Nonlinear optics in gallium phosphide cavities: simultaneous second and third harmonic generation

Blaine McLaughlin; David P. Lake; David P. Lake; Matthew Mitchell; Matthew Mitchell; Paul E. Barclay

doi:10.1364/JOSAB.455234

Journal of the Optical Society of America B
Vol. 39,
Issue 7,
pp. 1853-1860
(2022)
•https://doi.org/10.1364/JOSAB.455234

Nonlinear optics in gallium phosphide cavities: simultaneous second and third harmonic generation

Blaine McLaughlin, David P. Lake, Matthew Mitchell, and Paul E. Barclay

Open Access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Blaine McLaughlin, David P. Lake, Matthew Mitchell, and Paul E. Barclay, "Nonlinear optics in gallium phosphide cavities: simultaneous second and third harmonic generation," J. Opt. Soc. Am. B 39, 1853-1860 (2022)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Check for updates

Abstract

We demonstrate the simultaneous generation of second and third harmonic signals from a telecom wavelength pump in a gallium phosphide (GaP) microdisk. Using analysis of the power scaling of both the second and third harmonic outputs and calculations of nonlinear cavity mode coupling factors, we study contributions to the third harmonic signal from direct and cascaded sum frequency generation processes. We find that despite the relatively high material absorption in GaP at the third harmonic wavelength, both of these processes can be significant, with relative magnitudes that depend closely on the detuning between the second harmonic wavelengths of the cavity modes.

Full Article | PDF Article

More Like This

Second harmonic generation in gallium phosphide nano-waveguides

Aravind P. Anthur, Haizhong Zhang, Yuriy Akimov, Jun Rong Ong, Dmitry Kalashnikov, Arseniy I. Kuznetsov, and Leonid Krivitsky
Opt. Express 29(7) 10307-10320 (2021)

Optimal third-harmonic generation in an optical microcavity with χ⁽²⁾ and χ⁽³⁾ nonlinearities

Ming Li, Chang-Ling Zou, Chun-Hua Dong, and Dao-Xin Dai
Opt. Express 26(21) 27294-27304 (2018)

Cascaded third-harmonic generation of ultrashort optical pulses in two-dimensional quasi-phase-matching gratings

Nobuhide Fujioka, Satoshi Ashihara, Hidenobu Ono, Tsutomu Shimura, and Kazuo Kuroda
J. Opt. Soc. Am. B 24(9) 2394-2405 (2007)

Previous Article Next Article

Supplementary Material (1)

Name	Description
Supplement 1	Derivations of equations used in main text.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.

Fig. 1. (a) Energy level diagram of SHG, CSFG, and THG processes. Solid lines indicate WGM resonant modes, while dashed lines represent virtual energy levels. (b) Image of FDTD simulated normalized absolute field magnitude of the

${{\rm TE}_{{23,1}}}$

microdisk mode. White outline corresponds to the edge of the microdisk. (c) Image of FDTD simulated normalized absolute field magnitude of the

${{\rm TM}_{{48,2}}}$

microdisk mode.

Download Full Size | PDF

Fig. 2. Absolute values of second-order (outlined in red circles) and third-order (outlined in green squares) nonlinear coupling factors with the

${{\rm TE}_{{23,1}}}$

first harmonic mode. Groups of phase matched microdisk modes are plotted by the frequency and azimuthal number of the highest harmonic mode in the wave mixing process.

Download Full Size | PDF

Fig. 3. (a) Transmission spectrum of GaP microdisk pump mode around 1557 nm for 8.7 mW pump power. The Fano-like line shape of the observed resonance is attributed to a phase mismatch between the coupled fiber taper modes. (b) Second and (c) third harmonic output signal powers for several pump wavelengths and input powers. Top axes show the observed peak harmonic wavelength measured in the spectrometer.

Download Full Size | PDF

Fig. 4. On-resonance output power for second (orange) and third harmonic (green) signals. Solid lines are fits to the saturated resonance theory. The dashed line corresponds to quadratic power scaling predicted from zero depletion.

