## Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides

Optics Express, Vol. 17, Issue 16, pp. 13502-13515 (2009)

http://dx.doi.org/10.1364/OE.17.013502

Acrobat PDF (432 KB)

### Abstract

A metallic slot waveguide, with a dielectric strip embedded within, is investigated for the purpose of enhancing the optics-to-THz conversion efficiency using the difference-frequency generation (DFG) process. To describe the frequency conversion process in such lossy waveguides, a fully-vectorial coupled-mode theory is developed. Using the coupled-mode theory, we outline the basic theoretical requirements for efficient frequency conversion, which include the needs to achieve large coupling coefficients, phase matching, and low propagation loss for both the optical and THz waves. Following these requirements, a metallic waveguide is designed by considering the trade-off between modal confinement and propagation loss. Our numerical calculation shows that the conversion efficiency in these waveguide structures can be more than one order of magnitude larger than what has been achieved using dielectric waveguides. Based on the distinct impact of the slot width on the optical and THz modal dispersion, we propose a two-step method to realize the phase matching for general pump wavelengths.

© 2009 Optical Society of America

## 1. Introduction

1. M. Tonouchi, “Cutting-edge terahertz technology,” Nature Photonics **1**, 97 (2007). [CrossRef]

*χ*

^{(2)}process to generate a THz beam. In general, the conversion efficiency of DFG is proportional to the intensities of the pump beams [2, 3]. Consequently, in bulk crystals, it is desirable to use a beam with a small radius. On the other hand, an excessively small beam radius can result in strong diffraction effects. As a result, there exists an optimal beam radius. In a bulk GaSe nonlinear crystal, for example, when generating 0.914 THz wave from the mixing of two CO

_{2}lasers near 10

*µ*m, the maximum efficiency of 3.9×10

^{-9}W

^{-1}occurs at an optimal optical beam radius of 10.59

*µ*m [4

4. Y. Jiang and Y. J. Ding, “Efficient terahertz generation from two collinearly propagating CO2 laser pulses,” Appl. Phys. Lett. **91**, 091108 (2007). [CrossRef]

5. D. E. Thompson and P. D. Coleman, “Step-Tunable Far Infrared Radiation by Phase Matched Mixing in Planar-Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. **22**, 995–1000 (1974). [CrossRef]

6. W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. **82**, 4435 (2003). [CrossRef]

7. H. Cao, R. A. Linke, and A. Nahata, “Broadband generation of terahertz radiation in a waveguide,” Opt. Lett. **29**, 1751–1753 (2004). [CrossRef] [PubMed]

8. V. Berger and C. Sirtori, “Nonlinear phase matching in THz semiconductor waveguides,” Semicond. Sci. Technol. **19**, 964–970 (2004). [CrossRef]

9. 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**, 3392–3394 (2005). [CrossRef]

10. Y. Takushima, S. Y. Shin, and Y. C. Chung, “Design of a LiNbO_{3} ribbon waveguide for efficient difference-frequency generation of terahertz wave in the collinear configuration,” Opt. Express **15**, 14783–14792 (2007). [CrossRef] [PubMed]

11. C. Staus, T. Kuech, and L. McCaughan, “Continuously phase-matched terahertz difference frequency generation in an embedded-waveguide structure supporting only fundamental modes,” Opt. Express **16**, 13296–13303 (2008). [CrossRef] [PubMed]

12. K. L. Vodopyanov and Y. H. Avetisyan, “Optical terahertz wave generation in a planar GaAs waveguide,” Opt. Lett. **33**, 2314–2316 (2008). [CrossRef] [PubMed]

13. A. Marandi, T. E. Darcie, and P. P. M. So, “Design of a continuous-wave tunable terahertz source using waveguide-phase-matched GaAs,” Opt. Express **16**, 10427–10433 (2008). [CrossRef] [PubMed]

11. C. Staus, T. Kuech, and L. McCaughan, “Continuously phase-matched terahertz difference frequency generation in an embedded-waveguide structure supporting only fundamental modes,” Opt. Express **16**, 13296–13303 (2008). [CrossRef] [PubMed]

14. S. S. Dhillon, C. Sirtori, J. Alton, S. Barbieri, A. de Rossi, H. E. Beere, and D. A. Ritchie, “Terahertz transfer onto a telecom optical carrier,” Nature Photonics **1**, 411–415 (2007). [CrossRef]

11. C. Staus, T. Kuech, and L. McCaughan, “Continuously phase-matched terahertz difference frequency generation in an embedded-waveguide structure supporting only fundamental modes,” Opt. Express **16**, 13296–13303 (2008). [CrossRef] [PubMed]

15. E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. **66**, 285, (1995). [CrossRef]

*µ*m wavelength. In Section 4, we discuss in detail many of the considerations that lead to the design in Section 3. Finally, in Section 5, we propose a general method for designing such waveguides at different pump wavelengths.

