Abstract

Frequency combs in the mid-IR wavelength are usually implemented by difference-frequency generation (DFG) that mixes pump pulses and signal pulses. Different from most optical parametric amplifiers that operate at a typical low repetition rate of <0.1 MHz, mid-IR frequency combs require that pump/signal pulse repetition rate must be at least as high as tens of MHz (normally >30 MHz). The DFG mixing high repetition rate (HRR) pulses limits the allowed pulse energy to prevent crystal damage. In this paper, we numerically investigate HRR DFG with a focus on the energy scalability of idler pulses. We show that HRR DFG–unlike optical parametric amplifiers–may operate in the linear regime, in which the idler pulse energy scales linearly with respect to the pump/signal pulse energy. Our simulation results suggest an efficient approach to energy scaling the idler mid-IR pulses in a HRR DFG: increase the signal pulse energy to the same level as the pump pulse energy. We also show that DFG seeded by pump/signal pulses at ∼2-µm range benefits from reduced group-velocity mismatch and exhibits better idler energy scalability. For example, 44.2-nJ pulses at 9.87 µm can be achieved by mixing 500-nJ, 2.0-µm pump pulses and 100-nJ, 2.508-µm signal pulses in a 2-mm-thick GaSe crystal. At the end of this paper, we show that such high-energy signal pulses can be derived from the pump pulses using a recently invented fiber-optic method. Therefore, implementation of high-power (>2 W) longwave mid-IR frequency combs is practically feasible.

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References

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2019 (4)

2018 (7)

H.-Y. Chung, W. Liu, Q. Cao, L. Song, F. X. Kärtner, and G. Chang, “Megawatt peak power tunable femtosecond source based on self-phase modulation enabled spectral selection,” Opt. Express 26(3), 3684–3695 (2018).
[Crossref]

H. Timmers, A. Kowligy, A. Lind, F. C. Cruz, N. Nader, M. Silfies, G. Ycas, T. K. Allison, P. G. Schunemann, S. B. Papp, and S. A. Diddams, “Molecular fingerprinting with bright, broadband infrared frequency combs,” Optica 5(6), 727–732 (2018).
[Crossref]

G. Zhou, Q. Cao, F. X. Kärtner, and G. Chang, “Energy scalable, offset-free ultrafast mid-infrared source harnessing self-phase-modulation-enabled spectral selection,” Opt. Lett. 43(12), 2953–2956 (2018).
[Crossref]

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 µm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

K. Iwakuni, G. Porat, T. Q. Bui, B. J. Bjork, S. B. Schoun, O. H. Heckl, M. E. Fermann, and J. Ye, “Phase-stabilized 100 mW frequency comb near 10 µm,” Appl. Phys. B 124(7), 128 (2018).
[Crossref]

J. Zhang, K. F. Mak, N. Nagl, M. Seidel, D. Bauer, D. Sutter, V. Pervak, F. Krausz, and O. Pronin, “Multi-mW, few-cycle mid-infrared continuum spanning from 500 to 2250 cm−1,” Light: Sci. Appl. 7(2), 17180 (2018).
[Crossref]

C. Gaida, M. Gebhardt, T. Heuermann, F. Stutzki, C. Jauregui, J. Antonio-Lopez, A. Schülzgen, R. Amezcua-Correa, A. Tünnermann, I. Pupeza, and J. Limpert, “Watt-scale super-octave mid-infrared intrapulse difference frequency generation,” Light: Sci. Appl. 7(1), 94 (2018).
[Crossref]

2016 (5)

2015 (3)

M. Beutler, I. Rimke, E. Büttner, P. Farinello, A. Agnesi, V. Badikov, D. Badikov, and V. Petrov, “Difference-frequency generation of ultrashort pulses in the mid-IR using Yb-fiber pump systems and AgGaSe2,” Opt. Express 23(3), 2730–2736 (2015).
[Crossref]

