OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 17 — Aug. 17, 2009
  • pp: 14839–14850
« Show journal navigation

Comparison of the lowest-order transverse-electric (TE1) and transverse-magnetic (TEM) modes of the parallel-plate waveguide for terahertz pulse applications

Rajind Mendis and Daniel M. Mittleman  »View Author Affiliations


Optics Express, Vol. 17, Issue 17, pp. 14839-14850 (2009)
http://dx.doi.org/10.1364/OE.17.014839


View Full Text Article

Acrobat PDF (345 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present a comprehensive experimental study comparing the propagation characteristics of the virtually unknown TE1 mode to the well-known TEM mode of the parallel-plate waveguide (PPWG), for THz pulse applications. We demonstrate that it is possible to overcome the undesirable effects caused by the TE1 mode’s inherent low-frequency cutoff, making it a viable THz wave-guiding option, and that for certain applications, the TE1 mode may even be more desirable than the TEM mode. This study presents a whole new dimension to the THz technological capabilities offered by the PPWG, via the possible use of the TE1 mode.

© 2009 OSA

1. Introduction

Ever since the first demonstration of the parallel-plate waveguide (PPWG) for undistorted terahertz (THz) pulse propagation [1

1. R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001). [CrossRef]

], the PPWG geometry has proven to be a breakthrough technology, enabling numerous THz applications. These include THz interconnects [2

2. R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001). [CrossRef]

], pulse generation [3

3. H. Cao, R. A. Linke, and A. Nahata, “Broadband generation of terahertz radiation in a waveguide,” Opt. Lett. 29(15), 1751–1753 (2004). [CrossRef] [PubMed]

,4

4. S. Coleman and D. Grischkowsky, “Parallel plate THz transmitter,” Appl. Phys. Lett. 84(5), 654–656 (2004). [CrossRef]

], spectroscopy [5

5. R. Mendis, “Guided-wave THz time-domain spectroscopy of highly doped silicon using parallel-plate waveguides,” Electron. Lett. 42(1), 19–21 (2006). [CrossRef]

8

8. N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008). [CrossRef]

], sensing [9

9. J. Zhang and D. Grischkowsky, “Waveguide THz time-domain spectroscopy of nm water layers,” Opt. Lett. 29(14), 1617–1619 (2004). [CrossRef] [PubMed]

,10

10. M. Nagel, M. Forst, and H. Kurz, “THz biosensing devices: fundamentals and technology,” J. Phys. Condens. Matter 18(18), S601–S618 (2006). [CrossRef]

], imaging [11

11. M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86(22), 221107 (2005). [CrossRef]

], and signal processing [12

12. D. G. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16(19), 15123–15129 (2008). [CrossRef] [PubMed]

]. The PPWG has also been employed as a convenient two-dimensional environment for many THz experiments, such as to study photonic crystals [13

13. Z. Jian, J. Pearce, and D. M. Mittleman, “Defect modes in photonic crystal slabs studied using terahertz time-domain spectroscopy,” Opt. Lett. 29(17), 2067–2069 (2004). [CrossRef] [PubMed]

,14

14. Y. Zhao and D. Grischkowsky, “2-D terahertz metallic photonic crystals in parallel-plate waveguides,” IEEE Trans. Microw. Theory Tech. 55(4), 656–663 (2007). [CrossRef]

], photonic waveguides [15

15. A. L. Bingham and D. Grischkowsky, “High Q, one-dimensional terahertz photonic waveguides,” Appl. Phys. Lett. 90(9), 091105 (2007). [CrossRef]

], the super-prism effect [16

16. T. Prasad, V. L. Colvin, Z. Jian, and D. M. Mittleman, “Superprism effect in a metal-clad terahertz photonic crystal slab,” Opt. Lett. 32(6), 683–685 (2007). [CrossRef] [PubMed]

], and Bragg resonances [17

17. S. S. Harsha, N. Laman, and D. Grischkowsky, “High-Q terahertz Bragg resonances within a metal parallel plate waveguide,” Appl. Phys. Lett. 94(9), 091118 (2009). [CrossRef]

]. Interestingly, all of these THz applications have exploited the lowest-order transverse-magnetic (TM0) mode, which is also the transverse-electromagnetic (TEM) mode of the PPWG. The TEM mode has been the obvious choice due to its low loss and ease of quasi-optic coupling, and perhaps most importantly, due to its negligible group-velocity-dispersion (GVD), as a result of having no low-frequency cutoff.

