Spatial mode behavior of second harmonic ...

REGULAR PAPER

Japanese Journal of Applied Physics 53, 062201 (2014) http://dx.doi.org/10.7567/JJAP.53.062201

Spatial mode behavior of second harmonic generation in a ridge-type waveguide with a periodically poled MgO-doped lithium niobate crystal Jun-Hee Park*, Tai-Young Kang, Jeong-Ho Ha, and Han-Young Lee Korea Electronics Technology Institute, Seongnam, Gyeonggi 463-816, Korea E-mail: [email protected] Received October 29, 2013; accepted April 1, 2014; published online May 20, 2014 We report on spatial mode behavior of the second harmonic (SH) generated by nonlinear interaction in the a z-cut Mg-doped periodically poled LiNbO3 (MgO:PPLN) ridge-type waveguide. Specific SH modes were selectively generated by mode mixing of the fundamental harmonic (FH) waves. In addition, high-order SH modes TM10 and TM01 were simultaneously generated under similar phase-matching conditions in a quasi-phase matching (QPM) grating structure. The interfered mode profiles of high-order SH modes demonstrated specific mode distribution to have a diagonal angle and the Laguerre–Gaussian (LG) mode at a certain phase-matching condition obtained by temperature control. © 2014 The Japan Society of Applied Physics

1.

Introduction

Continuous-wave (CW) visible light sources are of interest in various industrial areas such as display technologies, optical data storage, material processing, and biomedical applications. One of attractive methods to obtain a visible light source is quasi-phase matching (QPM) second harmonic generation (SHG) technology in a periodically poled lithium niobate (PPLN) crystal. Waveguide-integrated QPM SHG is a strongly beneficial technology to realize optical devices in practice by taking advantage of its long interaction length, strong light confinement, and controllability of propagation modes. Recent researches on this technology have focused on achieving high conversion efficiency.1,2) The key points for obtaining efficient and high-power SHG waveguide devices include the confinement of the fundamental wave (FH) into the waveguide and the good overlap of the fundamental and second harmonic (SH) modes. Although the fundamental SH modes generally provide the best conversion efficiency, high-order SH modes are also currently being focused on owing to their unique physical properties and promising applications such as optical tweezers,3,4) orbital angular momentum,5,6) optical frequency mixers,7–9) and particularly multi-mode quantum information with high-order SH mode interference.10–14) In this paper, we present the spatial mode behavior of SHG in a z-cut MgO:PPLN crystal integrated in a ridge-type waveguide. The fundamental and high-order SH modes were obtained from selectively satisfied phase-matching conditions in a ridge-type waveguide with a QPM structure. Theoretical and experimental results verified that mode mixing with the FH mode contributes to the SH mode generation. High-order SH modes generated from an integrated QPM ridge-type waveguide demonstrated the specific mode interference between the two spatially orthogonal SH modes, TM2! 10 and TM2! 01 . The two modes were observed to be simultaneously generated and closely overlapped by crystal temperature adjustment which allowed intentional control of the phase difference between high-order SH modes. 2. High-order SH mode generation in a ridge-type PPLN waveguide

Consider fundamental and high-order SH mode generation with phase-matching conditions in a multimode waveguide

with a periodically poled QPM structure and coupling coefficient ©.15,16) The electric fields E2½ of frequency 2½ of the m-th SH mode can be expressed as 2! E2! ðx; y; zÞ ¼ A2! m ðzÞEm ðx; yÞ expðjm zÞ;

ð1Þ

is the normalized mode profile satisfying where E2! m ð1=2Þ E2! H2! m m ¼ 1 and ¢m is the propagation constant of the m-th mode. We then obtain the well-known coupled mode equation between FH and SH as d 2! A ðzÞ dz m ! Z Z 2! E2! ¼ j m ðx; yÞ expðjm zÞP ðx; y; zÞ dx dy; ð2Þ 2 where P 2½ is the nonlinear polarization for SHG with frequency 2½ and can be written as P2! ¼ 2"0 deff ðE! Þ2 :

ð3Þ

We can also define the electric field E½ of frequency ½ in the waveguide as the combination of guided FH modes as X E! ðx; y; zÞ ¼ A!n ðzÞEn ðx; yÞ expðjn zÞ: ð4Þ n