## 2. Theory

*ω*

_{2}and

*ω*

_{3}mix to produce a THz beam at

*ω*

_{1}=

*ω*

_{3}-

*ω*

_{2}. For each frequency

*ω*

*, we assume that the corresponding electromagnetic fields {*

_{j}**E**

*,*

_{j}**H**

*} are in a single mode that propagates along the +*

_{j}*z*direction, and can be written in the following form:

*β*is the real part of the wave number,

_{j}*A*

*is the mode amplitude, and {*

_{j}**e**

*,*

_{j,t(z)}**h**

*} are the modal profiles, with the subscripts*

_{j,t(z)}*t*and

*z*representing the transverse and longitudinal components, respectively. The modal profile is normalized such that

*dσ*is a vector along the z-direction. With such normalization, the e and h in the modal profile have units of V/(m√W) and A/(m√W), respectively, and |

*A*|

_{j}^{2}has unit of W. We note that such normalization is valid for any reciprocal waveguide structure, including waveguides with substantial loss. With such normalization, a wave in a single mode with unit amplitude (i.e.

*A*(

*j**z*)=1) carries a time-averaged power of

*c*W, where

*j**and h*

_{j,t}*can be taken to be real, and hence*

_{j,t}*c*=1, reproducing the usual normalization condition [16]. Our normalization relation of Eq. (2), however, is more general, and is necessary for the lossy waveguide cases.

_{j}*A*(

_{j}*z*), the coupled-mode equations that describe the DFG process in the waveguide are:

*α*

*is the power propagation loss coefficient for the*

_{j}*j*-th mode, Δ

*β*≡

*β*

_{3}-

*β*

_{2}-

*β*

_{1}, and the coupling coefficients are

*L*, pumped by two optical beams with amplitudes

*A*

_{2}(0) and

*A*

_{3}(0) at

*z*=0, the conversion efficiency is:

*P*

_{1}is the generated THz power and

*P*

_{2}and

*P*

_{3}are the pump powers. Under the approximation where the pump is not depleted by the nonlinear conversion process, one can solve Eq. (4) analytically to obtain the conversion efficiency:

*κ*

_{1}. To do so, from Eq. (5) we see that with respect to the modal profile, the orientation of the nonlinear crystal needs to be appropriately chosen. Moreover, since the amplitude of the electric field in a modal profile in general scales inversely with the modal size, as can be seen from the normalization relation of Eq. (2), tightly confining both the THz and the optical waves in the same waveguide structure is of great advantage.

*β*=0. As an illustration, assuming that loss is zero, the efficiency

*η*[Eq. (6)] is then proportional to

*L*

^{2}. Thus, one can achieve high conversion efficiency simply by increasing the length of the waveguide. Since

*ω*

_{1}=

*ω*

_{3}-

*ω*

_{2}, the phase matching condition can equivalently be described as

*n*=

_{THz}*n*, where

_{g}*n*=

_{THz}*cβ*

_{1}/

*ω*

_{1}is the phase index of the THz waves,

*c*is the speed of light in vacuum.

*β*=0 in Eq. (6) and solving

*dη*/

*dL*=0, we obtain the optimal waveguide length which maximizes the conversion efficiency:

## 3. An example of a high-efficiency waveguide device

*h*=0.3

*µ*m. The width of the slot and the GaAs strip are

*w*

_{1}=4

*µ*m and

*w*

_{2}=0.24

*µ*m respectively.