The lowest-order transverse-electric (TE1) mode of the PPWG has not been considered for THz pulse applications, mainly due to the presence of a low-frequency cutoff at fc = c/(2nb), where b is the plate separation, and n is the refractive index of the medium between the plates. This cutoff causes spectral filtering and introduces high GVD that results in broadening and reshaping of input broadband THz pulses, which has discouraged the use of the TE1 mode in the past. In this work, we compare the propagation characteristics of the TE1 mode with those of the TEM mode for possible THz pulse applications. We demonstrate how to negate the undesirable properties of the TE1 mode, making it a viable option for wave guiding, and further demonstrate that for certain THz applications, the TE1 mode may be more desirable than the TEM mode. Specifically, we show that one could achieve undistorted THz pulse propagation using the TE1 mode, similar to the TEM mode, but with the added potential for ultra-low ohmic losses in the dB/km range. We also show that it is possible to excite a practically simple, but highly effective, resonant cavity that is integrated with a PPWG, via the TE1 mode, and that this is not possible via the TEM mode.

2. Short path-length experiment

shown in Fig. 1(a)
Fig. 1 Time scans corresponding to (a) input reference, (b) TEM-mode propagation, (c) TE1-mode propagation in a 2.5 cm long PPWG with b = 0.5 mm, (d) TE1-mode propagation in a 2.5 cm long PPWG with b = 5 mm. The two insets (circled) show the excitation polarization axes with respect to the transverse cross-section of the PPWG. Although some of the TE1-mode data has been previously published [20], they are presented again here to emphasize the comparison with the TEM results.
. The positive peak of the main transient has a FWHM of 0.8 ps, and the observed secondary features are inherent to the THz-TDS system. Figure 1(b) shows the pulse after propagating through a 2.5 cm long, air-filled PPWG having b = 0.5 mm, with the input beam polarized perpendicular to the plates [inset of Fig. 1(b)] to excite the TEM mode. As expected, there is no change in the shape of the pulse compared to the reference, indicating single TEM mode propagation. This is confirmed by the corresponding amplitude spectrum shown in Fig. 2(a)
Fig. 2 (a) Amplitude spectra corresponding to the scans in Figs. 1(b) and 1(c), obtained by Fourier-transforming the truncated time-domain waveforms. The latter is given by the dots. (b) Phase and group velocity for the TE1 mode. The thick and thin red curves give the theoretical values for b = 0.5 mm and 5 mm, respectively. The dots and open circles are experimental. (c) Close-up of the phase velocity for b = 5 mm. The red curve is theoretical and the dots are experimental.
by the open circles, derived by Fourier transforming the truncated pulse, which gives no indication of a low-frequency cutoff. Figure 1(c) shows the pulse after propagating through the same PPWG, but with the input beam polarized parallel to the plates

In order to analyze the propagation behavior, we can write the frequency-domain input-output relationship for the single-mode waveguide as
Eout=ErefTCy2Cxej(βzβo)LeαL/2,
(1)
where Eout and Eref are the complex spectral components, T is the total transmission coefficient that takes into account the impedance mismatch at both the input and output, Cy is the coupling coefficient for the y direction as designated in the insets of Fig. 1 (squared, since it is the same at the input and output), and Cx is the coupling coefficient for the x direction (not squared, since it is 100% at the input). The coupling coefficients are analyzed using the standard overlap-integral method [2

2. R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001). [CrossRef]

], where Cy takes into account the similarity of the input/output Gaussian beam to the guided mode in the y direction, while Cx takes into account the spreading of the beam in the x direction due to diffraction. L is the propagation length, α is the attenuation constant, βz is the phase constant, and βo = 2π/λo, where λo is the free-space wavelength. The βo-term accounts for the fixed THz transmitter and receiver positions during the experiment.

Applying Eq. (1) to the data corresponding to two different propagation lengths, taking the complex ratio, and extracting the phase and amplitude information, we can derive the experimental βz and α for the propagating mode. This assumes that Cx is the same for the two lengths, which is justified since both lengths are relatively short. Using βz, we can derive the phase velocity υp ( = ω/βz) and the group velocity υg ( = ∂ω/∂βz), where the TE1-mode values are plotted in Fig. 2(b) by the dots and open circles, respectively. These show excellent agreement with the theoretical (thick red) curves calculated using classical guided-wave theory [18

18. N. Marcuvitz, Waveguide Handbook (Peregrinus, 1993).

,19

19. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

] for the TE1 mode of the PPWG with b = 0.5 mm. The curves clearly demonstrate the highly dispersive nature of propagation due to the cutoff at 0.3 THz, where the high-frequency components travel faster, resulting in the observed negative chirp.

