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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 2 — Jan. 28, 2013
  • pp: 2452–2462
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Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain

Tsong-Dong Wang, Yen-Chieh Huang, Ming-Yun Chuang, Yen-Hou Lin, Ching-Han Lee, Yen-Yin Lin, Fan-Yi Lin, and Galiya Kh. Kitaeva  »View Author Affiliations


Optics Express, Vol. 21, Issue 2, pp. 2452-2462 (2013)
http://dx.doi.org/10.1364/OE.21.002452


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Abstract

Optical parametric mixing is a popular scheme to generate an idler wave at THz frequencies, although the THz wave is often absorbing in the nonlinear optical material. It is widely suggested that the useful material length for co-directional parametric mixing with strong THz-wave absorption is comparable to the THz-wave absorption length in the material. Here we show that, even in the limit of the absorption loss exceeding parametric gain, the THz idler wave can grows monotonically from optical parametric amplification over a much longer distance in a nonlinear optical material until pump depletion. The coherent production of the non-absorbing signal wave can assist the growth of the highly absorbing idler wave. We also show that, for the case of an equal input pump and signal in difference frequency generation, the quick saturation of the THz idler wave predicted from a much simplified and yet popular plane-wave model fails when fast diffraction of the THz wave from the co-propagating optical mixing waves is considered.

© 2013 OSA

1. Introduction

In an ordinary optical device, optical amplification or oscillation is not possible for absorption loss exceeding amplification gain. Therefore, the operation wavelength of an optical amplifier or oscillator is usually designed in the transparent range of a gain material. This design rule is also widely adopted for an optical parametric amplifier. However, in the electromagnetic spectrum, the THz-frequency is relatively unexplored due to the scarcity of THz radiation sources. In order to generate a valuable THz wave, one often chooses to perform optical parametric amplification (OPA, input signal much weaker than the pump) or difference frequency generation (DFG, input signal comparable to the pump) in some quadratic nonlinear optical material with appreciable idler absorption at THz frequencies. One notable example is the THz-wave optical parametric generation in lithium niobate developed in the late 1960s and 1970s [1

1. J. M. Yarborough, S. S. Sussman, H. E. Purhoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett. 15(3), 102–105 (1969). [CrossRef]

3

3. M. A. Piestrup, R. N. Fleming, and R. H. Pantell, “Continuously tunable submillimeter wave source,” Appl. Phys. Lett. 26(8), 418–421 (1975). [CrossRef]

], which has been closely followed by Ito and his associates [4

4. K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D Appl. Phys. 35(3), R1–R14 (2002). [CrossRef]

] with great improvements on output coherence and efficiency. However, the absorption length of a THz wave in lithium niobate is usually shorter than a millimeter distance [5

5. L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005), doi:. [CrossRef]

]. Birefringence phase matching in lithium niobate requires the THz wave to propagate away from the nearly co-directional optical pump and signal beams at about a 65° angle. As soon as the THz wave propagates away from the optical beams, the THz wave is quickly absorbed in lithium niobate within a distance comparable to the THz absorption length. This walkoff-and-absorption phenomenon has prompted implementation of schemes of either coupling out the THz wave as fast as possible [6

6. K. Kawase, M. Sato, K. Nakamura, T. Taniuchi, and H. Ito, “Unidirectional radiation of widely tunable THz wave using a prism coupler under noncollinear phase matching condition,” Appl. Phys. Lett. 71(6), 753–755 (1997). [CrossRef]

10

10. J. B. Khurgin, D. Yang, and Y. J. Ding, “Generation of mid-infrared radiation in the highly-absorbing nonlinear medium,” J. Opt. Soc. Am. B 18(3), 340–343 (2001). [CrossRef]

] or increasing the overlap of mixing waves in the THz-wave walkoff direction [11

11. A. G. Stepanov, J. Hebling, and J. Kuhl, “Efficient generation of subpicosecond terahertz radiation by phase-matched optical rectification using ultrashort laser pulses with tilted pulse fronts,” Appl Phys Lett 83, 3000–3002 doi:Doi (2003). [CrossRef]

].The notion of THz OPA/DFG limited by the idler absorption was also at the same time developed across the literatures [12

12. T. Taniuchi and H. Nakanishi, “Collinear phase-matched terahertz-wave generation in GaP crystal using a dual-wavelength optical parametric oscillator,” J. Appl. Phys. 95, 7588–7591, doi:Doi (2004). [CrossRef]

15

15. J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quant. 14, 354–362, doi:Doi (2008). [CrossRef]

] and even emphasized in some summary papers [16

16. G. Kh. Kitaeva, “THz generation by means of optical laser,” Laser Phys. Lett. 5, 559–576 doi: (2008). [CrossRef]

19

19. 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]

].

In the following, we begin our discussion with the plane-wave model for parametric mixing in Sec. 2. This plane-wave model is valid when the beam size of the optical pump and signal is much larger than the THz wavelength or when the THz wave is confined in a waveguide. In Sec. 3, we modify the plane-wave model to take into account the fast diffraction of the THz wave when the optical beam size or the THz-wave’s radiation aperture is comparable to the THz wavelength. We then report a typical THz DFG experiment in Sec. 4 to show the growth of a THz wave over tens of absorption lengths in lithium niobate with an equal input intensity for the signal and pump. Sec. 5 is the conclusion.