17. P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K. Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air-bridge microcavities,” Appl. Phys. Lett. **67**, 167 (1995). [CrossRef]

18. K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y. S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. **89**, 141,119 (2006). [CrossRef]

19. I. Mehdi, S. C. Martin, R. J. Dengler, R. P. Smith, and P. H. Siegel, “Fabrication and performance of planar Schottky diodes withT-gate-like anodes in 200-GHz subharmonically pumped waveguide mixers,” IEEE Microwave and Guided Wave Lett. **6**, 49–51 (1996) [CrossRef]

20. S. M. Marazita, W. L. Bishop, J. L. Hesler, K. Hui, W. E. Bowen, T. W. Crowe, V. M. W. Inc, and V. A. Charlottesville, “Integrated GaAs Schottky mixers by spin-on-dielectric wafer bonding,” IEEE Trans. Electron Devices **47**, 1152–1157 (2000) [CrossRef]

21. P. H. Siegel, R. P. Smith, M. C. Graidis, and S. C. Martin, “2.5-THz GaAs monolithic membrane-diode mixer,” IEEE Trans. Microwave Theory Tech. **47**, 596–604 (1999) [CrossRef]

22. K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nature Materials **2**, 117–121 (2003). [CrossRef] [PubMed]

*µ*m). These two optical pumps will mix to generate a wave at 3THz. The refractive indices of all materials involved at these frequencies are summarized in Table 1.

*y*direction, and the THz wave has its electric field along the

*x*direction. In order for these waves to interact, the orientation of GaAs is chosen such that a [011] direction coincides with the

*y*-axis, and a [100] direction coincides with the

*x*-axis [Fig. 1(b)]. As a result, the two optical pump beams can generate a polarization in THz along the

*x*-axis through the

*d*

_{14}component in the

*χ*̿

^{(2)}tensor of GaAs. Here we use

*d*

_{14}=46.1 pm/V [27

27. K. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser and Photonics Reviews **2**, 11 (2008). [CrossRef]

*β*), the loss coefficient (

_{j}*α*), and the modal profile of all the relevant modes. To take into account the field penetration into the metal, a variable grid is used. For the THz wave, we use a computational window size of 200

_{j}*µ*m by 200

*µ*m, with a minimal grid spacing of 10 nm. For the optical wave, we use a computational window size of 20

*µ*m by 20

*µ*m with a minimal grid spacing of 5 nm. After obtaining the modal information, the nonlinear coupling coefficient

*κ*is then calculated with Eq. (5). By numerically solving the nonlinear coupled-mode equations [Eq. (4)] (we assume that the two pumps have equal power), we obtain the THz output power and hence the conversion efficiency. Such a calculation does not assume the undepleted-pump approximation.

_{j}*L*=10.4 mm calculated by Eq. (7) under the undepleted-pump approximation. Figure 2(b) shows the THz output power for a 10 mm long waveguide as a function of the pump power. The conversion efficiency is 5.66×10

_{max}^{-6}W

^{-1}, as compared to

*η*=5.71×10

^{-6}W

^{-1}calculated by Eq. (6). Thus, the full solution of the nonlinear ordinary differential equations of Eq. (4) indicates that the non-depleted pump approximation is generally valid in this system. The conversion efficiency is more than one order of magnitude larger than the highest previously reported for conventional dielectric waveguides [11

**16**, 13296–13303 (2008). [CrossRef] [PubMed]

## 4. Discussion of the design requirement

*µ*m that is much smaller than the 100

*µ*m free space wavelength of a 3 THz wave. Since the THz mode is a quasi-TEM mode, its dispersion relation is strongly influenced by the materials in the slot, which for our geometry is mostly filled with quartz. Our FDFD calculations show a

*n*≃2.14, as compared to the refractive index of 2.13 for quartz at the same wavelength. In the THz wavelength range, there is typically substantial material loss due to phonon-polariton excitations. At 3 THz, the loss coefficient of quartz is approximately 0.6 cm

_{THz}^{-1}. The use of metal induces additional THz loss due to the finite penetration of fields into the metal. The penetration depth is approximately 50 nm. The FDFD calculations indicate that the THz mode has a loss coefficient

*α*

_{1}≃4.59 cm

^{-1}. Thus, in this structure the loss at the THz wavelength range is dominated by metal loss.

*w*

_{2}=0.24 and

*h*=0.3

*µ*m such that the optical mode substantially extends into quartz, which lowers the group index to

*n*=2.14, satisfying the phase matching constraint.