The experimentally derived α, for both the TE1 and TEM modes, are plotted in Fig. 3(a)
Fig. 3 (a) Comparison of the experimental and theoretical attenuation constant for b = 0.5 mm. The dots and open circles give the experimental values, while the red and blue theoretical curves correspond to the TE1 and TEM modes, respectively. The inset shows the power coupling efficiency to the TE1 and TEM modes from an input Gaussian beam. (b) Theoretical attenuation constant for b = 5 mm, where the thick and thin lines correspond to air-filled and Si-filled PPWGs, respectively. Same color association as above. (c) Close-up of the baselines of the TE1 curves.
by the dots and open circles, respectively. Also plotted are the corresponding theoretical (red and blue) ohmic loss curves, computed using the expressions [18

18. N. Marcuvitz, Waveguide Handbook (Peregrinus, 1993).

,19

19. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

]

αTE=4nRs(fc/f)2Zob1(fc/f)2,
(2)
αTEM=2nRsZob.
(3)

Here, Zo is the free-space impedance and Rs = [π fμ /σ]1/2 is the surface resistance, where μ is the permeability and σ is the DC conductivity. The experimental and theoretical curves agree reasonably well, and reveal a remarkable counter-intuitive property of the TE1 mode, where the attenuation actually decreases with increasing frequency for all frequencies above cutoff. This dependence is in direct contrast to that of the TEM mode, which increases with frequency, and has not been observed with any other THz waveguide to date. The frequency dependence in the TEM-mode’s attenuation can be physically attributed to the decrease in skin depth, resulting in an increased ohmic loss as the frequency increases, and is the reason the observed TE1-mode’s dependence is counterintuitive, since one would expect the same skin-depth dependence. However, it turns out that in the TE1 mode, this physical effect is

offset by a more dominant geometric effect. An in-depth discussion of this remarkable phenomenon is presented elsewhere [20

20. R. Mendis and D. M. Mittleman, “An investigation of the lowest-order transverse-electric (TE1) mode of the parallel-plate waveguide for THz pulse propagation,” J. Opt. Soc. Am. B 26(9), A6–A13 (2009). [CrossRef]

].

This frequency dependence suggests that we should be able to reduce the TE1-mode’s attenuation by pushing fc to lower frequencies. We can lower fc by increasing b; for example, for an air-filled PPWG, when b = 5 mm, fc = 30 GHz, which is at the low end of the input spectrum. The corresponding αTE is plotted in Fig. 3(b) by the thick red curve, along with the analogous (same b) αTEM by the thick blue curve. For clarity, a close-up of the baseline of the αTE curve is shown in Fig. 3(c). We note that when b increases from 0.5 mm to 5 mm, by a factor of 10, αTE varies in a highly non-linear fashion, reducing from 2.7 × 10−2 dB/cm to 2.6 × 10−5 dB/cm (@ 1 THz), by a factor of more than 1000. In contrast, αTEM varies in a linear fashion, reducing from 1.5 × 10−1 dB/cm to 1.5 × 10−2 dB/cm (@ 1 THz), by the same factor of 10. Therefore, increasing b actually decreases both αTE and αTEM, although the effective reduction can be several orders of magnitude stronger in αTE, which is a clear advantage. The larger b predicts an extraordinarily low attenuation for the TE1 mode, where the calculated value of 2.6 × 10−5 dB/cm ( = 2.6 dB/km) is only an order of magnitude higher than that of telecommunications-grade optical fiber operating at 1550 nm.

It is also interesting to consider a situation where the PPWG is filled with a dielectric medium other than air. For example, when the above PPWG is filled with a 5 mm thick high-resistivity silicon (n = 3.42) slab, this would affect αTE and αTEM according to Eqs. (2) and (3). In fact, αTEM would proportionately increase, which is attributed to an increase in the magnetic field, generating higher conduction currents, and therefore, a higher ohmic loss in the metal plates [21

21. R. Mendis, “THz transmission characteristics of dielectric-filled parallel-plate waveguides,” J. Appl. Phys. 101(8), 083115 (2007). [CrossRef]

], as indicated by the thin blue curve in Fig. 3(b). Although, at first glance of Eq. (2), one might predict the same dependence for αTE, the fc terms bring about a more complex n dependence. Interestingly, αTE is actually reduced due to the high-index dielectric, as shown by the thin red curve in Fig. 3(c). One way to understand this is to realize that fc is being pushed to lower frequencies by the high-index medium, thereby naturally reducing the loss, similar to that observed when increasing b. However, although it is possible to reduce the ohmic loss αTE via the use of a dielectric filling, one need to be aware that an additional loss would be introduced by the dielectric medium (the dielectric loss), which would contribute to the overall loss. In fact, it is likely that the dielectric loss may turn out to be the more dominant loss in the TE1 case.

