Abstract

We describe a robust system for laser-driven narrowband terahertz generation with high conversion efficiency in periodically poled Lithium Niobate (PPLN). In the multi-stage terahertz generation system, the pump pulse is recycled after each PPLN stage for further terahertz generation. By out-coupling the terahertz radiation generated in each stage, extra absorption is circumvented and effective interaction length is increased. The separation of the terahertz and optical pulses at each stage is accomplished by an appropriately designed out-coupler. To evaluate the proposed architecture, the governing 2-D coupled wave equations in a cylindrically symmetric geometry are numerically solved using the finite difference method. Compared to the 1-D calculation which cannot capture the self-focusing and diffraction effects, our 2-D numerical method captures the effects of difference frequency generation, self-phase modulation, self-focusing, beam diffraction, dispersion and terahertz absorption. We found that the terahertz generation efficiency can be greatly enhanced by compensating the dispersion of the pump pulse after each stage. With a two-stage system, we predict the generation of a 17.6 mJ terahertz pulse with total conversion efficiency ηtotal = 1.6% at 0.3 THz using a 1.1 J pump laser with a two-lines spectrum centered at 1 μm. The generation efficiency of each stage is above 0.8% with the out-coupling efficiencies above 93.0%.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

P. Nugraha, G. Krizsán, G. Polónyi, M. Mechler, J. Hebling, G. Tóth, and J. Fülöp, “Efficient semiconductor multicycle terahertz pulse source,” J. Phys. B: At. Mol. Opt. Phys. 51, 094007 (2018).
[Crossref]

2017 (5)

2016 (2)

2015 (4)

2014 (2)

T. Kubacka, J. Johnson, M. Hoffmann, C. Vicario, S. de Jong, P. Beaud, S. Grübel, S.-W. Huang, L. Huber, L. Patthey, Y.-D. Chuang, J. J. Turner, G. L. Dakovski, W.-S. Lee, M. P. Minitti, W. Schlotter, R. G. Moore, C. P. Hauri, S. M. Koohpayeh, V. Scagnoli, G. Ingold, S. L. Johnson, and U. Staub, “Large-amplitude spin dynamics driven by a THz pulse in resonance with an electromagnon,” Science 343, 1333–1336 (2014).
[Crossref] [PubMed]

K. Ravi, W. R. Huang, S. Carbajo, X. Wu, and F. Kärtner, “Limitations to THz generation by optical rectification using tilted pulse fronts,” Opt. Express 22, 20239–20251 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (2)

2011 (2)

T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, “Coherent terahertz control of antiferromagnetic spin waves,” Nat. Photonics 5, 31–34 (2011).
[Crossref]

Z. Chen, X. Zhou, C. A. Werley, and K. A. Nelson, “Generation of high power tunable multicycle teraherz pulses,” Appl. Phys. Lett 99, 071102 (2011).
[Crossref]

2009 (1)

2008 (3)

2007 (6)

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[Crossref]

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

M. A. Belkin, F. Capasso, A. Belyanin, D. L. Sivco, A. Y. Cho, D. C. Oakley, C. J. Vineis, and G. W. Turner, “Terahertz quantum-cascade-laser source based on intracavity difference-frequency generation,” Nat. Photonics 1, 288–292 (2007).
[Crossref]

M. Naftaly and R. E. Miles, “Terahertz time-domain spectroscopy for material characterization,” Proc. IEEE 95, 1658–1665 (2007).
[Crossref]

A. Chafiq, Z. Hricha, and A. Belafhal, “Flat-topped mathieu-gauss beam and its transformation by paraxial optical systems,” Opt. Commun 278, 142–146 (2007).
[Crossref]

M. C. Hoffmann, K.-L. Yeh, J. Hebling, and K. A. Nelson, “Efficient terahertz generation by optical rectification at 1035 nm,” Opt. Express 15, 11706–11713 (2007).
[Crossref] [PubMed]

2006 (4)

2005 (1)