I. Pupeza, D. Sánchez, J. Zhang, N. Lilienfein, M. Seidel, N. Karpowicz, T. Paasch-Colberg, I. Znakovskaya, M. Pescher, W. Schweinberger, V. Pervak, E. Fill, O. Pronin, Z. Wei, F. Krausz, A. Apolonski, and J. Biegert, “High-power sub-two-cycle mid-infrared pulses at 100 MHz repetition rate,” Nat. Photonics 9(11), 721–724 (2015).
[Crossref]

H. Pires, M. Baudisch, D. Sanchez, M. Hemmer, and J. Biegert, “Ultrashort pulse generation in the mid-IR,” Prog. Quantum Electron. 43, 1–30 (2015).
[Crossref]

2014 (1)

2013 (2)

A. Gambetta, N. Coluccelli, M. Cassinerio, D. Gatti, P. Laporta, G. Galzerano, and M. Marangoni, “Milliwatt-level frequency combs in the 8–14 µm range via difference frequency generation from an Er:fiber oscillator,” Opt. Lett. 38(7), 1155–1157 (2013).
[Crossref]

A. Foltynowicz, P. Masłowski, A. J. Fleisher, B. J. Bjork, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide,” Appl. Phys. B 110(2), 163–175 (2013).
[Crossref]

2012 (5)

2010 (1)

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
[Crossref]

2007 (1)

2004 (1)

2003 (1)

2002 (1)

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88(13), 133901 (2002).
[Crossref]

2000 (1)

R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, “Generation and field-resolved detection of femtosecond electromagnetic pulses tunable up to 41 THz,” Appl. Phys. Lett. 76(22), 3191–3193 (2000).
[Crossref]

1998 (1)

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Abedin, K. S.

Agnesi, A.

Allison, T. K.

Amarie, S.

F. Keilmann and S. Amarie, “Mid-infrared frequency comb spanning an octave based on an Er fiber laser and difference-frequency generation,” J. Infrared, Millimeter, Terahertz Waves 33(5), 479–484 (2012).
[Crossref]

Amezcua-Correa, R.

C. Gaida, M. Gebhardt, T. Heuermann, F. Stutzki, C. Jauregui, J. Antonio-Lopez, A. Schülzgen, R. Amezcua-Correa, A. Tünnermann, I. Pupeza, and J. Limpert, “Watt-scale super-octave mid-infrared intrapulse difference frequency generation,” Light: Sci. Appl. 7(1), 94 (2018).
[Crossref]

Antonio-Lopez, J.

C. Gaida, M. Gebhardt, T. Heuermann, F. Stutzki, C. Jauregui, J. Antonio-Lopez, A. Schülzgen, R. Amezcua-Correa, A. Tünnermann, I. Pupeza, and J. Limpert, “Watt-scale super-octave mid-infrared intrapulse difference frequency generation,” Light: Sci. Appl. 7(1), 94 (2018).
[Crossref]

Apolonski, A.

T. P. Butler, D. Gerz, C. Hofer, J. Xu, C. Gaida, T. Heuermann, M. Gebhardt, L. Vamos, W. Schweinberger, J. A. Gessner, T. Siefke, M. Heusinger, U. Zeitner, A. Apolonski, N. Karpowicz, J. Limpert, F. Krausz, and I. Pupeza, “Watt-scale 50-MHz source of single-cycle waveform-stable pulses in the molecular fingerprint region,” Opt. Lett. 44(7), 1730–1733 (2019).
[Crossref]

I. Pupeza, D. Sánchez, J. Zhang, N. Lilienfein, M. Seidel, N. Karpowicz, T. Paasch-Colberg, I. Znakovskaya, M. Pescher, W. Schweinberger, V. Pervak, E. Fill, O. Pronin, Z. Wei, F. Krausz, A. Apolonski, and J. Biegert, “High-power sub-two-cycle mid-infrared pulses at 100 MHz repetition rate,” Nat. Photonics 9(11), 721–724 (2015).
[Crossref]

Armstrong, D.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Badikov, D.