There are other important advantages in lowering the cutoff of the TE1 mode. This would assist to maintain the spectral integrity of the input pulses, while reducing the GVD to almost negligible values, as seen by the (thin red) velocity curves shown in Fig. 2(b) for an air-filled PPWG with b = 5 mm. Except for the low end of the spectrum, these curves indicate virtually zero dispersion. However, this method of lowering the cutoff by increasing the plate separation has the obvious disadvantage of permitting multimode propagation, and is also a problem even for the TEM case. Since the cutoff frequencies of many higher-order modes now fall within the input spectrum, multiple modes could be simultaneously excited, leading to excessive loss and dispersion. Nevertheless, this problem can be overcome if the input coupling is optimized to selectively excite only the mode of interest via mode-matching. We note that the electric field of the TE1 mode has a ‘sin(πy/b)’ spatial dependence (where y = 0 is at one of the plate surfaces), whereas the TEM mode has a flat-top profile, independent of y. Therefore, the TE1 profile is better matched to a Gaussian profile, and should enable better coupling and selectivity. To quantify this, we calculate the power coupling efficiency (η) from an input Gaussian beam to the TE1 and TEM modes, as a function of b/D, where D is the 1/e beam size of the Gaussian. This result, shown inset of Fig. 3(a), predicts that we can couple to the TE1 mode with a maximum possible η of 99%, achieved when b/D = 1.42, whereas to the TEM mode, the maximum possible η is only 89%, achieved when bD. Additionally, the η curve for the TE1 mode is much broader than that for the TEM mode, which implies that we can achieve single-mode propagation for a larger range of input beam sizes when exciting the TE1 mode, compared to the TEM mode. This would mean that, when utilizing a possible multimode (or over-moded) PPWG configuration (having a large b), it would be easier to achieve single-TE1 mode propagation than to achieve single-TEM mode propagation.

To test an over-moded configuration for the TE1 case, we used the same aluminum plates as in our earlier experiment, and constructed PPWGs with a large b = 5 mm. We directly excited the guided-wave with a weakly focused (≈10 mm 1/e-diameter) THz input beam polarized parallel to the plates, without using cylindrical lenses. In practice, when using a large b, it is important to ensure that the input beam size is sufficiently large, so that it interacts with the (inside) surfaces of the plates, right at the input plane, to setup the guided mode. Figure 1(d) shows the resulting pulse after propagating though a 2.5 cm long PPWG, which indicates only a mild reshaping, in sharp contrast to the severe pulse distortion seen in Fig. 1(c). The experimentally derived phase velocity for this larger value of b, shown by the dots in Fig. 2(c), is in excellent agreement with the theoretical prediction (red curve) for the TE1 mode and indicates negligible dispersion. This clearly demonstrates that we have achieved single TE1 mode propagation, confirming the high selectivity of the input coupling, and moreover, demonstrates that we have overcome the problems due to the cutoff. Determining the experimental attenuation is not possible here, because the ohmic losses [Fig. 3(c)] are far too small to measure with these propagation lengths.

3. Long path-length experiment

An important consideration when using relatively long PPWGs is the energy leakage caused by wave diffraction in the unconfined (transverse) direction [2

2. R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001). [CrossRef]

]. This would result in an additional loss process termed as the “diffraction loss”. In the case of the TEM mode, the diffraction is identical to that of a freely propagating wave in space, and the loss can be quantified accordingly [2

2. R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001). [CrossRef]

]. However, in the case of the TE1 mode, there is a subtle difference, as demonstrated in the following experiment and subsequent analysis.

composite PPWG [22

22. R. Mendis and D. M. Mittleman, “Whispering-gallery-mode THz-pulse propagation on a single curved metallic plate,” in Conference on Lasers and Electro-Optics 2009, paper CThQ1.

].

In order to investigate the loss behavior observed in the long path-length PPWG [Fig. 5(a)], we again resort to the fundamental input-output expression given in Eq. (1). As mentioned before, the one-dimensional amplitude-coupling-coefficient Cx takes into account the spreading of the beam in the unconfined x direction, and was assumed to be the same for the considered (two) path lengths in the first experiment, due to the relatively short lengths used. However, since the current experiment deals with longer path lengths, Cx plays a major role. The longer path lengths would result in much higher lateral spreading of the beam, and in the case of the TEM mode, this spreading would be identical to that of a freely propagating beam in space, allowing the direct application of Gaussian-beam optics in one dimension to quantify this effect [2

2. R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001). [CrossRef]

]. In the case of the TE1 mode, however, this spreading cannot be immediately generalized to be identical to a freely-propagating beam, for the simple reason that it is not a TEM wave. Nevertheless, if we could assign an “effective refractive index” for the wave propagating in the TE1 mode, then mathematically, it would still be possible to apply Gaussian-beam optics, using this equivalent index, to determine the lateral spreading in the air-filled PPWG. In fact, analogous to a conventional dielectric medium, we can define an effective index as neff = c/υp, based on the phase-velocity curves presented in Fig. 2(b). These curves predict an neff that varies between zero and unity, since υp varies from ∞ to c, as the frequency increases from cutoff. This plasma-like behavior mimicked by the TE1 mode actually opens up the possibility for a whole new class of artificial dielectric media having a refractive index less than unity [23

23. R. Mendis and D. M. Mittleman, “A beam-scanning THz prism with effective refractive index less than unity,” presented at the International Workshop on Optical Terahertz Science and Technology, California, USA, 2009.