A. Dreyhaupt, S. Winnerl, T. Dekorsy, and M. Helm, “High-intensity terahertz radiation from a microstructured large-area photoconductor,” Appl. Phys. Lett 86, 121114 (2005).
[Crossref]

2004 (2)

2002 (2)

J. Hebling, G. Almasi, I. Z. Kozma, and J. Kuhl, “Velocity matching by pulse front tilting for large-area THz-pulse generation,” Opt. Express 10, 1161–1166 (2002).
[Crossref] [PubMed]

M. Nagel, P. Haring Bolivar, M. Brucherseifer, H. Kurz, A. Bosserhoff, and R. Büttner, “Integrated THz technology for label-free genetic diagnostics,” Appl. Phys. Lett 80, 154–156 (2002).
[Crossref]

2000 (4)

A. Markelz, A. Roitberg, and E. J. Heilweil, “Pulsed terahertz spectroscopy of DNA, bovine serum albumin and collagen between 0.1 and 2.0 THz,” Chem. Phys. Lett 320, 42–48 (2000).
[Crossref]

Y.-S. Lee, T. Meade, V. Perlin, H. Winful, T. Norris, and A. Galvanauskas, “Generation of narrow-band terahertz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate,” Appl. Phys. Lett 76, 2505–2507 (2000).
[Crossref]

Y.-S. Lee, T. Meade, M. DeCamp, T. Norris, and A. Galvanauskas, “Temperature dependence of narrow-band terahertz generation from periodically poled lithium niobate,” Appl. Phys. Lett 77, 1244–1246 (2000).
[Crossref]

K. Kawase, T. Hatanaka, H. Takahashi, K. Nakamura, T. Taniuchi, and H. Ito, “Tunable terahertz-wave generation from dast crystal by dual signal-wave parametric oscillation of periodically poled lithium niobate,” Opt. Lett. 25, 1714–1716 (2000).
[Crossref]

1999 (2)

J.-i. Shikata, M. Sato, T. Taniuchi, H. Ito, and K. Kawase, “Enhancement of terahertz-wave output from LiNbO3 optical parametric oscillators by cryogenic cooling,” Opt. Lett. 24, 202–204 (1999).
[Crossref]

G. Ghosh, “Dispersion-equation coefficients for the refractive index and birefringence of calcite and quartz crystals,” Opt. Commun 163, 95–102 (1999).
[Crossref]

1997 (5)

1996 (2)

R. DeSalvo, A. A. Said, D. J. Hagan, E. W. Van Stryland, and M. Sheik-Bahae, “Infrared to ultraviolet measurements of two-photon absorption and n2 in wide bandgap solids,” IEEE J. Quantum Electron 32, 1324–1333 (1996).
[Crossref]

P. U. Jepsen, R. H. Jacobsen, and S. Keiding, “Generation and detection of terahertz pulses from biased semiconductor antennas,” J. Opt. Soc. Am. B 13, 2424–2436 (1996).
[Crossref]

1994 (1)

A. Rice, Y. Jin, X. Ma, X.-C. Zhang, D. Bliss, J. Larkin, and M. Alexander, “Terahertz optical rectification from< 110> zinc-blende crystals,” Appl. Phys. Lett 64, 1324–1326 (1994).
[Crossref]

1993 (1)

M. Cree and P. Bones, “Algorithms to numerically evaluate the Hankel transform,” Comput. & Math. with Appl. 26, 1–12 (1993).
[Crossref]

1992 (3)

A. Parent, M. Morin, and P. Lavigne, “Propagation of super-gaussian field distributions,” Opt. Quantum Electron. 24, S1071–S1079 (1992).
[Crossref]

M. Gupta, “Power combining efficiency and its optimisation,” IEE Proc. H (Microwaves, Antennas Propagation) 139, 233–238 (1992).
[Crossref]

G. R. Hadley, “Transparent boundary condition for the beam propagation method,” IEEE J. Quantum Electron 28, 363–370 (1992).
[Crossref]

1990 (1)

1985 (1)

R. Weis and T. Gaylord, “Lithium niobate: summary of physical properties and crystal structure,” Appl. Phys. A: Mater. Sci. & Process. 37, 191–203 (1985).
[Crossref]

1980 (1)

J. Williamson, “Low-storage Runge-Kutta schemes,” J. Comput. Phys 35, 48–56 (1980).
[Crossref]

1977 (1)

1956 (1)

J. Manley and H. Rowe, “Some general properties of nonlinear elements-part I. general energy relations,” Proc. IRE 44, 904–913 (1956).
[Crossref]

Ahr, F.