2. Different regimes of OPA/DFG with idler absorption

The plane-wave formulism and solution for parametric mixing without absorption or without phase mismatch can be found in some publication and textbook [30

30. L. Lefort, K. Puech, G. W. Ross, Y. P. Svirko, and D. C. Hanna, “Optical parametric oscillation out to 6.3 μm in periodically poled lithium niobate under strong idler absorption,” Appl. Phys. Lett. 73(12), 1610–1612 (1998). [CrossRef]

, 31

31. A. Yariv and P. Yeh, Photonics, 6th Ed. (Oxford University Press, New York, Oxford, 2007).

]. We first extend the theory to include both idler absorption and phase mismatch. To clearly show the influence of the idler absorption, we break down the solution into several regimes characterized by a gain-to-loss ratio. We then discuss the difference between our result and a solution widely adopted for THz OPA/DFG.

To justify the saturation predicted by Eq. (1), one has to carefully examine the assumptions made to derive Eq. (1). Removing the pump and signal equations requires a negligible change of the pump and signal amplitudes throughout the parametric mixing process. A constant-pump assumption is possible for a process without pump depletion. A constant-signal assumption is apparently invalid for an OPA process, in which the signal grows from a small value to some appreciable one. For example, the injection-seeded THz parametric generator [38

38. S. Hayashi, K. Nawata, H. Sakai, T. Taira, H. Minamide, and K. Kawase, “High-power, single-longitudinal-mode terahertz-wave generation pumped by a microchip Nd:YAG laser [Invited],” Opt. Express 20(3), 2881–2886 (2012). [CrossRef] [PubMed]

] seeds a pulsed optical parametric amplifier with a weak signal in a lithium niobate crystal to generate a coherent THz wave. The constant-signal assumption could be valid over a very short crystal length when the input amplitude of the signal is comparable to the pump one. In this regard, the condition of an equal input pump and signal is sometimes satisfied for some DFG experiment. The validity of Eq. (1) has never been rigorously and quantitatively defined within the context of relevant physical parameters. In the following, we first show that, with a variable signal and a strong pump (typical to THz OPA), the growth of the highly absorptive idler wave is not limited to a saturation length predicted by Eq. (1). We then quantitatively show that Eq. (1) can be obtained from a joint consideration of the signal and idler equations under three conditions: (1) no pump depletion, (2) absorption loss much larger than parametric gain, and (3) material length much shorter than the absorption length. Finally we show in an experiment that the fast diffraction of the THz wave in a nonlinear optical material leaves the plane-wave model invalid even in the limit of an equal input pump and signal (typical to THz DFG).

If one allows both the signal and idler to vary in a parametric mixing process without pump depletion, only the pump equation can be abandoned from the three coupled-wave equations. The output photon flux density of the idler wave without any initial idler photon can be deduced from a general solution [39

39. G. Kh. Kitaeva and A. N. Penin, “Parametric frequency conversion in layered nonlinear media,” J. Exp. Theor. Phys. 98(2), 272–286 (2004). [CrossRef]

] of the same plane-wave model, given by
ϕi(L)=ϕs(0)eαiL/2Γ2|g|2|sinh(gL)|2
(2)
where g=Γ2+(αi/4jΔkf/2)2). For what follows, we set Δkf = 0 and g=Γ2+(αi/4)2) in Eq. (2) until we come back to fit the THz spectral tuning curve from our experiment. The corresponding signal photon flux density can be found to be ϕs(L)=ϕs(0)eαiL/2|cosh(gL)+αi/(4g)×sinh(gL)|2. The dependence of the output idler power on the idler absorption loss is not transparent from Eq. (2) as is. In the following, we break down Eq. (2) into approximate expressions in different limits of a characteristic gain-to-loss ratio defined as R = (2Γ)/(αi/2) = 4Γ/αi, where 2Γ is the intensity parametric gain coefficient and αi/2 is the effective loss of the parametric mixing process (see Eq. (4) below).

2.1 High-gain and short-gain-length regime

In the high-gain R2 >>1 and short-gain-length ΓL << 1 limit, Eq. (2) reduces to a compact expression
ϕi(L)ϕs(0)Γ2L2eαiL/2,
(3)
which has the maximum value at the crystal length L = 2/αi. However, when the crystal length approaches 2/αi, the condition ΓL << 1 is violated due to the constraint R2 = (4Γ/αi)2 >> 1. Therefore, it is incorrect to conclude from this regime that the maximum idler output occurs at a length comparable to the idler absorption length or L = 2/αi.

2.2 High-gain and long-gain-length regime

In the high-gain R2 >>1 and long-gain-length ΓL >> 1 limit, the idler output at z = L becomes
ϕi(L)ϕs(0)4e(2Γαi/2)L
(4)
Equation (4) indicates an exponential growth of the idler intensity along z similar to that for lossless OPA. It can be understood from Eq. (4) that 2Γ is the intensity parametric gain coefficient and αi/2 is effectively the idler-absorption induced parametric loss coefficient in a high-gain OPA process. In this regime, the idler power grows exponentially until pump depletion.

