Abstract

We report forward and backward THz-wave difference frequency generations at 197 and 469 μm from a PPLN rectangular crystal rod with an aperture of 0.5 (height in z) × 0.6 (width in y) mm2 and a length of 25 mm in x. The crystal rod appears as a waveguide for the THz waves but as a bulk material for the optical mixing waves near 1.54 μm. We measured enhancement factors of 1.6 and 1.8 for the forward and backward THz-wave output powers, respectively, from the rectangular waveguide in comparison with those from a PPLN slab waveguide of the same length, thickness, and domain period under the same pump and signal intensity of 100 MW/cm2.

© 2011 OSA

1. Introduction

Difference frequency generation (DFG) of two lasers beating at THz frequencies in a nonlinear optical material is a popular optical technique to generate coherent THz wave radiation. However, owing to the vast difference of the mixing wavelengths, the THz wave is usually more absorptive in the material than the optical mixing waves. For example, lithium niobate, while being transparent in the optical spectrum, has a typical absorption coefficient of a few tens of cm−1 at THz frequencies [1]. The THz wave experiences a pure absorption loss as soon as it leaves the gain region of the optical pump and signal beams. To overcome this problem, several schemes have been successfully implemented to couple out the THz wave as soon as possible for non-collinearly phase matched THz-wave DFG in lithium niobate [2]. For parametric frequency mixing, however, collinear phase matching is a preferred configuration to increase the parametric gain length and thus the wavelength conversion efficiency. With quasi-phase-matching (QPM), we have previously demonstrated collinearly phase matched THz-wave DFG in bulk periodically poled lithium niobate (PPLN) [3]. Unfortunately, the much longer wavelength of the THz wave could still make the generated THz wave quickly diffracted and absorbed outside the gain region of the optical pump and signal beams. GaAs is also a demonstrated QPM material for THz-wave DFG with much less absorption in the THz spectrum [4]. However, LN has a three-time larger nonlinear coefficient. If the diffraction induced absorption in LN can be alleviated, LN is still a promising material for high-efficiency THz DFG.

To reduce the diffraction-induced absorption, one could in principle design a nonlinear optical waveguide that guides the THz wave as well as the optical waves [5]. However, guiding an optical wave requires a waveguide aperture comparable to the optical wavelengths, which severely restricts the input and output powers of the mixing waves. Previously we have shown an experimental evidence of enhanced, non-collinearly phase matched THz-wave DFG from a 0.5-mm thick crystal slab of lithium niobate [6]. This crystal slab guides the THz wave in one transverse direction but behaves like a bulk crystal to the optical mixing waves. For what follows, we call such a waveguide a one-dimensional (1-D) nonlinear optical semi-waveguide (NOSW). In this paper, we compare collinearly phase matched THz-wave DFG in rectangular (2-D) and 1-D NOSWs of the same length made of PPLN. As will be shown below, the additional confinement of the THz wave in the other transverse dimension of the crystal indeed enhances the THz-wave output power under the same pump condition.

2. Theory

To be consistent with our following experiment using type-0 phase matched PPLN crystals, we choose z as the direction of polarization for all mixing waves and + x as the propagation direction for the pump and signal waves. Forward or backward THz-wave DFG refers to the propagation of the THz wave in the +x or −x direction, respectively. In a NOSW, the unguided optical component has a varying beam size along the propagation direction x. However, in our case, the optical mixing waves have a depth of focus significantly longer than the crystal length and the mode-radius variation is less than 2% over the whole crystal length. Therefore, it is a good approximation to write the electric fields of the collinearly propagating optical pump and signal waves with a constant Gaussian field profile in the transverse direction, given by Ei(t,y,z,x)=Re[2ηiei(y,z)Ai(x)ej(ωitβix)], where the subscript i = p, s denote the pump and signal waves, respectively, β is the propagation constant in the x direction, η = η0/n is the intrinsic wave impedance in a material of refractive index n, and e(y,z) is the transverse field profile with the normalization |e(x,y)|2dxdy=1, so that |A(x)|2=P(x) is the power of the wave at x. For the THz-wave DFG, the optical pump and signal wavelengths are nearly the same and ep(y,z)es(y,z) for a fundamental Gaussian beam can be written as

ep,s(y,z)=1w2πe(y2+z2)/w2,
where w is the average mode radius of the pump and signal waves in the nonlinear optical material. Likewise, the electric field of the guided THz wave can be expressed as ETHz(t,y,z,x)=Re[2ηTHzeTHz(y,z)ATHz(x)ej(ωTHztβTHzx)], where the sign preceding the propagation constant βTHz denotes a THz wave propagating along ± x.