Using Eqs. (3) and (4), Eq. (2) can be transformed to the coupled-mode equation, which describes the contribution of FH wave (combination of p-th and q-th guided modes) to the specific m-th SH mode generation as d 2! A ðzÞ ¼ jA!p ðzÞA!q ðzÞ expðjzÞ; dz m

ð5Þ

where ¼ ð2 pq Þ!"0 deff ZZ ! ! E2! m ðx; yÞ½Ep ðx; yÞEq ðx; yÞ dx dy; 1 if p ¼ q ; pq ¼ 0 if p 6¼ q ! ! ¼ 2! m p q :

ð6Þ ð7Þ ð8Þ

Equation (6) explains that, the non-linear coupling coefficient © can be increased in proportion to an overlap integral of SH modes and the non-linearity proportionally. In addition, the equation implies that the SH modes can be generated through a high conversion process by efficient mixing

062201-1

© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 062201 (2014)

J.-H. Park et al.

Fig. 2. Schematic view of the experimental setup for the blue-light emission by SHG with a tunable laser.

Fig. 1. (Color online) Microscope images of the ridge-type waveguide: (a) cross-sectional view and (b) top-view. For this sample H = 7.5 µm, hridge = 5.5 µm, and width W = 5 µm.

between the FH modes E!p and E!q , which should have intensity profiles similar to the generated SH modes with a high overlap integral. A waveguide-integrated QPM structure for 460 nm SHG was fabricated from a 500-µm-thick z-cut 5 mol % MgO:LN wafer. The wafer was polished down to 150 µm thickness prior to a periodical poling process, as described in Ref. 17. The periodic poling was performed in a poling jig with electrolyte electrodes at room temperature by applying an external electric voltage of 0.7 kV during 120 ms. The duty cycle of the poling structure was very close to 50%, which was determined by observation of the poled sample under a polarization microscope and which was confirmed by optical microscopic observation of the sample after chemical wetetching treatment. Subsequently, the periodically poled and 150-µm-thick sample, which was bonded to a dummy LN substrate for easy handling and bottom cladding function, was thinned down to 7.5 µm by polishing to have thickness uniformity better than 0.1 µm. Thickness monitoring was paralleled during the polishing process. The 7.5 µm thick wafer was dry-etched using a modified reactive ion etching (RIE) technique to form several dimensions of ridgetype waveguides with 5.5 µm ridge height and different widths. The 2-µm-thick residual slab was not etched for better sample reliability, higher physical stability and lower optical propagation loss of ridge-type waveguides. Finally, the poled, thinned, and dry-etched sample was covered by another LN substrate to form an upper cladding layer. Figure 1 shows microscope images of the fabricated ridgetype waveguides. In this experiment, we used a z-cut MgO:PPLN ridge-type waveguides, with a period of ª = 4.3 µm, satisfying the quasi-phase matching condition of ¦¢ = 2³/ª in Eq. (8);

poled region of 11 mm and a total crystal length and 12 mm. The insertion loss of these waveguides was 2.85 dB, the value of which incorporated a propagation loss of 0.64 dB/cm measured by the cut-back method involving a set of waveguides of varying lengths as well as a coupling loss of an incident beam to the waveguide. Both facets of the waveguide were cut at 5.4° and optically polished and uncoated for the fundamental and SH wave. During the SHG test of blue light generation, a continuous-wave diode-pumped solid-state Ti:Sapphire tunable ring laser was used as the fundamental light source at 920 nm, which was coupled into a ridge-type waveguide through a single-mode polarizationmaintaining fiber (Nufern PM980-XP). The polarization state of the fundamental light incident to the waveguides was set at the TM field in order to achieve maximum coupling efficiency. The waveguide chip was placed on a temperaturecontrolled plate with 0.1 °C controllability, which was used to set the QPM temperature of each waveguide for maximal conversion efficiency. The FH wave was subsequently transmitted to the fabricated PPLN ridge-type waveguides and the output beam was focused to a beam analyzer using an objective lens and IR cut filter. Near-field images of generated SH waves were recorded on a charge coupled device (CCD) as shown in Fig. 2. The waveguides were tested under various conditions of fundamental light wavelength and crystal temperatures, and the IR light was coupled to the waveguide positioned with a six-axis controller. In a multimode waveguide, it was difficult to confirm the specific mode characteristics owing to the interference of other occupied modes. However, wavelength conversion waveguides using second harmonic generation could measure the specific mode characteristic because the SH modes can be selectively generated at the QPM condition tuned by the external factors of fundamental light wavelength and crystal temperature. To confirm the specific mode propagation in the fabricated MgO:PPLN ridge-type waveguide, incident IR light wavelength was adjusted for the SH mode propagation because each mode satisfies a different phase-matching condition. Figure 3 shows various CCD images of the normalized fundamental and high-order SH modes, exhibiting a measured pumping light wavelength around 920 nm, and simulation results calculated by the finite element method (FEM) of the SHG process for mixing of the first harmonic wave. The measured and simulated SH mode images showed similar SH mode patterns, which verifying the good agreement between measured and simulated results. The fundamental SH mode, TM2! 00 , showed the maximum output power of 1.2 mW at 921.5 nm with a pumping