Alexander, M.

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[Crossref]

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Figures (15)

Fig. 1
Fig. 1 Schematic illustration of the multi-stage system. Detailed information about the quartz coupler (QC) can be found in Fig. 7. In the sketch, the angular deflection of the optical pump caused by the refraction at the output of each stage is not delineated for illustration purposes. The dark arrows on the PPLN crystals represent the poling of the nonlinear material.
Fig. 2
Fig. 2 Schematic illustration of the simulated geometry: the dark thick arrows represent the polarization direction of both pump and terahertz beams. The polarization direction is aligned with the extraordinary optical axis of PPLN. The origin of the cylindrical coordinate is at the center of the beam. r and z represent the transverse and propagation directions, respectively.
Fig. 3
Fig. 3 Comparison of a 4 stage system with input pump pulse parameters σ = 5 mm, τFWHM = 150 ps. The effective length of each stage is chosen to be the distance where efficiency saturates. (a,c,e) depict the terahertz spectra generated after each stage, the conversion efficiency, and the terahertz electric field by recycling the pump pulse directly without dispersion compensation (No Comp.). (b,d,f) show the terahertz spectra, the conversion efficiency, and the terahertz electric field with pump pulse dispersion compensation (Comp.) after each stage.
Fig. 4
Fig. 4 (a) shows the input pump pulse (b) shows the output pump pulse after one 2.5 cm PPLN stage. (c) shows the output pump pulse after dispersion compensation by adding the opposite second order dispersion of Lithium Niobate at the pump center frequency (GDD= 6300 fs2) to (b). The contour plot in the second and third rows are the short time Fourier transforms of the corresponding selected temporal range (indicated by the dotted red box).
Fig. 5
Fig. 5 (a–d) show the terahertz spectral density generated by 4 consecutive stages respectively. The first and second rows show the terahertz spectra generated without and with dispersion compensation, respectively.
Fig. 6
Fig. 6 (a–d) represent pump pulse spectral density after each corresponding stage. The first and second rows show the pump pulse spectra at the output of each stage generated without and with dispersion compensation, respectively.
Fig. 7
Fig. 7 (a) Schematic illustration of the output coupler and the angle definitions. In (b) and (c), comparison of the terahertz transmission from PPLN to air for ’Air’ and ’QC’ cases are shown. Additionally, the transmission of the generated flat-top terahertz beam with different beam sizes σt = 1 mm (dashed lines) and σt = 5 mm (solid lines) are analyzed. (b) shows terahertz transmission versus the refractive index of the PPLN at the given Brewster angles (BA) at S1 surface. The BA is calculated with the PPLN refractive index at terahertz frequency marked by the black dash-dotted line. (c) shows terahertz transmission versus the incident angle at surface S1 with given refractive index where the black dash-dotted lines mark the BA.
Fig. 8
Fig. 8 Numerical results of the terahertz generation in a single stage: (a) shows the conversion efficiency versus the pump pulse duration. The maximum efficiency η = 1.05 % is obtained at τFWHM = 150 ps. The input pump energy is calculated from Eq. (3) with the pump beam size σ = 5 mm. (b) shows the L0, Leff versus pump pulse duration. (c) shows the terahertz efficiency versus the propagation distance for τFWHM = 150 ps, where the steepest efficiency increase rate (L0) and effective length (Leff) are labeled.
Fig. 9
Fig. 9 (a) shows the efficiency of terahertz generation versus propagation distance for various beam sizes. (b) shows the spatial profile of the input pump pulse (dashed lines) and output pump pulse (solid lines). (c) shows the output terahertz beam spatial profile. For different beam sizes, the peak fluence is kept constant. The output spatial profiles of both terahertz radiation and the pump are obtained at the end of the interaction length, i.e. z = 25 mm.
Fig. 10
Fig. 10 (a) and (b) show the spectral density (first row) and flat phase front (second row) of the input pump spectral lines. (c) shows the spatial profile of the input and output pump pulse. (d) shows the terahertz spatial profile.
Fig. 11
Fig. 11 (a) and (b) show the spectral density (first row) and flat phase front (second row) of the input pump spectral lines. (c) shows the spatial profile of the input and output pump pulse. (d) shows the terahertz spatial profile.
Fig. 12
Fig. 12 (a) and (b) show the spectral density (first row) and phase front (second row) of the input pump spectral lines. (c) shows the spatial profile of the input and output pump pulse. (d) shows the terahertz spatial profile.
Fig. 13
Fig. 13 In (a,b) the first row shows the spatial profiles of the pump spectral lines and the second row represents the phase front of the corresponding spectral lines. (c) shows the pump input and output spatial profile. (d) shows the generated terahertz spatial profile.
Fig. 14
Fig. 14 (a,b) and (c,d) represent terahetz spatial profiles in PPLN in xy coordinate before S1 surface (see Fig. 7(a)) generated by a two-stage system with pump beam size σ = 5 mm and σ = 1 mm respectively. (e–h) represent coupled out terahertz spatial profiles of (a–d) after S2 surface in x′y coordinate in the air. The color bar represents fluence in the unite of J/m2. Each figure window size is 15 mm × 15 mm. Terahertz out-coupling efficiency from (a–d) to (e–h) is ηa = 96.1%, ηb = 93.7%, ηc = 62.5%, ηd = 60.3% respectively.
Fig. 15
Fig. 15 Illustration of the matrix representation of Eq. (17). The numbers of the mesh grids at r and ω dimensions are represented by Nr and Nω respectively. Each color of the corresponding column vector represents the coupled wave equation at a specific frequency ωm.