In our experiment, pump depletion was negligible. Without pump depletion and signal absorption, the coupled-mode equations for continuous-wave, collinear DFG are given by [7]

Asx=jκsApATHz*ejΔβx,
ATHzx=jκTHzApAs*ejΔβxαTHz2ATHz,
where αTHz is the absorption coefficient of the THz wave, κi is the nonlinear coupling coefficient, and Δβ=βpβsβTHzkQPM is the wave-number mismatch among the collinear pump, signal, THz waves, and the quasi-phase-matching (QPM) grating kQPM. Without any initial THz-wave power at x = 0, the forward THz-wave output power at x = L normalized to the input signal power Ps(0) is given by
PTHz(L)Ps(0)=λsλTHzeαTHzL/2Γ2|gf|2|sinh(gfL)|2,
where λ is the wavelength in vacuum, Γ is the parametric gain coefficient, and gf(αTHz/4jΔβf/2)2+Γ2 with Δβf=βpβsβTHzkQPM. The specific expression of the parametric gain coefficient Γ is given by
Γ2=κsκTHzPp(0)=Γ02Apϑ2=8π2deff2η0npnsnTHzλsλTHzIp(0)Apϑ2,
where Pp(0) and Ip(0) are the initial pump power and intensity at x = 0, respectively, Γ0 is the free-space plane-wave parametric gain coefficient [8], deff is the effective nonlinear coefficient, Ap is the pump-mode area, and Apϑ is a modification factor to the free-space plane-wave parametric gain coefficient Γ0 with the mode-overlapping integral ϑ defined as

ϑ=ep(y,z)es(y,z)eTHz(y,z)dydz.

It is straightforward to show that in the limit of a much larger THz-wave mode size than the optical one, ϑ2 approaches the inverse of the THz-wave mode area or ϑ21/ATHz and Γ2 is reduced from its free-space plane-wave value by a factor of Ap/ATHz. Since the THz wavelength is much longer than that of the optical mixing waves, this parametric gain reduction can be very significant due to fast diffraction of the THz wave in a bulk nonlinear optical material.

For the case of a backward THz wave propagating in the −x direction, we derive the THz-wave output power at x = 0 with zero initial THz-wave power at x = L, given by

PTHz(0)Ps(0)=λsλTHzΓ2|sin(gbL)αTHz4sin(gbL)+gbcos(gbL)|2,
where gbΓ2(αTHz/4jΔβb/2)2 with Δβb=βpβs+βTHzkQPM. It can be seen from Eq. (7) that the THz absorption increases the oscillation threshold and broadens the parametric gain bandwidth.

3. Experiment

We fabricated three 2-D PPLN NOSWs from congruent lithium niobate, as shown in Fig. 1(a) , but unfortunately broke the two shorter ones during polishing. For comparison, we also fabricated a 1-D PPLN NOSW with no wave confinement in the y direction. Both NOSWs are 25 mm long and 0.5 mm thick in the crystallographic x and z directions, respectively. The 2-D NOSW has a width of 0.6 mm along the y direction. All the guiding surfaces of the two crystals were optically polished. The ±x faces of the crystals were coated with anti-reflection layers at the pump and signal wavelengths. The QPM domain period of the two PPLN NOSWs is 65 μm, which permits phase matching for the generation of forward and backward THz waves at λTHz = 197 and 469 μm, respectively, at room temperature with a pump wavelength at λp = 1538.9 nm.

 

Fig. 1 (a) Photograph of the three 2-D NOSWs fabricated from PPLN for our experiment. Experimental data in this paper were taken from the longest one. (b) Schematic of the forward and backward THz-wave DFG in PPLN NOSW. The pump and signal are initially combined from a distributed feed-back diode laser (DFBDL) and a tunable external cavity diode laser (ECDL), and then boosted up in power by an Erbium-doped fiber amplifier (EDFA) and a pulsed optical parametric amplifier (OPA). A 4K silicon bolometer detects the backward and forward THz waves before and after the PPLN NOSW, respectively.

