Abstract

Dispersion control is a key objective in the field of photonics and spectroscopy, since it enhances non-linear effects by both enabling phase matching and offering slow light generation. In addition, it is essential for frequency comb generation, which requires a phase-lock mechanism that is provided by broadband compensation of group velocity dispersion (GVD). At optical frequencies, there are several well-established concepts for dispersion control such as prism or grating pairs. However, terahertz dispersion control is still a challenge, thus hindering further progress in the field of terahertz science and technology. In this work, we present a hybrid waveguide with both broadband, tuneable positive and more than octave-spanning negative terahertz GVD on the order of 10−22 s2/m, which is suitable for either intra- or extra cavity operation. This new terahertz device will enable ultra-short pulse compression, allow soliton propagation, improve frequency comb operation and foster the development of novel non-linear applications.

© 2016 Optical Society of America

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References

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2016 (1)

T. Fobbe, H. Nong, R. Schott, S. Pal, S. Markmann, N. Hekmat, J. Zhu, Y. Han, L. Li, P. Dean, E. H. Linfield, A. G. Davies, A. D. Wieck, and N. Jukam, “Improving the out-coupling of a metal-metal terahertz frequency quantum cascade laser through integration of a hybrid mode section into the waveguide,” J. Infrar. Millim. THz Waves 37(5), 426–434 (2016).
[Crossref]

2015 (3)

S. Pal, H. Nong, S. Markmann, N. Kukharchyk, S. Valentin, S. Scholz, A. Ludwig, C. Bock, U. Kunze, A. D. Wieck, and N. Jukam, “Ultrawide electrical tuning of light matter interaction in a high electron mobility transistor structure,” Sci. Rep. 5, 16812 (2015).
[Crossref] [PubMed]

M. S. Vitiello, G. Scalari, B. Williams, and P. De Natale, “Quantum cascade lasers: 20 years of challenges,” Opt. Express 23(4), 5167–5182 (2015).
[Crossref] [PubMed]

G. Villares and J. Faist, “Quantum cascade laser combs: effects of modulation and dispersion,” Opt. Express 23(2), 1651–1669 (2015).
[Crossref] [PubMed]

2014 (4)

D. Burghoff, T. Kao, N. Han, C. Chan, X. Cai, Y. Yang, D. Hayton, J. Gao, J. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave-spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2014).
[Crossref]

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

H. Nong, S. Pal, S. Markmann, N. Hekmat, R. Mohandas, P. Dean, L. Li, E. H. Linfield, A. G. Davies, A. D. Wieck, and N. Jukam, “Narrow-band injection seeding of a terahertz frequency quantum cascade laser: Selection and suppression of longitudinal modes,” Appl. Phys. Lett. 105(11), 111113 (2014).
[Crossref]

2012 (2)

A. Schliesser, N. Picqué, and T. Hänsch, “Mid-infrared frequency combs,” Nat. Photonics 6(7), 440–449 (2012).
[Crossref]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref] [PubMed]

2011 (1)

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5(5), 306–313 (2011).
[Crossref]

2010 (1)

M. Strain and M. Sorel, “Design and fabrication of integrated chirped bragg gratings for on-chip dispersion control,” IEEE J. Quantum Electron. 46(5), 774–782 (2010).
[Crossref]

2009 (1)

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photonics Rev. 3(1-2), 45–66 (2009).
[Crossref]

2008 (3)

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2(8), 474–481 (2008).
[Crossref]

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

M. Cho, J. Kim, H. Park, Y. Han, K. Moon, E. Jung, and H. Han, “Highly birefringent terahertz polarization maintaining plastic photonic crystal fibers,” Opt. Express 16(1), 7–12 (2008).
[Crossref] [PubMed]

2007 (2)

2006 (1)

2005 (1)

Y. A. Vlasov, M. O’Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438(7064), 65–69 (2005).
[Crossref] [PubMed]

2004 (3)

2003 (5)

K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11(8), 843–852 (2003).
[Crossref] [PubMed]

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[Crossref] [PubMed]

P. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
[Crossref] [PubMed]

U. Keller, “Recent developments in compact ultrafast lasers,” Nature 424(6950), 831–838 (2003).
[Crossref] [PubMed]

2002 (3)