2.3 High-loss and short-loss-length regime

OPA or DFG with strong idler absorption is the focus of this study. In the high-loss and short-loss-length limit, R2 << 1 and αiL/2 << 1, the general solution Eq. (2) reduces to Eq. (1). Therefore, quantitatively, Eq. (1) is valid under three conditions: (1) no pump depletion, (2) absorption loss much larger than parametric gain R2 << 1, (3) material length much shorter than the absorption length αiL/2 << 1. Condition (3) is not typical in most THz DFG experiments. For example, the THz absorption coefficient in lithium niobate is in the range of 1-100 cm−1. If one chooses αiL/2 = 0.1 to satisfy the condition αiL/2 << 1, Eq. (1) is valid only for a crystal length L between 2 and 0.02 mm. This length is unrealistically short for a practical application. On the other hand, if one chooses a crystal length L << 2/αi in the first place to satisfy Condition (3), the experimental result is indeed limited to the idler absorption length as a consequence of that choice, but cannot be generalized to conclude that OPA or DFG with idler absorption is limited to a crystal length comparable to the idler absorption length.

2.4 High-loss and long-loss-length regime

If one allows the crystal length to increase, in the high-loss and long-loss-length limit, R2 << 1 and αiL/2 >> 1, the idler photon flux density at L, according to Eq. (2), becomes
ϕi(L)ϕs(0)(2Γαi)2e(4Γ2/αi)L
(5)
Equation (5) is most interesting in that, in spite of the strong idler absorption R2 << 1, the idler intensity increases monotonically with L and does not saturate until pump depletion. This result is somewhat counter-intuitive but is a consequence of the paired signal-idler photon generation in an optical parametric process. The growth of the non-absorbing signal can assist the growth of the highly absorbing idler.

Figure 1
Fig. 1 Idler photon flux density normalized to the initial signal one versus crystal length for R = 0.2. Equation (1) (dashed green curve) only overlaps with Eq. (2) (solid blue curve) over a few idler absorption lengths. The inset shows fast growth of the non-absorbing signal without pump depletion, which has assisted the growth of the idler predicted by Eq. (2). For comparison, red curves are the idler photon flux densities numerically calculated from the three coupled-wave equations with r = ϕs(0)/ϕp(0) = 0.01 (OPA) and 1 (DFG), where ϕp(0) is the initial pump photon flux density.
plots Eq. (1) and Eq. (2), indicated by a dashed green line and a solid blue line, respectively, versus crystal length with idler loss 5 times the parametric gain or R = 0.2. The horizontal axis is the crystal length in units of the idler absorption length L¯=Lαi. It is seen that the simplified theory, Eq. (1), only overlaps with the more accurate theory, Eq. (2), for a crystal length comparable to the idler absorption length. This is a direct consequence of the short-length assumption (Condition (3)) made in deriving Eq. (1). Equation (2), the dashed curve, clearly shows monotonic growth of the idler power over the entire crystal length. Exponential growth of the idler power is also evident when L¯ becomes large, even though in the plot the effective parametric loss is 5 times the parametric gain. The inset is the corresponding signal photon flux density (assuming no pump depletion) normalized to its initial value versus distance, in which the fast growth of the non-absorbing signal has assisted the growth of the idler.

The discussion above holds true under the plane-wave model without pump depletion. When the input signal intensity approaches the pump one, pump depletion and thus idler saturation could occur in a short crystal length. For comparison, we also plot in Fig. 1 the idler photon flux density numerically solved from the three coupled-wave equations with r = ϕs(0)/ϕp(0) = 0.01 (OPA) and 1 (DFG), where ϕp(0) is the initial pump photon flux density. As expected, pump depletion, occurring much faster for DFG (r ~1), results in over-estimated output power from both Eqs. (1) and (2). The saturation value of Eq. (1) is somewhat useful for estimating the maximum idler power from a DFG process with idler absorption. However, a THz wave usually diffracts away from the optical beam aperture in THz OPA/DFG. As will be shown below, given the diffraction and an equal input signal and pump, the growth distance of the idler wave is still much longer than the THz absorption length.

3. Diffraction-modified plane-wave model

In THz OPA/DFG, the THz wave radiates from an aperture comparable to the transverse cross section of the optical beams. The plane-wave model in the last section is only valid for an optical beam size much larger than the THz wavelength or for a THz wave confined in a waveguide. However, to obtain a strong optical intensity in a bulk nonlinear optical material, the optical beams are often focused to a size comparable to the THz wavelength, which makes the THz wave quickly diffract as soon as it is generated. Under strong THz-wave diffraction and absorption, we propose the following two modifications to the plane-wave model.

4. Experiment with equal input pump and signal

Figure 2
Fig. 2 Experimental setup for studying THz-wave DFG with an equal input intensity for the pump and signal. The pump and signal were initially combined from a distributed feed-back diode laser (DFBDL) and tunable external cavity diode laser (ECDL), and then boosted up in power by an Erbium-doped fiber amplifier (EDFA) followed by a pulsed optical parametric amplifier. The polarization controllers after the two diode lasers control the polarization directions of the pump and signal in the nonlinear crystal. A 4k silicon bolometer detects the forward generated idler wave at 1.5 THz after the THz DFG PPLN crystal.
shows the experimental setup. The pump and signal waves were first combined in a single-mode optical fiber from a distributed-feedback diode laser (DFBDL) with a fixed wavelength at 1.5389 μm and an external-cavity diode laser (ECDL) with a tunable wavelength covering the bandwidth of the downstream THz DFG crystal. Two independent polarization controllers were used to align the polarizations of the pump and signal waves along the crystallographic z direction of the PPLN crystals. A passively Q-switched Nd:YAG microchip laser pumped a pulsed optical parametric amplifier following the Erbium-doped fiber amplifier (EDFA) to produce 9.7-μJ energy in a 360-ps width for each of the pump and signal pulse. The equal-energy signal and pump pulses were then focused to a 127-μm waist radius to the center of the PPLN array crystal for THz DFG. A Ni-metal wire mesh with uniform 45 μm × 45 μm square apertures was installed between the THz-DFG PPLN crystal and the collimating off-axis parabolic mirrors to reflect 86% of the THz wave toward the 4k Si bolometer and dump 84% of the optical waves. A 3-mm thick Germanium THz filter was installed before the 4k Si bolometer to block all the residue optical waves and transmit 35% of the THz wave into the bolometer.