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In our experiment, the waist radius of the optical pump and signal waves was 127-μm at the center of the PPLN crystals. Since the aperture of the PPLN crystals is 4-5 times the waist radius of the signal and pump waves, the PPLN crystals appear as a bulk material to the optical mixing waves. However, the very same crystals act as a waveguide for the THz waves, because the diffraction angles of the forward and backward THz waves are 0.1 and 0.23 rad, respectively, for an initial beam radius comparable to that of the optical waves. The crystal apertures are relatively large and capable of accommodating many waveguide modes for the THz waves. However, the fundamental THz-wave mode overlaps well with the Gaussian optical mode and is the dominant mode to build up in such a highly absorptive NOSW [6].

Figure 1(b) shows the schematic of the THz-wave DFG experiment. The pump and signal waves are first combined from a fixed-frequency distributed-feedback diode laser (DFBDL) at 1538.9 nm and an external-cavity diode laser (ECDL) with its wavelength tuned to the phase matching one for the downstream THz-wave DFG. An amplifier system, consisting of an Erbium-doped fiber amplifier (EDFA) followed by a pulsed two-color optical parameter amplifier (OPA), boosts each of the pump and signal energy to 9.7 μJ/pulse in a 360-ps pulse width. The forward propagating signal and pump pulses were then focused to the center of the PPLN NOSW. A silicon bolometer was installed before and after the PPLN NOSW to detect the backward and forward THz waves, respectively [3].

The largest possible THz mode area is the aperture area of the 2-D PPLN NOSW, which can be described by eTHz(y,z)=rect(y/ly)×rect(z/lz)/lylz, where rect(r/l) is a rectangular function with a unit amplitude inside and zero amplitude outside the range of −l/2 < r < l/2. The maximum gain reduction factor thus estimated from Eq. (6) is Apϑ0.29, which is about the square root of the area ratio Ap/ATHz, as expected for a large mode-area mismatch. Therefore, the actual parametric gain coefficient Γ for the 2-D NOSW could be reduced to about 1/3 of its free-space plane-wave value. Given deff = 168 × 2/π = 107 pm/V [9] and np = ns = 2.14 [10], the reduced parametric gain is estimated to be Γ=Γ0Apϑ=0.65,0.44cm−1 for the forward and backward THz waves with refractive indices of 5.22 and 5.05 [3], respectively. For the 1-D NOSW, the aforementioned theory is not valid due to the fast variation of the THz wave beam size along the propagation direction. However, one would expect a smaller effective parametric gain coefficient Γ and thus a smaller growth rate for the THz wave resulting from worsened mode mismatch and diffraction-induced absorption in the 1-D NOSW.

Figure 2(a) shows the measured DFG tuning curves for the forward THz waves at 197 μm generated from the 1-D (crosses) and 2-D (dots) PPLN NOSWs with a pump intensity of 102 MW/cm2. In the plot, the dashed and continuous lines are fitting curves using Eq. (4) with Γ = 0.53 and 0.65 cm−1 for the 1-D and 2-D NOSWs, respectively, given αTHz = 40 cm−1 at 1.5 THz for congruent lithium niobate [1]. As expected, the effective parametric gain coefficient for the 1-D NOSW is smaller due to diffraction of the THz wave in the y direction. The parametric gain of Γ = 0.65 cm−1 for the 2-D NOSW agrees well with the theory for a large mode-area mismatch. The measured tuning curves clearly show an enhancement factor of 1.6 at the phase matching wavelength for the THz-wave output power from the 2-D NOSW. Figure 2(b) shows the THz-wave output power versus pump intensity from the 1-D (squares) and 2-D (circles) NOSWs at the phase matching wavelength. During the measurement, the ratio of the pump to signal intensity remained one. The power enhancement factor of the THz wave is nonlinearly increased with the pump intensity, which indicates some exponential gain for the THz wave as predicted by Eq. (4). The estimated forward THz-wave pulse energies generated inside the 1-D and 2-D NOSWs are 41 and 63 pJ, respectively.

