Abstract

The strategies and approaches of designing chirped Distributed Bragg Reflector for group velocity compensation in metal-metal waveguide terahertz quantum cascade laser are investigated through 1D and 3D models. The results show the depth of the corrugation periods plays an important role on achieving broad-band group velocity compensation in terahertz range. However, the deep corrugation also brings distortion to the group delay behavior. A two-section chirped DBR is proposed to provide smoother group delay compensation while still maintain the broad frequency range (octave) operation within 2 THz to 4 THz.

© 2016 Optical Society of America

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References

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2014 (2)

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

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

2013 (1)

2012 (1)

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]

2007 (1)

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

2005 (1)

M. Sumetsky and B. J. Eggleton, “Fiber Bragg gratings for dispersion compensation in optical communication systems,” J. Opt. Fiber Commun. Rep. 2(3), 256–278 (2005).
[Crossref]

2003 (1)

S. T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

2002 (1)

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

2001 (1)

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hänsch, “Optical clockworks and the measurement of laser frequencies with a mode-locked frequency comb,” IEEE J. Quantum Electron. 37(12), 1493–1501 (2001).
[Crossref]

1987 (1)

1982 (1)

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53(10), R123–R181 (1982).
[Crossref]

1964 (1)

F. Gires and P. Tournois, “Interferometre utilisable pour la compression d’impulsions lumineuses modulees en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).

Ban, D.

Beck, M.

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

Blakemore, J. S.

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53(10), R123–R181 (1982).
[Crossref]

Blaser, S.

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]

Burghoff, D.

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

Cai, X.

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

Chan, C. W. I.

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

Cundiff, S. T.

S. T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

Eggleton, B. J.

M. Sumetsky and B. J. Eggleton, “Fiber Bragg gratings for dispersion compensation in optical communication systems,” J. Opt. Fiber Commun. Rep. 2(3), 256–278 (2005).
[Crossref]

Faist, J.

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

Gao, J.-R.

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

Gires, F.

F. Gires and P. Tournois, “Interferometre utilisable pour la compression d’impulsions lumineuses modulees en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).

Han, N.

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

Hänsch, T. W.

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

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hänsch, “Optical clockworks and the measurement of laser frequencies with a mode-locked frequency comb,” IEEE J. Quantum Electron. 37(12), 1493–1501 (2001).
[Crossref]

Hayton, D. J.

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

Holzwarth, R.

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

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hänsch, “Optical clockworks and the measurement of laser frequencies with a mode-locked frequency comb,” IEEE J. Quantum Electron. 37(12), 1493–1501 (2001).
[Crossref]

Hu, Q.

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

Hugi, A.

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]

Kao, T.-Y.

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

Liu, H. C.

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]

Ouellette, F.

Razavipour, S. G.

Reno, J. L.

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

Rosch, M.

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

Scalari, G.

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

Sumetsky, M.

M. Sumetsky and B. J. Eggleton, “Fiber Bragg gratings for dispersion compensation in optical communication systems,” J. Opt. Fiber Commun. Rep. 2(3), 256–278 (2005).
[Crossref]

Tournois, P.

F. Gires and P. Tournois, “Interferometre utilisable pour la compression d’impulsions lumineuses modulees en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).

Udem, T.

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

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hänsch, “Optical clockworks and the measurement of laser frequencies with a mode-locked frequency comb,” IEEE J. Quantum Electron. 37(12), 1493–1501 (2001).
[Crossref]

Villares, G.

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]

Wasilewski, Z.

Williams, B. S.

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

Xu, C.

Yang, Y.

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

Ye, J.

S. T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

Zimmermann, M.

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hänsch, “Optical clockworks and the measurement of laser frequencies with a mode-locked frequency comb,” IEEE J. Quantum Electron. 37(12), 1493–1501 (2001).
[Crossref]

C. R. Acad. Sci. Paris (1)

F. Gires and P. Tournois, “Interferometre utilisable pour la compression d’impulsions lumineuses modulees en frequence,” C. R. Acad. Sci. Paris 258, 6112–6115 (1964).

IEEE J. Quantum Electron. (1)

R. Holzwarth, M. Zimmermann, T. Udem, and T. W. Hänsch, “Optical clockworks and the measurement of laser frequencies with a mode-locked frequency comb,” IEEE J. Quantum Electron. 37(12), 1493–1501 (2001).
[Crossref]

J. Appl. Phys. (1)

J. S. Blakemore, “Semiconducting and other major properties of gallium arsenide,” J. Appl. Phys. 53(10), R123–R181 (1982).
[Crossref]

J. Opt. Fiber Commun. Rep. (1)

M. Sumetsky and B. J. Eggleton, “Fiber Bragg gratings for dispersion compensation in optical communication systems,” J. Opt. Fiber Commun. Rep. 2(3), 256–278 (2005).
[Crossref]

Nat. Photonics (3)

