Simultaneous perfect phase matching for second and third harmonic generations in ZnS/YF<sub>3</sub> photonic crystal for visible emissions

doi:10.1364/OE.14.012353

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Simultaneous perfect phase matching for second and third harmonic generations in ZnS/YF₃ photonic crystal for visible emissions

Weixin Lu, Ping Xie, Zhao-Qing Zhang, George K. L. Wong, and Kam S. Wong »View Author Affiliations

Optics Express, Vol. 14, Issue 25, pp. 12353-12358 (2006)
http://dx.doi.org/10.1364/OE.14.012353

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– Abstract
1. Introduction
2. The method of simulation
3. The experiment results compared with the simulation
4. Conclusion
– References and links

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Abstract

Theoretically designed and experimentally realized simultaneous perfect phase matching of second and third harmonic generations were demonstrated in a one-dimensional ZnS/YF₃ photonic crystal (PC) structure. Dramatic enhancement of second harmonic generation (SHG) and third harmonic generation (THG) in forward and backward directions near the photonic band edge were observed. This enhancement came from a combination of large ZnS nonlinear susceptibility coefficients, high density of optical modes and perfect phase matching of the fundamental and the harmonic waves near the photonic band edge due to modification of the dispersion curve by the PC structure. Total SHG and THG conversion efficiency over 4% is measured in only six micrometers length of photonic crystal. Theoretical calculations show good agreement with experimental measurements.

1. Introduction

The photonic crystals (PCs) have been extensively studied over the last decade [1–2

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]

]. The photonic band gaps of the PCs attracted the most attentions because of confining and controlling the propagation of photons in these materials, leading to many potential applications [3

Photonic crystals: physics, fabrication and applications , edited by K. Inoue and K. Ohtaka (Springer Verlag, Berlin, 2004)

]. In the last few years, the study of nonlinear optical properties such as the second harmonic generation (SHG) and the third harmonic generation (THG) is of particular interest in PCs [4

Nonlinear Photonic Crystals , edited by R. E. Slusher and B. J. Eggleton (Springer, Berlin 2003)

]. It is well known that for harmonic generation, the phase matching between pump laser and the harmonics signals is an important condition. Traditionally birefringent crystal or quasi-phase matching structures are used to satisfy the condition [5–7

H. Cheng and P. B. Miller, “Nonlinear Optical Theory in Solids,” Phys. Rev. 134, A683–A687 (1964). [CrossRef]

]. However, one-dimension (1-D) PC structures, which use spatial modulation of the linear refractive index, are similar as the quasi-phase matching schemes which use modulation of the nonlinear susceptibility as quasi-phase matching interaction for efficient SHG. In PCs, if the parts of sign reversion of the nonlinear materials are replaced by linear materials to compensate the dispersion of nonlinear materials, the phase matching condition for harmonic generation in terms of an effective index of refraction can be satisfied [8–11

M. Centini, M. Scalora, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Dispersive properties of one-dimensional photonic band gap structures for second harmonic generation,” J. Opt. A: Pure Appl. Opt. 2, 121–126 (2000). [CrossRef]

]. Thus, any material with large nonlinear susceptibility such as some semiconductors can be used and birefringent and/or ferroelectric effects are dispensable as long as it is transparent in wavelengths of interest. Another remarkable property of the PC structure is associated with the transmission resonance that appears near to the band gap, where the optical field is strongly confined which consequently further enhances the harmonic generation. Thus well-designed semiconductor-based PCs with thickness of a few microns can produce a dramatic enhancement of harmonic signals near the photonic band edge.

The enhancement of second harmonic generation (SHG) or third harmonic generation (THG) have been shown in the theory and the experiments in 1-D PCs for several years[11–15

Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D. Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001). [CrossRef]

]. The SHG in GaAlAs/AlAs PC structure was reported by Dumeige et al. [11

]. However, in this 1-D PC structure the phase matching cannot be realized and the conversion efficiency is only 10^-4 %. The optical field enhancement at fundamental frequency near the photonic band edge enhance the SHG in the visible spectral region was shown in the ZnS/SrF2 periodic structure [14

A. V. Balakin, V. A. ushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “Enhancement of second-harmonicgeneration with femtosecond laser pulses near the photonicband edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999). [CrossRef]

]. More recently, we have demonstrated efficient SHG in ZnSe-based PC due to both good phase matching and optical field enhancement at the photonic band edge [16

H. Yang, P. Xie, S. K. Chan, Z. Q. Zhang, I. K. Sou, G. K. L. Wong, and K. S. Wong, “Efficienct second harmonic generation form large band gap II–VI semiconductor photonic crstal”, Appl. Phys. Lett. 97, 131106 (2005). [CrossRef]