_{g}*µ*m, the optical photon energy is below half of the band gap of GaAs [28

28. W. C. Hurlbut, Y. S. Lee, K. L. Vodopyanov, P. S. Kuo, and M. M. Fejer, “Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared,” Opt. Lett. **32**, 668–670 (2007). [CrossRef] [PubMed]

_{2}as a function of slot width. As the slot width increases beyond 4

*µ*m, the loss of the optical modes drops below 1cm

^{-1}. For the slot width

*w*

_{1}=4

*µ*m, the loss coefficients for the two pumps are

*α*

_{2}=0.36 cm

^{-1}and

*α*

_{3}=0.20 cm

^{-1}.

*κ*. Figures 6(a–b) show the coupling coefficient and the maximum conversion efficiency, respectively, as a function of slot width. Without considering the phase mismatching induced by the slot width variation, i.e. by setting Δ

*β*=0 in the calculation, the conversion efficiency has a maximum value of 7.1×10

^{-6}W

^{-1}at

*w*

_{1}=6

*µ*m. The use of a narrower slot leads to higher optical propagation loss, whereas the use of a wider slot reduces the coupling coefficient. Figure 6(b) also shows that the phase mismatching further reduces the conversion efficiency.

## 5. Design procedure for general pump wavelengths

*w*

_{1}=3

*µ*m almost coincides with that in a GaAs strip waveguide without the metal, as seen in Fig. 7. Thus, to design a waveguide with the correct optical mode index, it is sufficient to consider only the GaAs strip waveguide, which greatly reduces the dimensions of the parameter space and hence simplifies the design process.

*µ*m, which is the regime of interest due to the consideration of losses in the optical modes, the index of the THz mode is essentially that of quartz.

*w*

_{2}and

*h*, such that the group index at the pump wavelength

*n*′

*is approximately equal but slightly larger than the refractive index of quartz*

_{g}*n*at the THz wavelength range. We then consider a slot waveguide with such GaAs strip embedded in it. For simplicity, the thickness of the metal layer is chosen to be the same as that of the GaAs strip. Thus, we will be aiming to determine the width

_{b}*w*

_{1}of the slot. To do so, we first search for an initial value of

*w*

_{1}, such that the corresponding optical propagation loss is low, and the group index of the pumps

*n*″

*and the effect index of the THz mode*

_{g}*n*″

*are subject to*

_{THz}*n*″

*≈*

_{g}*n*′

*and*

_{g}*n*″

*>*

_{THz}*n*′

*; then we gradually increase the slot width until the phase matching condition*

_{g}*n*″

*=*

_{THz}*n*″

*is satisfied. This process allows to always find a width*

_{g}*w*

_{1}since with increasing

*w*

_{1},

*n*″

*is still roughly equal to*

_{g}*n*′

*while*

_{g}*n*″

*monotonically decreases and approaches to*

_{THz}*n*that is less than

_{b}*n*′

*.*

_{g}## 6. Conclusion

## Appendix: Derivation of the coupled-mode equations for difference frequency generation in a lossy waveguide under nonlinear interaction

*Reciprocity theorem for waveguides*- Consider two guided waves {

**E**

*,*

_{i}**H**

*} (*

_{i}*i*=1, 2) in a z-invariant waveguide, each excited by a current density

**J**

*, respectively. From Maxwell’s equations:*

_{i}**J**

*are continuously varying along*

_{i}*z*, we obtain the reciprocity theorem:

*S*is any slice of the waveguide normal to

*z*. Importantly, this theorem is valid for both lossless and lossy media, i.e. it applies to the case where ε is complex.