062201-2


Jpn. J. Appl. Phys. 53, 062201 (2014)

J.-H. Park et al.

(a)

(b)

Fig. 3. (Color online) Diagrams of fundamental and high-order mode generation and normalized CCD images. The blue and black background images indicate simulation and observed experimental results, respectively.

power of 66 mW and normalized conversion efficiency of 22.8%/(W0cm2) [1.41 mW blue internal power with 35.7%/ 2! (W0cm2)].18) In addition, both the TM2! 10 and TM01 modes were generated around FH wavelength 923 nm, while 2! TM2! 20 and TM11 were generated at 924.5 and 923.35 nm, respectively. The measured maximum output powers of high-order SH modes were 0.34, 0.86, 0.048, and 0.024 mW, respectively at the identical pumping. High-order SH mode generation in the waveguide is the result of fundamental and high-order mode mixing of the FH wave. The efficiencies of the high-order SH modes are relatively lower than the standard fundamental SH mode owing to the nonstandard pump input coupling to excite a mode combination and poor stability caused by the high-order SH mode interference. TM2! 11 showed a phase-matching condition process different from the high-order SH modes due to the fundamental mode contribution of the FH wave in the ridge-type waveguide. Unlike the previous high-order SH modes in Figs. 3(b)–3(d), TM2! 11 originated from high-order mode mixing of TM!10 and TM!01 in Fig. 3(e), which satisfied the QPM grating period of ª = 4.3 µm, as Eq. (8). In addition, the high-order SH mode TM2! 11 was expected to appear at a longer FH wavelength than TM2! 20 , but owing to the highorder FH modes’ mixing characteristic, the TM2! 11 phasematching condition was obtained at shorter FH wavelength than TM2! 20 . The significant difference between the conver2! sion efficiencies of TM2! 10 and TM01 was due to an effect of the higher overlap integral of TM2! 01 compared to the fundamental FH mode. Similarly, the conversion efficiency 2! difference of TM2! 20 and TM11 resulted from the relatively higher overlap integral to the fundamental FH mode. 3. Interfered SH mode generation in a ridge-type PPLN waveguide

The dependence of the QPM curve on the temperature

Fig. 4. (Color online) Conversion efficiencies of the SH wave. (a) Fundamental SH mode conversion efficiency at 921.5 nm and (b) TM2! 10 and TM2! 01 mode conversion efficiencies as a function of temperature at an FH wavelength of 923 nm.