Figure 3
Fig. 3 THz-wave tuning curve measured from the 2.5 cm long PPLN crystal strip. The data is fit to Eq. (2) with αi = 40 cm−1, Γ = 0.53 cm−1, and L = 2.5 cm.
shows the measured THz-wave tuning curve from the 25 mm long PPLN strip. The plot was generated by recording the THz-wave output power in the bolometer while scanning the wavelength of the ECDL across the phase matching bandwidth of the THz DFG PPLN. It is possible to use the phase matching bandwidth of Eq. (2) to fit the experimental data to determine the absorption and parametric gain coefficients of the crystal. The continuous curve in Fig. 3 fits to the data with αi = 40 cm−1, Γ = 0.53 cm−1, and L = 2.5 cm. The measured absorption coefficient is consistent with the reported value for THz DFG in bulk congruent lithium niobate [21

21. D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase matching scheme in lithium niobate,” Opt. Express 17(8), 6623–6628 (2009). [CrossRef] [PubMed]

, 40

40. Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express 19(24), 24577–24582 (2011). [CrossRef] [PubMed]

, 41

41. 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,” J. Infrared. Millim. Te. 32(10), 1144–1156 (2011). [CrossRef]

]. With αi = 40 cm−1 and Γ = 0.53 cm−1, the gain-to-loss ratio is R = 5.3 × 10−2, which sets our experiment in the high-loss regime. Given deff = 168☓2/π = 107 pm/V [42

42. 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]

] and np = ns = 2.14 [43

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

], the parametric gain coefficient calculated from the free-space continuous plane-wave model is 2.2, which is about 4.2 times that obtained from the curve fitting in Fig. 3. The gain reduction factor RΓ calculated from Eq. (6) is 4.8 with an average w of 130 μm and αi = 40 cm−1. Given the uncertainty in the THz material parameters for lithium niobate, the experimentally deduced RΓ = 4.2 is reasonably close to the theoretically estimated RΓ = 4.8.

We further translated the PPLN crystal array in the transverse direction and allowed the incident optical beams to sample the PPLN gratings one by one, while keeping the input condition unchanged and measuring the generated THz-wave power in the Si bolometer. The measured THz-wave power versus the PPLN crystal length is shown in Fig. 4
Fig. 4 Measured output THz-wave power (blue dots) versus PPLN crystal length with an equal input intensity for the signal and pump, indicating growth of the power over a crystal length > 1 cm (40 idler absorption lengths). The position-dependent idler loss, Eq. (8), has been introduced into the three coupled-wave equations (dashed blue curve) to fit the experimental data with αi = 37 cm−1 and A = 10. The quick saturation of Eq. (1) (solid green curve) is not consistent with the measured experimental data.
(blue dots). The error bar is the range of data fluctuation about the fitted wavelength tuning curve taken for each PPLN strip. To fit the experimental data in Fig. 4, we introduced the position-dependent power absorption coefficient, Eq. (8), into the three coupled-wave equations (blue dashed curve) with A = 10 and an initial αi = 37 cm−1. With initial signal energy of 9.7 μJ at 1539 nm and an output THz wavelength at 200 μm, the fitted curve suggests 45-pJ peak energy at 1.5 THz generated from the 25-mm long PPLN crystal. This amount of output THz-wave energy matches well to our previously reported experimental value measured by a calibrated bolometer [40

40. Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express 19(24), 24577–24582 (2011). [CrossRef] [PubMed]

]. Equation (1) (green curve) is also plot in Fig. 4 for comparison. It is seen that Eq. (1), showing fast rise and quick saturation of the THz-wave power, is clearly inconsistent with the experimental result.

5. Conclusion

We have studied THz-wave OPA and DFG with strong THz-wave absorption in the regime without pump depletion. This is the regime most THz-wave OPA/DFG experiments were carried out. As indicated by Eq. (2), a theory derived under a plane-wave model without pump depletion, the highly absorptive THz wave in a THz OPA process can grow monotonically over a long crystal length until pump depletion. The coherent production of the non-absorbing signal can assist the growth of the absorbing idler. The long-range parametric amplification revealed by Eq. (5), reduced from Eq. (2) in the high-loss and long-loss-length limit, is particularly useful for co-directionally phase matched THz-wave parametric amplification or oscillation built up from a small signal. For the plane-wave model to be valid, the optical beam size of the pump and signal has to be much larger than the THz wavelength or the THz wave has to be confined in a waveguide [40

40. Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express 19(24), 24577–24582 (2011). [CrossRef] [PubMed]

].