*Orthogonality theorem of guided modes*- We consider a source-free waveguide. Suppose {

**E**

*,*

_{i}**H**

*} (*

_{i}*i*=1, 2) are two guided modes satisfying Eq. (8) with

**J**

_{1}=

**J**

_{2}=0. Splitting each of these two modes into the transverse {

**e**

*,*

_{i,t}**h**

*} and longitudinal parts {*

_{i,t}**e**

*,*

_{i,z}**h**

*}, we obtain*

_{i,z}*q*are the corresponding propagation constants that in general can be complex. The orthogonality theorem states that, when

_{i}*q*

_{1}≠

*q*

_{2}, the transversal parts of the two modes satisfy the following condition [29]:

*Coupled-mode equations for the nonlinear interaction in waveguides*- We now consider a waveguide with a source current density

**J**

_{1}=-

*iω*

**P**

^{NL}_{1}that arises from the nonlinear interaction. Such a source generates a guided wave {

**E**

_{1},

**H**

_{1}} propagating along the +

*z*direction, which can be expanded in terms of all guided modes at the same frequency:

**e**

*,*

_{l,t(z)}**h**

*} is the transverse (longitudinal) component of each guided mode propagating along +*

_{l,t(z)}*z*in the source-free case, and

*l*is the index for each mode. For the

*L*-th mode, applying the mirror symmetry operation of the waveguide about the plane normal to

*z*, one can show that

*z*.

**J**

_{1}=-

*iω*

**P**

^{NL}_{1},

**J**

_{2}=0, and Eqs. (12) and (13) into Eq. (9), we observe that on the left hand of Eq. (9), only the

**e**

*×*

_{l,t}**h**

*+*

_{L,t}**e**

*×*

_{L,t}**h**

*term is along the*

_{l,t}*z*-direction, the other terms are perpendicular to

*z*, and therefore it is the only non-vanishing term once the surface integral along

*z*is performed. By further applying the orthogonality condition [Eq. (11)], we obtain

*ω*

_{2}and

*ω*

_{3}, mix to produce a THz beam at

*ω*

_{1}=

*ω*

_{3}-

*ω*

_{2}. For each frequency

*ω*, the guided wave {

_{j}**E**

*,*

_{j}**H**

*} propagating along +*

_{j}*z*, has the following form

*α*and

_{j}*β*, which are both real and positive, are the power propagation loss coefficient and the wave number, respectively. The modal profile {

_{j}**e**

*,*

_{j,t(z)}**h**

*} satisfies the orthonormal relation of Eq. (2). Comparing Eq. (15) with Eq. (1), we have*

_{j,t(z)}**P**

^{NL}_{1}=

*χ*̿ :

**E***

_{2}

**E**

_{3}at the frequency

*ω*

_{1}can be written as

*χ*̿ is the second-order susceptibility tensor. By substituting Eqs. (2), (15), and (17) into Eq. (14), we have

*β*=

*β*

_{3}-

*β*

_{2}-

*β*

_{1}, and

*κ*

_{1}is the coupling coefficient

## References and links

1. | M. Tonouchi, “Cutting-edge terahertz technology,” Nature Photonics |

2. | Y. R. Shen, |

3. | R. W. Boyd, |

4. | Y. Jiang and Y. J. Ding, “Efficient terahertz generation from two collinearly propagating CO2 laser pulses,” Appl. Phys. Lett. |

5. | D. E. Thompson and P. D. Coleman, “Step-Tunable Far Infrared Radiation by Phase Matched Mixing in Planar-Dielectric Waveguides,” IEEE Trans. Microwave Theory Tech. |

6. | W. Shi and Y. J. Ding, “Designs of terahertz waveguides for efficient parametric terahertz generation,” Appl. Phys. Lett. |

7. | H. Cao, R. A. Linke, and A. Nahata, “Broadband generation of terahertz radiation in a waveguide,” Opt. Lett. |

8. | V. Berger and C. Sirtori, “Nonlinear phase matching in THz semiconductor waveguides,” Semicond. Sci. Technol. |

9. | 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. |

10. | Y. Takushima, S. Y. Shin, and Y. C. Chung, “Design of a LiNbO |

11. | C. Staus, T. Kuech, and L. McCaughan, “Continuously phase-matched terahertz difference frequency generation in an embedded-waveguide structure supporting only fundamental modes,” Opt. Express |

12. | K. L. Vodopyanov and Y. H. Avetisyan, “Optical terahertz wave generation in a planar GaAs waveguide,” Opt. Lett. |

13. | A. Marandi, T. E. Darcie, and P. P. M. So, “Design of a continuous-wave tunable terahertz source using waveguide-phase-matched GaAs,” Opt. Express |

14. | S. S. Dhillon, C. Sirtori, J. Alton, S. Barbieri, A. de Rossi, H. E. Beere, and D. A. Ritchie, “Terahertz transfer onto a telecom optical carrier,” Nature Photonics |

