We have observed Raman spectra of optical phonons at 1.34 μm in an air-bridge type of GaAs photonic-crystal (PC) slab waveguides (WGs) of 0.6 mm in length. Unlike the bulk GaAs case, both longitudinal (LO)- and transverse (TO) phonons were observed not only in the forward direction, but also in the backward direction. This anomalous feature can be well interpreted as arising from strong confinement of light in PC WGs. The scattering efficiency of LO phonon at 292 cm-1 is estimated as 1.9 × 10-7 cm-1sr-1 in the forward scattering. Based on the present information, the possibility of developing an optical amplifier with use of stimulated Raman scattering in a future ultrafast and ultrasmall PC WGs-based optical circuit is discussed.
©2006 Optical Society of America
Recently, stimulated Raman scattering (SRS) in semiconductor waveguides (WGs) has been actively studied [1–6], because SRS provides the potential of optical amplification and lasing in future compact planar optical circuits; such a proposal was first put forward in 1996 . Very recently, Raman laser was successfully developed in silicon WGs at 1.54 μm . As for ultrasmall and ultrafast integrated optical circuits for future communication system , two-dimensional (2D) semiconductor-based photonic-crystal (PC) WGs composing of the line-defect are very attractive , and have been extensively studied both theoretically and experimentally . In such a PC WG, extremely strong confinement of light is realized due to a large difference of the refractive-index vertically and photonic band-gap effect laterally, and as a result, the cross sectional area of the WG is ultrasmall, typically as small as 1.0 × 10-9 cm2. This fact is of great advantage to observing nonlinear-optical phenomena, since pulse energy needed to give rise to those phenomena becomes very small. In this sense, SRS for the above-mentioned purpose, due to optical phonon in the PC WG material is also attractive. However, even spontaneous Raman scattering (RS) in such a PC WG has never been reported up until now in near-infrared region. It is noted that behavior of RS itself in PC WGs is of interest, since it should be different from the bulk case  and, also different, because of the anomalous dispersion, from that in the conventional WGs .
As the first step toward developing Raman amplification and Raman lasing, we have successfully observed RS signal at 1.34 μm in an air-bridge type of GaAs-PC-slab-WG. As a result, we find that both the transverse (TO)- and longitudinal (LO) optical phonons of GaAs can be observed by utilizing the line-defect guided modes in the 2D photonic band gap (PBG). We also find that those are observed both in the forward and backward directions, which can be interpreted as appearing due to strong confinement of light . Based on information extracted about the scattering efficiency and the spectral width, we discuss the possibility of Raman amplification and lasing in a low propagation-loss PC WGs of 4 mm in length . The result reveals that those should be within reach at 1.55 μm for AlxGa1-xAs PC WGs, where two photon absorption (TPA) can be avoided for x> 0.2 .
Samples used in this work are the PC-slab WGs of triple-line-defect (W3), surrounded by 10-row air-holes on both sides . More specifically, three-missing rows of air-holes along the Γ-K direction were fabricated in a prototype PC slab, i.e., an air-bridge type GaAs PC slab of air-holes (radius r = 90 nm) with a 2D triangular lattice structure; the fabrication method is similar to the previous one . The lattice constant a, thickness d, and length L are 330 nm, 250 nm, and 600 μm, respectively. The slab plane is normal to <001>, and the light propagation direction is along <110>. In Fig. 1(a) is shown a scanning electron microscope (SEM) image of the sample. The samples were used without coating for anti-reflection in this work.
In Fig. 1(b) is shown the band structure of the TE-like W3 line-defect modes, which was calculated by using 2D finite-difference-time-domain (FDTD) method assuming the effective refractive index. In the present W3 case, there exist six line-defect bands in the 2D band gap from 1,420 to 1,160 nm, including one for the fundamental (the lowest) refractive-like band. Those can be classified into the even (red) and odd (green) modes (bands), which are symmetric and anti-symmetric, respectively, with respect to the mirror plane parallel to the propagation direction and normal to the slab plane. It is noted that the modes below the air light-line drawn in the Fig. 1(b) are guided ones, and that the odd modes are usually uncoupled to the external light. So, a high transmittance region due to the even guided bands is expected to range from 1,190 to 1420 nm. The second-lowest even band is mainly relevant to the present Raman experiment, since wavelengths of exciting laser and Raman signal (LO phonon) are 1,285 and 1,337 nm, respectively.
