SCALABLE MANUFACTURING WITH LASER INDUCED REFRACTIVE INDEX CHANGE

Abstract

Methods of designing a laser writing system for modifying a plurality of ophthalmic devices, and systems designed in accordance with those methods. One example of such a method includes: (a) determining at least one material characteristic of the ophthalmic devices, determined over a range of laser writing system parameters; (b) determining at least one design characteristic of the ophthalmic device; and (c) using at least the determined material and design characteristics, configuring at least one system parameter of the laser writing system to optimize throughput of the laser writing system, the laser writing system including: (i) a laser configured to generate a laser beam, (ii) a splitter configured to split the laser beam into a plurality of outputs, and (iii) a plurality of writing heads, each writing head configured to direct at least one of the outputs to an ophthalmic device to write one or more localized refractive index modifications into the ophthalmic device.

Claims

1. A method of designing a laser writing system for modifying a plurality of ophthalmic devices, the method comprising: (a) determining at least one material characteristic of the ophthalmic devices, determined over a range of laser writing system parameters; (b) determining at least one design characteristic of the ophthalmic device; and (c) using at least the determined material and design characteristics, configuring at least one system parameter of the laser writing system to optimize throughput of the laser writing system, the laser writing system comprising: (i) a laser configured to generate a laser beam, (ii) a splitter configured to split the laser beam into a plurality of outputs, and (iii) a plurality of writing heads, each writing head configured to direct at least one of the outputs to an ophthalmic device to write one or more localized refractive index modifications into the ophthalmic device.

2. The method of claim 1: wherein the at least one material characteristic includes a damage threshold for an induced single layer optical phase shift of the ophthalmic device; and wherein the at least one design characteristic includes a maximum phase shift designed for the ophthalmic device.

3. The method of claim 2, wherein the at least one material characteristic includes at least a first damage threshold for an induced single layer optical phase shift of the ophthalmic device at a first laser repetition rate, and a second damage threshold for an induced single layer optical phase shift of the ophthalmic device at a second laser repetition rate.

4. The method of claim 2 or 3, wherein the range of laser writing system parameters used for determining the at least one material characteristic includes at least one of a power range, a scan speed range, a laser repetition rate range, and a range of focusing lens numerical aperture.

5. The method of claim 4, wherein the range of laser writing system parameters used for determining the at least one material characteristic includes at least two of the power range, the scan speed range, the laser repetition rate range, and the focusing lens numerical aperture.

6. The method of claim 4 or 5, wherein the determined material characteristics also include at least one fitting parameter of a quantitative model relating an induced phase shift in the ophthalmic device to a configuration of the laser writing system.

7. The method of claim 6, wherein the determined material characteristics also include a multiphoton order of the quantitative model.

8. The method of claim 7, wherein the quantitative model is a two photon regime model comprising: $\Delta \varphi \left(P,\upsilon ,S,\mathrm{NA}\right):=\beta .Math.\left(\frac{P^2.Math.\mathrm{NA}}{\upsilon .Math.{\lambda }^3.Math.S.Math.\tau }\right)$ wherein Δϕ is a single layer written phase shift, P is an average power, NA is a numerical aperture, ν is a laser repetition rate, λ is a laser wavelength, S is a scan speed, π is a pulse duration, and β is the fitting parameter.

9. The method of claim 7, wherein the quantitative model is a three photon regime model comprising: $\Delta \Phi :=\frac{\gamma .Math.P^3.Math.{\mathrm{NA}}^3}{{\upsilon }^2.Math.{\tau }^2.Math.{\lambda }^5.Math.S}$ wherein Δϕ is a single layer written phase shift, P is an average power, NA is a numerical aperture, ν is a laser repetition rate, λ is a laser wavelength, S is a scan speed, π is a pulse duration, and γ is the fitting parameter.

10. The method of claim 7, wherein the quantitative model is a four photon regime model comprising: $\Delta \varphi =\gamma .Math.\frac{P^4.Math.{\mathrm{NA}}^5}{{\upsilon }^3.Math.{\tau }^3.Math.S.Math.{\lambda }^7}$ wherein Δϕ is a written single layer phase shift, P is an average power, NA is a numerical aperture, ν is a laser repetition rate, λ is a laser wavelength, S is a scan speed, π is a pulse duration, and γ is the fitting parameter.

11. The method of claim 9, wherein the quantitative model further comprises a saturation factor.

12. The method of claim 7, wherein the quantitative model is an N.sup.th photon regime model comprising: $\Delta \Phi :=\frac{\gamma .Math.P^N.Math.{\mathrm{NA}}^{2.Math.N-3}}{{\upsilon }^{N-1}.Math.{\tau }^{N-1}.Math.{\lambda }^{2.Math.N-1}.Math.S}$ wherein Δϕ is a single layer written phase shift, P is an average power, NA is a numerical aperture, ν is a laser repetition rate, λ is a laser wavelength, S is a scan speed, π is a pulse duration, and γ is the fitting parameter.

