5.4 Waveguides in bulk wafers (1974 to today)

L1 Phenomenon

Before thin films, light was guided in a slightly raised-index skin near the surface of a bulk wafer. Two routes made it: baking titanium stripes into the crystal at about 1000 °C, or swapping lithium for hydrogen in hot benzoic acid. Both give waveguides several micrometres wide with weak confinement (Ti stripes 7 µm wide Luo et al. 2019; ion-diffused index contrast below 0.02 Wang et al. 2018; proton exchange +0.12 on the extraordinary index only Jackel et al. 1982), which is why bulk LN circuits have large footprints Sun et al. 2020. Etched thin films reach an index contrast of 0.67 against SiO₂ Wang et al. 2018.

Proton exchange in benzoic acid, x-cutE_a 0.90 eV derived

(a) exchange depth vs time at T; dashed outside 217–249 °C

Temperature T249 °C

Time t 4.0 h

Rate read as

d²/t

Time axis

linear

T 249 °Ct 4.0 hd 2.34 µmr 1.37 µm²/hderived

(b) Ti indiffusion: reported recipes

Ti 80 nm, 7 µm stripes, z-cut	1060 °C, 9 h	P
Ti on −z face, O₂ flow, z-cut	1035 °C, 12 h	P
First report: Ti, V, Ni films	confined within about 1 µm	P(abs)

No sourced Ti diffusion coefficient: recipes are shown as points, and no Ti depth curve is drawn.

PE index step +0.12 on n_e only, step profile at 633 nm; loss < 0.5 dB/cm P(abs)

r(T) = r(249 °C) exp[−(E_a/k_B)(1/T − 1/522.15 K)] through the two reported points; whether the reported rate means d²/t or D is not confirmed from the full text, so both readings are offered.

Melt temperature249 °C

Exchange time4.0 h

Light at 1550 nm (false color), polarization

Ti indiffusion: no sourced diffusion coefficient, so no Ti depth curve; reported recipes 80 nm Ti at 1060 °C for 9 h P and 1035 °C for 12 h P. PE index step +0.12 on n_e only P(abs).

Depth: 2.34 µm
Guided mode: yes: n_e + 0.12

Inside the reported 217–249 °C window. Mode outline is a sketch, not a solved mode. derived

L2 Model and data

Titanium indiffusion

Quantity	Value	Source; status
First report	Ti, V, and Ni films diffused into LiNbO₃; Ti gives single-mode low-loss guides confined within about 1 µm of the surface	P(abs)
Recipe, z-cut, telecom	7 µm wide, 80 nm thick Ti stripes; 1060 °C for 9 h	P
Recipe, z-cut	Ti on the -z face; 1035 °C with constant O₂ flow for 12 h	P
Commercial Ti:LN modulators	up to 40 GHz (Exail catalogue)	V

Proton exchange (PE), annealed PE (APE), reverse PE (RPE)

Quantity	Value	Source; status
Melt	benzoic acid, 200-250 °C	P(abs)
Index change	+0.12 for the extraordinary index only; step profile (633 nm)	P(abs)
Diffusion rate, x-cut	1.37 µm²/h at 249 °C; 0.37 µm²/h at 217 °C; slower along z	P(abs)
Apparent activation energy from those two points	0.90 eV	derived Arrhenius fit through two points; meaning of "rate" (d²/t vs D) not confirmed from the full text, so this is a template-grade estimate
Loss	< 0.5 dB/cm, x-cut, 633 nm	P(abs)
RPE waveguides	normalized SHG efficiency about 100 %/W/cm² (1 W⁻¹ cm⁻²); 0.1-0.2 dB/cm loss typical	P
Ridge vs PE for power handling	vendor statement (HC Photonics) that ridge waveguides handle more power	V

L3 Details and open points

APE and RPE add a high-temperature anneal and a Li-rich reverse exchange that bury the index profile; the as-exchanged layer has strongly reduced nonlinearity P.
Out-diffusion of Li₂O at high temperature also raises the surface index; the 1973 "thin-film LiNbO₃" modulator used such an out-diffused planar guide in bulk LN P(abs).
Ion-beam-enhanced etching produced ridge waveguides in bulk (Zn:LN) before thin films existed P(title), S, S.

← 5.3 Wafers 5.5 Thin film: LNOI →