UV second harmonic generation in AlN waveguides with modal phase matching

T. Troha; M. Rigler; D. Alden; I. Bryan; W. Guo; R. Kirste; S. Mita; M. D. Gerhold; R. Collazo; Z. Sitar; M. Zgonik

doi:10.1364/OME.6.002014

1. Introduction

Recently, there has been interest in smaller, more efficient, robust and low cost deep UV laser sources for applications in chemical and biological detectors, non-line-of-sight communications, and water purification. The wide bandgap semiconductors GaN, AlN, and their ternary alloys are promising materials for efficient light generation in the deep UV spectral range [1–4]. They possess large thermal conductivity [5] that is also of advantage in electronics applications. Many breakthroughs have been made towards the fabrication of electrically injected deep UV laser diodes (LDs) using the AlGaN system. However, challenges in doping, carrier injection and defect control are still limiting these efforts.

As an alternative, UV laser light generation can be obtained by nonlinear frequency conversion. Conventional materials such as BBO, LBO, PPLN, or OPGaAs offer only limited opportunities for frequency doubling in the UV due to either lower efficiency, high absorption, or challenges in fabrication. The advantage of AlN is in its wide transparency window (0.2 – 14 µm), which allows for highly efficient second harmonic generation (SHG) of laser light down to 200 nm. AlN has three nonzero nonlinear coefficients, d₃₃, d_31, and d₃₃ being the largest one with a value of approximately 5 pm/V [6,7].

There are many methods to achieve phase matching of the pump and SH wave, such as birefringence phase matching [8], coupling-length phase matching [9], quasi phase matching [8,10] and modal dispersion phase matching [8,11–14]. For efficient SH conversion using the latter method, it is essential to combine the waveguide modes with the highest overlap integral. Several works investigated AlN waveguides and low propagation loss of 1.7 dB/ cm was observed [15]. For SHG using modal phase matching in AlN, only very limited data is available [15–17]. All works focused on SHG in the VIS or near IR but no data for SHG in the UV is available. This lack of data for UV SHG in AlN is explained by the fact that the AlN films were almost exclusively deposited by sputtering, where transparency in the UV is compromised by the incorporation of copious point defects [18].

In this study AlN waveguides were grown on sapphire substrates by Metal Organic Chemical Vapor Deposition (MOCVD). They were used for SHG using a modal dispersion phase matching (MDPM) technique.

2. Experimental

The waveguides employed in this study were fabricated from AlN thin films deposited on c-plane sapphire substrates. Films were grown via MOCVD in a vertical, cold-wall reactor. First, a 30 nm thick AlN nucleation layer was deposited at 650°C followed by a 550 nm thick AlN layer deposited at 1100°C in H₂ atmosphere at a total reactor pressure of 20 Torr [19]. Trimethylaluminum (TMA) and NH₃ were used as the aluminum and nitrogen precursors. The samples were patterned post growth with 10 µm wide stripes using standard photolithography and anisotropic plasma etching in a Minilock II reactive ion etcher using an RF power of 100 W and a gas mixture of 25 sccm BCl₃ and 25 sccm Cl₂ under a total chamber pressure of 75 mTorr, leading to 550 nm thick and 10 µm wide Al-polar AlN waveguides.

The AlN waveguides tested in this study were rectangular and are schematically shown in Fig. 1. The coordinate system was chosen with the z-axis perpendicular to the surface of the waveguide and light propagated in the x-direction. Optical measurements of SHG were performed with pump light in the wavelength range between 600 nm and 720 nm. A femtosecond laser system with tunable wavelength was used as a source emitting optical pulses with a duration of 40fs, spectral width of 30 nm (FWHM) and with repetition of 1 kHz. The energy per pulse ranged from 1 to 100 µJ depending on the chosen wavelength. The output beam was focused onto the front face of the waveguide using a lens with a 10 mm focal length. The size of the beam at the waveguide facet was around 10 μm. This is equal to the waveguide width in order to excite dominantly the fundamental mode in the y-direction.

Fig. 1 Cross section of a waveguide consisting of the film with thickness W between media with lower refractive indices. The c-axis of the wurtzite AlN is parallel to the z-axis. The scalar dielectric constants of substrate, waveguide core and air are ε₁, ε₂ and ε₃, respectively.

