Design of an efficient terahertz wave source from a GaP waveguide embedded in a silicon slot waveguide

Here, we propose an efﬁcient scheme for terahertz (THz) wave generation on the basis of difference frequency mixing (DFM) using a GaP ridge waveguide embedded in a silicon slot waveguide. Phase matching in the DFM process, between the nonlinear polarisation wave induced by two near-infrared pumps and the generated THz wave in the low-refractive-index slot waveguide, was achieved by utilising the modal birefringence of the fundamental transverse electric-and transverse magnetic-like modes at telecom wavelengths in the GaP ridge waveguide. The effective cross-sectional area of the THz wave in the waveguide was small, 220 µ m 2 at 2.26 THz, resulting in a photon conversion efﬁciency of 5.7 × 10 -2 %. The THz output power approached the multi-µ W level using the proposed waveguide structure. [DOI: http://dx.doi.org/10.2971/jeos.2015.15024]


INTRODUCTION
Terahertz (THz) sources, which operate in the wavelength range of 0.1-10 THz, have attracted a great deal of attention with regard to material science, biochemistry, security, and non-destructive testing applications; the availability of THz sources has advanced development in numerous areas by tuning to the specific eigenmodes of materials derived from optical phonons, inter-or intra-molecular vibration, and hydrogen bonding [1]- [6].
Nonlinear optics (NLO) facilitate efficient generation of THz waves, by converting near-infrared frequencies to the THz regime.Difference frequency mixing (DFM), in particular, has demonstrated high-power, frequency-tuneable, THz wave generation at room temperature [7]- [11].Effective DFM requires strong nonlinear interaction among the pump, signal, and THz waves; for this to occur, the nonlinear interaction cross-section must be sufficiently small to satisfy the quantum conversion efficiency limit specified by the Manley-Rowe relation.Especially, a semi-insulating GaP single crystal is one of the promising NLO materials compared with other ones such as GaAs, GaSe, and LiNbO 3 due to the following features: relatively high nonlinear optical susceptibility (50 pm/V at 1.55 µm [12]) wide transparency ranges for both infrared and THz regions, and low multiphoton absorption coefficient at telecom wavelength.In addition, semiconductor fabrication processes have been established, and is advantageous as THz optical devices.
Compared with bulk NLO crystals, THz waveguides made from NLO crystals, such as GaAs, GaP, and LiNbO 3 , with a cross-sectional size on the order of the THz wavelength considered, effectively confine the generated THz waves [13]- [21].However, despite strong confinement of the generated THz wave through DFM processes, THz wave absorption is relatively large compared with that of optical waves, due to optical phonon and free-carrier absorption.High-resistivity silicon crystal-based THz waveguides exhibit a smaller absorption coefficient than that of NLO crystals.The cross-sectional dimensions of THz waveguides, however, are limited by the nearly THz-wavelength-scale, in the order of a few hundred microns.
Slot waveguides use a low-refractive index region to strongly confine optical waves, sub-wavelength in scale, via total internal reflection [22]- [25].The high electric field amplitude in the low-index material, unattainable with conventional dielectric waveguides, enhances nonlinear interactions between the optical waves and NLOs.Slot waveguides and their operating principles have been applied to optical switching, optical amplifiers, optical detectors, and biosensing devices with integrated silicon photonic circuits [26]- [30].Slot waveguides are expected to facilitate efficient THz wave generation, due to their light-confinement capabilities and low propagation-loss properties.
In this paper, we describe a GaP ridge waveguide-based THzwave generator embedded in a silicon-slot THz-waveguide structure.Phase-matching analysis of the DFM process and estimation of the resulting THz conversion efficiency were conducted for the proposed waveguide structure.Utilising the birefringence of the GaP ridge waveguide, phase matching was achieved between the nonlinear polarisation wave and resulting THz wave by satisfying the low group index.
Strong confinement of the THz wave in the air-gap region of slot waveguide resulted in a high conversion efficiency, compared with that obtained using conventional dielectric waveguides.The waveguide assembly was installed on a quartz substrate.