Badikov, V.

Baltuška, A.

A. Baltuška, T. Fuji, and T. Kobayashi, “Controlling the carrier-envelope phase of ultrashort light pulses with optical parametric amplifiers,” Phys. Rev. Lett. 88(13), 133901 (2002).
[Crossref]

Baudisch, M.

Bauer, D.

J. Zhang, K. F. Mak, N. Nagl, M. Seidel, D. Bauer, D. Sutter, V. Pervak, F. Krausz, and O. Pronin, “Multi-mW, few-cycle mid-infrared continuum spanning from 500 to 2250 cm−1,” Light: Sci. Appl. 7(2), 17180 (2018).
[Crossref]

Baumann, E.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 µm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

Bernhardt, B.

B. Bernhardt, A. Ozawa, P. Jacquet, M. Jacquey, Y. Kobayashi, T. Udem, R. Holzwarth, G. Guelachvili, T. W. Hänsch, and N. Picqué, “Cavity-enhanced dual-comb spectroscopy,” Nat. Photonics 4(1), 55–57 (2010).
[Crossref]

Beutler, M.

Biegert, J.

D. Sanchez, M. Hemmer, M. Baudisch, S. L. Cousin, K. Zawilski, P. Schunemann, O. Chalus, C. Simon-Boisson, and J. Biegert, “7 µm, ultrafast, sub-millijoule-level mid-infrared optical parametric chirped pulse amplifier pumped at 2 µm,” Optica 3(2), 147–150 (2016).
[Crossref]

I. Pupeza, D. Sánchez, J. Zhang, N. Lilienfein, M. Seidel, N. Karpowicz, T. Paasch-Colberg, I. Znakovskaya, M. Pescher, W. Schweinberger, V. Pervak, E. Fill, O. Pronin, Z. Wei, F. Krausz, A. Apolonski, and J. Biegert, “High-power sub-two-cycle mid-infrared pulses at 100 MHz repetition rate,” Nat. Photonics 9(11), 721–724 (2015).
[Crossref]

H. Pires, M. Baudisch, D. Sanchez, M. Hemmer, and J. Biegert, “Ultrashort pulse generation in the mid-IR,” Prog. Quantum Electron. 43, 1–30 (2015).
[Crossref]

D. Sanchez, M. Hemmer, M. Baudisch, K. Zawilski, P. Schunemann, H. Hoogland, R. Holzwarth, and J. Biegert, “Broadband mid-ir frequency comb with CdSiP2 and AgGaS2 from an Er,Tm:Ho fiber laser,” Opt. Lett. 39(24), 6883–6886 (2014).
[Crossref]

Bjork, B. J.

K. Iwakuni, G. Porat, T. Q. Bui, B. J. Bjork, S. B. Schoun, O. H. Heckl, M. E. Fermann, and J. Ye, “Phase-stabilized 100 mW frequency comb near 10 µm,” Appl. Phys. B 124(7), 128 (2018).
[Crossref]

A. Foltynowicz, P. Masłowski, A. J. Fleisher, B. J. Bjork, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide,” Appl. Phys. B 110(2), 163–175 (2013).
[Crossref]

Bliss, D.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Brodschelm, A.

R. Huber, A. Brodschelm, F. Tauser, and A. Leitenstorfer, “Generation and field-resolved detection of femtosecond electromagnetic pulses tunable up to 41 THz,” Appl. Phys. Lett. 76(22), 3191–3193 (2000).
[Crossref]

Bui, T. Q.

K. Iwakuni, G. Porat, T. Q. Bui, B. J. Bjork, S. B. Schoun, O. H. Heckl, M. E. Fermann, and J. Ye, “Phase-stabilized 100 mW frequency comb near 10 µm,” Appl. Phys. B 124(7), 128 (2018).
[Crossref]

Butler, T. P.