 

Fig. 2 (a) Measured forward THz-wave tuning curves from the 1-D (dots) and 2-D (crosses) PPLN NOSWs. The dashed and continuous lines are fitting curves of Eq. (4) with Γ = 0.53 and 0.65 cm−1 for the 1-D and 2-D NOSW, respectively, given an attenuation coefficient of 40 cm−1. (b) The Measured THz-wave output power versus pump intensity from the 1-D (squares) and 2-D (circles) NOSWs, indicating some nonlinear THz-wave power enhancement in the 2-D NOSW.

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Figure 3(a) shows the measured DFG tuning curves for the backward THz wave at 469 μm generated from the 1-D (cross) and 2-D (dot) PPLN NOSWs with a pump intensity of 104 MW/cm2. The dashed and continuous lines are fitting curves using Eq. (7) with Γ = 0.34 and 0.44 cm−1 for the 1-D and 2-D NOSWs, respectively, and with an assumed attenuation coefficient of 6 cm−1. The reduced parametric gain coefficient for the 1-D NOSW also indicates a poorer beam overlap between the backward THz and forward optical waves due to diffraction of the THz wave in the y direction. The parametric gain of Γ = 0.44 cm−1 for the 2-D NOSW agrees well with the theory for a large mode-area mismatch. The measured tuning curves clearly show a power enhancement factor of 1.8 at the phase matching wavelength for the 2-D NOSW. Figure 3(b) shows the THz-wave output power versus pump intensity from the 1-D (squares) and 2-D (circles) NOSWs at the phase matching wavelength, indicating enhanced output power from the 2-D NOSW over the whole range of measurement. The estimated backward THz-wave pulse energies generated inside the 1-D and 2-D NOSWs are 0.3 and 0.5 nJ, respectively.

 

Fig. 3 (a) Measured backward THz-wave tuning curves from the 1-D (dots) and 2-D (crosses) PPLN NOSWs. The dashed and continuous lines are fitting curves of Eq. (7) with Γ = 0.34 and 0.44 cm−1 for the 1-D and 2-D NOSWs, respectively, and with an assumed attenuation coefficient of 6 cm−1. (b) The Measured backward THz-wave output power versus pump intensity from the 1-D (squares) and 2-D (circles) NOSWs, indicating enhanced THz-wave power from the 2-D NOSW over the whole range of measurement.

Download Full Size | PPT Slide | PDF

It should be pointed out that the THz wave in the 1-D NOSW could have a smaller diffraction angle in the unconfined y direction. With a fixed detection path for the THz wave from the 1-D and 2-D NOSW, the bolometer could have collected less THz-wave power from the 2-D NOSW. If so, the power enhancement factor reported above is conservative. However, the high absorption of the THz wave in lithium niobate would have concentrated the THz-wave power to an emitting aperture comparable to that of the optical beam for both NOSWs. Under this situation, the comparison curves reported above do not require further correction.

4. Summary

In summary, we have reported enhanced THz-wave DFG from a rectangular PPLN crystal rod with an aperture of 0.5 × 0.6 mm2. This crystal appears as a bulk material to the optical mixing waves near 1.54 μm but behaves like a 2-D waveguide to the forward and backward THz waves at 197 and 469 μm, respectively. The THz-wave output power from this 2-D NOSW is increased by a factor of 1.6 and 1.8 for the forward and backward THz waves, respectively, at pump and signal intensities of ~100 MW/cm2, when compared with that from a 1-D PPLN NOSW of the same thickness and length under the same pump condition. The 2-D waveguide confinement reduces the diffraction-induced absorption for the THz wave during the DFG process. In addition, we pointed out that, for most low-efficiency THz-wave DFG in bulk nonlinear optical materials, the major gain reduction mechanism could be the large mode-area mismatch between the THz and optical waves. This proof-of-principle experiment indeed points out a direction of potentially high-efficiency THz-wave DFG in a PPLN NOSW with further improved mode-area overlap for the THz and optical waves.

Acknowledgments

Shayeganrad has helped to correct some minor mistakes in this paper. This work is supported by National Science Council under Contract NSC99-2622-M-007-001-CC1.