3. Optical phonon to be observed in PC-slab WGs
There are two atoms in the unit cell of cubic GaAs (T d), so that only triply-degenerate optical phonon modes F 2 [F(x), F(y), F(z)] exist at Γ point in the Brillouin zone (BZ), where the letter in the parenthesis represents the direction of mechanical phonon vibration; x, y, and z refer to the crystallographic axes. Due to polar character, those are further split into two TO- and one LO phonons. In bulk crystal both types of phonons can be observed, typically in 90° scattering geometry, since the non-vanishing Raman tensors R ij for T d symmetry are Rxy and R yx, and those with x and y replaced in the cyclic way . The eigenvalues observed for TO and LO modes at room temperature are 268 and 292 cm-1, respectively . In thin WGs, where only the forward and backward scatterings make sense, the situation is different from the bulk case , as will be described below.
In the present PC WG, the guided modes possess TE-like polarization, which requires that both polarizations of incident and scattered lights must be parallel to <1-10>. Consequently, from the Raman tensor it follows that the direction of the phonon vibration must be in parallel to <001>. So, it seems that only TO phonon can be observed, whereas LO one can not. However, this is no longer true for a very thin sample like the present one. That this is indeed the case has already been confirmed by a pioneering work in a conventional WG in ref. 12).
Let us consider first the forward scattering geometry. In doing so, we basically follow the concept in ref. 12); note that the present dispersion is quite different from that in the conventional WG. The wave vectors k i and k s of incident and scattered light are both parallel to <110>. Then, q ∥ (the component of q parallel to the WG, i.e., <110>) is given by q ∥ =|k i - k s|, where q is the wave vector of the phonon. From the dispersion curve for the second-lowest band of even-symmetry guided modes shown in Fig. 1(b), q ∥ can be crudely estimated as (2π/a) × (0.063), or (2π/5.2) μm-1. On the other hand, both the thickness d and the width w of the present WG are very small, so that both components of q parallel to <001> and <1-10> direction are nonzero. Those are estimated as 2π/d = 2π/0.25 μm-1 and 2π/w = 2π/0.80 μm-1 in the former and the latter direction, respectively; actually, the effective width is to a considerable extent samller than this value of 0.80 μm because of strong confinement due to band-gap effect, but here we are rather concerned with order of the magnitude among three components. Since 2π/d > 2π/w >> q ∥, the q-vector should be not parallel to <110>, but almost in a plane normal to <110>. That 2π/d is the largest implies that the Raman signal due to LO phonon should be larger than that due to TO phonon in the forward direction.
Similarly, in the backward direction, q ∥ is given by q ∥ = k i - (-k s), and is estimated as (2π/0.41) μm-1. So, we have 2π/d > q ∥ > 2π/w. Notice that even in the backward direction, the q-component along the thickness direction is still the largest, in contrast to the case in a conventional WG, where q ∥ is the largest . This is because on one hand, q ∥ is considerably small as compared to the conventional WG, due to the anomalous dispersion arising from folding into the first BZ in a PC WG, and on the other hand, the thickness is by a factor of 4 smaller than that in ref. 12). Therefore, it is predicted that both TO and LO phonons should be observed in the backward direction too.
4. 1 Transmittance spectrum of the sample
In Fig. 2 is shown the transmittance spectrum of the 600-μm-long sample used in this work. The spectrum over a broad wavelength region was measured by using a newly-developed spectrometer suited for a sample with very thin and ultrasmall input-facet like the present one. The spectrometer consists of a halogen-lamp, a pair of polarization-preserving lensed fibers and a monochromator (home-made one) equipped with a multichannel InGaAs detector (OMA-V, Princeton Inst. Inc.), which was cooled down to -100 °C . In Fig. 2 a broad wavelength region with high transmittance from ~ 1,240 to 1,395 nm corresponds to that of the guided modes of two lower even-symmetry bands below the air light-line. The agreement of this region between the observed and the calculated (1190 – 1420 nm) is fairly good, considering the errors of the parameters involved. It seems that from Fig. 2 the propagation losses at the wavelengths of the exciting light and the signals in the Raman experiment are apparently 6.0 and 4.4 dB, respectively. However, notice that the exciting light at 1,285 nm should excite both the lowest and second-lowest even bands simultaneously, but the former light can not pass through the WG. This is because it belongs to the leaky band above the light line. In other words, this light is ineffective in exciting Raman signal. Assuming that the external light equally couples to the respective modes for simplicity, the propagation losses of the effective exciting light and the signal light are estimated approximately 3 and 2.0 dB, respectively; however, these values contain large uncertainty.