13. The method of claim 7, wherein the multiphoton order of the quantitative model is a two photon regime, a three photon regime, or a four photon regime.

14. The method of claim 6, wherein the quantitative model comprises a sum of a plurality of multi-photon regime models.

15. The method of claim 14, wherein the quantitative model comprises: $\Delta \Phi :=\beta .Math.\frac{P^2.Math.\mathrm{NA}}{\upsilon .Math.\tau .Math.{\lambda }^3.Math.S}+\gamma .Math.\frac{P^3.Math.{\mathrm{NA}}^3}{{\upsilon }^2.Math.{\tau }^2.Math.{\lambda }^5.Math.S}+\delta .Math.\frac{P^4.Math.{\mathrm{NA}}^5}{{\upsilon }^3.Math.{\tau }^3.Math.{\lambda }^7.Math.S}$ wherein Δϕ is a single layer written phase shift, P is an average power, NA is a numerical aperture, ν is a laser repetition rate, λ is a laser wavelength, S is a scan speed, π is a pulse duration, β is a second order fitting parameter, γ is a third order fitting parameter, and 6 is a fourth order fitting parameter.

16. The method of any one of claims 2-15, wherein optimizing throughput of the laser writing system comprises determining an optimal number of writing layers for modifying the ophthalmic devices in combination with an optimal number of writing heads of the laser writing system for optimizing throughput of the laser writing system.

17. The method of any one of claims 2-16, wherein optimizing throughput of the laser writing system comprises determining at least one of an optimal laser repetition rate, laser wavelength, laser pulsewidth, and scan speed for optimizing throughput of the laser writing system.

18. The method of any one of claims 2-17, wherein determining the at least one material characteristic of the ophthalmic devices includes determining the at least one material characteristic over a first range of laser writing system parameters and a second range of laser writing system parameters, the first and second ranges including at least one different laser repetition rate parameter, laser wavelength parameter, laser pulsewidth parameter, and scan speed parameter.

19. The method of any one of claims 2-18, further comprising determining a line spacing characteristic of the ophthalmic device.

20. A laser writing system for modifying a plurality of ophthalmic devices, the laser writing system comprising: (a) a laser configured to generate a laser beam, (b) a splitter configured to split the laser beam into a plurality of outputs, and (c) a plurality of writing heads, each writing head configured to direct at least one of the outputs to an ophthalmic device to write one or more localized refractive index modifications into the ophthalmic device; wherein the laser writing system is configured in accordance with the method of any one of claims 1-19.

21. The system of claim 20, wherein the laser is configured to generate a pulsed laser beam having a pulsewidth less than 350 femtoseconds and a repetition rate between 1 and 60 MHz.

22. The system of claim 21, wherein the laser is configured to generate a pulsed laser beam having a wavelength in the range of 340 nm to 1100 nm.

23. The system of claim 22, wherein the laser is configured to generate a pulsed laser beam having a wavelength in the range of 515 nm to 520 nm, or 1030 nm to 1040 nm, or 400 nm to 410 nm, or 795 nm to 805 nm.

24. The system of claim 20, wherein the splitter is configured to split the laser beam into 2 to 64 outputs.

25. The system of claim 20, wherein the ophthalmic devices are contact lenses or intraocular lenses, or hydrogel corneal implants.

26. A method of using a laser writing system for writing localized refractive index changes into ophthalmic devices, the method comprising providing a laser writing system in accordance with any one of claims 20-25, and (a) generating a pulsed laser beam in the laser writing system; (b) splitting the pulsed laser beam into a plurality of outputs, at least some of the outputs each associated with a writing head in the laser writing system; and (c) at each writing head, scanning the pulsed laser beam relative to an ophthalmic device to write one or more refractive index changes into the ophthalmic device.

27. A method using a laser writing system for writing localized refractive index changes into ophthalmic devices, the method comprising: (a) generating a pulsed laser beam having a wavelength in the range of 1030 nm to 1040 nm, a pulsewidth less than 350 femtoseconds, and a repetition rate less than 20 MHz; (b) splitting the pulsed laser beam into a plurality of outputs, at least some of the outputs each associated with a writing head; (c) at each writing head, scanning the pulsed laser beam relative to an ophthalmic device to write one or more refractive index changes into the ophthalmic device, wherein the laser writing system is configured such that it is capable of inducing a single writing layer phase shift of at least 0.3 waves at an average power at the writing head of less than 1500 mW and a scan speed greater than 100 mm/s.

28. The method of claim 27, wherein the ophthalmic device is a hydrogel material having a four photon absorption parameter in the range of 1e-59 m.sup.6.Math.waves/(W.sup.4.Math.s) to 3e-59 m.sup.6.Math.waves/(W.sup.4.Math.s) in the equation: $\Delta \varphi =\gamma .Math.\frac{P^4.Math.{\mathrm{NA}}^5}{{\upsilon }^3.Math.{\tau }^3.Math.S.Math.{\lambda }^7}$ wherein Δϕ is a written single layer phase shift, P is an average power of the pulsed laser beam at the writing head, NA is a numerical aperture of the writing head, ν is a laser repetition rate, λ is a laser wavelength, S is a scan speed, π is a laser pulse duration, and γ is the four photon absorption parameter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] FIG. 1 illustrates a femtosecond writing system. The Yb doped fiber laser is able to deliver femtosecond pulses at a series of adjustable repetition rates and with maximum output power up to 30 W.