References and links

1. G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” Int. J. Infrared Millim. Waves 32(10), 1144–1156 (2011).

2. K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron. 14(2), 295–306 (2008). [CrossRef]  

3. T. D. Wang, S. T. Lin, Y. Y. Lin, A. C. Chiang, and Y. C. Huang, “Forward and backward terahertz-wave difference-frequency generations from periodically poled lithium niobate,” Opt. Express 16(9), 6471–6478 (2008). [CrossRef]   [PubMed]  

4. K. L. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser Photonics Rev. 2(1–2), 11–25 (2008). [CrossRef]  

5. Y. Takushima, S. Y. Shin, and Y. C. Chung, “Design of a LiNbO3 ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration,” Opt. Express 15(22), 14783–14792 (2007). [CrossRef]   [PubMed]  

6. A. C. Chiang, T. D. Wang, Y. Y. Lin, S. T. Lin, H. H. Lee, Y. C. Huang, and Y. H. Chen, “Enhanced terahertz-wave parametric generation and oscillation in lithium niobate waveguides at terahertz frequencies,” Opt. Lett. 30(24), 3392–3394 (2005). [CrossRef]   [PubMed]  

7. M. H. Chou, “Optical frequency mixers using three-wave mixing for optical fiber communications,” PhD thesis, (Stanford University, 1999).

8. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

9. J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004). [CrossRef]  

10. D. H. Jundt, “Temperature-dependent Sellmeier equation for index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22(20), 1553–1555 (1997). [CrossRef]   [PubMed]  

References

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  1. G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” Int. J. Infrared Millim. Waves 32(10), 1144–1156 (2011).
  2. K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron. 14(2), 295–306 (2008).
    [Crossref]
  3. T. D. Wang, S. T. Lin, Y. Y. Lin, A. C. Chiang, and Y. C. Huang, “Forward and backward terahertz-wave difference-frequency generations from periodically poled lithium niobate,” Opt. Express 16(9), 6471–6478 (2008).
    [Crossref] [PubMed]
  4. K. L. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser Photonics Rev. 2(1–2), 11–25 (2008).
    [Crossref]
  5. Y. Takushima, S. Y. Shin, and Y. C. Chung, “Design of a LiNbO3 ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration,” Opt. Express 15(22), 14783–14792 (2007).
    [Crossref] [PubMed]
  6. A. C. Chiang, T. D. Wang, Y. Y. Lin, S. T. Lin, H. H. Lee, Y. C. Huang, and Y. H. Chen, “Enhanced terahertz-wave parametric generation and oscillation in lithium niobate waveguides at terahertz frequencies,” Opt. Lett. 30(24), 3392–3394 (2005).
    [Crossref] [PubMed]
  7. M. H. Chou, “Optical frequency mixers using three-wave mixing for optical fiber communications,” PhD thesis, (Stanford University, 1999).
  8. R. W. Boyd, Nonlinear Optics (Academic Press, 2008).
  9. J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
    [Crossref]
  10. D. H. Jundt, “Temperature-dependent Sellmeier equation for index of refraction, ne, in congruent lithium niobate,” Opt. Lett. 22(20), 1553–1555 (1997).
    [Crossref] [PubMed]

2011 (1)

G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” Int. J. Infrared Millim. Waves 32(10), 1144–1156 (2011).

2008 (3)

K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron. 14(2), 295–306 (2008).
[Crossref]

T. D. Wang, S. T. Lin, Y. Y. Lin, A. C. Chiang, and Y. C. Huang, “Forward and backward terahertz-wave difference-frequency generations from periodically poled lithium niobate,” Opt. Express 16(9), 6471–6478 (2008).
[Crossref] [PubMed]

K. L. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser Photonics Rev. 2(1–2), 11–25 (2008).
[Crossref]

2007 (1)

2005 (1)

2004 (1)

J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

1997 (1)

Almasi, G.

J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

Bartal, B.

J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

Chen, Y. H.

Chiang, A. C.

Chung, Y. C.

Hebling, J.

J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

Huang, Y. C.

Jundt, D. H.

Kawase, K.

K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron. 14(2), 295–306 (2008).
[Crossref]

Kitaeva, G. Kh.

G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” Int. J. Infrared Millim. Waves 32(10), 1144–1156 (2011).

Kovalev, S. P.

G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” Int. J. Infrared Millim. Waves 32(10), 1144–1156 (2011).

Kuhl, J.

J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

Lee, H. H.

Lin, S. T.

Lin, Y. Y.

Penin, A. N.

G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” Int. J. Infrared Millim. Waves 32(10), 1144–1156 (2011).

Shin, S. Y.

Stepanov, A. G.

J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

Suizu, K.

