Abstract

Chirped pulse amplification of a 1.6 GHz Ti:sapphire femtosecond frequency comb was achieved using a GaAs-based tapered semiconductor amplifier. The spectral component of 855–865 nm was coherently amplified up to 379 mW at 2.5 A, corresponding to a peak power of 1.48 kW and an average power of 150 µW per mode. A chirped Bragg grating was used for pulse stretching and compression, resulting in a ${150}\;{\rm mm} \times {200}\;{\rm mm}$ compact amplification system. Competition between the amplified spontaneous emission and the coherent signal was observed at high driving currents. A numerical analysis was presented to account for the observed gain suppression. This amplification method is useful for the realization of high repetition rate frequency combs with a wider spectral range, including the UV and mid-infrared regions.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Optical frequency combs using gigahertz mode-locked oscillators have unique advantages compared with typical combs with repetition rates of tens of megahertz. The higher optical power per mode makes it possible to measure the optical frequency with a high signal-to-noise ratio. The wider mode spacing enables us to directly resolve the frequency of Doppler-broadened transitions. In addition, the compactness is beneficial in practical applications such as astronomical observations [1,2]. However, the low pulse energy results in less nonlinear conversion efficiency, for example, to the UV region. Thus, coherent amplification that maintains a high repetition rate is necessary to realize a broader spectral range via nonlinear conversion. For example, a bright gigahertz frequency comb in the UV region would extend the application range of precision spectroscopy to electronic transitions in non-metallic atoms. However, amplification of femtosecond pulses using chirped pulse amplification [3] or passive resonators [4] reduces the repetition rate. Multipass amplification under steady-state excitation cannot achieve sufficient gain.

In this Letter, we propose chirped pulse amplification of a 1.6 GHz Ti:sapphire comb using a tapered semiconductor amplifier (TSA). TSAs are highly efficient amplifiers usually used in continuous-wave (CW) lasers and can amplify several milliwatts of CW radiation to several watts. On the other hand, a TSA is not suitable for amplifying pulses owing to its short carrier lifetime. However, temporal stretching of the input pulse is effective for increasing the amplification efficiency of pulsed light using TSAs. In a previous study, a femtosecond Ti:sapphire mode-locked laser with a repetition rate of 100 MHz, center wavelength of 780 nm, and spectral widths of 3 and 14 nm was amplified using pulse stretching with frequency chirping in optical fibers [5]. They showed that the phase coherence of the input was maintained at a level higher than ${10^{- 15}}$ after the amplification process. Chirped pulse amplification of a semiconductor mode-locked laser with a repetition rate of 95 MHz, a center wavelength of 975 nm, and a spectral width of 6 nm was also performed using pulse stretching and compression by a fiber Bragg grating [6]. This method achieved a pulse width of 590 fs and a peak power of 1.4 kW. In the high repetition rate regime, a semiconductor mode-locked laser with a repetition rate of 4 GHz, center wavelength of 922 nm, and spectral width of 4.4 nm was successfully amplified up to 366 W peak power using frequency chirping in the oscillator [7].

Here we amplified a stretched Ti:sapphire frequency comb with a repetition rate of 1.6 GHz, followed by pulse compression to near the Fourier transform limit. A chirped Bragg grating (CBG) was used to stretch and compress pulses, resulting in a compact amplification system of ${150}\;{\rm mm} \times {200}\;{\rm mm}$. During the amplification process, competition between the coherent signal and the amplified spontaneous emission (ASE) was observed. The results are discussed through numerical calculations using a simple rate equation.

Figure 1 shows the experimental setup. An in-house built Ti:sapphire frequency comb with a repetition rate of 1.6 GHz was used as the light source. An 855–865 nm component of the Ti:sapphire frequency comb spectrum (corresponding to a transform-limited pulse width of 110 fs) was extracted using a bandpass filter. The pulse with a filtered spectrum was normally incident on a CBG (fabricated by OptiGrate Corp.) and reflected back. The stretched pulse, which had a designed pulse duration of 450 ps, was extracted using a polarizing beam splitter (PBS) and a quarter-wave plate (QWP), and then injected into the single-mode waveguide of a GaAs-based TSA (DILAS, TA-0860-3000) using an aspheric lens. The TSA had a gain in the wavelength range of 850–868 nm with its temperature stabilized at 20°C. The 5000 µm long waveguide had an aperture size of ${1.2}\;{\unicode{x00B5}{\rm m}} \times {1.2}\;{\unicode{x00B5}{\rm m}}$ on the input side, and mode matching was performed carefully.

 figure: Fig. 1.