Büttner, E.

Cao, Q.

Cassinerio, M.

Chalus, O.

Chang, G.

Chung, H.-Y.

Coddington, I.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 µm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

I. Coddington, N. Newbury, and W. Swann, “Dual-comb spectroscopy,” Optica 3(4), 414–426 (2016).
[Crossref]

Coluccelli, N.

Cousin, S. L.

Cruz, F. C.

Dergachev, A.

Diddams, S. A.

G. Ycas, F. R. Giorgetta, E. Baumann, I. Coddington, D. Herman, S. A. Diddams, and N. R. Newbury, “High-coherence mid-infrared dual-comb spectroscopy spanning 2.6 to 5.2 µm,” Nat. Photonics 12(4), 202–208 (2018).
[Crossref]

H. Timmers, A. Kowligy, A. Lind, F. C. Cruz, N. Nader, M. Silfies, G. Ycas, T. K. Allison, P. G. Schunemann, S. B. Papp, and S. A. Diddams, “Molecular fingerprinting with bright, broadband infrared frequency combs,” Optica 5(6), 727–732 (2018).
[Crossref]

Drake, T.

Dubois, M.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127(6), 1918–1939 (1962).
[Crossref]

Eikema, K. S. E.

Farinello, P.

Fejer, M. M.

Fermann, M. E.

Fill, E.

I. Pupeza, D. Sánchez, J. Zhang, N. Lilienfein, M. Seidel, N. Karpowicz, T. Paasch-Colberg, I. Znakovskaya, M. Pescher, W. Schweinberger, V. Pervak, E. Fill, O. Pronin, Z. Wei, F. Krausz, A. Apolonski, and J. Biegert, “High-power sub-two-cycle mid-infrared pulses at 100 MHz repetition rate,” Nat. Photonics 9(11), 721–724 (2015).
[Crossref]

Fleisher, A. J.

A. Foltynowicz, P. Masłowski, A. J. Fleisher, B. J. Bjork, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide,” Appl. Phys. B 110(2), 163–175 (2013).
[Crossref]

Foltynowicz, A.

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[Crossref]

A. Foltynowicz, P. Masłowski, A. J. Fleisher, B. J. Bjork, and J. Ye, “Cavity-enhanced optical frequency comb spectroscopy in the mid-infrared application to trace detection of hydrogen peroxide,” Appl. Phys. B 110(2), 163–175 (2013).
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Figures (7)