]. Usually, a cascaded two-step process based on χ⁽²⁾ for THG (i.e., sum frequency generation between the second harmonic light with the fundamental to produce the third harmonic wavelength) was used to get the third harmonic (TH) signal, because of the low conversion efficiency of the direct THG based on χ⁽³⁾ [17

Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, New York 1984)

]. However, large enhancement of direct THG as the result of perfect phase matching and optical field enhancement near the band edge was recently demonstrated in polymer-based PCs [18

P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, Nick N. Lepeshkin, and Robert W. Boyd, “Dramatic Enhancement of Third-Harmonic Generation in Three-Dimensional Photonic Crystals,” Phys. Rev. Lett. 92, 083903 (2004). [CrossRef] [PubMed]

]. Theoretically, the simultaneous enhancement of SHG and THG via perfect phase matching has been shown to be possible in 1-D PC [12

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. E 64, 046606 (2001). [CrossRef]

, 13

V. V. Konotop and V. Kuzmiak, “Simultaneous second- and third-harmonic generation in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 16, 1370–1376 (1999). [CrossRef]

], however, no convincing experimental confirmation of this effect were demonstrated. Although simultaneous SHG and THG were seen in ZnSe/ZnMgS PC [19

Hui Yang, Ping Xie, S. K. Chan, Weixin Lu, Zhao-Qing Zhang, I. K. Sou, George K. L. Wong, and K. S. Wong, “Simultaneous enhancement of the second- and third-harmonic generations in one-dimensional semicounductor photonic crystals”, IEEE Quantum Electronic , 42, 447–451 (2006) [CrossRef]

], the THG in this case is largely due to field enhancement effect and the strong absorption of electronic bandgap of ZnSe limited the harmonic generations above the green spectral region.

In this paper, we demonstrate a dramatic enhancement of the SHG and THG in a 1-D PC structure. The perfect phase matching condition for SHG and THG are simultaneously satisfied in this PC. In addition to the localization enhancement effect of the electromagnetic field near the photonic band edge, the high conversion efficiency of SHG and THG are realized simultaneously for forward and backward directions. The total conversion efficiency of ~4% was obtained in a PC structure composed of ZnS/YF₃ multilayer of only a few microns in total thickness. The theoretical simulation of the spectral response and conversion efficiency of the SHG and THG from this PC structure by the transfer-matrix method [20–21

D. S. Bethune, “Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques,” J. Opt. Soc. Am. B 6, 910–916 (1989). [CrossRef]

] are in reasonable agreement with the experimental results.

2. The method of simulation

Consider a 1D nonlinear PC with N periods. One layer in each period is linear, with the refractive index n ₀ and width l ₀. The other layer is nonlinear, with the weak-field refractive index n, a second-order nonlinear susceptibility χ⁽²⁾ and a third-order susceptibility χ⁽³⁾. The width of the nonlinear layer is l. A pump wave Ẽ ₁ of frequency ω is incident ormally upon the sample along z axis. Due to the χ⁽²⁾ and χ⁽³⁾ nonlinearity, a SH wave and a TH wave can be generated. We represent the fundamental, the SH and the TH waves by Ẽ ₁(z, t)=E ₁(z)e ^-iωt+c.c., Ẽ ₂(z, t)=E ₂(z)e ^-2iωt+c.c. and Ẽ ₃(z, t)=E ₃(z)e ^-3iωt+c.c., where E_α (z, t)=

E_{α}^{+}

(z)+

E_{α}^{-}

(z) and

E_{α}^{\pm} (z) = A_{α}^{\pm} (z) e^{\pm i k_{α} z}

(α=1, 2, 3). Here

E_{α}^{+}

and

E_{α}^{-}

denote the forward and backward propagating components, respectively. Assuming

A_{α}^{\pm} = B_{α}^{\pm} e^{i κ_{α} z}

(α=1, 2, 3) in a nonlinear layer, the coupled wave equations for the fundamental, the SH and the TH waves are described as follows:

\frac{d B_{1}^{\pm}}{d z} = \pm i \frac{4 π ω}{n (ω) c} χ^{(2)} (B_{1}^{\pm *} B_{2}^{\pm} e^{\pm i Δ {k_{1}}^{'} z} + B_{2}^{\pm *} B_{3}^{\pm} e^{\pm i Δ {k_{2}}^{'} z}) \pm i \frac{6 π ω}{n (ω) c} χ^{(3)} (B_{1}^{\pm *^{2}} B_{3}^{\pm} e^{\pm i Δ {k_{3}}^{'} z} + B_{2}^{\pm^{2}} B_{3}^{\pm *} e^{\mp i Δ {k_{4}}^{'} z}),