The widely adopted THz-DFG theory, Eq. (1), which shows quick saturation of an absorbing idler wave, is an approximation of a more general expression, Eq. (2), in the limit of high absorption loss R2 << 1 and short crystal length L << 2/αi. The only assumptions made to derive Eq. (2) are: (1) the slowly varying envelope approximation, (2) plane-wave like fields, and (3) an undepleted pump. When the signal-to-pump ratio r approaches 1 for DFG, pump depletion can occur quickly in a short crystal and the valid regime of Eq. (2) merges with that of Eq. (1) in the short-crystal limit. However, in practice, the THz wave in THz DFG can diffract much faster than the optical mixing waves for an optical beam size comparable to the THz wavelength. Consequently, the pump-depletion induced idler saturation does not occur in a short crystal as predicted by Eq. (1). By using equal-amplitude pump and signal as the inputs to a co-directional THz difference frequency generator, we show the growth of an idler wave at 1.5 THz over a crystal length exceeding 40 idler absorption lengths. In this experiment, the effective parametric loss is nearly 20 times the parametric gain.

Acknowledgments

Huang thanks Fejer and Vodopyanov of Stanford University for helpful discussion on absorptive OPA in 2009. This work was supported by National Science Council under Contract NSC 98-2923-M-007-004-MY3 and the Frontier Research Centers of National Tsinghua University.

References and links

1.

J. M. Yarborough, S. S. Sussman, H. E. Purhoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett. 15(3), 102–105 (1969). [CrossRef]

2.

B. C. Johnson, H. E. Puthoff, J. Soohoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far-infrared emission in LiNbO3,” Appl. Phys. Lett. 18(5), 181–183 (1971). [CrossRef]

3.

M. A. Piestrup, R. N. Fleming, and R. H. Pantell, “Continuously tunable submillimeter wave source,” Appl. Phys. Lett. 26(8), 418–421 (1975). [CrossRef]

4.

K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D Appl. Phys. 35(3), R1–R14 (2002). [CrossRef]

5.

L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys. 97, 123505 (2005), doi:. [CrossRef]

6.

K. Kawase, M. Sato, K. Nakamura, T. Taniuchi, and H. Ito, “Unidirectional radiation of widely tunable THz wave using a prism coupler under noncollinear phase matching condition,” Appl. Phys. Lett. 71(6), 753–755 (1997). [CrossRef]

7.

K. Kawase, M. Sato, T. Taniuchi, and H. Ito, “Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler,” Appl. Phys. Lett. 68(18), 2483–2485 (1996). [CrossRef]

8.

K. Kawase, J. Shikata, H. Minamide, K. Imai, and H. Ito, “Arrayed silicon prism coupler for a terahertz-wave parametric oscillator,” Appl. Opt. 40(9), 1423–1426 (2001). [CrossRef] [PubMed]

9.

K. Suizu, T. Tsutsui, T. Shibuya, T. Akiba, and K. Kawase, “Cherenkov phase matched THz-wave generation with surfing configuration for bulk lithium nobate crystal,” Opt. Express 17(9), 7102–7109 (2009). [CrossRef] [PubMed]

10.

J. B. Khurgin, D. Yang, and Y. J. Ding, “Generation of mid-infrared radiation in the highly-absorbing nonlinear medium,” J. Opt. Soc. Am. B 18(3), 340–343 (2001). [CrossRef]

11.

A. G. Stepanov, J. Hebling, and J. Kuhl, “Efficient generation of subpicosecond terahertz radiation by phase-matched optical rectification using ultrashort laser pulses with tilted pulse fronts,” Appl Phys Lett 83, 3000–3002 doi:Doi (2003). [CrossRef]

12.

T. Taniuchi and H. Nakanishi, “Collinear phase-matched terahertz-wave generation in GaP crystal using a dual-wavelength optical parametric oscillator,” J. Appl. Phys. 95, 7588–7591, doi:Doi (2004). [CrossRef]

13.

M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett. 29(17), 2046–2048 (2004). [CrossRef] [PubMed]

14.

K. Kawase, K. Suizu, and S. Hayashi, and T. Shibuya” Nonlinear optical terahertz wave sources,” Opt. Spectroscopy 108, 841–845, doi:Doi (2010). [CrossRef]

15.

J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quant. 14, 354–362, doi:Doi (2008). [CrossRef]

16.

G. Kh. Kitaeva, “THz generation by means of optical laser,” Laser Phys. Lett. 5, 559–576 doi: (2008). [CrossRef]

17.

J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate – Part 1: Theory,” Appl. Phys. B. 86(2), 185–196 (2007). [CrossRef]

18.

J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, R. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate – Part 2: Experiments,” Appl. Phys. B. 86(2), 197–208 (2007). [CrossRef]

19.

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]

20.

L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B 12(11), 2102–2116 (1995). [CrossRef]

21.

D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase matching scheme in lithium niobate,” Opt. Express 17(8), 6623–6628 (2009). [CrossRef] [PubMed]

22.

C. Weiss, G. Torosyan, Y. Avetisyan, and R. Beigang, “Generation of tunable narrow-band surface-emitted terahertz radiation in periodically poled lithium niobate,” Opt. Lett. 26(8), 563–565 (2001). [CrossRef] [PubMed]

23.

Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett. 35(15), 2508–2510 (2010). [CrossRef] [PubMed]

24.

K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, “Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves,” Opt. Lett. 31(7), 957–959 (2006). [CrossRef] [PubMed]

25.

Y. Avetisyan, Y. Sasaki, and H. Ito, “Analysis of THz-wave surface-emitted difference-frequency generation in periodically poled lithium niobate waveguide,” Appl. Phys. B. 73(5), 511–514 (2001). [CrossRef]

26.

Y. Sasaki, Y. Avetisyan, K. Kawase, and H. Ito, “Terahertz-wave surface-emitted difference-frequency generation in slant-stripe-type periodically poled LiNbO3 crystal,” Appl. Phys. Lett. 81, 3323–3325 (2002).

27.

Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, “Surface-emitted terahertz-wave difference-frequency generation in two-dimensional periodically poled lithium niobate,” Opt. Lett. 30(21), 2927–2929 (2005). [CrossRef] [PubMed]

28.

Y. Sasaki, H. Yokoyama, and H. Ito, “Surface-emitted continuous-wave terahertz radiation using periodically poled lithium niobate,” Electron. Lett. 41(12), 712–713 (2005). [CrossRef]

29.

T. Suhara, Y. Avetisyan, and H. Ito, “Theoretical analysis of laterally emitting Terahertz-wave generation by difference-frequency generation in channel waveguides,” IEEE J. Quantum Electron. 39(1), 166–171 (2003). [CrossRef]

30.

L. Lefort, K. Puech, G. W. Ross, Y. P. Svirko, and D. C. Hanna, “Optical parametric oscillation out to 6.3 μm in periodically poled lithium niobate under strong idler absorption,” Appl. Phys. Lett. 73(12), 1610–1612 (1998). [CrossRef]

31.

A. Yariv and P. Yeh, Photonics, 6th Ed. (Oxford University Press, New York, Oxford, 2007).

32.

D. Zheng, L. A. Gordon, Y. S. Wu, R. S. Feigelson, M. M. Fejer, R. L. Byer, and K. L. Vodopyanov, “16-microm infrared generation by difference-frequency mixing in diffusion-bonded-stacked GaAs,” Opt. Lett. 23(13), 1010–1012 (1998). [CrossRef] [PubMed]

33.

W. Shi, Y. J. Ding, N. Fernelius, and K. Vodopyanov, “Efficient, tunable, and coherent 0.18-5.27-THz source based on GaSe crystal,” Opt. Lett. 27(16), 1454–1456 (2002). [CrossRef] [PubMed]

34.

K. Zhong, J. Yao, D. Xu, Z. Wang, Z. Li, H. Zhang, and P. Wang, “Enhancement of terahertz wave difference frequency generation based on a compact walk-off compensated KTP OPO,” Opt. Commun. 283(18), 3520–3524 (2010). [CrossRef]

35.

K. Suizu, T. Shibuya, S. Nagano, T. Akiba, K. Edamatsu, H. Ito, and K. Kawase, “Pulsed high peak power millimeter wave generation via difference frequency generation using periodically poled lithium niobate,” Jpn. J. Appl. Phys. 46(40), L982–L984 (2007). [CrossRef]

36.

K. Kawase, M. Mizuno, S. Sohma, H. Takahashi, T. Taniuchi, Y. Urata, S. Wada, H. Tashiro, and H. Ito, “Difference-frequency terahertz-wave generation from 4-dimethylamino-N-methyl-4-stilbazolium-tosylate by use of an electronically tuned Ti:sapphire laser,” Opt. Lett. 24(15), 1065–1067 (1999). [CrossRef] [PubMed]

37.

S. Ohno, K. Miyamoto, H. Minamide, and H. Ito, “New method to determine the refractive index and the absorption coefficient of organic nonlinear crystals in the ultra-wideband THz region,” Opt. Express 18(16), 17306–17312 (2010). [CrossRef] [PubMed]

38.

S. Hayashi, K. Nawata, H. Sakai, T. Taira, H. Minamide, and K. Kawase, “High-power, single-longitudinal-mode terahertz-wave generation pumped by a microchip Nd:YAG laser [Invited],” Opt. Express 20(3), 2881–2886 (2012). [CrossRef] [PubMed]

39.

G. Kh. Kitaeva and A. N. Penin, “Parametric frequency conversion in layered nonlinear media,” J. Exp. Theor. Phys. 98(2), 272–286 (2004). [CrossRef]

40.

Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express 19(24), 24577–24582 (2011). [CrossRef] [PubMed]

41.

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,” J. Infrared. Millim. Te. 32(10), 1144–1156 (2011). [CrossRef]

42.

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]

43.