[0040] FIGS. 2(a)-(b) are DIC images of the grating lines written at an average power of ˜500 mW, at scan speeds of 5 mm/s, 50 mm/s and 100 mm/s (from top to bottom), and at repetition rates of 15 MHz (a) and 60 MHz (b), respectively.

[0041] FIGS. 2(c)-(d) are DIC images of the grating lines written at average powers of ˜500 mW, 1000 mW and 1500 mW (from top to bottom), at a scan speed of 100 mm/s, and at repetition rates of 15 MHz (c) and 60 MHz (d), respectively.

[0042] FIG. 3(a) is a DIC image of four phase bars written in a J+J contact lens at two different powers, 1075 mW (top two) and 1105 mW (bottom two).

[0043] FIG. 3(b) is a schematic diagram showing two different scanning methods—raster scanning (left) and rectangular loop scanning (right).

[0044] FIG. 3(c) is an interferogram of the two phase bars written at a power of 1105 mW, a scan speed of 200 mm/s, and a repetition rate of 15 MHz.

[0045] FIG. 3(d) is a phase map showing phase difference between the laser-treated area and the surroundings.

[0046] FIGS. 4(a)-(d) illustrate quantitative results showing the phase change magnitude measured at 543 nm for the phase bars written in a J+J Acuvue contact lens as a function of power (FIG. 4(a)) and as a function of single pulse energy (FIG. 4(b)); phase bars written in a Contaflex GM Advance 58 sample as a function of power (FIG. 4(c)) and as a function of single pulse energy (FIG. 4(d)) at different repetition rates, 5 MHz, 10 MHz, 15 MHz and 60 MHz.

[0047] FIGS. 5(a) and 5(b) are plots of logarithm of the induced phase change at 543 nm versus logarithm of the average power in the focal volume at 5 MHz, 10 MHz, 15 MHz and 60 MHz for the Contaflex sample (a) and the J+J contact lens (b) for the purpose of the determination of the order of multiphoton absorption process.

[0048] FIG. 6 illustrates quantitative results showing the phase change magnitude measured at 543 nm written in a Contamac 58 sample as a function of power.

[0049] FIG. 7 is a plot of logarithm of the induced phase change at 543 nm versus logarithm of the average power in the focal volume for the Contamac 58 sample.

[0050] FIG. 8 schematically illustrates one example of LIRIC multi-head writing system.

[0051] FIG. 9 schematically illustrates one example of a high power splitter arrangement usable with the LIRIC multi-head writing system of FIG. 8.

[0052] FIG. 10 schematically illustrates one example of a scanning and delivery subsystem usable with the LIRIC multi-head writing system of FIG. 8.

[0053] FIG. 11 illustrates a pulse energy range in which a refractive index change occurs below a threshold in which gross material damage or scattering effects would occur.

[0054] FIG. 12 illustrates a scan speed range in which a refractive index change occurs above a threshold in which gross material damage or scattering effects would occur.

[0055] FIG. 13 illustrates examples of LIRIC lenses created in plano hydrogel.

[0056] FIG. 14 illustrates an example of a Fresnel-type phase-wrapped optical lens written in a thin layer.

[0057] FIG. 15 is data plotting phase change as a function of power and speed in Johnson & Johnson Acuvue2 contacts in response to 100 fs laser pulses at a repetition rate of 80 MHz and 800 nm, for speeds of (a) 3 mm/s, (b) 5 mm/s, (c) 10 mm/s, (d) 15 mm/s, (e) 20 mm/s, (f) 30 mm/s, and (g) 40 mm/s.

[0058] FIG. 16 is a three-dimensional visualization of the data in FIG. 15.

DETAILED DESCRIPTION

[0059] The following detailed description sets out examples of LIRIC writing systems and methods for ophthalmic materials, as well as techniques using our photochemical models for improving LIRIC manufacturing systems and methods. The specific examples described below are for illustrative purposes only, and are not intended to limit the scope of our inventions. Changes could be made to the systems, methods, and techniques described below without departing from the scope or spirit of our inventions.

Laser Pulse Repetition Rate

[0060] In some of the examples described in this patent, in order to enhance the feasibility and practicability of the femtosecond micromachining in vision correction, we rely on the laser pulse repetition rate to reduce the average power and to enhance the scan speed needed for inducing detectable refractive index (RI) change inside ophthalmic materials. There are several research groups that have reported the effect of the repetition rate on the microstructure formation inside fused silica and metals with the range of Hz and KHz. Most of the studies are focused on the effect of repetition rate on ablation efficiency, laser drilling of metals, defects formation, or surface texture of the laser induced microstructures. A comparison between kilohertz and megahertz laser systems made by Reichman et al. showed that megahertz repetition rate modification resulted in better quality waveguides with a greater refractive index increase than kilohertz repetition rate modification. However, to our best knowledge, no studies so far have illustrated the effect of repetition rate on the RI change induced by femtosecond micromachining in hydrogel-based polymers.