(1a)

\frac{d B_{2}^{\pm}}{d z} = \pm i \frac{4 π ω}{n (2 ω) c} χ^{(2)} (B_{1}^{\pm 2} e^{\mp i Δ {k_{1}}^{'} z} + {2 B}_{1}^{\pm *} B_{3}^{\pm} e^{\pm i Δ {k_{2}}^{'} z}) \pm i \frac{24 π ω}{n (2 ω) c} χ^{(3)} B_{1}^{\pm} B_{2}^{\pm *} B_{3}^{\pm} e^{\pm i Δ {k_{4}}^{'} z},

(1b)

\frac{d B_{3}^{\pm}}{d z} = \pm i \frac{12 π ω}{n (3 ω) c} χ^{(2)} B_{1}^{\pm} B_{2}^{\pm} e^{\mp i Δ {k_{2}}^{'} z} \pm i \frac{6 π ω}{n (3 ω) c} χ^{(3)} (B_{1}^{\pm^{3}} e^{\mp i Δ {k_{3}}^{'} z} + {3 B}_{1}^{\pm *} B_{2}^{\pm^{2}} e^{\mp i Δ {k_{4}}^{'} z}),

(1c)

where Δk ₁′=(k ₂-2k ₁)+(κ ₂-2κ ₁), Δk ₂′=(k ₃-k ₁-k ₂)+(κ ₃-κ ₁-κ ₂), Δk ₃′=(k ₃-3k ₁)+(κ ₃-3κ ₁), Δk ₄′=(k ₃+k ₁-2k ₂)+(κ ₃+κ ₁-2κ ₂) denote the phase mismatches in the case of strong field. The parameters κ_α(α=1,2,3) are defined as

κ_{1} = \frac{6 π ω}{n (ω) c} χ_{Kerr}^{(3)} (ω) [{∣ E_{1} ∣}^{2} + 2 {∣ E_{2} ∣}^{2} + 2 {∣ E_{3} ∣}^{2}]

κ_{2} = \frac{12 π ω}{n (2 ω) c} χ_{Kerr}^{(3)} (2 ω) [{2 ∣ E_{1} ∣}^{2} + {∣ E_{2} ∣}^{2} + 2 {∣ E_{3} ∣}^{2}]

and

κ_{3} = \frac{18 π ω}{n (3 ω) c} χ_{Kerr}^{(3)} (3 ω) [{2 ∣ E_{1} ∣}^{2} + {2 ∣ E_{2} ∣}^{2} + {∣ E_{3} ∣}^{2}]

. Note that

χ_{Kerr}^{(3)}

(ω),

χ_{Kerr}^{(3)}

(2ω) and

χ_{Kerr}^{(3)}

(3ω) are χ ⁽³⁾ susceptibility for Kerr effect of the nonlinear layer, χ ⁽²⁾ and χ ⁽³⁾ are, respectively, the susceptibilities for SH and TH generations. In Eq. (1), we have set χ ⁽²⁾≡χ ⁽²⁾(ω)=χ ⁽²⁾(2ω)=χ ⁽²⁾(3ω) and χ ⁽³⁾≡χ ⁽³⁾(ω)=χ ⁽³⁾(2ω)=χ ⁽³⁾(3ω) as required by conservation of energy flow. Using the Eq. (1) and an iterative procedure described elsewhere^{21
P. Xie and Z.Q. Zhang, “Optical phase conjugation in third-order nonlinear photonic crystals,” Phys. Rev. A
69, 053806 (2004). [CrossRef]}, we can obtain the SH and TH of forward and backward waves.

3. The experiment results compared with the simulation

The PC structure we designed and fabricated in this letter consists 18 periods of ZnS/YF₃ for the high/low index layers with layer thickness of 250/83.5nm respectively. The ZnS/YF₃ multilayers were grown commercially using conventional e-beam evaporation technique by Chroma Technology Corp. The sample is polycrystalline in nature as expected grown from evaporation technique. However, it is known that there is a net grain orientation distribution direction and thus the effective χ⁽²⁾ coefficient for polycrystalline material is only a few times smaller that the bulk crystal [22

M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature , 432, 374–376, (2004). [CrossRef] [PubMed]

]. Thus, the demonstration of efficient harmonic generations based on 1-D PC grown from e-beam evaporation is a major advantage compared to the slow and expensive MBE technique previously used [11

, 16

We use the refractive index of SiO₂ for YF₃ since they are almost the same in the frequency region of interest [23

Refractive index (n) for YF₃ is the proprietary information of the manufacturer. However, according to the manufacturer, the n of SiO₂ is almost the same as the YF₃ in the wavelength region of our interest, and indeed, experimental measured transmission curve is in excellent agreement with our simulation (Fig. 1a).

