Yun-feng Xiao - Ultra-high-q Optical Microcavities

Cheng Wang

*Department of Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong, China

HyperLight Corporation, 501 Massachusetts Avenue, Cambridge, MA 02139, USA

John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA

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Lithium niobate (LN) is an excellent nonlinear optical and electro-optic material that has found many applications in classical nonlinear optics, optical fiber communications and quantum photonics. Here we review the recent development of thin-film LN technology that has allowed the miniaturization of LN photonic devices and microcavities with ultra-high quality factors. We discuss the design principle of LN devices that makes use of the largest nonlinear coefficients, various device fabrication approaches and resulting device performances, and the current and potential applications of LN microcavities.

Since the discovery of optical nonlinearities in the 1960s, lithium niobate (LiNbO3, or LN) has been the most widely used second-order ((2)) material, with applications ranging from nonlinear wavelength conversion for classical and quantum light source,.

Table 1.1 Optical properties of representative (2) materials (~1,500 nm wavelength).

Since the (2) nonlinear processes are much weaker than linear optical processes, it is a natural choice to use high-Q microcavities to enhance the (2) processes. However, standard photonic device fabrication techniques commonly used in other material systems are not readily compatible with LN, the challenges of which will be discussed in more details in The low index contrast results in weak light confinement and large bending radii (~10 cm), preventing the realization of tightly confined microcavities in LN.

Where there is a will, there is a way, or perhaps more than one way. Many different technological approaches have been extensively studied in recent years in order to realize high-Q microcavities in LN. Along with such technology development, we see a continuous improvement in the Q factors of these cavities, as well as the emergence of a variety of applications.

In this chapter, we provide an overview of basic design principles for LN devices, recent advances in LN fabrication technology, as well as their applications in nonlinear optics and electro-optics.

Fig. 1.1 Schematic of traditional ion-diffused waveguides. The low index contrast between the waveguide core and cladding results in large mode areas and weak nonlinear interactions.

Needless to say, most applications of LN photonic devices are closely associated with (2) processes. However, a rigorous mathematic treatment of (2) processes can be quite complicated, since solving a three-wave-mixing process requires tensor analysis at the rank 3. The full (2) tensor has a total of 27 components, connecting the 3 waves and a total of 9 vector field components. Taking sum-frequency generation (1 + 23) as an example, the generated nonlinear polarization at 3 can be expressed as:

where i, j, k {x, y, z}.

Fortunately, in most LN applications, such full treatment is not required. Instead, there is only one critical component out of the 27 the , since this component is much larger than all other ones. Equation (1.1) can therefore be reduced to a scalar equation. Note that different notations such as d33 and r33 are often used for certain processes, which we will explain next, but keep in mind that they all correspond to .

Long story short, there is only one design rule for almost all LN photonic devices: align the directions of all electric fields with the z axis.

As shown in , taking a z-cut LN crystal as an example, transverse-magnetic (TM) optical modes are preferred for optical waves, and electrical contacts should be placed on top and bottom of the optical waveguide.

For second harmonic generation (SHG) [], where pump light at a frequency of is frequency doubled to a signal frequency of 2, the generated nonlinear polarization at 2 can be expressed as:

where d33 = is ~30 pm/V for LN and Ez() is the pump electric field z component.

Fig. 1.2 Cross-section illustrations showing the ideal alignment of the electric fields with LN crystal (z-cut in this case) in order to utilize the components. (a) For SHG, TM modes are preferred. (b) For electro-optic modulation, TM optical modes and top-bottom electrodes are preferred.

For electro-optic modulation [], a DC (or microwave) electric field induces a change in optical index of refraction. For LN, the index change for z-polarized light can be expressed as:

where nz is the linear refractive index for z-polarized light, r33 = 30.9 pm/V for LN, and Ez is the DC (or microwave) electric field in z direction.

Just like the majority of silicon photonics integrated circuits rely on silicon-on-insulator (SOI) substrates, a straightforward approach to build nanophotonic devices in LN is to use sub-micron thick, single-crystalline LN films that stand on top of a transparent and lower refractive index substrate, typically silica (SiO2). These substrates are called lithium niobate on insulator (LNOI). The LNOI wafers are fabricated using a Smart-cut ion-slicing process (

Fig. 1.3 Schematic of LNOI wafer production.

Thanks to the industrial development of LNOI technology in the past decade, high-quality LNOI wafers are now commercially available at sizes up to 4 inches, with various choices of crystal orientations and bottom handles. There are two major choices of LNOI crystal orientations z-cut and x-cut. As we have discussed in

The LNOI production processes also allow for different choices of bottom substrates (). Apart from the possibility of pre-embedding the metal contact layer in the LNOI wafers, popular handle materials include LN, silicon and quartz. LN handles possess the same thermal expansion constants as the device layer, therefore provide the best wafer-bonding quality. Silicon handles offer the possibility of using thermally grown SiO2 as the bottom cladding layer. Thermal SiO2 possesses much lower optical absorption losses than SiO2 grown on top of LN or quartz handles using plasma-enhanced chemical vapor deposition (PECVD). Quartz is an attractive handle material for applications that require high-performance microwave delivery (e.g. high-speed electro-optic modulators) due to its low microwave loss.