15. | E. R. Brown, K. A. McIntosh, K. B. Nichols, and C. L. Dennis, “Photomixing up to 3.8 THz in low-temperature-grown GaAs,” Appl. Phys. Lett. |

16. | A. Snyder and J. Love, |

17. | P. R. Villeneuve, S. Fan, J. D. Joannopoulos, K. Y. Lim, G. S. Petrich, L. A. Kolodziejski, and R. Reif, “Air-bridge microcavities,” Appl. Phys. Lett. |

18. | K. L. Vodopyanov, M. M. Fejer, X. Yu, J. S. Harris, Y. S. Lee, W. C. Hurlbut, V. G. Kozlov, D. Bliss, and C. Lynch, “Terahertz-wave generation in quasi-phase-matched GaAs,” Appl. Phys. Lett. |

19. | I. Mehdi, S. C. Martin, R. J. Dengler, R. P. Smith, and P. H. Siegel, “Fabrication and performance of planar Schottky diodes withT-gate-like anodes in 200-GHz subharmonically pumped waveguide mixers,” IEEE Microwave and Guided Wave Lett. |

20. | S. M. Marazita, W. L. Bishop, J. L. Hesler, K. Hui, W. E. Bowen, T. W. Crowe, V. M. W. Inc, and V. A. Charlottesville, “Integrated GaAs Schottky mixers by spin-on-dielectric wafer bonding,” IEEE Trans. Electron Devices |

21. | P. H. Siegel, R. P. Smith, M. C. Graidis, and S. C. Martin, “2.5-THz GaAs monolithic membrane-diode mixer,” IEEE Trans. Microwave Theory Tech. |

22. | K. Aoki, H. T. Miyazaki, H. Hirayama, K. Inoshita, T. Baba, K. Sakoda, N. Shinya, and Y. Aoyagi, “Microassembly of semiconductor three-dimensional photonic crystals,” Nature Materials |

23. | E. E. Russell and E. Bell, “Measurement of the Optical Constants of Crystal Quartz in the Far Infrared with the Asymmetric Fourier-Transform Method,” J. Opt. Soc. Am. |

24. | D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B |

25. | M. Ordal, L. Long, R. Bell, S. Bell, R. Bell, and R. Alexander, “Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared,” Appl. Opt. |

26. | E. D. Palik, |

27. | K. Vodopyanov, “Optical THz-wave generation with periodically-inverted GaAs,” Laser and Photonics Reviews |

28. | W. C. Hurlbut, Y. S. Lee, K. L. Vodopyanov, P. S. Kuo, and M. M. Fejer, “Multiphoton absorption and nonlinear refraction of GaAs in the mid-infrared,” Opt. Lett. |

29. | P. Bienstman, “ |

**OCIS Codes**

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(230.7370) Optical devices : Waveguides

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: May 5, 2009

Revised Manuscript: June 16, 2009

Manuscript Accepted: June 18, 2009

Published: July 22, 2009

**Citation**

Zhichao Ruan, Georgios Veronis, Konstantin L. Vodopyanov, Marty M. Fejer, and Shanhui Fan, "Enhancement of optics-to-THz conversion efficiency by metallic slot waveguides," Opt. Express **17**, 13502-13515 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13502

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### References

- M. Tonouchi, "Cutting-edge terahertz technology," Nat. Photonics 1, 97 (2007). [CrossRef]
- Y. R. Shen, The Principles of Nonlinear Optics (New York, Wiley-Interscience, 1984).
- R. W. Boyd, Nonlinear Optics (Academic Press, 2003).
- Y. Jiang and Y. J. Ding, "Efficient terahertz generation from two collinearly propagating CO2 laser pulses," Appl. Phys. Lett. 91, 091108 (2007). [CrossRef]
- D. E. Thompson and P. D. Coleman, "Step-Tunable Far Infrared Radiation by Phase Matched Mixing in Planar-Dielectric Waveguides," IEEE Trans. Microwave Theory Tech. 22, 995-1000 (1974). [CrossRef]
- W. Shi and Y. J. Ding, "Designs of terahertz waveguides for efficient parametric terahertz generation," Appl. Phys. Lett. 82, 4435 (2003). [CrossRef]
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