S. Schiller, “Spectrometry with frequency combs,” Opt. Lett. 27(9), 766–768 (2002).
[Crossref] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, “Optical frequency metrology,” Nature 416(6877), 233–237 (2002).
[Crossref] [PubMed]

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80(15), 2634–2636 (2002).
[Crossref]

2001 (1)

2000 (1)

1994 (2)

R. Szipöcs, C. Spielmann, F. Krausz, and K. Ferencz, “Chirped multilayer coatings for broadband dispersion control in femtosecond lasers,” Opt. Lett. 19(3), 201–203 (1994).
[Crossref] [PubMed]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

1993 (1)

1987 (2)

F. M. Mitschke and L. F. Mollenauer, “Ultrashort pulses from the soliton laser,” Opt. Lett. 12(6), 407–409 (1987).
[Crossref] [PubMed]

O. Martinez, “3000 times grating compressor with positive group velocity dispersion: application to fiber compensation in 1.3-1.6 μm region,” IEEE J. Quantum Electron. 23(1), 59–64 (1987).
[Crossref]

1984 (1)

1962 (1)

P. Maker, R. Terhune, M. Nisenoff, and C. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett. 8(1), 21–22 (1962).
[Crossref]

1948 (1)

J. Ville, “Théorie et applications de la notion de signal analytique,” Cables Transm. 2, 61–74 (1948).

1932 (1)

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40(5), 749–759 (1932).
[Crossref]

Ahmad, F. R.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301(5640), 1702–1704 (2003).
[Crossref] [PubMed]

Angelow, G.

Austin, R. R.

Baba, T.

T. Baba, “Slow light in photonic crystals,” Nat. Photonics 2(8), 465–473 (2008).
[Crossref]

Barbieri, S.

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5(5), 306–313 (2011).
[Crossref]

Beck, M.

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave-spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2014).
[Crossref]

Beere, H.

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photonics Rev. 3(1-2), 45–66 (2009).
[Crossref]

Blaser, S.

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref] [PubMed]

Bock, C.

S. Pal, H. Nong, S. Markmann, N. Kukharchyk, S. Valentin, S. Scholz, A. Ludwig, C. Bock, U. Kunze, A. D. Wieck, and N. Jukam, “Ultrawide electrical tuning of light matter interaction in a high electron mobility transistor structure,” Sci. Rep. 5, 16812 (2015).
[Crossref] [PubMed]

Bolivar, P. H.

J. G. Rivas, M. Kuttge, P. H. Bolivar, H. Kurz, and J. A. Sánchez-Gil, “Propagation of surface plasmon polaritons on semiconductor gratings,” Phys. Rev. Lett. 93(25), 256804 (2004).
[Crossref] [PubMed]

Burghoff, D.

D. Burghoff, T. Kao, N. Han, C. Chan, X. Cai, Y. Yang, D. Hayton, J. Gao, J. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Cai, X.

D. Burghoff, T. Kao, N. Han, C. Chan, X. Cai, Y. Yang, D. Hayton, J. Gao, J. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Capasso, F.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Chan, C.

D. Burghoff, T. Kao, N. Han, C. Chan, X. Cai, Y. Yang, D. Hayton, J. Gao, J. Reno, and Q. Hu, “Terahertz laser frequency combs,” Nat. Photonics 8(6), 462–467 (2014).
[Crossref]

Chernikov, S. V.

Cho, A. Y.

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Cho, M.

M. Cho, J. Kim, H. Park, Y. Han, K. Moon, E. Jung, and H. Han, “Highly birefringent terahertz polarization maintaining plastic photonic crystal fibers,” Opt. Express 16(1), 7–12 (2008).
[Crossref] [PubMed]

H. Han, H. Park, M. Cho, and J. Kim, “Terahertz pulse propagation in a plastic photonic crystal fiber,” Appl. Phys. Lett. 80(15), 2634–2636 (2002).
[Crossref]

Davies, A. G.