Fig. 1.
Fig. 1. DFG outputs under different launching conditions. (a) DFG outputs when the signal is fixed at 20 MW/cm$^2$. The idler growth has three different stages. When the pump is below 10 GW/cm$^2$, the idler has a linear growth. (b) DFG process with a fixed signal at three different levels. The idler grows linearly as the pump is below the threshold level. (c) DFG process with a fixed pump. The idler grows linearly as the signal is below the saturation level.
Fig. 2.
Fig. 2. DFG process inside 2-mm-thick GaSe. (a) Pulse profile at the output. The input signal pulse is also plotted. The signal in the graph is magnified by a factor of 50 and the idler by 5,000. Inset: output idler spectrum. (b) Output idler pulse before compression, after compression, and its TL form. The dashed curve shows the instantaneous frequency. (c) Peak intensity of the dechirped pulse against dechirping GDD. Inset: compressed pulse profile (blue curve) and TL pulse profile (red dashed curve).
Fig. 3.
Fig. 3. Scaling of idler pulse energy under different input conditions. (a) Scaling of idler energy versus input pump energy given input signal energy fixed at 100 pJ, 1 nJ, and 10 nJ. GaSe thickness: 2 mm. (b) Scaling of idler energy versus input pump energy given input signal energy fixed at 1 nJ, 10 nJ, and 100 nJ. GaSe thickness: 2 mm.
Fig. 4.
Fig. 4. Effect of GaSe thickness on idler pulse in 1-${\mu} \textrm{m}$ driven DFG. (a) Idler pulse profiles for GaSe thickness of 0.5 mm, 1.0 mm, 2.0 mm, 3.0 mm, and 4.0 mm. (b) Idler pulse energy versus crystal thickness. (c) Pulse duration of output pulse (red circle), compressed pulse (black triangle), and TL pulse (blue square) and spectral bandwidth versus GaSe thickness. (d) Peak power of output pulse (red circle), compressed pulse (black triangle), and TL pulse (blue square) versus GaSe thickness.
Fig. 5.
Fig. 5. Comparison between 1-${\mu} \textrm{m}$ driven DFG and 2-${\mu} \textrm{m}$ driven type-I DFG inside GaSe. (a) GVM for 1-${\mu} \textrm{m}$ pump and 2-${\mu} \textrm{m}$ pump. The temporal walk-off between the pump and the signal is about 5 time less for the case of 2-${\mu} \textrm{m}$ pump. (b) Phase matching condition for type-I DFG process inside GaSe.
Fig. 6.
Fig. 6. Scaling of idler pulse energy under different input conditions. (a) Scaling of idler energy versus input pump energy given input signal energy fixed at 100 pJ, 1 nJ, and 10 nJ. GaSe thickness: 2 mm. (b) Scaling of idler energy versus input signal energy given input pump energy fixed at 1 nJ, 10 nJ, 100 nJ and 500 nJ. GaSe thickness: 2 mm.
Fig. 7.
Fig. 7. Effect of GaSe thickness on idler pulse in 2-${\mu} \textrm{m}$ driven DFG. (a) Idler pulse profiles for GaSe thickness of 0.5 mm, 1.0 mm, 2.0 mm, 3.0 mm, and 4.0 mm. Inset: idler pulse energy versus crystal thickness. (b) Pulse duration of output pulse (red circle), compressed pulse (black triangle), and TL pulse (blue square) and spectral bandwidth versus GaSe thickness. (c) Peak power of output pulse (red circle), compressed pulse (black triangle), and TL (blue square) versus GaSe thickness.

Equations (6)

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d A 1 ( z ) d z = i ω 1 n 1 c d eff A 3 ( z ) A 2 ( z ) e i Δ k z , d A 2 ( z ) d z = i ω 2 n 2 c d eff A 3 ( z ) A 1 ( z ) e i Δ k z , d A 3 ( z ) d z = i ω 3 n 3 c d eff A 1 ( z ) A 2 ( z ) e + i Δ k z ,
I 1 ( z ) = ω 3 ω 2 I 20 sinh 2 ( Γ z ) , Γ 2 = 2 ω 2 ω 1 d e ff 2 n 1 n 2 n 3 ε 0 c 3 I 30 .
I idler = 2 ω 1 ω 3 d eff 2 n 1 n 2 n 3 ε 0 c 3 I 20 I 30 L 2 .
I idler = 1 4 ω 3 ω 2 I 20 e 2 Γ z .
I th = n 1 n 2 n 3 ε 0 c 3 2 ω 1 ω 2 d eff 2 ( 1 L ) 2 .
A 1 ( z , τ ) z + ( 1 v g , 1 1 v g , 3 ) A 1 ( z , τ ) τ + i β 2 , 1 2 2 A 1 ( z , τ ) τ 2 = i ω 1 d eff n 1 c A 3 A 2 e i Δ k z , A 2 ( z , τ ) z + ( 1 v g , 2 1 v g , 3 ) A 2 ( z , τ ) τ + i β 2 , 2 2 2 A 2 ( z , τ ) τ 2 = i ω 2 d eff n 2 c A 3 A 1 e i Δ k z , A 3 ( z , τ ) z + i β 2 , 3 2 2 A 3 ( z , τ ) τ 2 = i ω 3 d eff n 3 c A 1 A 2 e + i Δ k z .