Patterned Illumination via Phase Mask using fs-LAP

Another form of patterning via interference is possible using a phase mask placed near the −z face of the crystal. To increase the intensity incident on the phase mask, the truncated Gaussian beam was lightly focused providing a large depth of focus. The target LN crystal was held near the phase mask by the O-rings, as shown in Figure 6.23. The phase mask was oriented such that the grating k-vector was parallel to the x axis of the LN crystal, producing grating intensity lines aligned along the y axis, similar to the photoresist gratings used in the fabrication of PPLN by EFP.

The design of a phase mask for the formation of a QPM LAP domain grating requires knowledge of the dispersion curve of the target material, discussed in Section 2.2.2.2, and the resulting coherence length, discussed in Section 2.1.1. For SHG interactions in Mg:CLN and choosing a fundamental wavelength of λf = 800 nm (which is readily pro-

vided by a Ti:sapphire laser), the coherence length was calculated to be`c = 1312.9 nm.

Therefore, the period of grating required for QPM is Λg = 2`c = 2625.8 nm. For a

+1/−1 phase mask configuration with normal incidence, the illumination pattern ac- quires half the period of the phase mask, meaning the phase mask should be designed with Λpm= 5251.5 nm. This period has the added benefit of resulting in phase matching

in undoped CLN forλf '813.5 nm, within the tuning range of a Ti:sapphire laser. The

wavelength of operation of the phase mask itself was designed to be λ= 514.5 nm.

Figure 6.23 also reveals the problem of the aqueous environment in which the phase mask was immersed. Several manufacturers were unable to provide phase masks designed for operation in water, and thus the phase mask used had been optimized for operation in air. Using a scalar approximation, the 0-order of the phase mask can be minimized

LiNbO

L

F

633 nm

Water

O-Ring

Fused Silica

-HV+

Phase Mask

P

L

L

z

x

y

CCD

fs

Figure 6.23: Patterned LAP setup, showing the fs-pulsed beam incident on a phase

mask in front of the−z face of a lithium niobate sample, held between water electrodes using transparent fused silica plates. The polarized beam ofλ= 633 nm light is of low intensity and used only for visualization of the poling process via the crossed polarizer and CCD camera. The 3D coordinate system describes the orientation of the target

sample. (F = red filter; L = lens; P = polarizer; HV = high voltage.)

when the groove depth is [Hegedus97],

d= λ

2(npm−na)

(6.4)

wherenpmandnaare the refractive indices of the phase mask and the ambient materials,

respectively, and λ is the design wavelength of the phase mask. Because the groove depth was optimized for na = nair = 1, not for nwater, the resulting interference

pattern is no longer a simple interference of +/−1 orders. Instead, there was a very significant 0-order component as well, measured to be∼50% of the incident power in an aqueous environment. In addition to these diffraction orders, higher orders must also be considered due to the wavelength of operation and the design period [Hecht02]:

sinθm=

mλ

Λg ∴

|m| ≤ Λg

λ (6.5)

where θm is the diffraction angle of order m, and Λg is the grating period. From this

equation, for a period of 5251.5 nm and wavelength of 514.5 nm, 10 diffraction orders are expected from the phase mask, and all were observed.

Due to these disadvantages of the phase mask setup, the ideal periodic diffraction pattern was not realized. The most important result was the production of a diffraction grating with a period equal to the phase mask period, rather than one-half as would be expected for a +1/−1 phase mask configuration. This period resulted from the interference of diffraction ordersm= 0, ±1. However, due to the 0-order, the modulation depth of the

diffraction grating changed with distance away from the phase mask [Mills01]. Experi- mentally this meant that the precise placement of the LN crystal was very important for the reliable fabrication of periodic domains, ideally with a modulation depth of 100% (sinusoidal on/off bands of illumination). A small modulation depth, in contrast, would encourage lateral spreading of the domains so that merging of adjacent periods was more likely.

Despite these issues, periodic domain formation was possible via static illumination of the phase mask by λ = 514.5 nm light, shown following HF etch in Figure 6.24. In all these typical examples, the period of 5.25µm was precisely replicated, and the amount of spreading from the spot center to the edges followed the intensity profile of this Gaussian beam. The images have been chosen to show a transition from merging throughout the illumination spot (a) to a separation between all adjacent periods throughout the spot width (f). In general, a reduction of any of the three parameters of E-field, intensity, and illumination time lead to less lateral spreading and more clearly separated domain periods. A more uniform pattern is expected for a more uniform intensity profile, as has been seen in other patterned illumination.

One of the benefits of the use of a phase mask is the ability to scan the beam across the phase mask along the direction of the gratingk-vector, greatly extending the number of periods illuminated while maintaining the exposure parameters ofE-field and intensity. In this way, the length of the periodic structure is limited only by the length of the phase mask, rather than the size of the beam itself. In this hybrid direct-write/interference technique, the parameter of illumination time is replaced by thedwell time of the laser, or equivalently the scan speed. Figure 6.25 shows various regions exposed using this scanning method in 5-mol% Mg:CLN using an intensity and E-field of 0.5 GW/cm2 and 1200 V/mm, respectively. In (a–b), slow manual scanning caused over-exposure, resulting in merged domains and jagged edges as the domains spread away from the intensity peaks. Under the improved faster manual scanning in (c–d), a high-quality periodically poled grating is formed, exhibiting straight domain walls aligned with the illumination pattern. The inverted/non-inverted duty-cycle of this example is ∼25/75. However, precise control of all exposure conditions should allow the formation of the optimal 50/50 duty-cycle. Nonetheless, the 25/75 duty-cycle obtained in these exposures is already optimal for even-ordered QPM [Fejer92], meaning this poled grating would be suitable for our designed SHG interaction.

Prior to chemical etching, these spots were investigated by illumination using a HeNe laser. Despite the absence of surface patterning, diffraction was caused by electro-optic contrast from internal fields [M¨uller03b] and the charged domain walls of the surface domains. The illuminated spots showed ±1 and ±2 diffraction orders, as depicted in Figure 6.26. Measuring the diffraction angles of them= 1 order allowed the calculation of the diffraction grating period,

Λg =

mλ

Figure 6.24: SEM micrographs of the domain patterns produced in 5-mol% Mg:CLN

using phase mask illumination with fs-pulsed light of wavelength λ = 514.5 nm with an illumination period Λ = 5.25µm. The exposure conditions appear at the top-right

corner of each image.

where m is the diffraction order, λ = 633 nm is the wavelength, and θ is the diffrac- tion angle. From this measurement, the diffraction grating period was determined to be 5138 nm. The design period of the phase mask (5251.5 nm) would produce a diffraction angle within 0.15◦ of the measured angle, well within the measurement accuracy, veri- fying that the induced pattern in the material closely follows the illumination pattern.