[0061] The typical repetition rate currently used in femtosecond micromachining hydrogel polymers is larger than 80 MHz. However, prior to our investigation, it has not been investigated whether the high repetition rate (>80 MHz) is the optimal repetition rate for writing ophthalmic materials without inflicting any optical damage. Given the same single pulse energy, the accumulated temperature rise induced by a high-repetition-rate pulse train is higher than a low-repetition-rate pulse train, indicating that the high repetition rate of the pulse train should be able to induce larger refractive index change if we assume a pyrolytic degradation of polymers. However, we have considered the possibility that the laser-induced RI change results from a combination of both thermal-induced decomposition process and direct photochemical changes made by the nonlinear multiphoton absorption process. Although the accumulated thermal effect might be more significant in high repetition rate region, the photon energy that can be absorbed by the material is diminished due to a smaller single pulse energy for the same amount of average power; on the other hand, the low-repetition-rate pulses may easily reach the optical breakdown threshold and cause gross damage at smaller average power due to a larger single pulse energy. Therefore, we investigated the effect of repetition rate on both the induced RI change and the optical damage threshold. As part of our investigation, we discovered that the optimal repetition rate can be taken advantage of to reduce the amount of power required and speed up the femtosecond machining process.

[0062] In the following sub-sections, we present both the qualitative and quantitative experimental results showing how the repetition rate affects the magnitude of the induced phase change, which is related to RI change via the following equation,

[00007]$\begin{array}{cc}\mathrm{\Delta \varphi }=\frac{\Delta n.Math.L}{\lambda }& \left(1\right)\end{array}$

where Δϕ is the magnitude of the induced phase change in number of waves and measured at a specific reference wavelength (e.g. in this example at λ=543 nm), Δn is the induced average RI change, and L is the longitudinal thickness of the laser induced region. Grating lines were written in hydrogel-based contact lenses at two different repetition rates, 15 MHz and 60 MHz, to show that the great discrepancy between low repetition rate modification and high repetition rate modification can be easily visualized from the differential interference contrast (DIC) images. More systematic quantitative results were obtained by fabricating continuous phase shifting bars at four different repetition rates, 5 MHz, 10 MHz, 15 MHz and 60 MHz. A calibration function is derived from a photochemical model by associating the induced phase change with the molecular density changes due to the multiphoton absorption process and a pulse overlapping effect. The coefficients in the calibration function are fitted by the least square method. Single pulse energy damage threshold as a function of repetition rate was also investigated so as to determine the maximum achievable phase change just below the material damage threshold and to obtain the dynamic range for the writing process.

[0063] 1. Experimental Setup

[0064] The system configuration used for our experiment is depicted in FIG. 1. The light source used for the writing process is a KM Lab Y-Fi (Ytterbium fiber) laser, which delivers femtosecond laser pulses with a pulse duration of ˜120 fs, a central wavelength at 1035±5 nm. The pulse duration is measured by a commercially available autocorrelator (Newport, PSCOUT2-NIR-PMT) and can be adjusted by an internal grating pair working as a pulse compressor. This powerful Y-Fi laser contains an all-normal-dispersion (ANDi) Yb doped fiber oscillator, which enables tunable repetition rates in the range from 1 MHz to 60 MHz via the usage of a pulse picker. The pulse repetition rate from the oscillator is fixed at 60 MHz, and a pulse picker extracts certain pulses from the fast pulse train with an identical temporal separation, resulting in a different repetition rate from the oscillator. The available repetition rates are 60/N MHz, where N is an integer number from 4 to 60. An amplifier is employed after the pulse picker to amplify the average power up to 30 W, corresponding to a maximum pulse energy of 0.5 μJ at 60 MHz. A HWP and a PBS are placed after the Y-Fi laser to split the incident linearly polarized beam into two beams with orthogonal polarization and controllable power. The split ratio of the HWP and PBS unit was set to be 90:10, where 90% of the incoming beam transmits through the PBS and 10% of the beam is reflected onto a power meter for monitoring the power used in the writing process. A beam expander, consisting of two positive lenses, is placed after the HWP and PBS unit to amplify the beam size so that the effective numerical aperture (NA) for writing the samples is 0.47, and the corresponding diffraction-limited spot size is 2.75 μm. Three low GDD mirrors (Thorlabs, UM10-45B) are inserted in the system to fold the optical beam path and then the beam is sent through a microscope objective (Olympus, LCPLN50XIR) to form a diffraction-limited spot inside a sample. The microscope objective is attached to a motorized vertical stage (Newport, GTS30V) which provides Z axis step control. A sample is sandwiched between a microscope glass slide and a cover slip and soaked with solution to maintain hydrated. The sample is then mounted on a 2D linear translation stage (Aerotech, PRO115LM) which allows XY axial scanning with a speed up to 3 m/s. A back reflection monitor consisting of a focusing lens and a CCD camera is used to locate the writing depth which is was usually set to be in the middle of the polymer sample.