Download Full Size | PDF

Equations (19)

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

SHG: m_{2} = 2 m_{1} \pm 2,

CSFG: m_{3} = m_{1} + m_{2} \pm 2,

DTHG: m_{3} = 3 m_{1} .

\frac{d}{d t} a_{k} = (i ω_{k} - \frac{κ_{k}}{2}) a_{k} + \sqrt{\frac{κ_{k, e x}}{2}} s_{+},

s_{-} = s_{+} - \sqrt{\frac{κ_{k, e x}}{2} a_{k}},

κ_{k} = κ_{k, i + p} + κ_{k, e x} .

\frac{d}{d t} a_{1} = (i ω_{1} - \frac{κ_{1}}{2}) a_{1} + \sqrt{\frac{κ_{1, e x}}{2}} s_{+},

\frac{d}{d t} a_{2} = (i ω_{2} - \frac{κ_{2}}{2}) a_{2} - i ω_{2} β_{C S F G} a_{1}^{*} a_{3} + i ω_{2} β_{S H G} a_{1}^{2},

\frac{d}{d t} a_{3} = (i ω_{3} - \frac{κ_{3}}{2}) a_{3} + i ω_{3} β_{C S F G}^{*} a_{1} a_{2} + i ω_{3} β_{D T H G} a_{1}^{3},

P_{2} = \frac{η_{S H G} P_{i n}^{2}}{{(1 + ζ P_{i n})}^{2}},

P_{3} = η_{D T H G} P_{i n}^{3} + \frac{η_{C S F G} P_{i n}^{3}}{{(1 + ζ P_{i n})}^{2}},

η_{S H G} = 32 ω_{1}^{2} | β_{S H G} |^{2} \frac{κ_{1, e x}^{2} κ_{2, e x}}{κ_{1}^{4} κ_{2}^{2}},

η_{D T H G} = 144 ω_{1}^{2} | β_{D T H G} |^{2} \frac{κ_{1, e x}^{3} κ_{3, e x}}{κ_{1}^{6} κ_{3}^{2}},

η_{C S F G} = 2304 ω_{1}^{4} | β_{S H G} |^{2} | β_{C S F G} |^{2} \frac{κ_{1, e x}^{3} κ_{3, e x}}{κ_{1}^{6} κ_{2}^{2} κ_{3}^{2}},

ζ = 96 ω_{1}^{2} | β_{C S F G} |^{2} \frac{κ_{1, e x}}{κ_{1}^{2} κ_{2} κ_{3}},

\frac{δ ω_{k}}{ω_{k}} = - \frac{1}{2} \frac{\int_{ε} E^{*} \cdot δ P_{k} d^{3} x}{\int ε | E |^{2} d^{3} x},

β_{S H G} = \frac{1}{4} \frac{\int d^{3} x \sum_{ijk} ε χ_{ijk}^{(2)} [E_{1 i}^{*} E_{2 j} E_{1 k}^{*} + E_{1 i}^{*} E_{1 j}^{*} E_{2 k}]}{\int d^{3} x ε | E_{1} |^{2} {(\int d^{3} x ε | E_{2} |^{2})}^{1 / 2}},

β_{C S F G} = \frac{1}{4} \frac{\int d^{3} x \sum_{ijk} ε χ_{ijk}^{(2)} [E_{2 i}^{*} E_{3 j} E_{1 k}^{*} + E_{2 i}^{*} E_{1 j}^{*} E_{3 k}]}{{(\int d^{3} x ε | E_{1} |^{2})}^{1 / 2} {(\int d^{3} x ε | E_{2} |^{2})}^{1 / 2} {(\int d^{3} x ε | E_{3} |^{2})}^{1 / 2}},

β_{D T H G} = \frac{3}{8} \frac{\int d^{3} x ε χ^{(3)} (E_{1}^{*} \cdot E_{1}^{*}) (E_{1}^{*} \cdot E_{3})}{{(\int d^{3} x ε | E_{1} |^{2})}^{1 / 2} {(\int d^{3} x ε | E_{3} |^{2})}^{3 / 2}},

Abstract

Supplementary Material (1)

Data availability

Cited By

Figures (4)

Equations (19)

Journal of the Optical Society of America B