Fig. 1. Experimental setup (TSA, tapered semiconductor amplifier; CBG, chirped Bragg grating; PBS, polarizing beam splitter; QWP, quarter-wave plate).

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After amplification, the laterally broadened beam from the ${1.2}\;{\unicode{x00B5}{\rm m}} \times {150}\;{\unicode{x00B5}{\rm m}}$ output facet was compensated for astigmatism by collimation and cylindrical lenses. The shaped beam was passed through an optical isolator to prevent optical feedback and injected from the opposite side of the CBG for compression. The CBG was 45 mm long, and the size of the entire amplification system was ${150}\;{\rm mm} \times {200}\;{\rm mm}$. The PBS used to extract the pulses had a transmission extinction ratio ${{T}_{p}}:{{T}_{s}}$ of 1000:1. The dispersion in the optical elements was compensated for by multiple reflections from a pair of chirped mirrors. The insertion loss in the elements and the coupling loss owing to mode mismatch were estimated to be approximately 0.96 and 0.22 dB, respectively. We measured the pulse duration by taking the intensity autocorrelation using a 300 µm thick barium borate crystal.

Figure 2(a) shows the driving current dependence of the total optical output power at an injection power of 17 mW and the output power of the ASE without injection. The total output power with injection began to increase linearly at 1.2 A and was amplified up to 625 mW at 2.5 A, with a slope efficiency of 496 mW/A. Without injection, the ASE power was suppressed at low currents, but increased up to 410 mW with a slope efficiency of 408 mW/A at currents above 1.6 A; a narrow spectral component also appeared [see Fig. 3(b)], which might be caused by the insufficiency in AR coatings on the TSA facets. Although the TSA is designed to operate at a maximum driving current of 5 A with optical injection, the measurement was limited to driving currents of up to 2.5 A because of the pronounced amplification by the ASE at higher driving currents.

 figure: Fig. 2.

Fig. 2. (a) Driving current dependence of the total optical output power at an injection power of 17 mW (red squares) and of the output power of the ASE without injection (red triangles). (b) Current dependence of the gain of the amplified frequency comb (red circles) and CW laser (blue circles). (c) Optical input power dependence of the gain of the amplified comb at 2.0 A.

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 figure: Fig. 3.

Fig. 3. (a) Spectra of the injected (dashed line) and output (solid line) pulses at 2.5 A. (b) Spectrum of the ASE without injection at the same current. (c) Intensity autocorrelation of pulses measured after compression.

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The optical output power with injection is the sum of the amplified frequency comb and the ASE. At high current values of typically ${\gt}{1.6}\;{\rm A}$, the competition between the coherent amplification and the ASE was observed, making it difficult to measure the optical power separately. We estimated the power of the amplified comb at high current values by measuring the power of the second harmonic. The correspondence between the power of the second harmonic and the power of the amplified comb was obtained at drive currents lower than 1.6 A.

Figure 2(b) shows the dependence of the gain of the amplified frequency comb on the driving current. We included the gain for an injected CW laser (taken from the manufacturer’s spec sheet) as a reference, although the coupling efficiency may be different from that in the present setup. The amplification of the comb began at 1.2 A and increased linearly up to 2.1 A (13 dB gain) with a slope efficiency of 348 mW/A. Above 2.1 A, the inhibition of amplification by the ASE became pronounced, and the slope efficiency decreased to 123 mW/A. The maximum output power of the amplified comb was 379 mW (corresponding to a gain of 13.4 dB and a pulse energy of 236 pJ) at 2.5 A, and the average power per mode was 150 µW. The 13.4 dB gain is 2.6 dB smaller than the expected gain for the CW injection. The ASE that caused the optical noise showed a maximum power of 246 mW (corresponding to an optical power spectral density of 60 fW/Hz) at 2.5 A. Better AR coatings of the TSA would improve the amplification efficiency.

Figure 2(c) shows the optical injection power dependence of the gain of the amplified comb at 2.0 A, which was measured to examine gain saturation. The power of the amplified comb was evaluated by subtracting the total output, which might be underestimated for high optical input powers. Although the gain at high optical input powers had a roll-off compared with the small signal gain, the strong saturation generally observed in the amplification of femtosecond pulses did not occur.

Figure 3(a) shows the spectra of the injected and output pulses at 2.5 A, and Fig. 3(b) shows the spectrum of the ASE without injection at the same driving current. The spectral widths of the injected and output pulses are 8.3 and 7.1 nm at full width at half-maximum, respectively. The peak on the long-wavelength side of the output spectrum was due to the contribution of the ASE. Apart from the decrease in the spectral width due to gain narrowing, this indicates that the pulses were amplified over the entire spectrum.

