2), 145–147 (2013).
[Crossref] [PubMed]

Pathol. Int. (1)

S. Satoh, Y. Otsuka, Y. Ozeki, K. Itoh, A. Hashiguchi, K. Yamazaki, H. Hashimoto, and M. Sakamoto, “Label-free visualization of acetaminophen-induced liver injury by high-speed stimulated Raman scattering spectral microscopy and multivariate image analysis,” Pathol. Int. 64(10), 518–526 (2014).
[Crossref] [PubMed]

Other (2)

J.-X. Cheng and X. S. Xie, Coherent Raman Scattering Microscopy (CRC Press, 2013).

L. Hong, “Wavelength tunable, polarization stable mode-locked fiber laser,” US Patent, PCT/US2000/019170.

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Figures (6)

Fig. 1
Fig. 1 Experimental setup. OSA: optical spectrum analyzer. AC: intensity autocorrelator. PD: photodetector. LD: 976-nm laser diode. GS: galvanometer scanner. L1-L4: lenses with focal lengths of f1 = 35 mm, f2 = 125 mm, f3 = –50 mm, and f4 = 11 mm, respectively. G: diffraction grating with a groove density of 600 /mm.
Fig. 2
Fig. 2 Measured characteristics of wavelength-tunable pulses. (a) Intensity autocorrelation traces. Red line: Gaussian fit. (b) Spectra. (c) Pulse width (left) and spectral width (right). (d) Time-bandwidth product (left) and optical power (right). (d) Repetition rate. Lines in (c) and (d) are for clarity.
Fig. 3
Fig. 3 Oscilloscope traces of optical pulses when the wavelength was changed (a) from 1565.4 nm to 1554.1 nm and (b) from 1554.1 nm to 1565.4 nm. Vertical axis: 400 µs/div. Horizontal axis: 20 mV/div.
Fig. 4
Fig. 4 Optical spectra measured in the peak-hold mode when GS was driven with sinusoidal waves. Red: 100 Hz. Green and blue: 500 Hz.
Fig. 5
Fig. 5 Experimental results of the compensation of repetition frequency. (a) Variation of repetition rates with respect to that at 1556 nm. Lines are for clarity. (b) The slope of curves shown in (a) plotted as a function of the position of the grating.
Fig. 6
Fig. 6 Geometric arrangement of the OBPF.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

y=xtanφ,
( x x 0 )cosθ+ysinθ=0.
x 1 = x 0 1+tanθtanφ ,
y 1 = x 0 tanφ 1+tanθtanφ .
l(φ)= OQ ¯ = x 1 2 + y 1 2 = x 0 (1+tanθtanφ)cosφ .
dl dφ = x 0 (tanφtanθ) (1+tanθtanφ) 2 cosφ .
2dsin(θφ)=λ.
dφ dλ = 1 2dcos(θφ) .
dl dλ = dl dφ dφ dλ = x 0 (tanφtanθ) 2d (1+tanθtanφ) 2 cosφcos(θφ) .
dl dλ = x 0 sinθ 2d(1 sin 2 θ) .
f= c 2L ,
df dl = df dL = c 2 L 2 = 2 f 2 c .
df dλ = df dl dl dλ = x 0 f 2 sinθ cd(1 sin 2 θ) = x 0 f 2 (λ/2d) cd[1 (λ/2d) 2 ]
d d X g df dλ = f 2 (λ/2d) cd[1 (λ/2d) 2 ] =1.68Hz/nm/mm.
Δ x 2 Δ x 1 = ( f 2 f 1 ) 2 .
1.68[Hz/nm/mm]×( f 2 X g Δ x 2 )[mm],
2DL f rep 2 =107Hz/nm.

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