T. Fobbe, H. Nong, R. Schott, S. Pal, S. Markmann, N. Hekmat, J. Zhu, Y. Han, L. Li, P. Dean, E. H. Linfield, A. G. Davies, A. D. Wieck, and N. Jukam, “Improving the out-coupling of a metal-metal terahertz frequency quantum cascade laser through integration of a hybrid mode section into the waveguide,” J. Infrar. Millim. THz Waves 37(5), 426–434 (2016).
[Crossref]

H. Nong, S. Pal, S. Markmann, N. Hekmat, R. Mohandas, P. Dean, L. Li, E. H. Linfield, A. G. Davies, A. D. Wieck, and N. Jukam, “Narrow-band injection seeding of a terahertz frequency quantum cascade laser: Selection and suppression of longitudinal modes,” Appl. Phys. Lett. 105(11), 111113 (2014).
[Crossref]

S. Barbieri, M. Ravaro, P. Gellie, G. Santarelli, C. Manquest, C. Sirtori, S. Khanna, E. H. Linfield, and A. G. Davies, “Coherent sampling of active mode-locked terahertz quantum cascade lasers and frequency synthesis,” Nat. Photonics 5(5), 306–313 (2011).
[Crossref]

De Natale, P.

Dean, P.

T. Fobbe, H. Nong, R. Schott, S. Pal, S. Markmann, N. Hekmat, J. Zhu, Y. Han, L. Li, P. Dean, E. H. Linfield, A. G. Davies, A. D. Wieck, and N. Jukam, “Improving the out-coupling of a metal-metal terahertz frequency quantum cascade laser through integration of a hybrid mode section into the waveguide,” J. Infrar. Millim. THz Waves 37(5), 426–434 (2016).
[Crossref]

H. Nong, S. Pal, S. Markmann, N. Hekmat, R. Mohandas, P. Dean, L. Li, E. H. Linfield, A. G. Davies, A. D. Wieck, and N. Jukam, “Narrow-band injection seeding of a terahertz frequency quantum cascade laser: Selection and suppression of longitudinal modes,” Appl. Phys. Lett. 105(11), 111113 (2014).
[Crossref]

Dianov, E. M.

Diddams, S. A.

Ell, R.

Engelen, R. J.

Faist, J.

G. Villares and J. Faist, “Quantum cascade laser combs: effects of modulation and dispersion,” Opt. Express 23(2), 1651–1669 (2015).
[Crossref] [PubMed]

M. Rösch, G. Scalari, M. Beck, and J. Faist, “Octave-spanning semiconductor laser,” Nat. Photonics 9(1), 42–47 (2014).
[Crossref]

G. Villares, A. Hugi, S. Blaser, and J. Faist, “Dual-comb spectroscopy based on quantum-cascade-laser frequency combs,” Nat. Commun. 5, 5192 (2014).
[Crossref] [PubMed]

A. Hugi, G. Villares, S. Blaser, H. C. Liu, and J. Faist, “Mid-infrared frequency comb based on a quantum cascade laser,” Nature 492(7428), 229–233 (2012).
[Crossref] [PubMed]

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photonics Rev. 3(1-2), 45–66 (2009).
[Crossref]

J. Faist, F. Capasso, D. L. Sivco, C. Sirtori, A. L. Hutchinson, and A. Y. Cho, “Quantum cascade laser,” Science 264(5158), 553–556 (1994).
[Crossref] [PubMed]

Ferencz, K.

Fischer, M.

G. Scalari, C. Walther, M. Fischer, R. Terazzi, H. Beere, D. Ritchie, and J. Faist, “THz and sub-THz quantum cascade lasers,” Laser Photonics Rev. 3(1-2), 45–66 (2009).
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Figures (5)