]. Figure 1 shows the simulation of the transmission, effective index neff and density of modes (DOM) for this PC structure and the experimental result of transmission. Due to the judicious choices of the materials and the parameters of the structure, the realization of near perfect phase matching at the fundamental wavelength about 1530nm for both SHG and THG is shown Fig. 1(b). As the result of the phasing matching effect, the coherence length L_c of the PC sample at the phase matching wavelengths are tens of millimeters, compared with ~6 microns and ~1 microns respectively for SHG and THG in the bulk ZnS. Furthermore, the fundamental and the harmonic wavelengths coincide exactly with very high DOM region at the photonic band edge. The existence of forward and backward propagation simultaneously in the PC permits the efficient generation of both forward and backward SHG and THG. The measured transmission spectrum is in good agreement with the simulation one in Fig. 1 which means our sample is a good 1-D PC with a clear photonic band gap and many transmission resonances.

Fig. 1. (a) The experimentally measured (dotted line) and the corresponding theoretically calculated (solid line) transmission. (b) Effective refractive index (solid line) and density of modes (DOM) (dashed line) as a function of wavelengths of the same PC.

The pump laser comes from an optical parametric amplifier tunable from 0.5 to 1.9µm at 10Hz repetition rate with pulse duration of about 35 ps. The laser splits into two parts. One is used as the reference to remove the fluctuation of the laser power and to normalize the signals at different wavelengths. The other is used as the fundamental wave for SHG and THG. The intensity of fundamental wave is controlled by variable neutral density filter from 200MW/cm² to 3GW/cm². The SH and TH signal are detected by a photomultiplier tube coupled to a monochrometer. Figure 2 shows the measured forward SHG and THG conversion efficiency and the corresponding simulations (dashed curves) as a function of fundamental wavelengths at excitation intensity of 3 GW/cm². In all our calculations χ⁽²⁾=7×10^-9 esu and χ⁽³⁾=1×10^-12 esu, which are close to the values given in references [24

Marvin J. Weber, CRC Handbook of Laser Science and Technology, Volume III Optical Materials: Part 1 (CRC Press, 1986).

] and [25

Marvin J. Weber, CRC Handbook of Laser Science and Technology, Supplement 2: Optical Materials (CRC Press, 1995).

]. The dramatic enhancements of SH and TH signals are shown in Fig. 2 when the fundamental excitation wavelengths are peaks at about 1530nm, 1605nm and 1700nm. Comparing with the Fig. 1 these enhancements coincide with the simulation results of SHG and THG due to the good phase matching and high DOM at these wavelengths near the photonic band edge. This is further verified from SHG (Fig. 2a) and THG spectra where no enhancement peaks are seen at shorter wavelength band edge (i.e., at ~1280nm) where DOM is still fairly high but poor phase matching for fundamental (1280nm) with the SHG and THG wavelengths (see Fig. 1(b)). This result show unambiguously that the enhancement of the SHG and THG is due to both phase matching and high DOM.

Although good agreement is obtained between theory and experiment in the SHG, we also observe some discrepancy in the THG. Despite the excellent agreements found between theory (dashed curve) and experiment in the peak positions of THG shown in Fig. 2(b), there exists a two orders of magnitude difference in the ratio of conversion efficiency at the first peak to that at the second peak. This large discrepancy cannot be reduced by adjusting the value of χ⁽³⁾ in our calculation. A possible source of the discrepancy is due to the presence of randomness in our sample. Both SEM cross-section and manufacturer specifications indicate that variation in layer thickness of a few % does exist in our sample. To study the effects due to layer randomness, we have repeated our calculations for many random configurations. For each configuration, the thickness of each layer is allowed to vary randomly within a given percentage. Our results indicate that a 3.5% randomness in the layer thickness is capable of reducing the above discrepancy significantly. The results of a particular configuration with 3.5% randomness are shown by solid curves in Fig. 2. This configuration is chosen so that the simulation result for the THG fits best the experimental data. It should be mentioned that the behavior of the forward SHG (see Fig. 2(a)) is insensitive to the presence such small randomness in the layer thickness. As will be shown later, this choice of random configuration also reduces the discrepancies between theory and experiments in the backward direction for both SHG and THG.

Fig. 2. The experimentally (solid circle) measured and theoretically (dash line without and solid line with the fluctuation of layer thickness) calculated SHG (a) and THG (b) conversion efficiency in the forward direction at excitation intensity of 3 GW/cm².

Due to very large field enhancement, the maximum conversion efficiency of THG almost equals to the one of SHG even in the low excitation. A cubic dependence of THG on the pump energy verifies that the direct THG is achieved. Theoretical calculation also shows the TH signal obtained from the direct THG base on χ⁽³⁾ is larger than obtained via a cascaded two-step process based on χ⁽²⁾.

Figure 3 shows the theoretically calculated and experimentally measured conversion efficiency of SHG and THG in the backward direction as a function of fundamental wavelengths at excitation intensity of 3 GW/cm². The behavior of SHG and THG in the backward direction is similar as the forward one. The magnitude and peak positions of conversion efficiency for both SHG and THG are found to be in good agreement between theory and experiments taking the randomness of layer thickness into account. The presence of layer randomness in a sample can modify the wave functions of the fundamental wave and higher harmonics within the sample, which can in turn alter the conversion efficiencies for both SHG and THG. Thus, some spectral regions where the simulated harmonic intensities are more enhanced in the sample with 3.5% layer fluctuation than the perfect crystal is the result of this effect. When the incident laser was about 3GW/cm² the maximum conversion efficiencies are 1% and 0.5% for SHG and THG respectively in the forward direction, 1.2% and 1.7% for SHG and THG respectively in the backward direction.

Fig. 3. Conversion efficiency of experimentally (solid circle) measured and theoretically calculated SHG(a) and THG(b) without (dash line) and with (solid line) fluctuation in layer thickness in the backward direction at excitation intensity of 3 GW/cm².

4. Conclusion

In this study we have observed the dramatic simultaneous enhancement for SHG and THG in forward and backward directions from 1-D ZnS/YF₃ PC structure. It is shown that good phase matching and simultaneous availability of the high DOM of fundamental and harmonic waves realize these enhancements near the photonic band gap. The conversion efficiencies for SHG and THG in forward and backward directions are in good agreement between the experimental results and theoretical simulations. The large conversion efficiency for THG is due to direct THG base on χ⁽³⁾ process instead of the cascaded two-step process based on χ⁽²⁾. The total SHG and THG conversion efficiency is 4.4% in a six microns thick sample pumped at 3GW/cm². Successful fabrication of this 1-D PC using conventional e-beam evaporation has considerable advantages compared to more complicated and expensive techniques such as MBE. Overall, our results exhibit a good prospect for PC in nonlinear optics applications in the near-UV to visible spectral region.

Acknowledgments

This work is partially supported by the Research Grant Council of Hong Kong (grant numbers HKUST6063/02P and 605804).

References and links

1.	E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]
2.	S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]
3.	Photonic crystals: physics, fabrication and applications , edited by K. Inoue and K. Ohtaka (Springer Verlag, Berlin, 2004)
4.	Nonlinear Photonic Crystals , edited by R. E. Slusher and B. J. Eggleton (Springer, Berlin 2003)
5.	H. Cheng and P. B. Miller, “Nonlinear Optical Theory in Solids,” Phys. Rev. 134, A683–A687 (1964). [CrossRef]
6.	J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. 127, 1918–1939 (1962) [CrossRef]
7.	P. A. Franken and J. F. Ward, “Optical Harmonics and Nonlinear Phenomena,” Rev. Mod. Phys. 35, 23–39 (1963). [CrossRef]
8.	M. Centini, M. Scalora, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Dispersive properties of one-dimensional photonic band gap structures for second harmonic generation,” J. Opt. A: Pure Appl. Opt. 2, 121–126 (2000). [CrossRef]
9.	N. Bloembergen and A. J. Sievers, “Nonlinear optical properties of periodic laminar structures,” Appl. Phys. Lett. 17, 483–486 (1970). [CrossRef]
10.	J. P. Van der Ziel and M. Ilegem, “Optical second harmonic generation in periodic multilayer GaAs-Al_0.3Ga_0.7As structures,” Appl. Phys. Lett. 28, 437–439 (1976). [CrossRef]
11.	Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D. Aguanno, and M. Scalora, “Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap,” Appl. Phys. Lett. 78, 3021–3023 (2001). [CrossRef]
12.	M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, “Simultaneously phase-matched enhanced second and third harmonic generation,” Phys. Rev. E 64, 046606 (2001). [CrossRef]
13.	V. V. Konotop and V. Kuzmiak, “Simultaneous second- and third-harmonic generation in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 16, 1370–1376 (1999). [CrossRef]
14.	A. V. Balakin, V. A. ushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher, and P. Masselin, “Enhancement of second-harmonicgeneration with femtosecond laser pulses near the photonicband edge for different polarizations of incident light,” Opt. Lett. 24, 793–795 (1999). [CrossRef]
15.	M. G. Martemyanov, T. V. Dolgova, and A. A. Fedyanin, “Optical third-harmonic generation in one-dimensional photonic crystals and microcavities,” J. of Exp. And Theor. Phys. 98, 463–477 (2004). [CrossRef]
16.	H. Yang, P. Xie, S. K. Chan, Z. Q. Zhang, I. K. Sou, G. K. L. Wong, and K. S. Wong, “Efficienct second harmonic generation form large band gap II–VI semiconductor photonic crstal”, Appl. Phys. Lett. 97, 131106 (2005). [CrossRef]
17.	Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, New York 1984)
18.	P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, Nick N. Lepeshkin, and Robert W. Boyd, “Dramatic Enhancement of Third-Harmonic Generation in Three-Dimensional Photonic Crystals,” Phys. Rev. Lett. 92, 083903 (2004). [CrossRef] [PubMed]
19.	Hui Yang, Ping Xie, S. K. Chan, Weixin Lu, Zhao-Qing Zhang, I. K. Sou, George K. L. Wong, and K. S. Wong, “Simultaneous enhancement of the second- and third-harmonic generations in one-dimensional semicounductor photonic crystals”, IEEE Quantum Electronic , 42, 447–451 (2006) [CrossRef]
20.	D. S. Bethune, “Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques,” J. Opt. Soc. Am. B 6, 910–916 (1989). [CrossRef]
21.	P. Xie and Z.Q. Zhang, “Optical phase conjugation in third-order nonlinear photonic crystals,” Phys. Rev. A 69, 053806 (2004). [CrossRef]
22.	M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, “Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials,” Nature , 432, 374–376, (2004). [CrossRef] [PubMed]
23.	Refractive index (n) for YF₃ is the proprietary information of the manufacturer. However, according to the manufacturer, the n of SiO₂ is almost the same as the YF₃ in the wavelength region of our interest, and indeed, experimental measured transmission curve is in excellent agreement with our simulation (Fig. 1a).
24.	Marvin J. Weber, CRC Handbook of Laser Science and Technology, Volume III Optical Materials: Part 1 (CRC Press, 1986).
25.	Marvin J. Weber, CRC Handbook of Laser Science and Technology, Supplement 2: Optical Materials (CRC Press, 1995).

OCIS Codes
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.4160) Nonlinear optics : Multiharmonic generation
(190.4360) Nonlinear optics : Nonlinear optics, devices

ToC Category:
Nonlinear Optics

History
Original Manuscript: September 26, 2006
Revised Manuscript: November 22, 2006
Manuscript Accepted: November 22, 2006
Published: December 11, 2006

Citation
Weixin Lu, Ping Xie, Zhao-Qing Zhang, George K. L. Wong, and Kam S. Wong, "Simultaneous perfect phase matching for second and third harmonic generations in ZnS/YF₃ photonic crystal for visible emissions," Opt. Express 14, 12353-12358 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-25-12353

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References

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
Photonic crystals: physics, fabrication and applications, edited by K. Inoue and K. Ohtaka (Springer Verlag, Berlin, 2004)
Nonlinear Photonic Crystals, edited by R. E. Slusher and B. J. Eggleton (Springer, Berlin 2003)
H. Cheng, P. B. Miller, "Nonlinear Optical Theory in Solids," Phys. Rev. 134, A683-A687 (1964). [CrossRef]
J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918-1939 (1962). [CrossRef]
P. A. Franken and J. F. Ward, "Optical Harmonics and Nonlinear Phenomena," Rev. Mod. Phys. 35, 23-39 (1963). [CrossRef]
M. Centini, M. Scalora, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Dispersive properties of one-dimensional photonic band gap structures for second harmonic generation," J. Opt. A: Pure Appl. Opt. 2, 121-126 (2000). [CrossRef]
N. Bloembergen and A. J. Sievers, "Nonlinear optical properties of periodic laminar structures," Appl. Phys. Lett. 17, 483-486 (1970). [CrossRef]
J. P. Van der Ziel and M. Ilegem, "Optical second harmonic generation in periodic multilayer GaAs-Al0.3Ga0.7As structures," Appl. Phys. Lett. 28, 437-439 (1976). [CrossRef]
Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D. Aguanno, and M. Scalora, "Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap," Appl. Phys. Lett. 78, 3021-3023 (2001). [CrossRef]
M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, C. M. Bowden, "Simultaneously phase-matched enhanced second and third harmonic generation," Phys. Rev. E 64, 046606 (2001). [CrossRef]
V. V. Konotop and V. Kuzmiak, "Simultaneous second- and third-harmonic generation in one-dimensional photonic crystals," J. Opt. Soc. Am. B 16, 1370-1376 (1999). [CrossRef]
A. V. Balakin, V. A. ushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher and P. Masselin, "Enhancement of second-harmonicgeneration with femtosecond laser pulses near the photonicband edge for different polarizations of incident light," Opt. Lett. 24, 793-795 (1999). [CrossRef]
M. G. Martemyanov, T. V. Dolgova and A. A. Fedyanin, "Optical third-harmonic generation in one-dimensional photonic crystals and microcavities," J. Exp. Theor. Phys. 98, 463-477 (2004). [CrossRef]
H. Yang, P. Xie, S. K. Chan, Z. Q. Zhang, I. K. Sou, G. K. L. Wong and K. S. Wong, "Efficient second harmonic generation form large band gap II-VI semiconductor photonic crystal," Appl. Phys. Lett. 97, 131106 (2005). [CrossRef]
Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, New York 1984).
P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, NickN. Lepeshkin and Robert W. Boyd, "Dramatic enhancement of Third-Harmonic Generation in Three-Dimensional Photonic Crystals," Phys. Rev. Lett. 92, 083903 (2004). [CrossRef] [PubMed]
Hui Yang, Ping Xie, S. K. Chan, Weixin Lu, Zhao-Qing Zhang, I. K. Sou, George K. L. Wong and K. S. Wong, "Simultaneous enhancement of the second- and third-harmonic generations in one-dimensional semicounductor photonic crystals," IEEE Quantum Electron. 42, 447-451 (2006) [CrossRef]
D. S. Bethune, "Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques," J. Opt. Soc. Am. B 6, 910-916 (1989). [CrossRef]
P. Xie and Z. Q. Zhang, "Optical phase conjugation in third-order nonlinear photonic crystals," Phys. Rev. A 69, 053806 (2004). [CrossRef]
M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature, 432, 374-376, (2004). [CrossRef] [PubMed]
Refractive index (n) for YF3 is the proprietary information of the manufacturer. However, according to the manufacturer, the n of SiO2 is almost the same as the YF3 in the wavelength region of our interest, and indeed, experimental measured transmission curve is in excellent agreement with our simulation [Fig. 1(a)].
MarvinJ. Weber, CRC Handbook of Laser Science and Technology, Volume III Optical Materials: Part 1 (CRC Press, 1986).
MarvinJ. Weber, CRC Handbook of Laser Science and Technology, Supplement 2: Optical Materials (CRC Press, 1995).

Aguanno, G. D.
Armstrong, J. A.
Balakin, A. V.
Baudrier-Raybaut, M.
Bertolotti, M.
Bethune, D. S.
Bloembergen, N.
Bloemer, M. J.
Bowden, C. M.
Centini, M.
Chan, S. K.
Cheng, H.
D’Aguanno, G.
Dolgova, T. V.
Ducuing, J.
Dumeige, Y.
Fedyanin, A. A.
Franken, P. A.
Haïdar, R.
Ilegem, M.
John, S.
Konotop, V. V.
Kupecek, Ph.
Kuzmiak, V.
Lemasson, Ph.
Levenson, J. A.
Markowicz, P. P.
Martemyanov, M. G.
Miller, P. B.
Nick, P. N.
Pershan, P. S.
Prasad, P. N.
Pudavar, H.
Rosencher, E.
Sagnes, I.
Sauvage, S.
Scalora, M.
Sibilia, C.
Sievers, A. J.
Sou, I. K.
Tiryaki, H.
Van der Ziel, J. P.
Vidakovic, P.
Ward, J. F.
Wong, G. K. L.
Wong, K. S.
Xie, P.
Yablonovitch, E.
Yang, H.
Zhang, Z. Q.

Appl. Phys. Lett.

N. Bloembergen and A. J. Sievers, "Nonlinear optical properties of periodic laminar structures," Appl. Phys. Lett. 17, 483-486 (1970). [CrossRef]
J. P. Van der Ziel and M. Ilegem, "Optical second harmonic generation in periodic multilayer GaAs-Al0.3Ga0.7As structures," Appl. Phys. Lett. 28, 437-439 (1976). [CrossRef]
Y. Dumeige, P. Vidakovic, S. Sauvage, I. Sagnes, J. A. Levenson, C. Sibilia, M. Centini, G. D. Aguanno, and M. Scalora, "Enhancement of second-harmonic generation in a one-dimensional semiconductor photonic band gap," Appl. Phys. Lett. 78, 3021-3023 (2001). [CrossRef]
H. Yang, P. Xie, S. K. Chan, Z. Q. Zhang, I. K. Sou, G. K. L. Wong and K. S. Wong, "Efficient second harmonic generation form large band gap II-VI semiconductor photonic crystal," Appl. Phys. Lett. 97, 131106 (2005). [CrossRef]

IEEE Quantum Electron.

Hui Yang, Ping Xie, S. K. Chan, Weixin Lu, Zhao-Qing Zhang, I. K. Sou, George K. L. Wong and K. S. Wong, "Simultaneous enhancement of the second- and third-harmonic generations in one-dimensional semicounductor photonic crystals," IEEE Quantum Electron. 42, 447-451 (2006) [CrossRef]

J. Exp. Theor. Phys.

M. G. Martemyanov, T. V. Dolgova and A. A. Fedyanin, "Optical third-harmonic generation in one-dimensional photonic crystals and microcavities," J. Exp. Theor. Phys. 98, 463-477 (2004). [CrossRef]

J. Opt. A: Pure Appl. Opt.

M. Centini, M. Scalora, C. Sibilia, G. D’Aguanno, M. Bertolotti, M. J. Bloemer, and C. M. Bowden, "Dispersive properties of one-dimensional photonic band gap structures for second harmonic generation," J. Opt. A: Pure Appl. Opt. 2, 121-126 (2000). [CrossRef]

J. Opt. Soc. Am. B

Nature

M. Baudrier-Raybaut, R. Haïdar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature, 432, 374-376, (2004). [CrossRef] [PubMed]

Opt. Lett.

A. V. Balakin, V. A. ushuev, N. I. Koroteev, B. I. Mantsyzov, I. A. Ozheredov, A. P. Shkurinov, D. Boucher and P. Masselin, "Enhancement of second-harmonicgeneration with femtosecond laser pulses near the photonicband edge for different polarizations of incident light," Opt. Lett. 24, 793-795 (1999). [CrossRef]

Phys. Rev.

H. Cheng, P. B. Miller, "Nonlinear Optical Theory in Solids," Phys. Rev. 134, A683-A687 (1964). [CrossRef]
J. A. Armstrong, N. Bloembergen, J. Ducuing, P. S. Pershan, "Interactions between Light Waves in a Nonlinear Dielectric," Phys. Rev. 127, 1918-1939 (1962). [CrossRef]

Phys. Rev. A

P. Xie and Z. Q. Zhang, "Optical phase conjugation in third-order nonlinear photonic crystals," Phys. Rev. A 69, 053806 (2004). [CrossRef]

Phys. Rev. E

M. Centini, G. D’Aguanno, M. Scalora, C. Sibilia, M. Bertolotti, M. J. Bloemer, C. M. Bowden, "Simultaneously phase-matched enhanced second and third harmonic generation," Phys. Rev. E 64, 046606 (2001). [CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
P. P. Markowicz, H. Tiryaki, H. Pudavar, P. N. Prasad, NickN. Lepeshkin and Robert W. Boyd, "Dramatic enhancement of Third-Harmonic Generation in Three-Dimensional Photonic Crystals," Phys. Rev. Lett. 92, 083903 (2004). [CrossRef] [PubMed]

Rev. Mod. Phys.

P. A. Franken and J. F. Ward, "Optical Harmonics and Nonlinear Phenomena," Rev. Mod. Phys. 35, 23-39 (1963). [CrossRef]

Other

Y. R. Shen, The Principles of Nonlinear Optics (John Wiley & Sons, New York 1984).
Photonic crystals: physics, fabrication and applications, edited by K. Inoue and K. Ohtaka (Springer Verlag, Berlin, 2004)
Nonlinear Photonic Crystals, edited by R. E. Slusher and B. J. Eggleton (Springer, Berlin 2003)
Refractive index (n) for YF3 is the proprietary information of the manufacturer. However, according to the manufacturer, the n of SiO2 is almost the same as the YF3 in the wavelength region of our interest, and indeed, experimental measured transmission curve is in excellent agreement with our simulation [Fig. 1(a)].
MarvinJ. Weber, CRC Handbook of Laser Science and Technology, Volume III Optical Materials: Part 1 (CRC Press, 1986).
MarvinJ. Weber, CRC Handbook of Laser Science and Technology, Supplement 2: Optical Materials (CRC Press, 1995).

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