Tables (2)

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Table 1 Simulation Parameters with Two-lines Input

Tables Icon

Table 2 Quartz Coupler Parameters

Equations (23)

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A op ( ω , r , z ) z = i 2 k ( ω ) 1 r r ( r A op ( ω , r , z ) r ) i ε 0 n ( ω ) n 2 ω 2 { | A op ( t , r , z ) | 2 A op ( t , r , z ) } i ω χ eff ( z ) 2 n ( ω ) c A op ( ω + Ω , r , z ) A THz * ( Ω , r , z ) e i Δ k z d Ω
A THz ( Ω , r , z ) z = i 2 k ( Ω ) 1 r r ( r A THz ( Ω , r , z ) r ) α ( Ω ) 2 A THz ( Ω , r , z ) i Ω χ eff ( z ) 2 n ( Ω ) c A op ( ω + Ω , r , z ) A op * ( ω , r , z ) e i Δ k z d ω
Energy = 2 π σ 2 Γ ( M + 1 M ) F d 2 1 M
1 e d η ( z ) d z | z = L 0 = d η ( z ) d z | z = L eff .
{ for short pump pulses , δ α 1 , L 0 = tan 1 ( δ α ) / δ for short pump pulses , δ α 1 , L 0 = 2 ln ( 2 ) / α , L eff = 2 α ln ( 2 1 1 e 1 )
{ E ( ω , r ) = E 0 ( ω , r ) ( 1 + 0.05 cos ( 2 π × 4 r r max ) ) , ω 2 π × 291.3 THz E ( ω , r ) = E 0 ( ω , r ) , ω > 2 π × 291.3 THz
E ( ω , r ) = E 0 ( ω , r ) ( 1 + 0.05 cos ( 2 π × 4 r r max ) )
E ( ω , r ) = E 0 ( ω , r ) e i π cos ( 2 π × 4 r r max )
{ E ( ω , r ) = E 0 ( ω , r ) e i π cos ( 2 π × 4 r r max ) , ω 2 π × 291.3 THz E ( ω , r ) = E 0 ( ω , r ) , ω > 2 π × 291.3 THz
η combine = | k = 1 N T E k ( x , y , t ) | 2 d x d y d t N T k = 1 N T | E k ( x , y , t ) | 2 d x d y d t
η total = η combine × ( η 1 × η a + η 2 × η b )
[ P 1 NL ( 2 ) P 2 NL ( 2 ) P 3 NL ( 2 ) ] = 2 0 [ 0 0 0 0 d 15 d 22 d 22 d 22 0 d 15 0 0 d 15 d 15 d 33 0 0 0 ] [ | E 1 | 2 | E 2 | 2 | E 3 | 2 E 2 E 3 * + E 2 * E 3 E 1 E 3 * + E 1 * E 3 E 1 E 2 * + E 1 * E 2 ]