Download Full Size | PDF

The polarization was chosen such that the TM modes were coupled into the waveguide. The generated SH signal was filtered out from the remaining pump signal and delivered to a detection system consisting of a spectrograph and a photon counting camera. The camera was operated in a gated mode and was synchronized with the femtosecond system.

3. Theoretical background

The planar waveguide approximation was used for the analysis of our measurements [20]. The review of the theory describing SHG in planar waveguides is provided to derive all possible MDPM interactions and to show that some of them can provide very high efficiencies. The waveguide was uniaxial AlN with a relatively low birefringence, which allowed us to use the isotropic approximation. Transverse electric (TE) waves with nonzero components of electromagnetic fields E_y, H_x, H_z and transverse magnetic (TM) solutions with nonzero values of E_z, E_x, H_y are the two families of solutions.

In the TM case, which is relevant for SHG in the AlN waveguides studied in this work, the resulting scalar wave equation is

\nabla^{2} H_{y} + \frac{ε}{c_{0}^{2}} \frac{\partial^{2} H_{y}}{\partial t^{2}} = 0,

where ε denotes the dielectric constant and c₀ the velocity of light in vacuum. The solutions of Eq. (1) are waveguide modes distinguished by the superscript s that are written in the form

H_{y}^{s} (x, z, t) = H_{0}^{s} ψ^{s} (z) e^{i (β^{s} x - ω t)} .

Each mode s propagates with a different propagation constant

β^{s}

and

ψ^{s} (z)

is the transverse distribution of the magnetic field, given in the three media as

\begin{array}{l} ψ_{1}^{s} (z) = η_{1} e^{κ_{1}^{s} z} z \leq 0 \\ ψ_{2}^{s} (z) = \sin (κ_{2}^{s} z + ϕ) 0 \leq z \leq W . \\ ψ_{3}^{s} (z) = η_{3} e^{- κ_{3}^{s} (z - W)} z \geq W \end{array}

In the waveguide,

ψ^{s} (z)

is defined by the sine function whereas in the surrounding layers it decays exponentially. The constants

η_{1}

,

η_{3}

, and ϕ are chosen to satisfy the boundary conditions and

H_{0}^{s}

is the normalization constant. The functions

ψ^{s} (z)

are orthogonal and are normalized as

\int ψ^{s} (z) ψ^{r} (z) d ​ z = δ_{s r} W / 2,

where W denotes waveguide thickness and

δ_{s r}

is the Kronecker delta. The wavevector-components in the z-direction

κ_{1}

,

κ_{2}

and

κ_{3}

are expressed as

\begin{array}{l} κ_{1}^{s} = \sqrt{{(β^{s})}^{2} - k_{0}^{2} ε_{1}}, \\ κ_{2}^{s} = \sqrt{k_{0}^{2} ε_{2} - {(β^{s})}^{2}} ​ and \\ κ_{3}^{s} = \sqrt{{(β^{s})}^{2} - k_{0}^{2} ε_{3}} . \end{array}

The equations above completely define the propagation and structure of the TM modes and the electric fields can be derived from them. We are interested in the nonlinear interaction of modes which are coupled through the nonlinear polarization

{\vec{P}}_{N L} = ε_{0} χ^{(2)} : \vec{E} \vec{E},

where

\vec{E}

denotes the electric field inside the waveguide,

ε_{0}

is the vacuum dielectric permittivity and

χ^{(2)}

is the second-order nonlinear susceptibility tensor. In AlN, the highest nonlinear coefficient is

d_{33}

and we only consider the case where both pump and SH electric fields are polarized in the z-direction. The electric field

E_{z}

of a TM mode is

E_{z} (x, z, t) = \frac{β^{s}}{ω ε ε_{0}} H_{y} (x, z, t) = E_{0}^{s} ψ^{s} (z) e^{i (β^{s} x - ω t)} .

