Introduction

Second-harmonic generation (SHG) is a case of nonlinear optical interaction; this phenomenon occurs when light (typically laser beam) goes through nonlinear material, generating a beam with higher energy. In other words, two photons of the same frequency generate a new photon with the double frequency of the input photons and shorter to half wavelength when they interact with nonlinear materials. SHG is also known as frequency doubling; this phenomenon was discovered by Franken and his colleagues about sixty years ago. (‎1) (‎2)

Frequency doubling occurs in a nonlinear material, crystals do not contain inversion centers, as determined by second-order nonlinear susceptibility .  Figure 1 a) illustrates geometry and b) illustrates energy-level of: (‎2)


Figure 1. a) represent SHG. b) illustration of energy-level for SHG. (Figure: Miriam Yakob)

Physical process

The insert beam generates a nonlinear polarization (P) wave interacting with nonlinear crystal because of the impact of  . The equation below describes nonlinear polarization P(t)   in a non-centrosymmetric material:

   P(t)=   ϵ0χE(t)          (1)

Where: E is the strength of an optical field, below is general equation for field strength:

E(t) = Ee^-iωt+...      (2)

By combing equations 1 and 2 for second-order nonlinear polarization equation:

                 P^2(t)= 2ϵ0χ^2EE+(2ϵ0χ^2E^2e^(-i2ωt)+...)             (3)

ϵ0 is the permittivity of free space, and t is for time. (‎2) (‎3)

The nonlinear polarization wave scatters higher energy beam with twice the frequency in the same direction of the input beam, generating two fields: electromagnetic, and due to phase-matching, second harmonic. Second-harmonic field interacts also with the inserted beam and results energy moving from input photons to the second harmonic photons. (‎3)

Phase matching

Phase matching in SHG-material means that the vectors of input wave and output second-harmonic wave are the same (𝞓k= 0), thus optical indices n(ω)= n(2ω). Phase matching is essential for SHG uses in different applications; even a small amount of mismatching has a huge negative impact on SHG efficiency. (‎3) ‎(4) (‎9) There are two types of phase-matching: Critical or angle phase matching and noncritical. In the first one, the wave is either refracts at an angle (extraordinary polarization) or goes straight through the material (ordinary polarization) (‎5)(‎6)(‎1). In the latter, phase matching is achieved by modifying the temperature of the material (‎7).  

SHG Materials

As mentioned before, SHG occurs in non-centrosymmetric materials meaning materials without inversion centers. For high performance in different applications, nonlinear crystal should include phase matching and large band gap, additionally to transparency. (‎8) some materials used for SHG:

  • borate crystals such as bismuth borate (BiB3O6), cesium lithium borate (CsLiB6O10), and β phase barium borate (β-BaB2O4). Figure 2 shows the crystal structure of a) bismuth borate b) cesium lithium borate c) (β-BaB2O4). (‎1‎) (10)


a                                                           b                                                             c

Figure 2. Crystal structures of a) BiB3O6 b) CsLiB6O10 c) β-BaB2O4. (Figure: Miriam Yakob)


  • Niobate crystals like lithium niobate (LiNbO3) and potassium niobate (KNbO3) (fig 3). (‎1) (‎10)

                                                                                    a                                                                        b


Figure 3. 3D crystal structure a) LiNbO3 b) KNbO3. (Figure: Miriam Yakob)


  • Other materials fabricated and used for SHG applications: monopotassium phosphate (KH2PO4) (fig 4 a) (‎8), and α- and β-silver polyiodates (α-AgI3O8 and β-AgI3O8) (fig 4 b).

                                                                                       a                                                                  b

Figure 4. Structures of a) AgI3O8.  b) KH2PO4  (Figure: Miriam Yakob)

Applications

SHG is used in laser technology to make specific types of lasers (‎8). SHG phenomena are utilized in microscope imaging for biomedical applications; SHG imaging microscopy is used for disease discovery (‎11).

References

  1. Second-harmonic generation. 2.2022 Wikipedia. Referred 14.03.2022.
  2. Boyd. (2007) “The Nonlinear Optical Susceptibility, book Elsevier”. Nonlinear Optics, book (third ed.) 1-67.
  3. Paschotta. N. d. Frequency doubling; RP Photonics Encyclopedia. Retrieved 14.3.2022. Website.
  4. Zhang et al., Phase-Matching in Nonlinear Optical Compounds: A Materials Perspective; Chemistry of Materials 2017 (7) 2655-2668.
  5. Paschotta. N. d. Critical phase matching; RP Photonics Encyclopedia. Retrieved 15.03.20212. Website.
  6. Double Refraction. N. d. Britannica. Retrieved 15.03.2022. Website.

https://www.britannica.com/science/double-refraction

  1. Paschotta, n. d. Noncritical Phase Matching; RP Photonics Encyclopedia. Retrieved 15.03.2022.
  2. Chen et al., High-Performance Second Harmonic-Generation (SHG) Materials: New Developments and New Strategies; American Chemical Society 2021 (12) 2775-2783.

https://doi.org/10.1021/acs.accounts.1c00188

  1. Eckardt et al., Phase Matching Limitations of High Efficiency Second-Harmonic Generation; IEEE Journal of Quantum Electronics 1984 (20) 1178-1187.
  2. Pascotta, n. d. Nonlinear Crystal Materials; RP Photonics Encyclopedia. Retrieved 16.03.2022.
  3. Campagnola, Second Harmonic Generation Imaging Microscopy: Applications to Diseases Diagnostics; Analytical chemistry 2011 (83) 3224-3231. (https://doi.org/10.1021/ac1032325)

 

 

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