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

OCIS Codes
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

ToC Category:
Nonlinear Optics

History
Original Manuscript: November 28, 2012
Manuscript Accepted: January 14, 2013
Published: January 24, 2013

Citation
Tsong-Dong Wang, Yen-Chieh Huang, Ming-Yun Chuang, Yen-Hou Lin, Ching-Han Lee, Yen-Yin Lin, Fan-Yi Lin, and Galiya Kh. Kitaeva, "Long-range parametric amplification of THz wave with absorption loss exceeding parametric gain," Opt. Express 21, 2452-2462 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-2452


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References

  1. J. M. Yarborough, S. S. Sussman, H. E. Purhoff, R. H. Pantell, and B. C. Johnson, “Efficient, tunable optical emission from LiNbO3 without a resonator,” Appl. Phys. Lett.15(3), 102–105 (1969). [CrossRef]
  2. B. C. Johnson, H. E. Puthoff, J. Soohoo, and S. S. Sussman, “Power and linewidth of tunable stimulated far-infrared emission in LiNbO3,” Appl. Phys. Lett.18(5), 181–183 (1971). [CrossRef]
  3. M. A. Piestrup, R. N. Fleming, and R. H. Pantell, “Continuously tunable submillimeter wave source,” Appl. Phys. Lett.26(8), 418–421 (1975). [CrossRef]
  4. K. Kawase, J. Shikata, and H. Ito, “Terahertz wave parametric source,” J. Phys. D Appl. Phys.35(3), R1–R14 (2002). [CrossRef]
  5. L. Pálfalvi, J. Hebling, J. Kuhl, Á. Péter, and K. Polgár, “Temperature dependence of the absorption and refraction of Mg-doped congruent and stoichiometric LiNbO3 in the THz range,” J. Appl. Phys.97, 123505 (2005), doi:. [CrossRef]
  6. K. Kawase, M. Sato, K. Nakamura, T. Taniuchi, and H. Ito, “Unidirectional radiation of widely tunable THz wave using a prism coupler under noncollinear phase matching condition,” Appl. Phys. Lett.71(6), 753–755 (1997). [CrossRef]
  7. K. Kawase, M. Sato, T. Taniuchi, and H. Ito, “Coherent tunable THz-wave generation from LiNbO3 with monolithic grating coupler,” Appl. Phys. Lett.68(18), 2483–2485 (1996). [CrossRef]
  8. K. Kawase, J. Shikata, H. Minamide, K. Imai, and H. Ito, “Arrayed silicon prism coupler for a terahertz-wave parametric oscillator,” Appl. Opt.40(9), 1423–1426 (2001). [CrossRef] [PubMed]
  9. K. Suizu, T. Tsutsui, T. Shibuya, T. Akiba, and K. Kawase, “Cherenkov phase matched THz-wave generation with surfing configuration for bulk lithium nobate crystal,” Opt. Express17(9), 7102–7109 (2009). [CrossRef] [PubMed]
  10. J. B. Khurgin, D. Yang, and Y. J. Ding, “Generation of mid-infrared radiation in the highly-absorbing nonlinear medium,” J. Opt. Soc. Am. B18(3), 340–343 (2001). [CrossRef]
  11. A. G. Stepanov, J. Hebling, and J. Kuhl, “Efficient generation of subpicosecond terahertz radiation by phase-matched optical rectification using ultrashort laser pulses with tilted pulse fronts,” Appl Phys Lett83, 3000–3002 doi:Doi (2003). [CrossRef]
  12. T. Taniuchi and H. Nakanishi, “Collinear phase-matched terahertz-wave generation in GaP crystal using a dual-wavelength optical parametric oscillator,” J. Appl. Phys. 95, 7588–7591, doi:Doi (2004). [CrossRef]
  13. M. Cronin-Golomb, “Cascaded nonlinear difference-frequency generation of enhanced terahertz wave production,” Opt. Lett.29(17), 2046–2048 (2004). [CrossRef] [PubMed]
  14. K. Kawase, K. Suizu, and S. Hayashi, and T. Shibuya” Nonlinear optical terahertz wave sources,” Opt. Spectroscopy 108, 841–845, doi:Doi (2010). [CrossRef]
  15. J. E. Schaar, K. L. Vodopyanov, P. S. Kuo, M. M. Fejer, X. Yu, A. Lin, J. S. Harris, D. Bliss, C. Lynch, V. G. Kozlov, and W. Hurlbut “Terahertz sources based on intracavity parametric down-conversion in quasi-phase-matched gallium arsenide,” IEEE J. Sel. Top. Quant. 14, 354–362, doi:Doi (2008). [CrossRef]
  16. G. Kh. Kitaeva, “THz generation by means of optical laser,” Laser Phys. Lett. 5, 559–576 doi: (2008). [CrossRef]
  17. J. A. L’huillier, G. Torosyan, M. Theuer, Y. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate – Part 1: Theory,” Appl. Phys. B.86(2), 185–196 (2007). [CrossRef]
  18. J. A. L’huillier, G. Torosyan, M. Theuer, C. Rau, R. Avetisyan, and R. Beigang, “Generation of THz radiation using bulk, periodically and aperiodically poled lithium niobate – Part 2: Experiments,” Appl. Phys. B.86(2), 197–208 (2007). [CrossRef]
  19. 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]
  20. L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3,” J. Opt. Soc. Am. B12(11), 2102–2116 (1995). [CrossRef]
  21. D. Molter, M. Theuer, and R. Beigang, “Nanosecond terahertz optical parametric oscillator with a novel quasi phase matching scheme in lithium niobate,” Opt. Express17(8), 6623–6628 (2009). [CrossRef] [PubMed]