According to Eq. (7),

E_{z}

is proportional to

H_{y}

, therefore the wave equation (Eq. (1) also holds for

E_{z}

. Consequently, the wave equation with the interaction term reads

\nabla^{2} E_{z} - \frac{ε}{c_{0}^{2}} \frac{\partial^{2} E_{z}}{\partial t^{2}} = μ_{0} \frac{\partial^{2} P_{z}^{N L}}{\partial t^{2}},

where

μ_{0}

is the magnetic constant. The total electric field

E = E_{ω} + E_{2 ω}

is the sum of optical waves at the fundamental frequency ω and the second harmonic frequency 2ω. The fields

E_{ω}

and

E_{2 ω}

are in general composed of several modes denoted with indices s and p and are written as

\begin{array}{l} E_{ω} (x, z, t) = \sum_{s} \frac{1}{2} (E_{ω}^{s} (x) ψ_{ω}^{s} (z) e^{i (β_{ω}^{s} x - ω t)} + c . c), \\ E_{2 ω} (x, z, t) = \sum_{p} \frac{1}{2} (E_{2 ω}^{p} (x) ψ_{2 ω}^{p} (z) e^{i (β_{2 ω}^{p} x - 2 ω t)} + c . c .), \end{array}

where

ψ_{ω}^{s} (z)

and

ψ_{2 ω}^{p} (z)

describe transverse distribution of the electric field. Each mode propagates with a different propagation constant denoted by

β_{ω}^{s}

and

β_{2 ω}^{p}

. Usually the propagation constant is expressed with the effective refractive index n_eff that is defined with the relation

β^{s} = k_{0} n_{eff}^{s}

, where k₀ is the vacuum propagation constant. The modal amplitudes of electric fields

E_{ω}^{s} (x)

and

E_{2 ω}^{p} (x)

slowly change with the propagation distance. Using the ansatz from Eq. (10), the nonlinear polarization that oscillates with frequency 2ω is expressed as

P_{2 ω}^{N L} (x, z, t) = \frac{ε_{0}}{4} \sum_{r s} d_{33} E_{ω}^{r} (x) E_{ω}^{s} (x) ψ_{ω}^{r} (z) ​ ​ ​ ψ_{ω}^{s} (z) e^{i ((β_{ω}^{r} + β_{ω}^{s}) x - 2 ω t)} .

Following the standard procedure Eq. (10) is inserted into a nonlinear wave Eq. (8) and solved separately for the frequencies ω and 2ω. For the frequency 2ω, taking into account the non-depleted pump and slowly varying envelope approximation, the following expression is derived

\sum_{p} \frac{\partial E_{2 ω}^{​ ​ p} (x)}{\partial x} ψ_{2 ω}^{p} (z) e^{i β_{2 ω}^{p} x} n_{eff}^{2 ω, p} = \frac{i ω}{2 c_{0}} d_{33} \sum_{r s} E_{ω}^{r} E_{ω}^{s} ψ_{ω}^{r} (z) ψ_{ω}^{s} (z) e^{i (β_{ω}^{r} +}^{β_{ω}^{s}) x} .

In the next step, Eq. (11) is multiplied with

ψ_{2 ω}^{p} (z) e^{- i β_{2 ω}^{p} x}

and integrated over the xz plane. The electric field amplitude of the p-th mode,

E_{2 ω}^{p} (x)

, is then

E_{2 ω}^{p} (x) = \frac{i 4 ω^{2} d_{33}}{3 π c_{0}^{2} n_{eff}^{2 ω, p}} \sum_{r s} E_{ω}^{r} E_{ω}^{s} \sqrt{Γ_{p, r, s}} (\frac{e^{i Δ β_{p, r, s} x} - 1}{i Δ β_{p, r, s}}),

where the fact that transverse field distributions of the waveguide modes are orthonormalized is utilized (Eq. (4). Two terms are introduced, namely the phase mismatch term

Δ β_{p, r, s} = β_{2 ω}^{p} - β_{ω}^{r} - β_{ω}^{s},

and the overlap integral

Γ_{p, r, s} = \frac{9 π^{2}}{16 W^{2}} {[\int ψ_{ω}^{​ ​ r} (z) ψ_{ω}^{s} (z) ψ_{2 ω}^{p} (z) d ​ z]}^{2},

which is a dimensionless quantity normalized to 1 when the three interacting modes perfectly overlap in the transverse direction. Phase matching can be achieved in the multimode optical waveguides by selecting a set of modes p, r, and s giving a zero mismatch

Δ β_{p, r, s} = 0

. In this case,

E_{2 ω}^{p} (x)

increases linearly with the x-coordinate. The power per unit length in y-direction of the p-th waveguide mode at frequency 2ω is then

P_{2 ω}^{p} (x) = \frac{32 ω^{2} d_{33}^{2} ε_{2 ω} n_{eff}^{ω, r} n_{eff}^{ω, s}}{9 π^{2} W ε_{0} c_{0}^{3} ε_{ω}^{2} {(n_{eff}^{2 ω, p})}^{3}} P_{ω}^{​ ​ ​ ​ r} P_{ω}^{s} Γ_{p, r, s} x^{2},

where the optical power per unit length in the y-direction is given as

P_{ω}^{r} (x) = {\int (H_{ω}^{r})}_{y}^{*} {(E_{ω}^{r})}_{z} d z = \frac{ω ε_{0} ε_{ω} W}{2 β_{ω}^{r}} {| E_{ω}^{r} (x) |}^{2} .