of MgO:PPLN crystal is shown in Fig. 4. The temperature full width at half-maximum (FWHM) of the fundamental and both the SH high-order modes was 1.2 °C. Since the phasematching conditions of the two high-order SH modes are overlapped, as shown in Fig. 4(b), the characterization of one mode should be performed while minimizing the other mode by adjusting fundamental light coupled to the waveguide position and monitoring mode image through CCD not to be interfered by the other mode, which will enable the determination of the amplitudes of the FH mode propagating in the waveguides. These overlapped phase-matching conditions between two SH high-order modes mean that ¢10 and ¢01 at both wavelengths ½ and 2½ should be similar, which is determined by the geometry and dimension of a ridge-type waveguide structure. To confirm the similarity between the two mode characteristics, we calculated the phase-matching conditions of both modes. The ridge-type waveguide was modeled by the Sellmeier equation for MgO:PPLN given by.19) Subsequently, the effective index for each mode was calculated using a FEM. Through Eq. (8), we obtained the FH wavelengths to be quasi-phase matched with the SH in the 4.3 µm periodically poled structures. The results are summarized in Table I and show a good agreement with the experiment results in Figs. 3(a)–3(c). Figure 4(b) shows that the ampli2! tude ratio of TM2! 10 and TM01 modes can be determined by temperature tuning. Thus we can express the spatial mode distribution of the total SH modes as a function of temperature change as

062201-3


Jpn. J. Appl. Phys. 53, 062201 (2014)

J.-H. Park et al.

Table I. Calculated effective indices and phase-matching wavelengths for each mode in the ridge-type waveguide with poling period ª = 4.3 µm to show the characteristics in Figs. 3(a)–3(c). ! NTM 00

2.154338

! NTM 10

2.151918

! NTM 01

2.151546

2! NTM 00

2.261481

2! NTM 10

2.260436

2! NTM 01

2.260252

TM00 (nm) TM10 (nm)

921.46 922.84

TM01 (nm)

923.13

at which the conversion efficiency of TM2! 01 was relatively very low. We can expect to have diagonally distributed mode profiles at temperatures between those for a vertically distributed mode profile and horizontally distributed mode profile. As expected, the diagonally distributed modes were generated at 24.4 and 25.4 °C, respectively as shown in Figs. 5(a) and 5(b), in which two modes had similar amplitudes that are confirmed from the results in Fig. 4(b). However, the two diagonally distributed mode profiles are spatially orthogonal because the phase of TM2! 01 lags by ³ at 25.4 °C, at which the amplitude of TM2! 01 is minimum owing to phase-mismatch. The Laguerre–Gaussian (LG) mode profile was generated around FH wavelength 923 nm from the combination of 2! 20) two Hermite–Gaussian (HG) modes, TM2! 10 and TM01 . Figure 5(c) shows the process of LG mode generation with a phase difference of ³/2 from two high-order SH modes. The conversion efficiencies of two modes in Fig. 4(b) shows that 2! TM2! 10 and TM01 were simultaneously generated in satisfying the phase-matching condition at 23.8 °C, at which TM2! 10 had a phase lag of ³/2 with respect to TM2! , which contributed 01 to LG mode generation. 4.

Fig. 5. (Color online) Diagram of interfered mode generation and normalized CCD images. Both (a) and (b) show diagonally declined mode profiles, and (c) shows the LG mode profile. The blue and black background images indicate simulation and observed experimental results, respectively.

2! 2! 2! E2! ðx; yÞ ¼ A2! TM10 ðTÞETM10 ðx; yÞ þ ATM01 ðTÞETM01 ðx; yÞ; ð9Þ 2! where A2! TM10 and ATM01 are the complex amplitudes of the 2! 2! TM10 and TM01 modes respectively. Equation (9) implies that the profile of the generated SH mode distribution is affected by the temperature. To confirm the interfered pattern change of the SH output mode resulting from temperature tuning, the incident IR light was coupled to the waveguide at a specific position where the maximum 2! SH intensity in both TM2! 10 and TM01 modes were similar. Then, the SHG measurements were performed for a 923 nm SH wave. Figure 5 shows the simulation and the measurement results that describe the processes of interfered mode generation and normalized SH mode profiles generated from the interference 2! between two modes, TM2! 10 and TM01 . The results of Fig. 5 can be understood clearly by considering that the transverse distribution is determined by the amplitude ratio and the phase difference between the two modes, and these are changed by altering the temperature, as shown in Fig. 4(b). The vertically distributed mode profiles in Fig. 3(c) were obtained at 23.4 and 26.0 °C, where the conversion efficiencies of TM2! 10 mode were nearly zero. On the other hand, the mode profile of TM2! 10 obtained at a temperature of 25.2 °C was horizontally distributed as shown in Fig. 3(b),