K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron. 14(2), 295–306 (2008).
[Crossref]

Takushima, Y.

Tuchak, A. N.

G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” Int. J. Infrared Millim. Waves 32(10), 1144–1156 (2011).

Vodopyanov, K. L.

K. L. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser Photonics Rev. 2(1–2), 11–25 (2008).
[Crossref]

Wang, T. D.

Yakunin, P. V.

G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” Int. J. Infrared Millim. Waves 32(10), 1144–1156 (2011).

Appl. Phys. B (1)

J. Hebling, A. G. Stepanov, G. Almasi, B. Bartal, and J. Kuhl, “Tunable THz pulse generation by optical rectification of ultrashort laser pulses with tilted pulse fronts,” Appl. Phys. B 78, 593–599 (2004).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

K. Suizu and K. Kawase, “Monochromatic-tunable terahertz-wave sources based on nonlinear frequency conversion using lithium niobate crystal,” IEEE J. Sel. Top. Quantum Electron. 14(2), 295–306 (2008).
[Crossref]

Int. J. Infrared Millim. Waves (1)

G. Kh. Kitaeva, S. P. Kovalev, A. N. Penin, A. N. Tuchak, and P. V. Yakunin, “A method of calibration of terahertz wave brightness under nonlinear-optical detection,” Int. J. Infrared Millim. Waves 32(10), 1144–1156 (2011).

Laser Photonics Rev. (1)

K. L. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser Photonics Rev. 2(1–2), 11–25 (2008).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Other (2)

M. H. Chou, “Optical frequency mixers using three-wave mixing for optical fiber communications,” PhD thesis, (Stanford University, 1999).

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

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Figures (3)

Fig. 1
Fig. 1

(a) Photograph of the three 2-D NOSWs fabricated from PPLN for our experiment. Experimental data in this paper were taken from the longest one. (b) Schematic of the forward and backward THz-wave DFG in PPLN NOSW. The pump and signal are initially combined from a distributed feed-back diode laser (DFBDL) and a tunable external cavity diode laser (ECDL), and then boosted up in power by an Erbium-doped fiber amplifier (EDFA) and a pulsed optical parametric amplifier (OPA). A 4K silicon bolometer detects the backward and forward THz waves before and after the PPLN NOSW, respectively.

Fig. 2
Fig. 2

(a) Measured forward THz-wave tuning curves from the 1-D (dots) and 2-D (crosses) PPLN NOSWs. The dashed and continuous lines are fitting curves of Eq. (4) with Γ = 0.53 and 0.65 cm−1 for the 1-D and 2-D NOSW, respectively, given an attenuation coefficient of 40 cm−1. (b) The Measured THz-wave output power versus pump intensity from the 1-D (squares) and 2-D (circles) NOSWs, indicating some nonlinear THz-wave power enhancement in the 2-D NOSW.

Fig. 3
Fig. 3

(a) Measured backward THz-wave tuning curves from the 1-D (dots) and 2-D (crosses) PPLN NOSWs. The dashed and continuous lines are fitting curves of Eq. (7) with Γ = 0.34 and 0.44 cm−1 for the 1-D and 2-D NOSWs, respectively, and with an assumed attenuation coefficient of 6 cm−1. (b) The Measured backward THz-wave output power versus pump intensity from the 1-D (squares) and 2-D (circles) NOSWs, indicating enhanced THz-wave power from the 2-D NOSW over the whole range of measurement.

Equations (7)

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e p,s (y,z)= 1 w 2 π e ( y 2 + z 2 )/ w 2 ,
A s x =j κ s A p A THz * e jΔβx ,
A THz x =j κ THz A p A s * e jΔβx α THz 2 A THz ,
P THz (L) P s (0) = λ s λ THz e α THz L/2 Γ 2 | g f | 2 | sinh( g f L) | 2 ,
Γ 2 = κ s κ THz P p (0)= Γ 0 2 A p ϑ 2 = 8 π 2 d eff 2 η 0 n p n s n THz λ s λ THz I p (0) A p ϑ 2 ,
ϑ= e p (y,z) e s (y,z) e THz (y,z) dydz.
P THz (0) P s (0) = λ s λ THz Γ 2 | sin( g b L) α THz 4 sin( g b L)+ g b cos( g b L) | 2 ,

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