Fig. 1
Fig. 1 (a) Mode profile of the absolute value of electric field in z-direction. The waveguide height is d = 56μm and the dielectric permittivities are set to ε1 = 11.7 (Si) and ε2 = 1 (air). (b) Frequency dependent penetration depth (inset), effective and group index (left axis) and confinement factor (right axis). The normal (orange) and anomalous (green) dispersion indicate positive and negative GVD, respectively. (c) Influence of waveguide height on both the dispersion relation (right axis, dashed curves) and GVD (left axis, bold curves). Interestingly, at typical QCL heights (d = 10−20 μm) the GVD zero crossing is at typical QCL frequencies (1.25−2.50 THz) offering broadband material and gain GVD compensation.
Fig. 2
Fig. 2 (a) Schematic of the experimental geometry including an Au-coated leakage blocker (yellow) and the waveguides for an experimental determination of the dispersion relation via THz time domain spectroscopy for a waveguide height of d = 40 μm. (b) Time domain signal for a 3.5 mm long hybrid waveguide (blue) with a l = 336 μm long DM section at the end of the ridge. (c) Time domain signal for a 3.5 mm long metal-metal (MM) waveguide (green). A minimized leakage at around 2 ps at the in-coupling facet is an essential factor for obtaining an accurate dispersion relation. The close-up illustrates the difference between both signals. The champagne-colored area corresponds to the time domain window that is used for the Fourier-transform and the spectral phase analysis. (d) Dispersion relation obtained from the spectral phase analysis (champagne circles) and the theoretical model (red line). The corresponding GVD is shown in the inset.
Fig. 3
Fig. 3 (a) Time domain signal and Wigner-Ville distribution (WVD) based time-frequency domain analysis for a 3.5 mm long hybrid waveguide (violet) with a L = 2.3 mm long DM section and a waveguide height of d = 60μm. (b) Repeated measurement as in Fig. 3(a) employing an optical low-pass THz filter that cuts off all frequencies above 1 THz (dark purple). (c) The increasing instantaneous frequency (positive chirp) reflects the positive GVD. (d) The decreasing instantaneous frequency (negative chirp) maps the negative GVD into the time domain. (e) Dispersion relation obtained from a Fourier-transform of the signal corresponding to the light purple area in Fig. 3(a) compared to the theoretical curve (blue). (f) GVD of the investigated hybrid waveguide as deduced from Fig. 3(e) (blue).
Fig. 4
Fig. 4 (a) DM section waveguide GVD for different top dielectrics and a waveguide height of d = 13μm demonstrating a GVD-flattening. (b) GaAs material GVD (blue), MM waveguide GVD (grey) [28] and hybrid waveguide GVD (black). For GVD compensation, a composite hybrid waveguide with two different top dielectric materials with n2,1 = 1.54 and n2,2 = 2 is used. The DM section lengths correspond to 16% and 40% of the ridge length, respectively. The broad hybrid waveguide GVD allows a broad material GVD compensation (turquoise).
Fig. 5
Fig. 5 (a) WVD of an un-chirped Gaussian pulse (numerical example) and constant instantaneous frequency (IF) (black curve). (b) Negatively chirped Gaussian pulse with linearly decreasing IF. (c) Positively chirped Gaussian pulse with linearly increasing IF. (d) Negatively chirped hybrid waveguide signal from Fig. 3(a) pulse with an approximately linear decrease of the IF. The IF data from Fig. 3(d) (red squares) is in good accordance with the IF obtained from the WVD (black curve). (e) Positively chirped hybrid waveguide signal from Fig. 3(b) with an approximately linear increase of the IF. The IF data from Fig. 3(c) (red squares) is compared to the IF obtained from the WVD (black curve: smoothed IF, grey: unsmoothed IF).

Equations (15)

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ϕ l DM (ω)= ϕ L,l Hyb (ω) Ll L ϕ L MM (ω).
n eff (ω)= c l ( ϕ l DM (ω) ω t 0 ),
(E,H)=( E m , H m )(z, β m )exp(i(ωt β m y)).
H x,m ={ Cexp(r( β m )z) z>0 Esin(h( β m )z)+Fcos(h( β m )z) 0<z<d Dexp(q( β m )z) z<0.
r( β m )= β m 2 ε 2 ω 2 c 2 , h( β m )= ε 1 ω 2 c 2 β m 2 , q( β m )= β m 2 ε m ω 2 c 2 .
tan(h( β m )d)= r( β m )h( β m ) ε 1 ε m +h( β m )q( β m ) ε 1 ε 2 h ( β m ) 2 ε 2 ε m q( β m )r( β m ) ε 1 2 .
GVD d 2 β m d ω 2 .
W(t,f)= 1 2π s(t τ 2 ) s * (t+ τ 2 ) exp(i2πτf)dτ,
s(t)=E(t)+iH[E(t)].
W(t,f)df =|s(t) | 2 .
IF(t)= 1 |s(t) | 2 fW(t,f)df .
W ch (t,f)= exp( i2πb ( t τ 2 ) 2 )exp( i2πb ( t+ τ 2 ) 2 )exp(i2πτf)dτ =δ(f2bt).
W G (t,f)~exp(m (t t 0 ) 2 n f 2 ),
W y (t,f)= W x (t,ρ) W h (t,fρ)dρ .
W ch,G (t,f)= W ch (t,ρ) W G (t,fρ)dρ ~exp(m(t t 0 ) 2 n (f2bt) 2 ).

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