Summary

In summary, we have successfully demonstrated spatial mode behavior in a fabricated z-cut MgO:PPLN ridge-type waveguide using second harmonic generation around a 460 nm wavelength region. The fundamental and high-order SH modes were selectively generated through mode mixing in FH waves and specific phase-matching conditions in a QPM grating structure. In addition, we have shown spatial mode interference between high-order SH modes, TM2! 10 and TM2! , the phase-matching conditions of which were close to 01 each other and overlapped. The experimental results suggest that SH modes can be simultaneously generated at a specific temperature range and that the power ratio of the two generated modes can be altered by temperature tuning. Finally, we can obtain the phase-matching condition by temperature change for the interfered SH mode distribution having diagonally declined angle and LG mode owing to the phase difference between the two SH modes. Acknowledgement

This research was supported by Ministry of Trade, Industry and Energy (MOTIE), as a project, “Development of Coherent optical transmitter and receiver component technologies (2010-GU-TD-200408-001)”.

1) S. Kurimura, Y. Kato, M. Maruyama, Y. Usui, and H. Nakajima, Appl. Phys. Lett. 89, 191123 (2006). 2) R. Kou, S. Kurimura, K. Kikuchi, A. Terasaki, H. Nakajima, K. Kondou, and J. Ichikawa, Opt. Express 19, 11867 (2011). 3) D. W. Zhang and X.-C. Yuan, Opt. Lett. 28, 740 (2003). 4) M. J. Snadden, A. S. Bell, R. B. M. Clarke, E. Riis, and D. H. McIntyre, J. Opt. Soc. Am. B 14, 544 (1997). 5) K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742(R) (1996). 6) J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997). 7) J. R. Kurz, J. Huang, X. Xie, T. Saida, and M. M. Fejer, Opt. Lett. 29, 551 (2004). 8) V. Delaubert, M. Lassen, D. R. N. Pulford, H.-A. Bachor, and C. C. Harb,

062201-4


Jpn. J. Appl. Phys. 53, 062201 (2014)

J.-H. Park et al.

Opt. Express 15, 5815 (2007). 9) J. R. Kurz, K. R. Parameswaran, R. V. Roussev, and M. M. Fejer, Opt. Lett. 26, 1283 (2001). 10) M. Lassen, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett. 102, 163602 (2009). 11) M. Lassen, V. Delaubert, J. Janousek, K. Wagner, H.-A. Bachor, P. K. Lam, N. Treps, P. Buchhave, C. Fabre, and C. C. Harb, Phys. Rev. Lett. 98, 083602 (2007). 12) M. T. L. Hsu, W. P. Bowen, and P. K. Lam, Phys. Rev. A 79, 043825 (2009). 13) J. Janousek, K. Wagner, J.-F. Morizur, N. Treps, P. K. Lam, C. C. Harb, and H.-A. Bachor, Nat. Photonics 3, 399 (2009). 14) K. Wagner, J. Janousek, V. Delaubert, H. Zou, C. Harb, N. Treps, J.-F.

Morizur, P. K. Lam, and H.-A. Bachor, Science 321, 541 (2008). 15) J. R. Kurz, X. P. Xie, and M. M. Fejer, Opt. Lett. 27, 1445 (2002). 16) T. Suhara and M. Fujimura, Waveguide Nonlinear-Optic Devices (Springer, New York, 2003) Chap. 2. 17) S. W. Kwon, W. S. Yang, H. M. Lee, W. K. Kim, H.-Y. Lee, W. J. Jeong, M. K. Song, and D. H. Yoon, Appl. Surf. Sci. 254, 1101 (2007). 18) M. Iwai, T. Yoshino, S. Yamaguchi, M. Imaeda, N. Pavel, I. Shoji, and T. Taira, Appl. Phys. Lett. 83, 3659 (2003). 19) D. E. Zelmon, D. L. Small, and D. Jundit, J. Opt. Soc. Am. B 14, 3319 (1997). 20) Y. L. Lee, W. Shin, B.-A. Yu, C. Jung, Y.-C. Noh, and D.-K. Ko, Opt. Express 18, 7678 (2010).

062201-5