GaP-BASED NLO WAVEGUIDE EMBBED IN Si SLOT WAVEGUIDE FOR THE DFM PROCESS
The special modal properties of the incident pump waves are defined by the ridge waveguide with cross-sectional dimensions, h ridge , w ridge , t slab , and w slab in Figure 1(b).In order to realize the single mode propagation of the pump waves in the ridge waveguide, these dimensions should be satisfied the following condition [31]: According to Eq. ( 1), we set the ridge waveguid dimensions, h ridge , w ridge , t slab and w slab to be 1.0 µm, 1.2 µm, 0.8 µm and 3.0 µm, respectively.
The fabrication process for the proposed waveguide is as follows.A GaP wafer was optically bonded to a single-crystal quartz substrate using direct wafer bonding.The thickness of the GaP layer was reduced by chemical mechanical polishing (CMP).Photolithography and reactive ion etching (RIE) were used to construct the ridge waveguide structure in GaP.The Si slot waveguide, fabricated using RIE, was bonded to the quartz substrate.
Figure 2 shows the effective refractive index n eff , and respective mode attenuation coefficient n eff , of the slot waveguide as a function of THz frequency.Calculations were conducted using a finite-difference mode solver [32].In the calculations, we took into account the refractive index and material attenuation at THz frequencies for GaP, silicon, and quartz.The complex refractive indices of GaP, silicon, and quartz, n + iκ, at 2.26 THz are 3.3615 + 0.002144i, 3.4180 + 0.0004974i, and 2.1406 + 0.00093i, respectively [33,34].
The numerically estimated effective index n eff and modal attenuation coefficient n eff are shown in Figure 2. The small refractive indices values, characteristic of the slot waveguide, were confirmed.The calculated refractive index of the slot waveguide was 1.366 at 2.4 THz, significantly smaller than that of the GaP core region (3.3 at 2 THz [35]); thus, the THz wave should be confined to the gap region of the slot waveguide, with a low modal attenuation coefficient of 0.77 cm −1 at 2.4 THz.
To satisfy phase-matching conditions among the optical pump, signal wave, and generated THz wave, we utilised modal birefringence of the GaP ridge waveguide.Two incident optical pump and signal waves, having frequencies of ω p and ω s , respectively, propagated collinearly along the [110] crystalline direction of the GaP ridge waveguide shown in Figure 1.When the polarisation directions of the pump and signal waves were set parallel with respect to the [001] (transverse magnetic (TM) mode) and [1 10] (transverse electric (TE) mode) directions, the group index of the induced nonlinear polarisation wave was reduced, compared with the refractive index of GaP, resulting in the generation of TE-like THz wave confined in the slot waveguide.sions, the group index of the nonlinear polarisation wave, n g , was estimated in Figure 3(b) for a fixed pump wavelength of 1.55 µm.The large modal index difference between the fundamental TM-like and TE-like modes produced a nonlinear polarisation wave with a low group index.The propagation constant of the nonlinear polarisation wave, generated by the pump and signal waves, is given by: where ω i (i = p and s) are the angular frequencies of the pump and signal waves.Here, we consider the propagation losses in the waveguide associated with the phase-matching conditions for the DFM process.Figure 4(a) illustrates the normalized optical intensity distribution of the TE-like pump wave at 1.5686 µm in the GaP ridge waveguide.The optical wave is confined into the ridge waveguide.The propagation losses for the optical wave were estimated by beam propagation method.Figure 4(a) shows the optical intensity change as a function of the ridge waveguide length.From this figure, the propagation loss in the ridge waveguide β IR was estimated to be 1.05 cm −1 .
We introduced a complex phase-mismatch factor associated with DFM, as follows: where ∆β R and ∆β I denote the real and imaginary parts of the phase-mismatch term.The imaginary part of Eq. ( 3) restricts the THz-wave power as it propagates along the waveguide.The coherence length L c in the DFM process satisfies the figure of merit in the designed NLO device, with the optimal length designed for maximum output power.The coherence length is calculated from the following equation [36]: Numerical estimation of the coherence length for 2.26-THz generation was 1.4 cm, where the phase-mismatch terms ∆β R and ∆β I , were 0 cm −1 and 0.67 cm −1 , respectively.

THz OUTPUT CHARACTERISTICS IN THE DFM PROCESS
The conversion efficiency in the DFM process for the GaPbased slot waveguide was estimated using the following [37]: where P i and α i (i = p, s, and THz) are the optical power and absorption coefficients for the pump, signal, and THz waves, respectively, and L is the waveguide length.Γ is the nonlinear coupling coefficient, given by: where d q is the second-order nonlinear coefficient of GaP, n i (i = p, s, and THz) are the refractive indices of the pump, signal, and THz waves, respectively, c is the speed of light, and µ 0 is the permeability in vacuum.
The second-order nonlinear coefficient of GaP, d q , is expressed by [38]: where d e is the electronic second-order nonlinear coefficient (d e = 50 pm V −1 [12]), and ν TO and γ correspond to the transverse optical (TO) phonon frequency (ν TO = 11.01THz) and its damping constant (γ = 0.03 THz).The effective nonlinear interaction area A eff is given by: where E i (i = p, s, and THz) are the normalised complex amplitudes of the electric field of the pump, signal, and THz waves, respectively.
where E(x, y) is the electric field profile of the waveguide, and α(x, y) is the absorption loss distribution for the entire waveguide.α eff,THz was estimated to be 0.78 cm −1 using the absorption coefficients of GaP, Si, and quartz at 2.26 THz: 0.5, 4, and 0.3 cm −1 , respectively.From this, the THz output power through the DFM process as a function of the waveguide length L was calculated, as shown in Figure 6.In this calculation, the power of the continuous wave (CW) pump and signal was assumed to be 1 W. The THz power increased monotonously with the waveguide length, reaching a maximum CW-THz wave power of 6.6 µW when the waveguide length was 1.5 cm, in agreement with the coherence length.
The power conversion efficiency was estimated at 6.5×10 −4 %, corresponding to a photon conversion efficiency of 5.7×10 −2 %.This value was much higher than that of the experimental results reported previously (η = 1.3×10 −5 %) [17].The THz output power was comparable to that produced by a quantum cascade-based DFM source [39].THz power exceeding the multi-µW level can be detected using a THz The estimated effective area A eff was 220 µm 2 .
FIG. 6 THz output power as a function of the waveguide length L. The input power of the pump and signal waves was fixed at 1 W, respectively.The maximum output power was obtained to be 6.6 µW, which corresponds to a photon-conversion efficiency of 5.7×10 -2 %.
detector operating at room temperature, such as a pyroelectric detector or Golay cell.Thus, the proposed waveguide structure described can be used as a compact, high-power THz source.