]. Therefore, neff = 0 at fc, and increases towards unity as the frequency increases.

An interesting consequence of this result is that the lateral spreading for a wave propagating in the TE1 mode would be generally more than if it were to freely propagate, starting from the same Gaussian beam (waist) size, due to the fact that the index is lower than that of free space. This spreading is more severe for frequencies near the cutoff, but becomes negligible at high frequencies, as shown in Fig. 5(c). This figure shows the frequency-dependent lateral output beam size after propagating through a 25 cm long PPWG, starting from a frequency-independent 2 cm diameter input beam, for b = 0.5 mm (thick red curve) and b = 10 mm (thin red curve), in the TE1 mode. Also shown (blue curve, which is almost perfectly overlapping with the thin red curve) is the frequency-dependent output beam size for the TEM mode, starting from the same input beam size, and after propagating 25 cm. Note that in the case of the TEM mode, the value of b does not affect the spreading. This demonstrates that for large values of b, the beam spreading associated with the TE1 mode is very similar to that of the TEM mode, or to a freely propagating beam, except for the very low frequency end (near fc), where it is slightly higher.

Once the diffractive spreading is known, we can determine Cx for the short (2.5 cm) and long (25.0 cm) PPWGs in the current experiment, using the standard overlap-integral method [2

2. R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001). [CrossRef]

]. These are plotted in Fig. 5(d), assuming a collecting-aperture size of 6 mm for the silicon-lens-coupled THz receiver. Now, applying Eq. (1) to the short and long path-lengths separately, taking the complex ratio, and extracting the amplitude information, we can write
|EoutlEouts|=[CxlCxs]eα(LlLs)/2,
(4)
where the subscripts ‘l ’and ‘s ’ stand for the long and short waveguides, respectively. Equation (4) would allow us to determine the experimental α due to the ohmic loss, provided there is a measurable change between |Eoutl| and |Eouts| × [Cxl /Cxs], where the latter term is the adjusted spectrum of the short waveguide (mathematically) accounting for the diffraction. These two spectra are plotted in Fig. 5(b) by the dots and open circles, respectively, and are experimentally indistinguishable. This implies that the experiment does not allow a meaningful measurement of the ohmic loss. However, this does demonstrate that the ohmic loss is virtually negligible, which is also confirmed by the theoretical loss, computed using Eq. (2) for b = 10 mm, where it is found to be 9.3 × 10−6 dB/cm at 0.5 THz and 3.3 × 10−6 dB/cm at 1 THz. To meaningfully measure these extraordinarily low ohmic losses, we would need to employ PPWGs that are several tens of meters in length, while overcoming the diffraction losses. This analysis clearly demonstrates that for a PPWG with a large enough b, the only appreciable loss for the TE1 mode is caused by diffraction. Therefore, mitigating this diffraction loss is an important consideration towards the practical realization of an ultra-low loss THz waveguide [20

20. R. Mendis and D. M. Mittleman, “An investigation of the lowest-order transverse-electric (TE1) mode of the parallel-plate waveguide for THz pulse propagation,” J. Opt. Soc. Am. B 26(9), A6–A13 (2009). [CrossRef]

].

4. Resonant-cavity experiment

In this experiment, we investigate the feasibility of exciting a resonant cavity integrated with a PPWG, via the TE1 and TEM modes. We note that there have been several interesting experimental THz studies demonstrating resonant spectral features using (modified) PPWG structures, fabricated using advanced lithographic techniques [10

10. M. Nagel, M. Forst, and H. Kurz, “THz biosensing devices: fundamentals and technology,” J. Phys. Condens. Matter 18(18), S601–S618 (2006). [CrossRef]

,13

13. Z. Jian, J. Pearce, and D. M. Mittleman, “Defect modes in photonic crystal slabs studied using terahertz time-domain spectroscopy,” Opt. Lett. 29(17), 2067–2069 (2004). [CrossRef] [PubMed]

15

15. A. L. Bingham and D. Grischkowsky, “High Q, one-dimensional terahertz photonic waveguides,” Appl. Phys. Lett. 90(9), 091105 (2007). [CrossRef]

,17

17. S. S. Harsha, N. Laman, and D. Grischkowsky, “High-Q terahertz Bragg resonances within a metal parallel plate waveguide,” Appl. Phys. Lett. 94(9), 091118 (2009). [CrossRef]

]. Here, we study a very simple cavity, which can be easily integrated with a PPWG, fabricated using conventional machining.