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

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

B. S. Williams, “Terahertz quantum-cascade lasers,” Nat. Photonics 1(9), 517–525 (2007).
[Crossref]

Nature (2)

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]

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

Opt. Express (1)

Opt. Lett. (1)

Rev. Mod. Phys. (1)

S. T. Cundiff and J. Ye, “Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[Crossref]

Other (2)

D. P. Burghoff, “Broadband terahertz photonics, ” Doctoral thesis, pp. 83–89 (2014)

P. Yeh, Optical Waves in Layered Media (John Wiley & Sons, 1991).

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Figures (4)

Fig. 1
Fig. 1 (a) An example of corrugation shape of a double chirped waveguide structure. The period lengths of sinusoidal shape gradually increase from left to right, while the corrugation depth tapers linearly from the starting period to the ending period. Inset: A full waveguide consisting of a chirped DBR structure (red) and a flat ridge waveguide section (blue). (b) The reflectance spectra of chirped DBRs with different period lengths (8 – 28 μm). The DBRs have a sinusoidal shape, similar to the one shown in (a). The period length in each DBR remains constant. The 1D simulation results show that the peak reflectance frequency shifts from 1.7 THz to 5.6 THz while the corrugation period length decreases from 28 to 8 μm. (c) The group delay from a 6 mm-long ridge waveguide (~ + 4.5 ps, blue curve) within 2.5 to 3.5 THz is compensated by that from a carefully designed chirped DBR structure (~-4.5 ps, red curve), resulting in a close to zero overall group delay (green curve).
Fig. 2
Fig. 2 (a) Six 20 μm wide chirped DBR structures are simulated by using the one dimensional model. Structure A (SA in red) is set as a baseline sample with following parameters: starting period length (10 μm), ending period length (26 μm), number of periods (30), ending period corrugation depth (8.5 μm), and starting period corrugation depth(0 μm). Structure B and C (SB in orange and SC in yellow) have the same parameters as those in SA, except the number of periods (35 periods in SB and 40 periods in SC). Structure D, E, and F (SD in green, SE in blue, and SF in purple) have the same parameters as those in SA, except the starting period corrugation depth(1, 2, 3 μm for SD, SE, SF, respectively). (b) The calculated reflectance spectra of SA (red), SB (orange) and SC (yellow). (c) The calculated group delay of SA (red), SB (orange) and SC (yellow). A difference of ~3.9 ps in group delay compensation between SA and SC is shown. (d) The calculated reflectance spectra of SA (red), SD (green), SE (blue) and SF (purple). (e) The calculated group delay of SA (red), SD (green), SE (blue) and SF (purple).
Fig. 3
Fig. 3 (a) Comparison of the corrugation shape of two 20 μm wide chirped DBR Structure G (SG) and Structure H (SH). These two structures share the same parameters of starting period length (10 μm), ending period length (26 μm), number of periods (40), starting period corrugation depth (4 μm), and ending period corrugation depth (8.5 μm). However, different from SG, SH has an additional 10 periods of corrugations as a transition buffer from the flat rectangular ridge waveguide to the chirped DBR section. (b) Calculated group delay of SG (blue) and SH (red). The buffer region provides SH with a smoother group delay curve between 2 THz and 4 THz with less modulation, but still retains the same decaying trend (~7 ps) as that in SG. (c) Calculated modulations of the group delays within the frequency band for DBR structures with different number of periods in the buffer region. All other dimensional parameters are the same as those in SH.
Fig. 4
Fig. 4 (a) Calculated reflectance of three chirped DBR structures (Structure I (SI in blue), Structure J (SJ in green), and Structure K (SK in red)) within a frequency range of 2 - 4 THz from simulations based on a 3D model. The dimensional parameters of the structures are listed in Table 2. SI only provides a sufficient reflectance frequency band from 2 THz to 3 THz, while SJ and SK still have close-to-unity reflectance at 4 THz. (b) Calculated group delay of SI (blue), SJ (green) and SK (red). For SI, the modulation on its group delay curve appears with the frequency increasing beyond its cutoff frequency (~2.8 THz at ~70% of reflectance) from its reflectance band. (c) Calculated mode distribution in SI at 3 THz. (d) Calculated mode distribution in SK at 4 THz. (e) Calculated mode distribution in SJ at 2.30 THz, 2.37 THz, and 2.44 THz corresponding to the resonance and off-resonance frequencies, labeled by vertical dashed lines in (b).

Tables (2)

Tables Icon

Table 1 Dimensional Parameters of SA, SB, SC, SD, SE, and SF

Tables Icon

Table 2 Dimensional Parameters of SI, SJ, and SK for the 3D Models in COMSOL

Equations (3)

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ε ( ω , T ) = ε ( T ) + ω T O 2 ( T ) [ ε 0 ( T ) ε ( T ) ] ω T O 2 ( T ) ω 2 + i γ P ω
λ i = 2 n e f f Λ i
τ g ( ω ) = d d ω arg [ r ( ω ) ]

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