Figure 3(c) shows the result of the intensity autocorrelation measurement, corrected for the dispersion caused in the measurement. The compressed pulse width was 160 fs, which is comparable to the Fourier transform limit (138 fs) derived from the spectral width of the injected pulse. This result confirms that the nonlinear phase modulation was minimal, and the amplified pulse was properly compressed by the setup of this Letter. This pulse width is the shortest among those obtained in studies that used a similar setup [57], which is important to extend of frequency combs to the UV region through wavelength conversion.

In pulse amplification using TSAs, temporal and spectral distortions due to nonlinear refractive index changes in the gain medium, including self-phase modulation, generally occur [8]. Therefore, we assessed the magnitude of the nonlinear optical effect induced by the stretched pulse used in this Letter. The nonlinear phase shift accumulated in the TSA, the B-integral, is expressed as follows:

$$B = \frac{{2\pi}}{\lambda}\int {n_2}I(z ){\rm d}z ,$$
where ${n_2}$ is the nonlinear refractive index, $I(z)$ is the pulse intensity along the beam axis, and $z$ is the position in propagating direction. The value of ${n_2}$ for the GaAs waveguide was ${\sim}1 \times {10^{- 14}}\;{{\rm cm}^2}/{\rm W}$, and the maximum pulse intensity in the waveguide was $3 \times {10^5}{\rm \;W}/{{\rm cm}^2}$. The phase shift originating from the nonlinear refractive index was $1 \times {10^{- 4}}$, and its effect on the spectrum and pulse waveform was negligible. The stretched pulse used in this Letter had a low instantaneous intensity owing to its high repetition rate and long pulse width, and it can be amplified without any distortion of the spectrum or pulse waveform apart from gain narrowing.

However, several factors reduce the amplification efficiency compared to the amplification of a CW laser [9]. Delayed gain recovery and non-equilibrium carrier dynamics lead to gain suppression for pulse widths less than several picoseconds. In addition, gain suppression due to the ASE is more pronounced in pulse amplification than in CW [7]. To better understand the amplification characteristics presented above, we performed numerical calculations and compared the results with those of the CW laser. The stretched pulse has a pulse width of 450 ps because of the linear chirp in the CBG, which is long enough for the pulse width to neglect the detailed carrier dynamics [9]. Assuming that the carrier distribution is uniform in the waveguide and that the carriers reach equilibrium fast enough compared to the time variation of the incident pulse, the time variation of the carrier number is described by the following rate equation:

$$\frac{{{\rm d}N}}{{{\rm d}t}} = \frac{{({I - {I_0}} )}}{q} - \frac{{{P_{{\rm laser}}}}}{{h\nu}} - \left({\frac{N}{{{\tau _{c}}}}} \right) ,$$
where $N$ is the total number of carriers, $I$ is the driving current value, ${I_0}$ is the bias current for transparency, $q$ is the charge element, ${P_{{\rm laser}}}$ is the optical output power of the laser, $h\nu$ is the photon energy, and ${\tau _{ c}}$ is the carrier lifetime. ${\tau _{c}}$ can be expressed in terms of the relaxation time due to the ASE, ${\tau _{{\rm ase}}}$, and the relaxation time due to the radiation-free transition, ${\tau _{{\rm nr}}}$, is as follows:
$$\frac{1}{{{\tau _{ c}}}} = \frac{1}{{{\tau _{{\rm ase}}}}} + \frac{1}{{{\tau _{{\rm nr}}}}}.$$

The laser power, ${P_{{\rm laser}}}$, and the ASE power, ${P_{{\rm ase}}}$, are expressed as follows:

$${P_{{\rm laser}}} = G(\nu )N{P_{{\rm in}}} ,$$
$${P_{{\rm ase}}} = \frac{{Nh\nu}}{{{\tau _{{\rm ase}}}}} ,$$
where ${P_{{\rm in}}}$ is the incident power of the laser, and $G(\nu)$ is the proportionality coefficient that relates the gain spectrum and the number of carriers. Considering the shape of the gain spectrum, we approximated $G(\nu)$ as a Gaussian with a full width at half-maximum of 10 nm. For a simplified and qualitative interpretation, we neglected the possible nonlinear gain for the ASE with respect to the driving current.