Figure 6(a)
Fig. 6 Time scans corresponding to TE1-mode propagation in (a) 6.4 mm long PPWG with b = 1 mm, (b) same PPWG with an integrated resonant cavity, formed by incorporating a square groove in the top plate. Longitudinal cross-sections (along the direction of propagation) are shown inset. (c) and (d) give the respective amplitude spectra, where the spectrum of the cavity-integrated-PPWG shows a strong and narrow resonance dip (red arrow) in addition to the water-vapor absorption lines (green arrows).
shows a 10,000-scan average of a THz pulse after propagating through a 6.4 mm long (reference) PPWG with b = 1 mm in the single TE1 mode. As expected, we observe a negative chirp with pulse broadening due to the cutoff. The corresponding amplitude spectrum derived by Fourier-transforming the original 320 ps time-scan, zero-padded to 5120 ps, is shown in Fig. 6(c) on a logarithmic scale. This exhibits a cutoff fc = 0.15 THz and two strong water-vapor absorption lines (green arrows) at 0.557 THz and 0.752 THz. Figure 6(b) shows the pulse after propagating through a PPWG with the same b, but where the top plate has a square groove with side d, situated perpendicular to the direction of propagation, and centered between the input and output planes of the waveguide. The longitudinal cross-section of the fully integrated cavity is shown schematically in the inset of Fig. 6(b), and a photograph of the top plate is shown in Fig. 7(b)
Fig. 7 (a) Power transmission (dots) in the vicinity of the resonance dip, fit to a Lorentzian line-shape indicating a resonance frequency of 0.280 THz, a linewidth of 5 GHz, and an extinction coefficient of 30 dB. (b) Photograph of the aluminum plate containing the square groove. The blue dashed lines demarcate the lateral extent of the propagating THz beam inside the assembled PPWG.
. When comparing the two time pulses, we can see the presence of a low-frequency envelope for the one with the cavity, with a more dramatic, but localized effect in the corresponding amplitude spectrum (derived as before) shown in Fig. 6(d). This

figure shows a very strong, narrow extinction feature (red arrow), in addition to the two water-vapor lines.

By comparing the spectra of the propagated pulses, with and without the cavity, we can derive the power transmission for the integrated device, which is plotted in Fig. 7(a) by the dots, in the vicinity of the extinction feature. This is fit with a Lorentzian-line shape (red curve), giving a center frequency fo = 0.280 THz, a 3-dB linewidth Δf = 5 GHz, and a peak extinction coefficient of almost 30 dB. Although the derived quality-factor Q = fof = 56, is not so impressive due to the relatively lower fo, these values of Δf and extinction-coefficient are the best ever measured in the THz regime for a PPWG-based device, to the best of our knowledge. In order to theoretically model the cavity, we resort to the well-known resonance-

frequency expression for an air-filled, generalized 3-D rectangular cavity, given by [19

19. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

]
fr=c2(m1d1)2+(m2d2)2+(m3d3)2,
(5)
where d 1, d 2, and d 3 are the dimensions of the three sides, and m 1, m 2, and m 3 are positive integers, which may also be equal to zero depending on the reduced dimensionality of the cavity. For the cavity under test, defined by the open-ended square groove of side d = 538 ± 13 μm, we find fr = 0.279 ± 0.007 THz assuming a 1-D cavity, where m 2 = m 3 = 0, m 1 = 1, and d 1 = d, from Eq. (5). This calculated value of fr is in excellent agreement with the experimental fo, and suggests that this groove behaves as a 1-D cavity, where standing waves are setup between the two vertical sidewalls of the groove, similar to a Fabry-Perot cavity.

due to the reduced energy density inside the PPWG. Nevertheless, the dispersive broadening due to a smaller b can be readily ignored in this type of application.

5. Conclusions

In this comprehensive study, we have compared the propagation characteristics of the virtually unknown (in the THz regime) TE1 mode of the PPWG with those of the well-known TEM mode. We demonstrate that by the proper choice of the plate separation and input excitation, we could negate the dispersive pulse broadening that has discouraged the use of the TE1 mode for THz-pulse applications, making it a viable wave-guiding option. We find that it is possible to achieve extraordinarily low ohmic losses with the TE1 mode, which would make this an ideal candidate for long-path-length applications, provided we could mitigate the diffraction losses. We also demonstrate that it is possible to excite a simple resonant cavity integrated with a PPWG using the TE1 mode, but not with the TEM mode, implying that the TE1 mode may be more advantageous than the TEM mode for certain THz applications. As a closing remark, we point out that this study in no way lessens the value of the plethora of unique THz applications made possible by the TEM mode of the PPWG, as presented in Refs. [1

1. R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001). [CrossRef]

17

17. S. S. Harsha, N. Laman, and D. Grischkowsky, “High-Q terahertz Bragg resonances within a metal parallel plate waveguide,” Appl. Phys. Lett. 94(9), 091118 (2009). [CrossRef]

], but rather, presents a whole new dimension to the technological capabilities offered by the PPWG, for many other possible THz applications via the use of its TE1 mode.