Modal dispersion phase matching in materials with normal dispersion relation can be achieved for the combinations p, r, and s that satisfy condition

r \leq s < p or r < s \leq p .

In addition to phase matching, the modes should also have a large overlap. In order to estimate the efficiency of various MDPM combinations, we make the following simplification: if the refractive index of the waveguide core is much larger than that of the surrounding layers, the transverse distributions of the electromagnetic field simplify into sine functions

ψ^{n} (z) = \sin (\frac{π}{W} (1 + n) z),

where n indicates the mode number. The overlap integral is then expressed as

Γ_{r, s, p} = \frac{9 π^{2}}{16 W^{2}} {(\int_{0}^{W} \sin (\frac{π}{W} (1 + r) z) \sin (\frac{π}{W} (1 + s) z) \sin (\frac{π}{W} (1 + p) z) d z)}^{2},

In Table 1, the values of the overlap integral for different combinations r, s, and p satisfying the condition (17) are presented. The perfect confinement of modes in the core is used as estimation of modal overlapping.

Table 1. Approximate values of normalized overlap integrals for different waveguide mode combinations {r, s, p} = {0, 1, 2, 3, 4, 5} for which Eq. (18) is true. Calculations were done in the limit of perfect confinement of modes inside the waveguide core. The experimentally observed combinations are underlined, the combinations with largest Г_r,s,p are highlighted yellow, however, they are not phase-matched in our waveguide.

View Table

In order to show the MDPM conditions, the dispersions of the effective refractive indices of the waveguide modes are presented in Fig. 2 with a common horizontal axis for the pump and SH wavelength. For the calculations, the waveguides were considered planar due to their large width to thickness ratio (18:1). We used the refractive index values for the AlN thin films – that were measured by ellipsometry [21] and extrapolated to UV – and the dispersion relation for sapphire that was reported in the literature [22]. As expected, the SH modes have a higher n_eff, that decreases as the mode order increases. Figure 2 shows n_eff for the two lower-order modes of the pump wavelength, as well as the average value of the two. Both the pump and SH modes show normal dispersion. Dotted lines are added in order to show the limits of n_eff represented by the refractive indices of bulk AlN and sapphire. At wavelengths where the n_eff curves for the pump and SH intersect, the phase matching condition, $Δ β_{r, s, p} = 0$ , is satisfied. Out of all the intersections, the three marked with circles are the ones with a relatively large overlap integral, as seen in Table 1. The other four intersections, labeled with squares, have negligible overlap integrals.

Fig. 2 The dispersions of n_eff for the pump (red dashed lines) and SH (blue solid lines) waveguide modes in AlN waveguide with a thickness of 550 nm. Dotted lines represent the dispersions of the extraordinary refractive indices of bulk AlN [13] and sapphire [14]. At wavelengths where blue and red lines intersect, phase matching occurs. The black circles indicate the MDPM interactions which are responsible for the measured SH signal. The inset schematically shows additional dispersion curves taking into account first excited mode in the y-direction of a rectangular waveguide. The three intersections marked with circles have significant overlap integrals.

Download Full Size | PDF

The use of the planar waveguide approximation can be justified by the following consideration. Firstly, the pump used was a well centered Gaussian beam with a diameter equal to the waveguide width, therefore mainly the y-direction-zero-order mode was excited. The amplitudes of the higher-order modes decrease with increasing order. The situation is similar with higher SH modes where only the low-order modes have to be considered due to very low overlap integrals with the pump. Secondly, due to a large width to thickness ratio the y-direction-low-order modes propagate with n_eff very close to the n_eff of the zero-order mode and therefore do not affect the phase matching intersection points considerably, as is schematically shown in the inset of Fig. 2. Taking into account that solutions for rectangular waveguide would give minimal corrections, we decided to use planar waveguide aproximation.