We calculated the average output power with injection of either a CW laser or a Gaussian pulse with a pulse width of 450 ps, both with an average input power of 20 mW. The repetition rate of the pulse is 1.6 GHz. The current dependence of the gain is shown in Fig. 4(a). Based on the output characteristics of the amplifier in free-running operation and the energy balance, we set ${I_0}$ to 1.35 A, ${\tau _{{\rm ase}}}$ to 400 ps, and ${\tau _{{\rm nr}}}$ to 130 ps. The result qualitatively explains the experimental fact that the amplification efficiency is lower for the pulse than for the CW. The physical origin of the reduced gain for the pulsed input is that the ASE predominates the amplification when the input power is weak in the modulated temporal distribution: the calculated time variation of the instantaneous output power of the coherent signal and the ASE for the CW and pulsed injection are shown in Fig. 4(b). For pulsed injection, the gain consumption due to the ASE amplification becomes significant at a low input such as approximately 0.3 ns whereas, for CW injection, the steady input suppresses the ASE and maintains a relatively high gain of the coherent signal. When the pulse width of the incident pulse was 450 ps, the calculated pulse width of the amplified pulse was 435 ps, and the decrease in pulse width due to amplification was estimated to be 3%. For a more quantitative analysis, it is necessary to consider the spatial dependence of the pulse intensity and the gain, as well as the internal reflection causing the enhanced ASE and the temperature effect at high driving currents.

 figure: Fig. 4.

Fig. 4. (a) Calculated current dependence of the gain for CW (blue circles) and pulsed (red circles) injection. (b) Calculated time variation of the instantaneous output power of the coherent signal (solid line) and the ASE (dashed line) for CW (blue line) and pulsed (red line) injection.

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The numerical calculation using this model shows that the amplification efficiency can be improved by 10% by extending the pulse width to 600 ps or increasing the repetition rate to 2 GHz. It is expected that the amplification efficiency can be further improved by using a CBG with higher dispersion rates or a light source with higher repetition rates.

In summary, we have demonstrated a compact and efficient chirped pulse amplification of a 1.6 GHz frequency comb using a TSA. A maximum power of 379 mW and an average mode power of 150 µW were achieved while maintaining the pulse width close to the Fourier transform limit. The size of the optical system was reduced to ${150}\;{\rm mm} \times {200}\;{\rm mm}$ using a CBG for pulse stretching and compression. Owing to the high repetition rate and stretching by the CBG, amplification was achieved without any distortion of the pulse waveform or spectrum due to nonlinear effects. Numerical calculations using a simple rate equation showed that the stretched pulse used in this Letter is more susceptible to gain suppression than the CW laser. Further improvement of the amplification efficiency by increasing the repetition rate or by further stretching the pulses is a future challenge. This amplification method is expected to enable the realization of bright high repetition rate frequency combs in the UV region and direct frequency comb spectroscopy with a high signal-to-noise ratio.

Funding

Precursory Research for Embryonic Science and Technology (JPMJPR190B).

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

REFERENCES

1. E. Chae, E. Kambe, K. Motohara, H. Izumiura, M. Doi, and K. Yoshioka, J. Opt. Soc. Am. B 38, A1 (2021). [CrossRef]  

2. D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Chang, A. J. Benedick, L.-J. Chen, F. X. Kärtner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, Opt. Express 20, 13711 (2012). [CrossRef]  

3. D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985). [CrossRef]  

4. R. J. Jones and J. Ye, Opt. Lett. 27, 1848 (2002). [CrossRef]  

5. F. C. Cruz, M. C. Stowe, and J. Ye, Opt. Lett. 31, 1337 (2006). [CrossRef]  

6. K. Kim, S. Lee, and P. J. Delfyett, Opt. Express 13, 4600 (2005). [CrossRef]  

7. T. Ulm, F. Harth, H. Fuchs, J. A. L’Huillier, and R. Wallenstein, Appl. Phys. B 92, 481 (2008). [CrossRef]  

8. G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989). [CrossRef]  

9. J. Mark and J. Mork, Appl. Phys. Lett. 61, 2281 (1992). [CrossRef]  

References

  • View by:

  1. E. Chae, E. Kambe, K. Motohara, H. Izumiura, M. Doi, and K. Yoshioka, J. Opt. Soc. Am. B 38, A1 (2021).
    [Crossref]
  2. D. F. Phillips, A. G. Glenday, C.-H. Li, C. Cramer, G. Furesz, G. Chang, A. J. Benedick, L.-J. Chen, F. X. Kärtner, S. Korzennik, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, Opt. Express 20, 13711 (2012).
    [Crossref]
  3. D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
    [Crossref]
  4. R. J. Jones and J. Ye, Opt. Lett. 27, 1848 (2002).
    [Crossref]
  5. F. C. Cruz, M. C. Stowe, and J. Ye, Opt. Lett. 31, 1337 (2006).
    [Crossref]
  6. K. Kim, S. Lee, and P. J. Delfyett, Opt. Express 13, 4600 (2005).
    [Crossref]
  7. T. Ulm, F. Harth, H. Fuchs, J. A. L’Huillier, and R. Wallenstein, Appl. Phys. B 92, 481 (2008).
    [Crossref]
  8. G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
    [Crossref]
  9. J. Mark and J. Mork, Appl. Phys. Lett. 61, 2281 (1992).
    [Crossref]