[0065] 2. Experimental Results

[0066] In order to illustrate the effect of repetition rates on the induced phase change, we conducted both qualitative and quantitative experiments at different repetition rates, with different powers and different scan speeds. Samples used in our qualitative experiments are hydrogel-based contact lenses (Acuvue2, Johnson & Johnson) made of a soft hydrophilic material known as “etafilcon A”, a copolymer of 2-hydroxyethyl methacrylate and methacrylic acid cross-linked with 1,1,1-trimethylol propane trimethacrylate and ethylene glycol dimethacrylate. Periodic grating structures were fabricated ˜50 μm below the top surface of a contact lens using a raster scanning method. FIGS. 2(a) and (b) show the DIC images of the gratings written with a power of ˜500 mW, at three different scan speeds, 5 mm/s, 50 mm/s and 100 mm/s and at two different repetition rates of 15 MHz and 60 MHz. Each grating consists of 10 grating lines with a line spacing of 5 μm, resulting in a total width of 50 μm. In order to maintain a constant velocity inside the sample, the length of each grating is set to be 20 mm, which is ensured to be long enough to compensate for the acceleration and deceleration travel distance of the stage. Given the same average power and the same repetition rate, the grating lines became fainter as the scan speed was increased, indicating that a larger RI change can be induced using a smaller scan speed. Distinct difference can be perceived between the DIC image obtained at 15 MHz (FIG. 2(a)) and 60 MHz (FIG. 2(b)). Grating lines micro-machined at 15 MHz can be seen at all the three scan speeds while the grating lines are difficult to be detected at 60 MHz even at the lowest scan speed. Results obtained at 100 mm/s using three different powers, 500 mW, 1000 mW and 1500 mW and two different repetition rates are shown in FIGS. 2(c) and (d), respectively. Similar results were obtained from the power scaling experiments as from the scan speed scaling experiments. Grating lines became brighter as the power was increased until the optical breakdown threshold was reached while the repetition rate and the scan speed were kept the same. The optical damage was indicated by the formation of dark carbon spots or material distortion with melting traces and porosities highly localized along the grating lines. The results obtained at the same repetition rate are consistent with the conclusions drawn in Ding et al.'s paper, implying that larger RI change can be achieved by increasing the average power and lowering the scan speed. However, comparing the DIC images at two different repetition rates while keeping other irradiation parameters the same leads to several new findings. As shown by the bright central grating lines written at 15 MHz (FIG. 2(c)) and the fairly faint grating lines at 60 MHz (FIG. 2(d)), the usage of a lower repetition rate pulse train can result in a much larger refractive index change at the same average power. Lower-repetition-rate pulses also cause optical damage at a smaller average power, as indicated in the images that for a given average power at 1500 mW, carbonized grating lines could be observed at 15 MHz while minor modification was induced at 60 MHz. The noteworthy difference between 15 MHz and 60 MHz can be explained from the single pulse energy point of view. Single pulse energy as a product of the average power and pulse interval is 4 times larger at 15 MHz than at 60 MHz for the same average power, meaning more energy per pulse can be absorbed by the material through multiphoton absorption at a lower repetition rate to induce more significant amount of RI change.

[0067] More systematic experiments were performed to generate quantitative results. We inscribed phase bars instead of grating lines inside a Acuvue J+J contact lens with +4 diopters and a base curvature of 8.7 mm. The travel distance of the 2D linear stage is still set to be 20 mm so as to keep the scan speed constant at 200 mm/s inside the sample. Each phase bar is made up of 30 grating lines separated by 1 μm, which is smaller than the focused spot size, thus creating a continuous phase carpet of dimensions 30 μm by 20 mm. As shown in FIG. 3(a), there are 4 phase bars written at two different exposure conditions. The top two phase bars were fabricated at 1075 mW while the bottom ones at 1105 mW. The difference between two writing conditions (as long as no damage occurs) cannot be detected directly from the DIC image but can be well spotted by measuring the phase change induced inside the written area with respect to the surroundings under a home built two-wavelength Mach-Zehnder interferometer (MZI). The scanning method used in the experiments is a rectangular loop scanning as shown in FIG. 3(b) rather than a raster scanning, which allows us to write side by side two same phase bars with a separation of 100 μm. Additionally, the rectangular loop scanning minimizes the spatial thermal effect induced by two adjacent grating lines since the separation between two adjacent grating lines is 100 times larger than that in the raster scanning. The amount of phase change measured with a reference light at 543 nm is extracted and unwrapped via the Goldstein's branch cut unwrapping algorithm and Fourier-transform method of fringe pattern analysis. The interferogram showing two phase bars written at the same irradiation parameters (used for creating the two bottom phase bars in FIG. 3(a)) and the corresponding retrieved phase map are displayed in FIGS. 3(c) and (d), respectively. Obvious phase shift can be observed from the interferogram and phase change inside the written region differs from the pristine region with sharp discontinuity at the edges. The average phase change was calculated to be −0.54 waves and the variation inside one phase bar was less than 0.05 waves. The difference of the induced phase change between the top phase bar and the bottom one in FIG. 3(d) is roughly 0.02 waves, indicating that consistent and stable phase change can be achieved by the femtosecond micromachining process. The longitudinal thickness of each scanning line is estimated to be around 8 μm by taking a cross section image of one grating structure consisting of 10 scanning lines and therefore the corresponding RI change to a phase change of −0.54 waves at 543 nm is calculated to be −0.037 from Eq. (1).