4. Results and discussion

Figure 3(a) shows a SEM image of an AlN waveguide. The dimension of the front surface was approximately 550 nm × 10 μm, and they were ~2 mm long. The front and top surfaces are almost atomically smooth whereas the side walls exhibit a relatively rough surface and some small curvature. From the set of produced waveguides only the smoothest ones were used for SHG. In Fig. 3(b) HeNe laser light is coupled into the waveguide from the bottom. Scattering can be observed from the front surface and along the waveguide arising from random but low density defects on the top surface, and from the sidewalls.

Fig. 3 a) SEM image of a rectangular AlN waveguide on sapphire substrate. b) Picture taken by a camera above the sample showing light coupling and scattering of a HeNe laser beam. The horizontal scattering line is coming from the sapphire substrate.

Download Full Size | PDF

The results of the SHG measurements are presented in Fig. 4. We observed three main SH peaks at wavelengths of 306 nm, 331 nm and 356 nm that we assign to mode-combinations $2 {TM}_{1}^{ω} \to {TM}_{4}^{2 ω}$ , ${TM}_{0}^{ω} + {TM}_{1}^{ω} \to {TM}_{3}^{2 ω}$ and $2 {TM}_{0}^{ω} \to {TM}_{2}^{2 ω}$ , respectively, marked with circles in Fig. 2.

Fig. 4 Second harmonic generation spectra in AlN waveguides for three different pump wavelengths. The SH response is a consequence of MDPM between the mode combinations $2 {TM}_{1}^{ω} \to {TM}_{4}^{2 ω}$ , ${TM}_{0}^{ω} + {TM}_{1}^{ω} \to {TM}_{3}^{2 ω}$ and $2 {TM}_{0}^{ω} \to {TM}_{2}^{2 ω}$ denoted with circles in Fig. 2. Blue solid curves show the SH spectra and the dashed red curves the pump spectra.

Download Full Size | PDF

The SHG spectra presented in Fig. 4 show some structure in addition to the main peaks. This structure was studied in more detail and is presented in Fig. 5. For the SHG peak at 356 nm, the pump spectrum was varied in the vicinity of the MDPM wavelength in order to observe the change of the structure of the SH response. The maximum power of the SH signal was observed for the pump spectrum with central wavelength at 713 nm (Fig. 5(c)), which is in good agreement with the predicted MDPM. A lower intensity side peak on the shorter wavelength side of the main SH peak can be observed in Figs. 5(a)–5(d). We explain this peak as the nonlinear coupling of the fundamental modes ${TM}_{00}^{ω}$ and ${TM}_{01}^{ω}$ with the SH mode ${TM}_{2 1}^{2 ω}$ , where the second number in subscript defines the number of nodes in the y-direction. The effective refractive index of the y-excited mode is slightly lower than the fundamental mode in the y–direction, therefore a peak is observed at a shorter wavelength. Keeping this in mind one could amend Fig. 2, which is based on the planar waveguide approximation, by adding additional curves for the y-excited modes for both the fundamental and SH modes. The number of intersections increases and additional spectral features may appear, as observed in Fig. 5. Additional support for our explanation comes also from the observation that the SH spectrum varies with focusing and lateral displacement of the pump beam, therefore exciting higher-order modes.

Fig. 5 The SH response in the AlN waveguide at different central wavelengths of the pump wave spectra. The solid blue lines show the spectrum of the SH signals and the dashed red lines show the pump spectra.

Download Full Size | PDF

We estimated the power of UV light that was generated in AlN waveguides. From the input beam with an average power of 1 mW 7% was coupled into the waveguide because of the large waveguide aspect ratio 1:18. Additional losses were caused by reflection at the front surface (~30%) and coupling to the unwanted waveguide modes (~10%). From this we estimated that around 43 μW of the pump power was coupled to the waveguide and could be used for conversion. Inside the waveguide, propagation losses were also observed, mainly due to the scattering from the waveguide side walls, but were negligible in comparison with the coupling losses. By using Eq. (15) we estimated that approximately 100 nW of UV power was generated.