4. 2 Raman scattering measurement
The experimental setup for observing Raman spectrum is shown in Fig. 3. A cw semiconductor laser diode (LD) having 10 mW output power at 1,287 nm was employed as a pumping source. After passing through a set of narrow-band-pass filters for removing the spontaneous emission, the laser was coupled to a polarization-preserving fiber (the core diameter of 9.9 μm), the other side of which was polished so as to be in the form of a lens with the radius of curvature being 10 μm. Thus, the output laser from the fiber was focused onto the cleaved edge-plane of the W3 sample by using this lens. In the case of scattering in the forward direction, the Raman signal was picked up by using another identical lensed fiber. The transmitted laser light was also picked up, but it was eliminated by a set of narrow-band-pass filters before being fed to a monochromator (Ackton SpectraPro 2300i). There, a grating of either 150 grooves/mm or 600 grooves /mm was used, depending on the case; the spectral resolution power is approximately 1.2 and 0.3 nm for the former and latter case, respectively. Thereby, only the signal light was detected with use of a cooled multichannel InGaAs detector, which is similar to but slightly different from the one used for transmittance measurement described in 4. 1.
In the backward scattering case, measurement was made with a beam splitter inserted between the LD and a special lens (a magnification of x 100) used instead of the lensed fiber (see Fig. 3). We were compelled to use such a lens for the following reason. In the case of a lensed fiber, the reflected light from the cleaved surface of the sample turned out so strong that a broad Raman spectrum of fused silica (core material) of the 2 m-long fiber masked the signal under study. So, the signal light emerging from the PC WG was picked up with use of fthe lens described above, and the signal light reflected at the beam splitter was fed to the mono chromator, and detected by the same detector. All measurements were performed at room temperature.
In Fig. 4 is shown an example of Raman spectra observed in the forward direction. There it is seen that two spectral lines clearly appear at 267 and 292 cm-1. The expanded spectrum is shown in Fig. 5. The spectral width Δω observed is estimated as 3.5 cm-1 (105 GHz) and 4.5 cm-1 (125 GHz) for the former and the latter line, respectively. We confirmed that the signal frequencies (shifts) remained unchanged, when the wavelength of the LD for excitation was slightly varied from 1284.95 nm to 1286.27 nm by heating. Besides, we also observed a similar spectrum with the same frequency shifts for another similar sample but with the different lattice constant of 315 nm. These facts together give firm evidence that the present signal is spontaneous RS in origin.
From a comparison of the present frequency values with those of bulk GaAs, i.e., 268 (TO) and 292 (LO) cm-1 , it is evident that the lower frequency spectrum is the Raman signal due to TO phonon, and the other due to LO phonon in the GaAs core layer. It is seen in Fig. 4(a) that the spectral intensity is stronger in LO phonon than in TO one, and that the spectral width is broader in the former than in the latter. The former fact is consistent with the prediction in §3, so this is quite reasonable.
In Fig. 5 is shown the Raman spectrum observed in the backward direction; actually, the signal turns out very weak, but we have successfully observed this signal. We mention that 30 % of the forward-scattered signal should contribute to their intensities, by reflection at the forward uncoated edge-plane. Nevertheless, it is evident that in this case also, both TO- and LO phonon signals are observed; it is noted that only TO phonon should be observed in the corresponding semiconductor (GaP) WG, since the q-vector is well defined as such that it is parallel to the propagation direction . The present observation is again consistent with the expectation in §3, which is that both signals should be observed. However, in contrast to the forward scattering case, the signal backward-scattered by TO phonon is observed with the intensity, roughly speaking, similar to, or even larger than that by LO one. This quantitative result is considered to be also in reasonable agreement with the expectation.
Now, we are in a position to evaluate the Raman scattering efficiency S (cm-1sr-1). For this purpose, first we need to experimentally estimate the proportional constant b to obtain the spontaneous Raman coefficient η, which is defined as,
where I s and I 0 refer to the intensity (power) of the scattered signal at the output facet of the WG and that of the pumping power at the input facet, respectively. Figure 6 shows variation of I s of the LO phonon signal with I 0. There, I 0 is estimated from the LD power by knowing a total transmittance of filters used, the coupling efficiency for the polarization-preserving optical fiber, and the coupling efficiency of ~-15 dB for the waveguide. Similarly, I s is evaluated from the measured signal intensity by knowing the effective transmittance (~ -20 dB) of the monochromator, a total of transmittance (- 6.1 dB) of four narrow-band-pass filters, and the coupling efficiency (-14.9 dB) between the signal intensity at the output facet of WG and the lensed fiber. We note that the scattered signal light from the WG emerges substantially in the directions of 2 π solid angle, but only the light scattered within a part of the solid angle can be coupled to the present fiber, causing the efficiency very small.