CONCLUSION
We demonstrated efficient THz wave generation from a GaPbased ridge waveguide embedded in a Si slot waveguide.Strong confinement and low propagation loss for the generated THz waves resulted in a THz output power of 6.6 µW at 2.26 THz, corresponding to a photon conversion efficiency of 5.7×10 −2 %.The proposed waveguide structure is an effective way to produce high-power CW-THz waves above the multi-µW level that can be detected by THz detectors operating at

FIG. 1 (
FIG. 1 (a) Cross-sectional view of a GaP-based nonlinear optic (NLO) waveguide embedded in a Si slot waveguide for terahertz (THz) wave generation via difference frequency mixing (DFM).(b) Detailed illustration of the GaP ridge waveguide structure.

Figure 1 (
Figure 1(a) shows a schematic drawing of a Si slot waveguide, including the GaP ridge waveguide for THz-wave generation.The Si slot waveguide, composed of high-resistivity silicon (cross-sectional height: 15 µm; cross-sectional width: 18 µm), sandwiched the GaP ridge waveguide, with a 6-µm spacing.The waveguide assembly was installed on a quartz substrate.The special modal properties of the incident pump waves are defined by the ridge waveguide with cross-sectional dimensions, h ridge , w ridge , t slab , and w slab in Figure1(b).In order to realize the single mode propagation of the pump waves in the ridge waveguide, these dimensions should be satisfied the following condition[31]:

FIG. 2
FIG. 2 Modal effective index and effective attenuation coefficient n eff ,THz and α eff , THz for fundamental transverse electric (TE)-like THz-waves in the slot waveguide as a function of THz frequency.

Figure 3 (FIG. 3
Figure 3(a)  shows the calculated modal indices of the TE and TM modes in a GaP ridge waveguide.We confirmed a large modal birefringence of ∆n ≈ 0.022 between the TE and TM modes in the GaP ridge waveguide.From these modal disper- The modal indices for the fundamental TM-like pump and TE-like signal waves, n p,TM-like and n s,TE-like , provide a group index for the nonlinear polarisation wave n g .The propagation constant of the nonlinear polarisation wave β IR is shown in Figure 3(b), as well as that for the guided THz wave in the slot waveguide obtained from the effective index n eff,THz .The frequency position, highlighted by an open circle, indicates that the phase-matching condition is satisfied at 2.26 THz for the designed waveguide structure.

FIG. 4
FIG. 4 (a) Normalised optical intensity distribution of the TE-like pump wave at 1.5686 µm in the GaP ridge waveguide.(b) The optical power change as a function of the waveguide length.The propagation loss was estimated to be 1.05 cm -1 .

Figure 5
shows the normalised electric field distribution of the THz wave in the slot waveguide at 2.26 THz (Figure5(a)) and effective nonlinear interaction area A eff expressed by Eq. (8) (Figure5(b)).The effective area A eff was estimated to be ∼220 µm 2 , resulting in a coupling coefficient Γ of 3.4×10 −14 (s/m W −1/2 ).The estimated value was twice lager than the area of slot region (90 µm 2 ) because the THz electric field overlaps the GaP ridge waveguide partially.The propagation loss of the slot waveguide for the THz wave α eff,THz is given by: A eff,THz = E 2 THz (x, y)α THz (x, y)dxdy E 2 THz (x, y)dxdy ,

FIG. 5
FIG. 5 (a) Normalised optical intensity distribution of the TE-like THz wave at 2.26 THz in the slot waveguide.(b) The nonlinear interaction area, A eff obtained from Eq. (8).