[0068] 3. Quantitative Photochemical Model of Phase Changes

[0069] To map out the induced phase change at different repetition rates, the power tested started from a small value at which a small phase change can be measured by the MZI and ended at a value where the sample damage occurs. The scanning pattern was the rectangular loop scanning and the writing speed was fixed at 200 mm/s. Two materials were laser-treated for collecting quantitative data at four different repetition rates, 5 MHz, 10 MHz, 15 MHz and 60 MHz. One of the materials is an Acuvue J+J Contact lens as described in the previous section and the other one is a plano hydrogel sample named Contaflex GM Advance 58 (Contamac Inc.), which is made of “Acofilcon A”, a synonym for “2-Butenedioic acid (2Z)-, di-2-propenyl ester, polymer with 2,3-Dihydroxypropyl 2-methyl-2-propenoate, 1-Ethenyl-2-pyrrolidinone, 2-Hydroxyethyl 2-methyl-2-propenoate and Methyl 2-methyl-2-propenoate”. The magnitude of the measured phase change at four repetition rates as a function of average power and single pulse energy is shown respectively in FIGS. 4(a) and 4(b) for the J+J contact lens as well as in FIGS. 4(c) and 4(d) for the Contaflex GM Advance 58 sample. Each experimental data was obtained by averaging the phase change values from 8 to 12 phase bars that were written with the same laser irradiation parameters. The variance assigned to each individual data shows the standard deviation obtained from these rectangles.

[0070] The fitting curves are derived from a photochemical model involving multiphoton absorption process and overwriting factor. RI change is assumed to be induced by the density change of polymer matrix in the excitation volume through multiphoton absorption. In our specific case where near infrared light at 1035 nm was used, a four photon absorption process was expected to occur during the writing process due to a strong UV linear absorption cut off wavelength around 300 nm. Then the excited molecular density change D can be expressed in the following form assuming a small absorption limit for simplicity,

[00008]$\begin{array}{cc}D=\mathrm{.Math.}.Math.\left(\frac{E}{\mathrm{VOL}}\right).Math.\left(\beta .Math.I_{\mathrm{peak}}^3.Math.L\right)& \left(2\right)\end{array}$

where ε is a material constant for relating the deposited energy to the molecule density change, E is the single pulse energy absorbed by the material, VOL is the light-matter interaction volume, β is the fourth photon absorption coefficient, I.sub.Peak is the peak pulse intensity and L is the longitudinal thickness of the interaction region. Apart from the four photon absorption process, accumulation effect originating from pulse overlapping should also be considered. The overwriting of spots can be accounted for as the spot size divided by the spacing between the spots by assuming a uniform (‘top-hat’) beam profile, denoted as for simplicity,

[00009]$\begin{array}{cc}N=\frac{\omega .Math.v}{S}& \left(3\right)\end{array}$

where ω is the diffraction limited laser spot size inside the material, ν is the pulse repetition rate and S is the scan speed. Eq. (3) represents the number of pulses per spot and the detailed illustration about the intersection of displaced laser pulses can be found in other research work. Therefore, the number of pulses per spot can be calculated based on Eq. (3) to be ˜18, ˜35, ˜53 and ˜210 at 5 MHz, 10 MHz, 15 MHz and 60 MHz, respectively.

[0071] Following Eq. (2) and Eq. (3), the overall excited molecule density change can be expressed as the product of the molecule density change caused by a single pulse times the overlapping effect N. After mathematica manipulation and expressing the single pulse energy in terms of average power and repetition rate, we are able to propose the final result of the phase change equation,

[00010]$\begin{array}{cc}\Delta \varphi =\gamma .Math.\frac{P^4.Math.{\mathrm{NA}}^5}{{\upsilon }^3.Math.{\tau }^3.Math.S.Math.{\lambda }^7}& \left(4\right)\end{array}$

where P is the average power, NA is the numerical aperture, π is the pulse duration. Parameter γ is a constant which contains the fourth photon absorption coefficient and associates the absorbed energy with the phase change. It can be determined by using a least square fitting method. Results show the fitting curve matches the experimental results well for the three low repetition rates but there is a deviation at 60 MHz between the experimental data and the fitting curve. The fitting parameter is found to be γ=2.82e-59 m.sup.6.Math.waves/(W.sup.4.Math.s) for J+J contact lenses and γ=1.33e-59 m.sup.6.Math.waves/(W.sup.4.Math.s) for Contaflex samples. The results may suggest that the fourth photon absorption rate or the ability of transferring the absorbed energy to induce RI change of Contaflex samples is smaller than that of J+J contact lenses. Therefore, it may be considered to add dopants into the Contaflex samples to increase absorption cross section or add quenchers to enhance the energy conversion efficiency.