2021 (1)

2012 (1)

2008 (1)

T. Ulm, F. Harth, H. Fuchs, J. A. L’Huillier, and R. Wallenstein, Appl. Phys. B 92, 481 (2008).
[Crossref]

2006 (1)

2005 (1)

2002 (1)

1992 (1)

J. Mark and J. Mork, Appl. Phys. Lett. 61, 2281 (1992).
[Crossref]

1989 (1)

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[Crossref]

1985 (1)

D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
[Crossref]

Agrawal, G. P.

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[Crossref]

Benedick, A. J.

Chae, E.

Chang, G.

Chen, L.-J.

Cramer, C.

Cruz, F. C.

Delfyett, P. J.

Doi, M.

Fuchs, H.

T. Ulm, F. Harth, H. Fuchs, J. A. L’Huillier, and R. Wallenstein, Appl. Phys. B 92, 481 (2008).
[Crossref]

Furesz, G.

Glenday, A. G.

Harth, F.

T. Ulm, F. Harth, H. Fuchs, J. A. L’Huillier, and R. Wallenstein, Appl. Phys. B 92, 481 (2008).
[Crossref]

Izumiura, H.

Jones, R. J.

Kambe, E.

Kärtner, F. X.

Kim, K.

Korzennik, S.

L’Huillier, J. A.

T. Ulm, F. Harth, H. Fuchs, J. A. L’Huillier, and R. Wallenstein, Appl. Phys. B 92, 481 (2008).
[Crossref]

Lee, S.

Li, C.-H.

Mark, J.

J. Mark and J. Mork, Appl. Phys. Lett. 61, 2281 (1992).
[Crossref]

Mork, J.

J. Mark and J. Mork, Appl. Phys. Lett. 61, 2281 (1992).
[Crossref]

Motohara, K.

Mourou, G.

D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
[Crossref]

Olsson, N. A.

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[Crossref]

Phillips, D. F.

Sasselov, D.

Stowe, M. C.

Strickland, D.

D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
[Crossref]

Szentgyorgyi, A.

Ulm, T.

T. Ulm, F. Harth, H. Fuchs, J. A. L’Huillier, and R. Wallenstein, Appl. Phys. B 92, 481 (2008).
[Crossref]

Wallenstein, R.

T. Ulm, F. Harth, H. Fuchs, J. A. L’Huillier, and R. Wallenstein, Appl. Phys. B 92, 481 (2008).
[Crossref]

Walsworth, R. L.

Ye, J.

Yoshioka, K.

Appl. Phys. B (1)

T. Ulm, F. Harth, H. Fuchs, J. A. L’Huillier, and R. Wallenstein, Appl. Phys. B 92, 481 (2008).
[Crossref]

Appl. Phys. Lett. (1)

J. Mark and J. Mork, Appl. Phys. Lett. 61, 2281 (1992).
[Crossref]

IEEE J. Quantum Electron. (1)

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (4)

Fig. 1.
Fig. 1. Experimental setup (TSA, tapered semiconductor amplifier; CBG, chirped Bragg grating; PBS, polarizing beam splitter; QWP, quarter-wave plate).
Fig. 2.
Fig. 2. (a) Driving current dependence of the total optical output power at an injection power of 17 mW (red squares) and of the output power of the ASE without injection (red triangles). (b) Current dependence of the gain of the amplified frequency comb (red circles) and CW laser (blue circles). (c) Optical input power dependence of the gain of the amplified comb at 2.0 A.
Fig. 3.
Fig. 3. (a) Spectra of the injected (dashed line) and output (solid line) pulses at 2.5 A. (b) Spectrum of the ASE without injection at the same current. (c) Intensity autocorrelation of pulses measured after compression.
Fig. 4.
Fig. 4. (a) Calculated current dependence of the gain for CW (blue circles) and pulsed (red circles) injection. (b) Calculated time variation of the instantaneous output power of the coherent signal (solid line) and the ASE (dashed line) for CW (blue line) and pulsed (red line) injection.

Equations (5)

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B = 2 π λ n 2 I ( z ) d z ,
d N d t = ( I I 0 ) q P l a s e r h ν ( N τ c ) ,
1 τ c = 1 τ a s e + 1 τ n r .
P l a s e r = G ( ν ) N P i n ,
P a s e = N h ν τ a s e ,