In this study we detected MDPM combinations that can be reached in multimode AlN waveguides on sapphire substrates. Higher SH efficiencies in MDPM combination seem to be possible (0pp, where p = 1, 2, etc. from Table 1). For higher-order modes, however, there exists a cut-off wavelength λ_cut-off. For the fundamental p-mode it is always below the anticipated wavelength where the MDPM would occur. Nevertheless, waveguide fabricated from the materials with appropriate dispersion relation would possibly allow the exploitation of the MDPM with these mode combinations.

5. Conclusions

We demonstrated second harmonic generation into the UV reaching the minimum wavelength of 306 nm by using AlN waveguides grown on a sapphire substrates. Several UV SH peaks were observed and were assigned to phase matching among various waveguide modes. The resulting SH peaks could be well explained by the presented theoretical model for MDPM using the measured refractive index dispersions of the bulk materials. While MDPM offers a relatively low conversion efficiency, this work provided several important findings that will guide future development of the more efficient, quasi phase matching approach in AlN: (1) it confirmed dispersion relations of the refractive indices measured by ellipsometry, (2) it showed that the d₃₃ coefficient could be effectively used for SHG, (3) it confirmed that MOCVD-grown AlN is of sufficient quality and transparency for SHG in the UV range, and (4) that waveguide fabrication used in this study produces sidewalls with minimal losses.

Acknowledgments

Partial financial support from NSF (DMR-1108071, DMR-1312582, ECCS-1508854, DMR-1508191), ARO (W911NF-15-2-0068, W911NF-14-C-0008), and ARRS (N1-0021) is greatly appreciated.

References and links

1. H. Morkoc, Nitride Semiconductors and Devices (Springer, 1999).

2. H. Yoshida, Y. Yamashita, M. Kuwabara, and H. Kan, “A 342-nm ultraviolet AlGaN multiple-quantum-well laser diode,” Nat. Photonics 2(9), 551–554 (2008). [CrossRef]

3. S. Nakamura, M. Senoh, N. Iwasa, and S. Nagahama, “High-power in GaN single-quantum-well-structure blue and violet light-emitting diodes,” Appl. Phys. Lett. 67(13), 1868 (1995). [CrossRef]

4. R. Paschotta, Encyclopedia of Laser Physics and Technology, 1st ed. (Wiley-VCH, 2008)

5. G. A. Slack, R. Tanzilli, R. O. Pohl, and J. W. Vandersande, “The intrinsic thermal conductivity of AIN,” J. Phys. Chem. Solids 48(7), 641–647 (1987). [CrossRef]

6. Y. Fujii, S. Yoshida, S. Misawa, S. Maekawa, and T. Sakudo, “Nonlinear optical susceptibilities of AlN film,” Appl. Phys. Lett. 31(12), 815 (1977). [CrossRef]

7. S. Strite and H. Morkoc, “GaN, AlN and InN: A review,” J. Vac. Sci. Technol. B Microelectron. Nanometer Struct. 10, 1237 (1992).

8. S. Venugopal Rao, K. Moutzouris, and M. Ebrahimzadeh, “Nonlinear frequency conversion in semiconductor optical waveguides using birefringent, modal and quasi-phase-matching techniques,” J. Opt. A, Pure Appl. Opt. 6(6), 569–584 (2004). [CrossRef]

9. I. Biaggio, V. Coda, and G. Montemezzani, “Coupling-length phase matching for nonlinear optical frequency conversion in parallel waveguides,” Phys. Rev. A 90(4), 043816 (2014). [CrossRef]

10. T. Sugita, K. Mizuuchi, Y. Kitaoka, and K. Yamamoto, “31%-efficient blue second-harmonic generation in a periodically poled MgO:LiNbO₃ waveguide by frequency doubling of an AlGaAs laser diode,” Opt. Lett. 24(22), 1590–1592 (1999). [CrossRef] [PubMed]

11. D. B. Anderson and J. T. Boyd, “Wideband CO₂ Laser Second Harmonic Generation Phase Matched in GaAs Thin-Film Waveguides,” Appl. Phys. Lett. 19(8), 266 (1971). [CrossRef]

12. D. Duchesne, K. A. Rutkowska, M. Volatier, F. Légaré, S. Delprat, M. Chaker, D. Modotto, A. Locatelli, C. De Angelis, M. Sorel, D. N. Christodoulides, G. Salamo, R. Arès, V. Aimez, and R. Morandotti, “Second harmonic generation in AlGaAs photonic wires using low power continuous wave light,” Opt. Express 19(13), 12408–12417 (2011). [CrossRef] [PubMed]