[0072] Several conclusions can be drawn from FIG. 4. As shown in FIGS. 4(a) and 4(c), the magnitude of the phase change measured at 543 nm rises as the power increases for a given repetition rate for both materials and lower repetition rates can induce the same amount of phase change at a much smaller power, which are consistent with the qualitative results shown in FIG. 2. Lower repetition rate, on the other hand, causes sample damage at a smaller power for both materials; however, the damage threshold in terms of the single pulse energy behaves differently for two materials. As shown in FIG. 4(b), the single pulse energy needed for initiating the optical breakdown in a J+J contact lens is ˜82 nJ at 5 MHz, ˜81 nJ at 10 MHz, ˜77 nJ at 15 MHz and ˜63 nJ at 60 MHz. Therefore, the experimental results indicate that the sample damage threshold of a J+J contact lens decreases as the repetition rate increases or equivalently the number of laser shots at the same spot increases. However, FIG. 4(d) shows that the single pulse energy damage threshold of a Contaflex sample is ˜83 nJ at 5 MHz, ˜82 nJ at 10 MHz, 84 nJ at 15 MHz and 82 nJ at 60 MHz, indicating a damage threshold independent of repetition rate. We assume the relationship between the optical breakdown threshold and the number of pulses per spot can be described by the incubation effect. Given the same single pulse energy, the magnitude of the phase change increases as the repetition rate rises, which could be attributed to the accumulation effect arising from the overlapping of two adjacent pulses. A higher-repetition-rate pulse train is able to produce a larger number of laser shots on the same spot, meaning more pulse energy could be absorbed by the material. Therefore, it is reasonable to conclude that the maximum achievable phase change just below the damage threshold also increases as the repetition rate increases by taking into account that the change in single pulse energy damage threshold is modest for the repetition rates from 5 MHz through 60 MHz. As shown in FIGS. 4(b) and 4(d), the maximum achievable phase change for the J+J contact lens is ˜0.38 waves at 5 MHz, ˜0.6 waves at 10 MHz, ˜0.7 waves at 15 MHz and ˜1 wave at 60 MHz and for the Contaflex sample, ˜0.17 waves at 5 MHz, ˜0.26 waves at 10 MHz, ˜0.33 waves at 15 MHz and 0.56 waves at 60 MHz. The increasing pulse overlapping effect at higher repetition rates and the roughly same single pulse energy threshold at different repetition rates together contribute to the growth of the maximum achievable phase change just below the damage threshold.

[0073] 4. Empirical Model of Phase Changes

[0074] As shown in FIG. 4, the fitting curves derived from the photochemical model and the overlapping effect work well for the low repetition rates at 5 MHz, 10 MHz and 15 MHz but less perfectly for 60 MHz. There are multiple reasons to account for the deviation at 60 MHz. The deviation at high repetition rate may indicate a reduced nonlinearity order from 4 at low number of pulses per spot to around 1 at high number of pulses per spot due to the accumulated linearly absorbing color centers via the incubation reaction. The formation of linearly absorbing defects were also confirmed by an increased absorbance of the laser irradiated area near the UV absorption edge after examining UV-visible transmission spectra. In order to show the decrease in the nonlinearity order we plot the experimental data in a double logarithmic scale. As shown in FIGS. 5(a) and 5(b), we plot the logarithm of the induced phase change at four different repetition rate versus the logarithm of the average power in the focal volume. The empirical model was obtained using linear fitting method and thus the order of the multiphoton absorption process was indicated by the linearly fitted trend line gradient. We also observed a decreasing trend line gradient as the repetition rate increases. However, in contrast to the diffraction efficiency used in their paper, which should scale quadratically as the RI change, a direct relationship between the induced phase/RI change and the average power was obtained to determine the order of the multiphoton absorption process. For the Contaflex sample (as shown in FIG. 5(a)), the line gradient decreases from 4.15 at 5 MHz to 3.17 at 60 MHz, which indicates the multiphoton process evolves from a pure four photon absorption process at low number of pulses per spot to a lower order of multiphoton absorption process at high number of pulses per spot due to the formation of larger number of color centers. For the J+J contact lens (as shown in FIG. 5(b)), the trend line gradient follows the decreasing rule as well and slightly reduces from 3.4 at 5 MHz to 3.1 at 60 MHz. The order of multiphoton absorption process keeps decreasing and the overall power dependence is lowered by taking account into both the four photon absorption of the material and the linear absorption of the color centers.