From the gradient of the straight line shown in Fig. 6, we can extract b = 1.5 × 10-9 per L eff in the forward scattering geometry. Thus, assuming L eff = 300 μm, we have η = 5.0 × 10-8 cm-1 as a value per unit length.
Finally, S is defined as,
where ΔΩ is the effective solid angle of scattered light in the WG. So, with ΔΩ= 0.26 sr-1, S is evaluated as 1.9 × 10-7 cm-1 sr-1.
First, let us compare the present efficiency with that of the bulk GaAs in ref 20). From the latter value of 1.27 × 10-7 cm-1 sr-1 at 1.24 μm, we have S = 9.4 × 10-8 cm-1sr-1 at 1.34 μm under study. So, the present value is in good agreement with this value. We remark that a large amount of uncertainty is involved in estimating the present S-value. Particularly, estimation of the coupling efficiency between a lensed fiber and a PC WG contains uncertainty by a factor of 2 in focusing and collecting light, respectively. We note that our value of S is by a factor of 3.5 smaller than a value of 37 × 10-7 cm-1 sr-1 at 1.55 μm for a Si-wire WG .
where ω S, N 0, c and ħ are angular frequency of Stokes Raman scattering, the Bose factor, the velocity of light in vacuum, and Planck constant, respectively; n s represent the effective refractive index at the Stokes frequency. With N 0 = 1.3, n s = 3.5, Δω = 2π × 1.35 × 1011 s-1 and S = 1.9 × 10-7 cm-1sr-1, we have
This value is very consistent with a value of ~ 10 cm/W in ref 23), although the latter one is not a directly observed value, but a deduced one from Raman scattering efficiency observed at 515 nm with help of the wavelength-dispersion in ref. 20). Now, from our value of g, an energy required to excite Raman lasing (SBS) at 1.55 μm can be evaluated for a similar but 4mm-long GaAs PC WG with negligibly small propagation loss . Substituting all relevant values, a value of 2 W (peak power) is obtained to give rise to SRS. This is a very small value, so it should be easily attained. Only thing is that TPA is a problem, because it prevents SRS occurring. It is noted that not only TPA itself but also TPA-induced free-carriers followed by one photon absorption suppress SRS. However, this problem is circumvented by using a sample made of AlxGa1-xAs with x > 0.18, for which a band gap becomes smaller than 760 nm, making TPA substantially neglected; thereby no remarkable free-carriers are excited. It is remarked that in the above the Raman scattering efficiency and the magnitude of g in AlxGa1-xAs with x = 0.2 is postulated to be not much different from that in GaAs.
Finally, let us briefly discuss which is more advantageous to SRS, AlGaAs-based PC WGs or Si-based PC WGs such as a SOI type one. The main advantage of Si-based ones is the compatibility of the fabrication technology with that of current CMOS. However, TPA followed by free-carriers described above is the main disadvantage of Si-based ones. Unlike AlGaAs-based PC WGs, there is not a good way to avoid TPA. Generally speaking, the free-carriers effect is more serious than TPA itself, since the carrier lifetime is very long, say, of the order of ns in Si. So, one of the best ways to suppress free-carrier effect is to remove those by electric field externally applied, although it makes an optical circuit very complicated. In this respect, no doubt AlGaAs-based PC WGs have an advantage over the Si-based ones for the above-mentioned reason. It is noted that even in the case where a small amount of free-carriers are excited, the free-carrier effect in AlGaAs-based ones is much relaxed because of much shorter carrier lifetime in AlGaAs as compared to Si .
We have successfully observed Raman scattering at 1.34 μm in an ultrasmall sample of GaAs-based PC-slab WG of line-defect with a small cross sectional area of 1 × 10-9 cm2 and a short length of 0.6 mm, by using an exciting power inside as weak as 10 μW. As a result, we have estimated the scattering efficiency of 1.9 × 10-7 cm-1sr-1. This fact implies that SRS is within reach at 1.55 μm in a similar but longer (4 mm) PC WG, which greatly benefits by strong confinement of light.
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