13. P. K. Tien, “Light waves in thin films and integrated optics,” Appl. Opt. 10(11), 2395–2413 (1971). [CrossRef] [PubMed]

14. Y. L. Lee, W. Shin, B.-A. Yu, C. Jung, Y.-C. Noh, and D.-K. Ko, “Mode tailoring in a ridge-type periodically poled lithium niobate waveguide,” Opt. Express 18(8), 7678–7684 (2010). [CrossRef] [PubMed]

15. W. H. P. Pernice, C. Xiong, C. Schuck, and H. X. Tang, “Second harmonic generation in phase matched aluminum nitride waveguides and micro-ring resonators,” Appl. Phys. Lett. 100(22), 223501 (2012). [CrossRef]

16. P. M. Lundquist, W. P. Lin, Z. Y. Xu, G. K. Wong, E. D. Rippert, J. A. Helfrich, and J. B. Ketterson, “Ultraviolet second harmonic generation in radio‐frequency sputter‐deposited aluminum nitride thin films,” Appl. Phys. Lett. 65(9), 1085 (1994). [CrossRef]

17. D. N. Hahn, G. T. Kiehne, J. B. Ketterson, G. K. L. Wong, P. Kung, A. Saxler, and M. Razeghi, “Phase-matched optical second-harmonic generation in GaN and AlN slab waveguides,” J. Appl. Phys. 85(5), 2497 (1999). [CrossRef]

18. D. Blanc, A. M. Bouchoux, C. Plumereau, A. Cachard, and J. F. Roux, “Phase-matching frequency doubling in an aluminum nitride waveguide with a tunable laser source,” Appl. Phys. Lett. 66(6), 659 (1995). [CrossRef]

19. A. Rice, R. Collazo, J. Tweedie, R. Dalmau, S. Mita, J. Xie, and Z. Sitar, “Surface preparation and homoepitaxial deposition of AlN on (0001)-oriented AlN substrates by metalorganic chemical vapor deposition,” J. Appl. Phys. 108(4), 043510 (2010). [CrossRef]

20. K. Kawano and T. Kitoh, Introduction to Optical Waveguide Analysis: Solving Maxwell’s Equation and the Schrodinger Equation (Wiley-Interscience, 2001)

21. M. Rigler, J. Buh, M. P. Hoffmann, R. Kirste, M. Bobea, S. Mita, M. D. Gerhold, R. Collazo, Z. Sitar, and M. Zgonik, “Optical characterization of Al- and N-polar AlN waveguides for integrated optics,” Appl. Phys. Express 8(4), 042603 (2015). [CrossRef]

22. M. Bass, V. N. Mahajan, and E. W. Van Stryland, Handbook of Optics - Design, Fabrication, and Testing; Sources and Detectors; Radiometry and Photometry, 3rd ed. (McGraw-Hill, Inc. 2010)

r s p	Г_r,s,p	r s p	Г_r,s,p	r s p	Г_,r,s,p
0 0 0	1	0 5 5	0.6	2 3 5	0.22
0 0 2	0.04	0 6 6	0.6	2 4 4	0.08
0 0 4	0.0008	1 1 2	0.30	2 4 6	0.22
0 0 6	0.00009	1 1 4	0.07	2 5 5	0.07
0 1 1	0.6	1 1 6	0.0027	2 6 6	0.07
0 1 3	0.05	1 2 3	0.28	3 4 4	0.06
0 1 5	0.0015	1 2 5	0.08	3 3 6	0.21
0 2 2	0.6	1 3 4	0.27	3 4 5	0.05
0 2 4	0.06	1 3 6	0.08	3 5 6	0.048
0 2 6	0.0018	1 4 5	0.26	4 4 6	0.044
0 3 3	0.6	1 5 6	0.26	4 6 6	0.030
0 3 5	0.06	2 2 4	0.24	5 5 6	0.026
0 4 4	0.57	2 2 6	0.09
0 4 6	0.06	2 3 3	0.08

UV second harmonic generation in AlN waveguides with modal phase matching

Abstract

1. Introduction

2. Experimental

3. Theoretical background

4. Results and discussion

5. Conclusions

Acknowledgments

References and links

Cited By

Figures (5)

Tables (1)

Equations (19)

Optical Materials Express