Acknowledgments

This work was supported in part by the National Science Foundation (NSF) and by the United States Air Force through the CONTACT program.

References and links

1.

R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001). [CrossRef]

2.

R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001). [CrossRef]

3.

H. Cao, R. A. Linke, and A. Nahata, “Broadband generation of terahertz radiation in a waveguide,” Opt. Lett. 29(15), 1751–1753 (2004). [CrossRef] [PubMed]

4.

S. Coleman and D. Grischkowsky, “Parallel plate THz transmitter,” Appl. Phys. Lett. 84(5), 654–656 (2004). [CrossRef]

5.

R. Mendis, “Guided-wave THz time-domain spectroscopy of highly doped silicon using parallel-plate waveguides,” Electron. Lett. 42(1), 19–21 (2006). [CrossRef]

6.

J. S. Melinger, N. Laman, S. S. Harsha, and D. Grischkowsky, “Line narrowing of terahertz vibrational modes for organic thin polycrystalline films within a parallel plate waveguide,” Appl. Phys. Lett. 89(25), 252221 (2006). [CrossRef]

7.

J. S. Melinger, N. Laman, S. S. Harsha, S. Cheng, and D. Grischkowsky, “High-resolution waveguide terahertz spectroscopy of partially oriented organic polycrystalline films,” J. Phys. Chem. A 111(43), 10977–10987 (2007). [CrossRef] [PubMed]

8.

N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008). [CrossRef]

9.

J. Zhang and D. Grischkowsky, “Waveguide THz time-domain spectroscopy of nm water layers,” Opt. Lett. 29(14), 1617–1619 (2004). [CrossRef] [PubMed]

10.

M. Nagel, M. Forst, and H. Kurz, “THz biosensing devices: fundamentals and technology,” J. Phys. Condens. Matter 18(18), S601–S618 (2006). [CrossRef]

11.

M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86(22), 221107 (2005). [CrossRef]

12.

D. G. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16(19), 15123–15129 (2008). [CrossRef] [PubMed]

13.

Z. Jian, J. Pearce, and D. M. Mittleman, “Defect modes in photonic crystal slabs studied using terahertz time-domain spectroscopy,” Opt. Lett. 29(17), 2067–2069 (2004). [CrossRef] [PubMed]

14.

Y. Zhao and D. Grischkowsky, “2-D terahertz metallic photonic crystals in parallel-plate waveguides,” IEEE Trans. Microw. Theory Tech. 55(4), 656–663 (2007). [CrossRef]

15.

A. L. Bingham and D. Grischkowsky, “High Q, one-dimensional terahertz photonic waveguides,” Appl. Phys. Lett. 90(9), 091105 (2007). [CrossRef]

16.

T. Prasad, V. L. Colvin, Z. Jian, and D. M. Mittleman, “Superprism effect in a metal-clad terahertz photonic crystal slab,” Opt. Lett. 32(6), 683–685 (2007). [CrossRef] [PubMed]

17.

S. S. Harsha, N. Laman, and D. Grischkowsky, “High-Q terahertz Bragg resonances within a metal parallel plate waveguide,” Appl. Phys. Lett. 94(9), 091118 (2009). [CrossRef]

18.

N. Marcuvitz, Waveguide Handbook (Peregrinus, 1993).

19.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

20.

R. Mendis and D. M. Mittleman, “An investigation of the lowest-order transverse-electric (TE1) mode of the parallel-plate waveguide for THz pulse propagation,” J. Opt. Soc. Am. B 26(9), A6–A13 (2009). [CrossRef]

21.

R. Mendis, “THz transmission characteristics of dielectric-filled parallel-plate waveguides,” J. Appl. Phys. 101(8), 083115 (2007). [CrossRef]

22.

R. Mendis and D. M. Mittleman, “Whispering-gallery-mode THz-pulse propagation on a single curved metallic plate,” in Conference on Lasers and Electro-Optics 2009, paper CThQ1.

23.

R. Mendis and D. M. Mittleman, “A beam-scanning THz prism with effective refractive index less than unity,” presented at the International Workshop on Optical Terahertz Science and Technology, California, USA, 2009.