  22. C. Weiss, G. Torosyan, Y. Avetisyan, and R. Beigang, “Generation of tunable narrow-band surface-emitted terahertz radiation in periodically poled lithium niobate,” Opt. Lett.26(8), 563–565 (2001). [CrossRef] [PubMed]
  23. Y. H. Avetisyan, “Terahertz-wave surface-emitted difference-frequency generation without quasi-phase-matching technique,” Opt. Lett.35(15), 2508–2510 (2010). [CrossRef] [PubMed]
  24. K. Suizu, Y. Suzuki, Y. Sasaki, H. Ito, and Y. Avetisyan, “Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves,” Opt. Lett.31(7), 957–959 (2006). [CrossRef] [PubMed]
  25. Y. Avetisyan, Y. Sasaki, and H. Ito, “Analysis of THz-wave surface-emitted difference-frequency generation in periodically poled lithium niobate waveguide,” Appl. Phys. B.73(5), 511–514 (2001). [CrossRef]
  26. Y. Sasaki, Y. Avetisyan, K. Kawase, and H. Ito, “Terahertz-wave surface-emitted difference-frequency generation in slant-stripe-type periodically poled LiNbO3 crystal,” Appl. Phys. Lett.81, 3323–3325 (2002).
  27. Y. Sasaki, Y. Avetisyan, H. Yokoyama, and H. Ito, “Surface-emitted terahertz-wave difference-frequency generation in two-dimensional periodically poled lithium niobate,” Opt. Lett.30(21), 2927–2929 (2005). [CrossRef] [PubMed]
  28. Y. Sasaki, H. Yokoyama, and H. Ito, “Surface-emitted continuous-wave terahertz radiation using periodically poled lithium niobate,” Electron. Lett.41(12), 712–713 (2005). [CrossRef]
  29. T. Suhara, Y. Avetisyan, and H. Ito, “Theoretical analysis of laterally emitting Terahertz-wave generation by difference-frequency generation in channel waveguides,” IEEE J. Quantum Electron.39(1), 166–171 (2003). [CrossRef]
  30. L. Lefort, K. Puech, G. W. Ross, Y. P. Svirko, and D. C. Hanna, “Optical parametric oscillation out to 6.3 μm in periodically poled lithium niobate under strong idler absorption,” Appl. Phys. Lett.73(12), 1610–1612 (1998). [CrossRef]
  31. A. Yariv and P. Yeh, Photonics, 6th Ed. (Oxford University Press, New York, Oxford, 2007).
  32. D. Zheng, L. A. Gordon, Y. S. Wu, R. S. Feigelson, M. M. Fejer, R. L. Byer, and K. L. Vodopyanov, “16-microm infrared generation by difference-frequency mixing in diffusion-bonded-stacked GaAs,” Opt. Lett.23(13), 1010–1012 (1998). [CrossRef] [PubMed]
  33. W. Shi, Y. J. Ding, N. Fernelius, and K. Vodopyanov, “Efficient, tunable, and coherent 0.18-5.27-THz source based on GaSe crystal,” Opt. Lett.27(16), 1454–1456 (2002). [CrossRef] [PubMed]
  34. K. Zhong, J. Yao, D. Xu, Z. Wang, Z. Li, H. Zhang, and P. Wang, “Enhancement of terahertz wave difference frequency generation based on a compact walk-off compensated KTP OPO,” Opt. Commun.283(18), 3520–3524 (2010). [CrossRef]
  35. K. Suizu, T. Shibuya, S. Nagano, T. Akiba, K. Edamatsu, H. Ito, and K. Kawase, “Pulsed high peak power millimeter wave generation via difference frequency generation using periodically poled lithium niobate,” Jpn. J. Appl. Phys.46(40), L982–L984 (2007). [CrossRef]
  36. K. Kawase, M. Mizuno, S. Sohma, H. Takahashi, T. Taniuchi, Y. Urata, S. Wada, H. Tashiro, and H. Ito, “Difference-frequency terahertz-wave generation from 4-dimethylamino-N-methyl-4-stilbazolium-tosylate by use of an electronically tuned Ti:sapphire laser,” Opt. Lett.24(15), 1065–1067 (1999). [CrossRef] [PubMed]
  37. S. Ohno, K. Miyamoto, H. Minamide, and H. Ito, “New method to determine the refractive index and the absorption coefficient of organic nonlinear crystals in the ultra-wideband THz region,” Opt. Express18(16), 17306–17312 (2010). [CrossRef] [PubMed]
  38. S. Hayashi, K. Nawata, H. Sakai, T. Taira, H. Minamide, and K. Kawase, “High-power, single-longitudinal-mode terahertz-wave generation pumped by a microchip Nd:YAG laser [Invited],” Opt. Express20(3), 2881–2886 (2012). [CrossRef] [PubMed]
  39. G. Kh. Kitaeva and A. N. Penin, “Parametric frequency conversion in layered nonlinear media,” J. Exp. Theor. Phys.98(2), 272–286 (2004). [CrossRef]
  40. Y. C. Huang, T. D. Wang, Y. H. Lin, C. H. Lee, M. Y. Chuang, Y. Y. Lin, and F. Y. Lin, “Forward and backward THz-wave difference frequency generations from a rectangular nonlinear waveguide,” Opt. Express19(24), 24577–24582 (2011). [CrossRef] [PubMed]
  41. 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,” J. Infrared. Millim. Te.32(10), 1144–1156 (2011). [CrossRef]
  42. 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]
  43. D. H. Jundt, “Temperature-dependent Sellmeier equation for the index of refraction, ne, in congruent lithium niobate,” Opt. Lett.22(20), 1553–1555 (1997). [CrossRef] [PubMed]

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