Ω [ 1 / v THz ( Ω ) 1 / v g ( ω ) ] Λ 2 = π + 2 π N N = 0 , 1 , 2 , 3
ω 0 { | A op ( t , r , z ) | 2 A op ( t , r , z ) i ω 0 | A op ( t , r , z ) | 2 A op ( t , r , z ) t } = ω 0 { | A op ( t , r , z ) | 2 A op ( t , r , z ) } + ( ω ω 0 ) { | A op ( t , r , z ) | 2 A op ( t , r , z ) } = ω { | A op ( t , r , z ) | 2 A p ( t , r , z ) } .
1 r j r ( r j A op ( ω m , r j , z k ) r ) = r j A op ( ω m , r j 1 , z k ) ( r j + r j + ) A op ( ω m , r j , z k ) + r j + A op ( ω m , r j + 1 , z k )
A op ( ω m , r j , z k ) z = P NL ( ω m , r j , z k ) + i 2 k ( ω m ) [ r j A op ( ω m , r j 1 , z k ) + ( r j + r j + ) A op ( ω m , r j , z k ) r j + A op ( ω m , r j + 1 , z k ) ]
A op ( ω , r 0 , z ) = A op ( ω , r 1 , z )
A op ( ω , r N r + 1 , z ) = A op ( ω , r N r , z ) n op 2 r N r n 2 r N r + 1
A op ( ω , r N r + 1 , z ) = 0
A op ( ω , r N r + 1 , z k + 1 ) = A op ( ω , r N r , z k + 1 ) A op ( ω , r N r + 1 , z k ) r N r A op ( ω , r N r , z k ) r N r + 1
A THz ( Ω , z ) = i Ω χ 333 ( 2 ) π n ( Ω ) c 0 A op ( ω + Ω , r , z ) A op * ( ω , r , z ) d ω [ e i δ z e α ( Ω ) z 2 α ( Ω ) 2 + i δ ] = P NL ( Ω ) [ e i δ z e α ( Ω ) z 2 α ( Ω ) 2 + i δ ]
δ = [ k ( Ω ) + k ( ω ) k ( ω + Ω ) 2 π Λ ] = [ Ω c ( n ( Ω ) n g ( ω ) ) 2 π Λ ] ( n ( Ω 0 ) n g ( ω 0 ) ) c τ FWHM .
e α z 2 = [ 1 2 cos ( δ z ) + 2 δ α sin ( δ z ) 2 δ 2 α 2 cos ( δ z ) ] { for short pump pulse , δ α 1 , 2 δ α sin ( δ z ) = 2 δ 2 α 2 cos ( δ z ) L 0 = tan 1 ( δ α ) / δ , for long pump pulse , δ α 1 , e α z 2 = 1 2 cos ( δ z ) 1 2 L 0 = 2 ln ( 2 ) / α , L eff = 2 α ln ( 2 1 1 e 1 )

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