OCIS Codes
(230.5750) Optical devices : Resonators
(230.7370) Optical devices : Waveguides
(320.5390) Ultrafast optics : Picosecond phenomena
(320.5540) Ultrafast optics : Pulse shaping

ToC Category:
Ultrafast Optics

History
Original Manuscript: June 22, 2009
Revised Manuscript: July 29, 2009
Manuscript Accepted: July 31, 2009
Published: August 6, 2009

Citation
Rajind Mendis and Daniel M. Mittleman, "Comparison of the lowest-order transverse-electric (TE1) and transverse-magnetic (TEM) modes of the parallel-plate waveguide for terahertz pulse applications," Opt. Express 17, 14839-14850 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14839


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Mendis and D. Grischkowsky, “Undistorted guided-wave propagation of subpicosecond terahertz pulses,” Opt. Lett. 26(11), 846–848 (2001). [CrossRef]
  2. R. Mendis and D. Grischkowsky, “THz interconnect with low loss and low group velocity dispersion,” IEEE Microw. Wirel. Compon. Lett. 11(11), 444–446 (2001). [CrossRef]
  3. H. Cao, R. A. Linke, and A. Nahata, “Broadband generation of terahertz radiation in a waveguide,” Opt. Lett. 29(15), 1751–1753 (2004). [CrossRef] [PubMed]
  4. S. Coleman and D. Grischkowsky, “Parallel plate THz transmitter,” Appl. Phys. Lett. 84(5), 654–656 (2004). [CrossRef]
  5. R. Mendis, “Guided-wave THz time-domain spectroscopy of highly doped silicon using parallel-plate waveguides,” Electron. Lett. 42(1), 19–21 (2006). [CrossRef]
  6. J. S. Melinger, N. Laman, S. S. Harsha, and D. Grischkowsky, “Line narrowing of terahertz vibrational modes for organic thin polycrystalline films within a parallel plate waveguide,” Appl. Phys. Lett. 89(25), 252221 (2006). [CrossRef]
  7. J. S. Melinger, N. Laman, S. S. Harsha, S. Cheng, and D. Grischkowsky, “High-resolution waveguide terahertz spectroscopy of partially oriented organic polycrystalline films,” J. Phys. Chem. A 111(43), 10977–10987 (2007). [CrossRef] [PubMed]
  8. N. Laman, S. S. Harsha, D. Grischkowsky, and J. S. Melinger, “High-resolution waveguide THz spectroscopy of biological molecules,” Biophys. J. 94(3), 1010–1020 (2008). [CrossRef]
  9. J. Zhang and D. Grischkowsky, “Waveguide THz time-domain spectroscopy of nm water layers,” Opt. Lett. 29(14), 1617–1619 (2004). [CrossRef] [PubMed]
  10. M. Nagel, M. Forst, and H. Kurz, “THz biosensing devices: fundamentals and technology,” J. Phys. Condens. Matter 18(18), S601–S618 (2006). [CrossRef]
  11. M. M. Awad and R. A. Cheville, “Transmission terahertz waveguide-based imaging below the diffraction limit,” Appl. Phys. Lett. 86(22), 221107 (2005). [CrossRef]
  12. D. G. Cooke and P. U. Jepsen, “Optical modulation of terahertz pulses in a parallel plate waveguide,” Opt. Express 16(19), 15123–15129 (2008). [CrossRef] [PubMed]
  13. Z. Jian, J. Pearce, and D. M. Mittleman, “Defect modes in photonic crystal slabs studied using terahertz time-domain spectroscopy,” Opt. Lett. 29(17), 2067–2069 (2004). [CrossRef] [PubMed]
  14. Y. Zhao and D. Grischkowsky, “2-D terahertz metallic photonic crystals in parallel-plate waveguides,” IEEE Trans. Microw. Theory Tech. 55(4), 656–663 (2007). [CrossRef]
  15. A. L. Bingham and D. Grischkowsky, “High Q, one-dimensional terahertz photonic waveguides,” Appl. Phys. Lett. 90(9), 091105 (2007). [CrossRef]
  16. T. Prasad, V. L. Colvin, Z. Jian, and D. M. Mittleman, “Superprism effect in a metal-clad terahertz photonic crystal slab,” Opt. Lett. 32(6), 683–685 (2007). [CrossRef] [PubMed]
  17. S. S. Harsha, N. Laman, and D. Grischkowsky, “High-Q terahertz Bragg resonances within a metal parallel plate waveguide,” Appl. Phys. Lett. 94(9), 091118 (2009). [CrossRef]
  18. N. Marcuvitz, Waveguide Handbook (Peregrinus, 1993).
  19. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
  20. R. Mendis and D. M. Mittleman, “An investigation of the lowest-order transverse-electric (TE1) mode of the parallel-plate waveguide for THz pulse propagation,” J. Opt. Soc. Am. B 26(9), A6–A13 (2009). [CrossRef]
  21. R. Mendis, “THz transmission characteristics of dielectric-filled parallel-plate waveguides,” J. Appl. Phys. 101(8), 083115 (2007). [CrossRef]
  22. R. Mendis and D. M. Mittleman, “Whispering-gallery-mode THz-pulse propagation on a single curved metallic plate,” in Conference on Lasers and Electro-Optics 2009, paper CThQ1.
  23. R. Mendis and D. M. Mittleman, “A beam-scanning THz prism with effective refractive index less than unity,” presented at the International Workshop on Optical Terahertz Science and Technology, California, USA, 2009.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited