Abstract

Chip-integrated whispering-gallery resonators (WGRs) enable compact and wavelength-agile nonlinear optical frequency synthesizers. So far, the most flexible phase-matching technique, i.e., quasi-phase matching, has not been applied in this configuration. The reason is the lack of suitable thin films with alternating crystal structure on a low-refractive-index substrate. Here, we demonstrate an innovative method of realizing thin film substrates suitable for quasi-phase matching by field-assisted domain engineering of lithium niobate, and subsequent direct bonding and polishing. We are able to fabricate high-Q on-chip WGRs with these substrates by using standard semiconductor manufacturing techniques. The Q-factors of the resonators are up to one million, which allows us to demonstrate quasi-phase-matched second-harmonic generation in on-chip WGRs for the first time, to the best of our knowledge. The normalized conversion efficiency is 9×104mW1. This method can also be transferred to other material systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Whispering-gallery resonators (WGRs) have proven to be highly attractive for nonlinear optics due to their high Q-factors larger than 109, small mode volumes, and mechanical robustness [13]. The achievable high internal intensities lead to efficient frequency conversion already at low input powers in the μW region [4]. Made of non-centrosymmetric materials, they are applied for optical-parametric oscillators working from the visible [5] to the mid-infrared [6] spectral region. They are used for frequency doublers generating light from the ultraviolet [7] to the near infrared as well as for infrared upconversion detectors [8,9]. To achieve phase matching, methods such as birefringent- [1012], cyclic- [13,14], and quasi-phase matching [15] have been employed. The latter gives ultimate flexibility regarding wavelengths and polarizations of the interacting light fields. Furthermore, it always provides access to the largest second-order nonlinear-optical coefficient of the material, e.g., in lithium niobate (LiNbO3, LN), this is d333=20.3pm/V compared with d311=3.4pm/V [16], which has to be used for birefringent phase matching. The d222=2.1pm/V [17] could also be accessed.

The majority of WGR frequency converters are based on bulk resonators. However, recently on-chip WGRs, e.g., out of LN [1820], aluminum nitride [21], aluminum gallium arsenide [22], and gallium nitride [23], have become very attractive. This is because of their small dimensions in the micrometer region and thus extremely small mode volumes, and the additional potential of building mixed photonic and electrical circuits [24], as well as the prospect of using parallel and reproducible semiconductor manufacturing techniques [25]. On-chip WGRs are fabricated from thin-film substrates to achieve a high refractive index step for sufficient light confinement. They have currently one major limitation: quasi-phase matching is hard to achieve. Although, in general, in ferroelectric crystals the domains can be patterned with the help of external electric fields, field-assisted domain inversion of thin films on substrates is difficult, since the backside of the thin film cannot be accessed electrically. For non-ferroelectric materials, the situation is also difficult, as one needs to grow periodically structured thin films, which cannot be done on any substrate.

We overcome this limitation for on-chip frequency converters here by introducing a method to obtain thin films with patterns of inverted second-order optical nonlinearity starting with patterned bulk material, which is bonded onto a substrate with lower refractive index and polished down to a thin film. This approach works for many material combinations. In this contribution, we demonstrate this method for periodically poled LN on quartz (pp-LNoQ).

The fabrication starts with field-assisted domain inversion of bulk LN by writing calligraphically a linear grating with a period length of 23 μm into a 300-μm-thick 5-mol.%-MgO-doped optically polished z-cut-LN chip (Fig. 1). A chromium layer serves as the backside electrode on the +z side of the crystal, and we write the domains with the help of a tungsten-carbide tip on the z side of the wafer, moving along the y-crystal axis. A detailed description of the poling procedure can be found in Ref. [26]. Next, we clean the periodically poled sample and also a z-cut-α-quartz chip, followed by a further cleaning and surface-functionalization procedure (for details, see Supplement 1). The aim of this procedure is to assure perfectly clean and OH-terminated surfaces, which are crucial for the direct bonding process [27,28].

 figure: Fig. 1.

Fig. 1. Process flow for the fabrication of periodically poled lithium-niobate-on-quartz (pp-LNoQ) substrates: (a) Domain inversion; (b) cleaning, surface functionalization; (c) thermal bonding; and (d) lapping and polishing.

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In a next step, we put the periodically poled sample and the quartz chip together. Hydrogen bonds at the OH-terminated surface already form at room temperature, such that the samples stick together. Hereafter, we increase the bond forces by tempering on a hot plate at 325°C for 5 h. We choose α quartz as the substrate, since the thermal-expansion coefficients α parallel to the a-crystal axis is close to that of LN (αa,quartz=12.4×106K1; αa,LN=14.8×106K1 [17]). Subsequently, we reduce the thickness of the periodically poled LN to 2 μm by lapping and polishing with a standard wafer-polishing machine (PM5, Logitech; for details, see Supplement 1).

To obtain on-chip WGRs, we structure micro-rings with a diameter of 216 μm into the pp-LNoQ thin films by standard semiconductor manufacturing techniques, including lithography, reactive-ion etching, and a polishing process. A detailed description can be found in Ref. [25]. Figure 2 shows the final result. For this image, we made the domains visible by etching a dummy sample in a 40% potassium hydrochloride (KOH) solution at 90°C for 45 min, since the z surface of LN etches faster than the +z surface. The linear domain structure with a 23 μm periodicity and a 5 μm domain width can be clearly seen.

 figure: Fig. 2.

Fig. 2. False-color SEM images of (a) a pp-LNoQ on-chip WGR with a diameter of 216 μm and (b) zoomed view. Dark blue: LN with z axis pointing up. Light blue: LN with z axis pointing down. Brown: quartz substrate.

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For optical characterization, we use the setup shown in Fig. 3. An amplified distributed feedback (DFB) laser diode (Eblana Photonics, EP1550-DM-B with amplifier IPG Laser, EAD-3-C-PM), which emits at 1551 nm and is tunable over 2 nm, serves as the light source. To couple light into the WGR, we use a setup with a fixed chip containing a straight coupling waveguide and a second chip on top comprising the WGRs. We couple light into the coupling waveguide via end-fire coupling with a 40× microscope objective lens. Light penetrates from the coupling waveguide to the WGR via evanescent field coupling. Both the horizontal position of the WGR with respect to that of the coupling waveguide and the vertical distance between the coupling waveguide and the WGR can be adjusted via a x,y,z-piezo-actuator stage, and hence the coupling strength can be tuned.

 figure: Fig. 3.

Fig. 3. Schematic of the setup for Q-factor measurement and investigation of second-harmonic generation.

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First, we determine the Q-factor of ordinarily (o) and extraordinarily (e) polarized whispering-gallery modes (WGMs). The first is in the range of 4×105 to 1.3×106, while the second is significantly lower, ranging from 7×104 to 2×105. We are able to reach critical coupling and overcoupling for o-polarized light only. The reason for the higher loss for e-polarized modes most likely stems from the fabrication used for the on-chip WGRs: after structuring of ring resonators into the top LN thin film by lithography and reactive-ion etching, we use a polishing process to reduce the side-wall roughness and thus the scattering loss [25]. To clean the chips after polishing and to remove the polishing particles, we deploy a wet-chemical cleaning procedure with KOH. This is uncritical and does not affect the quality factor of either the o- or the e-polarized modes for resonators having no domain pattern [25]. However, since KOH etches the z surface of LN faster than the +z surface, we generate nm-large steps on top of the on-chip WGRs by this final cleaning process. This roughness has a larger effect on the Q-factors of the e-polarized modes than on the o-polarized modes, hence the higher losses. This is not a fundamental problem and can be solved by revising of the final polishing and cleaning procedure.

Due to the advantages regarding Q-factor and coupling efficiency, we pump the resonator with o-polarized light to generate frequency-doubled light, which is also o-polarized (type 0 phase matching, ooo). In doing so, we observe the generation of red light in the WGR with a CCD-camera. This light is coupled into the waveguide (Fig. 4). The light at the end facet is collimated, and one part is diverted for interrogation by a spectrometer. We use a long-pass filter (cut-on wavelength: 1100 nm), to separate the pump light from the converted one and measure the intensities with detectors operating in the visible and in the near-infrared spectral regions. The recorded spectrum shows that the wavelength of the converted light is 775.5 nm, confirming the second-harmonic generation (SHG). The second-harmonic light is also o-polarized.

 figure: Fig. 4.

Fig. 4. Measured conversion efficiency of SHG (blue dots) and theoretical curve fitted by the analytical model. Inset: Image of the WGR while second-harmonic light is generated and coupled out into the coupling waveguide.

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We optimized the phase matching of the conversion process by varying the resonator temperature in the sub-K range. This influences the coupling distance and is compensated with the piezo stage to achieve critical coupling again. Afterwards, we tuned the pump power from 0.5 to 5 mW internal pump power in the coupling waveguide, while recording the power of the converted light, to calculate the conversion efficiency (Fig. 4). The measured efficiency depends linearly on the pump power, and the normalized conversion efficiency is 9×104mW1. At higher pump powers around 5 mW, the light conversion starts to become unstable due to thermal effects.

To compare this result with the theoretically expected value, we start with the relation for the conversion efficiency η [2]:

ηPshPp=4rsh1+rshrp1+rpX(1+X)2
with
X(1+X)2=rp1+rpPpP0,
where Pp is the pump power, Psh the power of the second-harmonic light, and rp,sh are the ratios between the coupling losses and the internal losses in the resonator. This means that at rp,sh=1, we have critical coupling, where the internal loss equals the coupling loss. Furthermore, we have the characteristic power at which high efficiencies for the conversion process can be reached:
P0=νpπε0np4nsh28deff21Qi,p2Qi,shVeff(1+rp)2(1+rsh).
Here, νp is the frequency of the pump light, np,sh are the refractive indices of the resonator material, Qi,p,Qi,sh are the unloaded Q-factors for the two waves, and Veff is the effective mode volume. We have the effective nonlinear coefficient deff=|SM|d222 with a correction constant |SM|2/π, which originates from the domain pattern (for details on how SM is calculated, see Supplement 1).

In WGRs, the following selection rule for quasi-phase matching applies [2]:

2mpmsh±M=0,
with the azimuthal mode numbers mp, msh for the pump and the second-harmonic waves and the integer M, provided by the quasi-phase-matching structure. We calculate mp=940 and msh=1934 (Fig. 5) with a finite-element simulation (FEM) (Comsol, Wave Optics Module). Due to Eq. (4), the linear poling structure has to compensate for |M|=54. We used a poling structure with a periodicity of 23 μm and a domain width of approximately 5 μm. Figure 5 shows the Fourier coefficients of the poling structure with |SM=54|=0.06; thus, our structure is indeed expected to enable quasi-phase matching. Furthermore, we have an intrinsic Q-factor for the pump light of Qp=1.3×106, and since we assume that the Q-factor is limited by surface scattering, we can estimate the Q-factor of the second harmonic light to be Qsh=Qp(λsh/λp)3=Qp/8. We calculate the effective mode volume to be Veff=3.8×103μm3 with our FEM. With rp=1 and rsh=1, we can estimate the characteristic power with Eq. (3) to be P0=524mW, which means that PpP0.

 figure: Fig. 5.

Fig. 5. Mode cross section of (a) pump light and (b) second-harmonic light. (c) Fourier coefficients of a theoretical domain pattern with 23 μm periodicity and 5 μm domain width for type 0 phase matching, resulting in d(ϕ).

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From Eq. (2), it follows with rp=1 that also X1, and hence X(1+X)2X. Taking Eq. (2) and with PpP0, Eq. (1) can be approximated to

η(Pp)4(rp1+rp)2rsh1+rsh1P0Pp.

A fit to the experimental data gives rsh=0.6. This is reasonable, since we have just one coupling waveguide for both the pump light and the second-harmonic light, and therefore we are able optimize the coupling ratio just for one wave. If we have critical coupling for the pump light, it is obvious that we are in the undercoupled regime for the second-harmonic light due to a faster decay of the evanescent field for light with shorter wavelength and a slightly different mode position in the WGR. Critical coupling for both the pump light and the second-harmonic light could be achieved by using a second coupling waveguide, which gives the opportunity to optimize the coupling for the pump and second-harmonic waves independently.

From Eq. (5), it becomes evident that a highly effective nonlinear-optical coefficient and also high Q-factors are crucial for getting large conversion efficiencies. The pump light we use is o-polarized, which means that we employ the nonlinear-optical coefficient d222, which is relatively small compared to d333. If we can get also high Q-factors in the range of one million for modes pumped with e-polarized light, this would lead to P0=1.4mW, which means we leave the undepleted-pump regime with PpP0—the reason we cannot estimate η with Eq. (5) anymore. Using Eqs. (1) and (2), a conversion efficiency at Pp=1mW of 15.6% can be calculated even with the relatively low deff due to the linear domain pattern. Using a radial pattern, one could achieve deff=2/πd333 and get even higher efficiencies. Here, we are also in the depleted pump regime at 1 mW pump power—the reason we have to use Eqs. (1) and (2) to calculate the conversion efficiency. Assuming rp=rsh=1, we get η=24%. Applying radially domain structures is in principle possible; however, alignment structures have to be used to align the domains to the waveguide rings properly. Compared to single domain WGRs, the conversion efficiency should be (2d333/(πd311))214-times higher (see Supplement 1). This shows the high potential of pp-LNoQ WGRs.

In conclusion, we show how to achieve quasi-phase matching in on-chip WGRs, to the best of our knowledge, for the first time. We demonstrate SHG with a normalized conversion efficiency of 9×104mW1, which is on the same order of magnitude as reported in previous work where cyclic phase matching was used [14]. However, we want to emphasize that compared to cyclic phase matching, we can adjust the period length of the periodical poling structure, which gives us the freedom to tailor phase matching for every other spectral range. Furthermore, it gives full flexibility for the polarization of the interacting light fields, so that the largest nonlinear-optical coefficient d333 can be accessed or, e.g., polarization entanglement of the interacting waves can be achieved. Thus, the presented procedure for achieving periodically structured ferroelectric thin films overcomes the phase-matching limitation of on-chip WGRs. This limitation has so far prevented on-chip WGRs from fully unfolding their high potential, which they have due to their cheap and precise manufacturing by standard semiconductor fabrication techniques. Compared to waveguide-integrated frequency converters, where normalized efficiencies up to 2.4%/mW and maximum efficiencies up to 92% can be achieved [2], the here presented conversion efficiency using o-polarized light is still low. However the discussion above about e-polarized light shows the high potential of WGRs: by improving the Q-factor to just 106 and using radially domain structures, WGRs can catch up with waveguides easily; furthermore, the size of WGRs is just in the 100 μm range, and since WGRs are resonators, optical feedback is provided. This gives a promising perspective to demonstrate the first on-chip optical parametric oscillator or to realize compact photonic circuits comprising frequency synthesizers.

Funding

Bundesministerium für Bildung und Forschung (BMBF) (13N13648).

Acknowledgment

Richard Wolf appreciates the support by a Gisela and Erwin Sick Fellowship and Yuechen Jia from Alexander von Humboldt Foundation.

 

See Supplement 1 for supporting content.

REFERENCES

1. V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006). [CrossRef]  

2. I. Breunig, Laser Photon. Rev. 10, 569 (2016). [CrossRef]  

3. D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, J. Opt. 18, 123002 (2016). [CrossRef]  

4. J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010). [CrossRef]  

5. C. S. Werner, T. Beckmann, K. Buse, and I. Breunig, Opt. Lett. 37, 4224 (2012). [CrossRef]  

6. S.-K. Meisenheimer, J. U. Fürst, K. Buse, and I. Breunig, Optica 4, 189 (2017). [CrossRef]  

7. J. U. Fürst, K. Buse, I. Breunig, P. Becker, J. Liebertz, and L. Bohatý, Opt. Lett. 40, 1932 (2015). [CrossRef]  

8. D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, New J. Phys. 16, 053025 (2014). [CrossRef]  

9. A. Rueda, F. Sedlmeir, M. C. Collodo, U. Vogl, B. Stiller, G. Schunk, D. V. Strekalov, C. Marquardt, J. M. Fink, O. Painter, G. Leuchs, and H. G. L. Schwefel, Optica 3, 597 (2016). [CrossRef]  

10. J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010). [CrossRef]  

11. J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015). [CrossRef]  

12. C. Wang, M. J. Burek, Z. Lin, H. A. Atikian, V. Venkataraman, I.-C. Huang, P. Stark, and M. Loncar, Opt. Express 22, 30924 (2014). [CrossRef]  

13. G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, Appl. Phys. Lett. 103, 181107 (2013). [CrossRef]  

14. J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016). [CrossRef]  

15. T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011). [CrossRef]  

16. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, J. Opt. Soc. Am. B 14, 2268 (1997). [CrossRef]  

17. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

18. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Nat. Photonics 1, 407 (2007). [CrossRef]  

19. R. Luo, H. Jiang, S. Rogers, H. Liang, Y. He, and Q. Lin, Opt. Express 25, 24531 (2017). [CrossRef]  

20. M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017). [CrossRef]  

21. X. Guo, C.-L. Zou, and H. X. Tang, Optica 3, 1126 (2016). [CrossRef]  

22. S. Mariani, A. Andronico, A. Lemaître, I. Favero, S. Ducci, and G. Leo, Opt. Lett. 39, 3062 (2014). [CrossRef]  

23. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, Opt. Express 19, 10462 (2011). [CrossRef]  

24. M. Wang, Y. Xu, Z. Fang, Y. Liao, P. Wang, W. Chu, L. Qiao, J. Lin, W. Fang, and Y. Cheng, Opt. Express 25, 124 (2017). [CrossRef]  

25. R. Wolf, I. Breunig, H. Zappe, and K. Buse, Opt. Express 25, 29927 (2017). [CrossRef]  

26. C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, and I. Breunig, Sci. Rep. 7, 9862 (2017). [CrossRef]  

27. A. Plößl, Mater. Sci. Eng. R 25, 1 (1999). [CrossRef]  

28. J. Haisma, B. A. Spierings, U. K. Biermann, and A. A. van Gorkum, Appl. Opt. 33, 1154 (1994). [CrossRef]  

References

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  1. V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006).
    [Crossref]
  2. I. Breunig, Laser Photon. Rev. 10, 569 (2016).
    [Crossref]
  3. D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, J. Opt. 18, 123002 (2016).
    [Crossref]
  4. J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
    [Crossref]
  5. C. S. Werner, T. Beckmann, K. Buse, and I. Breunig, Opt. Lett. 37, 4224 (2012).
    [Crossref]
  6. S.-K. Meisenheimer, J. U. Fürst, K. Buse, and I. Breunig, Optica 4, 189 (2017).
    [Crossref]
  7. J. U. Fürst, K. Buse, I. Breunig, P. Becker, J. Liebertz, and L. Bohatý, Opt. Lett. 40, 1932 (2015).
    [Crossref]
  8. D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, New J. Phys. 16, 053025 (2014).
    [Crossref]
  9. A. Rueda, F. Sedlmeir, M. C. Collodo, U. Vogl, B. Stiller, G. Schunk, D. V. Strekalov, C. Marquardt, J. M. Fink, O. Painter, G. Leuchs, and H. G. L. Schwefel, Optica 3, 597 (2016).
    [Crossref]
  10. J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
    [Crossref]
  11. J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
    [Crossref]
  12. C. Wang, M. J. Burek, Z. Lin, H. A. Atikian, V. Venkataraman, I.-C. Huang, P. Stark, and M. Loncar, Opt. Express 22, 30924 (2014).
    [Crossref]
  13. G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, Appl. Phys. Lett. 103, 181107 (2013).
    [Crossref]
  14. J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
    [Crossref]
  15. T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
    [Crossref]
  16. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, J. Opt. Soc. Am. B 14, 2268 (1997).
    [Crossref]
  17. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).
  18. A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Nat. Photonics 1, 407 (2007).
    [Crossref]
  19. R. Luo, H. Jiang, S. Rogers, H. Liang, Y. He, and Q. Lin, Opt. Express 25, 24531 (2017).
    [Crossref]
  20. M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
    [Crossref]
  21. X. Guo, C.-L. Zou, and H. X. Tang, Optica 3, 1126 (2016).
    [Crossref]
  22. S. Mariani, A. Andronico, A. Lemaître, I. Favero, S. Ducci, and G. Leo, Opt. Lett. 39, 3062 (2014).
    [Crossref]
  23. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, Opt. Express 19, 10462 (2011).
    [Crossref]
  24. M. Wang, Y. Xu, Z. Fang, Y. Liao, P. Wang, W. Chu, L. Qiao, J. Lin, W. Fang, and Y. Cheng, Opt. Express 25, 124 (2017).
    [Crossref]
  25. R. Wolf, I. Breunig, H. Zappe, and K. Buse, Opt. Express 25, 29927 (2017).
    [Crossref]
  26. C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, and I. Breunig, Sci. Rep. 7, 9862 (2017).
    [Crossref]
  27. A. Plößl, Mater. Sci. Eng. R 25, 1 (1999).
    [Crossref]
  28. J. Haisma, B. A. Spierings, U. K. Biermann, and A. A. van Gorkum, Appl. Opt. 33, 1154 (1994).
    [Crossref]

2017 (6)

2016 (5)

X. Guo, C.-L. Zou, and H. X. Tang, Optica 3, 1126 (2016).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

A. Rueda, F. Sedlmeir, M. C. Collodo, U. Vogl, B. Stiller, G. Schunk, D. V. Strekalov, C. Marquardt, J. M. Fink, O. Painter, G. Leuchs, and H. G. L. Schwefel, Optica 3, 597 (2016).
[Crossref]

I. Breunig, Laser Photon. Rev. 10, 569 (2016).
[Crossref]

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, J. Opt. 18, 123002 (2016).
[Crossref]

2015 (2)

J. U. Fürst, K. Buse, I. Breunig, P. Becker, J. Liebertz, and L. Bohatý, Opt. Lett. 40, 1932 (2015).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

2014 (3)

2013 (1)

G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, Appl. Phys. Lett. 103, 181107 (2013).
[Crossref]

2012 (1)

2011 (2)

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[Crossref]

C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, Opt. Express 19, 10462 (2011).
[Crossref]

2010 (2)

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

2007 (1)

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Nat. Photonics 1, 407 (2007).
[Crossref]

2006 (1)

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006).
[Crossref]

1999 (1)

A. Plößl, Mater. Sci. Eng. R 25, 1 (1999).
[Crossref]

1997 (1)

1994 (1)

Aiello, A.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

Andersen, U. L.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Andronico, A.

Atikian, H. A.

Becker, P.

Beckmann, T.

C. S. Werner, T. Beckmann, K. Buse, and I. Breunig, Opt. Lett. 37, 4224 (2012).
[Crossref]

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[Crossref]

Biermann, U. K.

Bohatý, L.

Breunig, I.

S.-K. Meisenheimer, J. U. Fürst, K. Buse, and I. Breunig, Optica 4, 189 (2017).
[Crossref]

R. Wolf, I. Breunig, H. Zappe, and K. Buse, Opt. Express 25, 29927 (2017).
[Crossref]

C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, and I. Breunig, Sci. Rep. 7, 9862 (2017).
[Crossref]

I. Breunig, Laser Photon. Rev. 10, 569 (2016).
[Crossref]

J. U. Fürst, K. Buse, I. Breunig, P. Becker, J. Liebertz, and L. Bohatý, Opt. Lett. 40, 1932 (2015).
[Crossref]

C. S. Werner, T. Beckmann, K. Buse, and I. Breunig, Opt. Lett. 37, 4224 (2012).
[Crossref]

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[Crossref]

Burek, M. J.

Buse, K.

Cheng, Y.

M. Wang, Y. Xu, Z. Fang, Y. Liao, P. Wang, W. Chu, L. Qiao, J. Lin, W. Fang, and Y. Cheng, Opt. Express 25, 124 (2017).
[Crossref]

M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Chu, W.

Collodo, M. C.

Degl’Innocenti, R.

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Nat. Photonics 1, 407 (2007).
[Crossref]

Ducci, S.

Elser, D.

J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

Fang, W.

M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
[Crossref]

M. Wang, Y. Xu, Z. Fang, Y. Liao, P. Wang, W. Chu, L. Qiao, J. Lin, W. Fang, and Y. Cheng, Opt. Express 25, 124 (2017).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Fang, Z.

M. Wang, Y. Xu, Z. Fang, Y. Liao, P. Wang, W. Chu, L. Qiao, J. Lin, W. Fang, and Y. Cheng, Opt. Express 25, 124 (2017).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Fang, Z.-W.

M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
[Crossref]

Favero, I.

Fink, J. M.

Fong, K. Y.

Fürst, J. U.

S.-K. Meisenheimer, J. U. Fürst, K. Buse, and I. Breunig, Optica 4, 189 (2017).
[Crossref]

J. U. Fürst, K. Buse, I. Breunig, P. Becker, J. Liebertz, and L. Bohatý, Opt. Lett. 40, 1932 (2015).
[Crossref]

G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, Appl. Phys. Lett. 103, 181107 (2013).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Guarino, A.

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Nat. Photonics 1, 407 (2007).
[Crossref]

Günter, P.

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Nat. Photonics 1, 407 (2007).
[Crossref]

Guo, X.

Haertle, D.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[Crossref]

Haisma, J.

He, Y.

Herr, S. J.

C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, and I. Breunig, Sci. Rep. 7, 9862 (2017).
[Crossref]

Huang, I.-C.

Huang, Y.-P.

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, New J. Phys. 16, 053025 (2014).
[Crossref]

Ilchenko, V. S.

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006).
[Crossref]

Ito, R.

Jiang, H.

Kitamoto, A.

Kondo, T.

Kowligy, A. S.

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, New J. Phys. 16, 053025 (2014).
[Crossref]

Kumar, P.

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, New J. Phys. 16, 053025 (2014).
[Crossref]

Lassen, M.

J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Lemaître, A.

Leo, G.

Leuchs, G.

A. Rueda, F. Sedlmeir, M. C. Collodo, U. Vogl, B. Stiller, G. Schunk, D. V. Strekalov, C. Marquardt, J. M. Fink, O. Painter, G. Leuchs, and H. G. L. Schwefel, Optica 3, 597 (2016).
[Crossref]

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, J. Opt. 18, 123002 (2016).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Liang, H.

Liao, Y.

Liebertz, J.

Lin, G.

G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, Appl. Phys. Lett. 103, 181107 (2013).
[Crossref]

Lin, J.

M. Wang, Y. Xu, Z. Fang, Y. Liao, P. Wang, W. Chu, L. Qiao, J. Lin, W. Fang, and Y. Cheng, Opt. Express 25, 124 (2017).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Lin, J.-T.

M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
[Crossref]

Lin, Q.

Lin, Z.

Linnenbank, H.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[Crossref]

Liu, Z.-M.

M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
[Crossref]

Loncar, M.

Luo, R.

Mariani, S.

Marquardt, C.

A. Rueda, F. Sedlmeir, M. C. Collodo, U. Vogl, B. Stiller, G. Schunk, D. V. Strekalov, C. Marquardt, J. M. Fink, O. Painter, G. Leuchs, and H. G. L. Schwefel, Optica 3, 597 (2016).
[Crossref]

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, J. Opt. 18, 123002 (2016).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Matsko, A. B.

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, J. Opt. 18, 123002 (2016).
[Crossref]

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006).
[Crossref]

Meisenheimer, S.-K.

Ni, J.

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

Painter, O.

Palacios, T.

Pernice, W.

Plößl, A.

A. Plößl, Mater. Sci. Eng. R 25, 1 (1999).
[Crossref]

Poberaj, G.

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Nat. Photonics 1, 407 (2007).
[Crossref]

Qiao, L.

M. Wang, Y. Xu, Z. Fang, Y. Liao, P. Wang, W. Chu, L. Qiao, J. Lin, W. Fang, and Y. Cheng, Opt. Express 25, 124 (2017).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Qiao, L.-L.

M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
[Crossref]

Razzaghi, C.

C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, and I. Breunig, Sci. Rep. 7, 9862 (2017).
[Crossref]

Rezzonico, D.

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Nat. Photonics 1, 407 (2007).
[Crossref]

Rogers, S.

Rueda, A.

Ryu, K. K.

Schuck, C.

Schunk, G.

Schwefel, H. G. L.

Sedlmeir, F.

Shirane, M.

Shoji, I.

Soergel, E.

C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, and I. Breunig, Sci. Rep. 7, 9862 (2017).
[Crossref]

Spierings, B. A.

Stark, P.

Steigerwald, H.

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[Crossref]

Stiller, B.

Strekalov, D. V.

A. Rueda, F. Sedlmeir, M. C. Collodo, U. Vogl, B. Stiller, G. Schunk, D. V. Strekalov, C. Marquardt, J. M. Fink, O. Painter, G. Leuchs, and H. G. L. Schwefel, Optica 3, 597 (2016).
[Crossref]

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, J. Opt. 18, 123002 (2016).
[Crossref]

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, New J. Phys. 16, 053025 (2014).
[Crossref]

G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, Appl. Phys. Lett. 103, 181107 (2013).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

Sturman, B.

C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, and I. Breunig, Sci. Rep. 7, 9862 (2017).
[Crossref]

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[Crossref]

Tang, H. X.

van Gorkum, A. A.

Venkataraman, V.

Vogl, U.

Wang, C.

Wang, M.

M. Wang, Y. Xu, Z. Fang, Y. Liao, P. Wang, W. Chu, L. Qiao, J. Lin, W. Fang, and Y. Cheng, Opt. Express 25, 124 (2017).
[Crossref]

M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Wang, N.

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Wang, P.

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

Werner, C. S.

C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, and I. Breunig, Sci. Rep. 7, 9862 (2017).
[Crossref]

C. S. Werner, T. Beckmann, K. Buse, and I. Breunig, Opt. Lett. 37, 4224 (2012).
[Crossref]

Wolf, R.

Xiong, C.

Xu, Y.

M. Wang, Y. Xu, Z. Fang, Y. Liao, P. Wang, W. Chu, L. Qiao, J. Lin, W. Fang, and Y. Cheng, Opt. Express 25, 124 (2017).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Xu, Y.-X.

M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
[Crossref]

Yu, N.

G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, Appl. Phys. Lett. 103, 181107 (2013).
[Crossref]

Zappe, H.

Zou, C.-L.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

G. Lin, J. U. Fürst, D. V. Strekalov, and N. Yu, Appl. Phys. Lett. 103, 181107 (2013).
[Crossref]

J. Lin, Y. Xu, J. Ni, M. Wang, Z. Fang, L. Qiao, W. Fang, and Y. Cheng, Appl. Phys. Lett. 6, 014002 (2016).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

V. S. Ilchenko and A. B. Matsko, IEEE J. Sel. Top. Quantum Electron. 12, 15 (2006).
[Crossref]

J. Opt. (1)

D. V. Strekalov, C. Marquardt, A. B. Matsko, H. G. L. Schwefel, and G. Leuchs, J. Opt. 18, 123002 (2016).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (1)

I. Breunig, Laser Photon. Rev. 10, 569 (2016).
[Crossref]

Mater. Sci. Eng. R (1)

A. Plößl, Mater. Sci. Eng. R 25, 1 (1999).
[Crossref]

Nat. Photonics (1)

A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, and P. Günter, Nat. Photonics 1, 407 (2007).
[Crossref]

New J. Phys. (1)

D. V. Strekalov, A. S. Kowligy, Y.-P. Huang, and P. Kumar, New J. Phys. 16, 053025 (2014).
[Crossref]

Opt. Commun. (1)

M. Wang, J.-T. Lin, Y.-X. Xu, Z.-W. Fang, L.-L. Qiao, Z.-M. Liu, W. Fang, and Y. Cheng, Opt. Commun. 395, 249 (2017).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Optica (3)

Phys. Rev. Lett. (3)

J. U. FÜrst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 104, 153901 (2010).
[Crossref]

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010).
[Crossref]

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011).
[Crossref]

Sci. China Phys. Mech. Astron. (1)

J. Lin, Y. Xu, Z. Fang, M. Wang, N. Wang, L. Qiao, W. Fang, and Y. Cheng, Sci. China Phys. Mech. Astron. 58, 114209 (2015).
[Crossref]

Sci. Rep. (1)

C. S. Werner, S. J. Herr, K. Buse, B. Sturman, E. Soergel, C. Razzaghi, and I. Breunig, Sci. Rep. 7, 9862 (2017).
[Crossref]

Other (1)

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003).

Supplementary Material (1)

NameDescription
» Supplement 1       Additional information about the fabrication and calculation of the effective nonlinear optical coefficient

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Figures (5)

Fig. 1.
Fig. 1. Process flow for the fabrication of periodically poled lithium-niobate-on-quartz (pp-LNoQ) substrates: (a) Domain inversion; (b) cleaning, surface functionalization; (c) thermal bonding; and (d) lapping and polishing.
Fig. 2.
Fig. 2. False-color SEM images of (a) a pp-LNoQ on-chip WGR with a diameter of 216 μm and (b) zoomed view. Dark blue: LN with z axis pointing up. Light blue: LN with z axis pointing down. Brown: quartz substrate.
Fig. 3.
Fig. 3. Schematic of the setup for Q -factor measurement and investigation of second-harmonic generation.
Fig. 4.
Fig. 4. Measured conversion efficiency of SHG (blue dots) and theoretical curve fitted by the analytical model. Inset: Image of the WGR while second-harmonic light is generated and coupled out into the coupling waveguide.
Fig. 5.
Fig. 5. Mode cross section of (a) pump light and (b) second-harmonic light. (c) Fourier coefficients of a theoretical domain pattern with 23 μm periodicity and 5 μm domain width for type 0 phase matching, resulting in d ( ϕ ) .

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

η P sh P p = 4 r sh 1 + r sh r p 1 + r p X ( 1 + X ) 2
X ( 1 + X ) 2 = r p 1 + r p P p P 0 ,
P 0 = ν p π ε 0 n p 4 n sh 2 8 d eff 2 1 Q i , p 2 Q i , sh V eff ( 1 + r p ) 2 ( 1 + r sh ) .
2 m p m sh ± M = 0 ,
η ( P p ) 4 ( r p 1 + r p ) 2 r sh 1 + r sh 1 P 0 P p .

Metrics