[0075] Other than the reduced nonlinearity order at high number of pulses due to color center formation, the deviation at 60 MHz could be attributed to a much higher accumulated temperature rise achieved inside the material after a high-repetition-rate laser exposure. The heat accumulation effect may play a more significant role at a high repetition rate domain and induce the phase change via a distinct photothermal effect which has a power dependency different from that of a photochemical effect. A third explanation for the deviation at 60 MHz could be a saturation effect at high intensities since we noticed the induced phase change cannot increase infinitively and tends to be saturated when the induced phase change reaches a high value. If the saturation factor is not introduced into the theoretical model, the fitting results would be higher than experimental results as the power and repetition rates increase. Therefore, a saturation factor can be incorporated into the photochemical model for the purpose of a better fitting. The saturation factor can be inserted under the material constants if we assume there is a possible limit on the finite number of available molecules, or the capability of the material to redirect the absorbed energy to induce phase change is limited or the depolymerization process is balanced by a recombination effect. On the other hand, the saturation factor can also be attached to the fourth photon absorption coefficient by analogy with the decreasing nonlinear absorption coefficient measured at high laser intensity. We then propose the modified photochemical model can be expressed in the following form by employing a classic saturation factor,

[00011]$\begin{array}{cc}\Delta \varphi =\frac{\Delta {\varphi }_0}{1+\frac{A}{A_{sat}}}& \left(5\right)\end{array}$

where Δϕ is a small signal induced phase change expressed in Eq. (4) and we tried to express A as the induced phase change, the excited molecular density, the average power/intensity, or the peak intensity. The best fitting results for all the repetition rates from 5 MHz to 60 MHz were obtained by denoting A as the average power/intensity and yielded a coefficient of determination R.sup.2 greater than 95% for J+J contact lenses and greater than 97% for Contaflex sample at all four repetition rates. However, the modified photochemical model does not work well at 60 MHz when A represents other parameters, including the induced phase change, the excited molecular density, and the peak intensity.

[0076] The exact mechanism associating the absorbed pulse energy to RI change is still controversial and could be subject to further investigation. The accumulated pulse energy absorbed by the material via multiphoton absorption can excite electrons to a high electronic state to induce direct bond dissociation or the absorbed energy can be transferred from electrons to lattice to heat the polymer matrix and induce subsequent pyrolysis of the polymer. Depolymerization, either a photolysis reaction or a thermal-driven process, usually increases polymer chain volume by random chain scission and direct bond breaking, thus causing monomer formation, internal tensile stress propagation and volume expansion which is confirmed by the shift of the molecular weight to a lower value and the broadening of the polymer molecular weight distribution. After the decomposition of polymer into smaller monomers or oligomers, we assume these smaller fragments may diffuse out from the laser-irradiated area into the surrounding and water molecules can then occupy the empty expanded area due to enhanced hydrolysis, thus resulting in an increasing water content in the laser treated area. Therefore, the negative sign of induced phase/RI change might be attributed to a lower refractive index of water than the sample itself and a reduced polymer density due to hydrodynamic expansion. One potential avenue for further research involves taking advantage of Raman spectroscopy to gain insight into the chemical composition change in the laser-irradiated area and then determine whether the RI change in hydrogel polymers arises from a thermal-induced decomposition process via non-radiative decay or a direct chemical bond breaking procedure via multiphoton ionization or a combined photothermal and photochemical effect.

[0077] 5. Effect of Repetition Rate on Femtosecond Micromachining Process

[0078] The effect of repetition rate has been demonstrated to play an important role in femtosecond micromachining process. The same amount of phase change can be achieved at a lower average power and a faster scan speed by taking advantage of low repetition rate pulses while the damage threshold in terms of single pulse energy maintains almost the same for all the tested repetition rates. Based on both the qualitative and quantitative results, we are able to conclude that the induced phase change depends on the amount of pulse energy absorbed by the material via both the multiphoton absorption and the overlapping effect induced by adjacent pulses. In order to fit the experimental data, we developed a calibration function based on a photochemical model. The induced phase change scales as the power to the fourth order as a consequence of four photon nonlinear absorption at 1035 nm. The optimal repetition rate for femtosecond micromachining contact lenses seems to be around 15 MHz for at least some manufacturing processes, for the reason that the maximum achievable phase change just below the damage is a little bit lower than that obtained at 60 MHz but the average power required is roughly 3 times smaller.

[0079] 6. Two Photon and Other Models

[0080] The above discussion is presented in the context of a four photon regime. For other systems and materials, a two photon regime may be the more appropriate photochemical model, and the following phase change equation may be utilized:

[00012]$\begin{array}{cc}\Delta \varphi \left(P,\upsilon ,S,\mathrm{NA}\right):=\beta .Math.\left(\frac{P^2.Math.\mathrm{NA}}{\upsilon .Math.{\lambda }^3.Math.S.Math.\tau }\right)& \left(6\right)\end{array}$

where P is the average power, NA is the numerical aperture, and π is the pulse duration. Parameter β is a constant which contains the second photon absorption coefficient and associates the absorbed energy with the phase change.

[0081] As a general matter, in at least some instances, a two photon model such as the one in eq. (6) may be more appropriate for relatively higher energy writing and a four photon model such as the one in eq. (4) may be more appropriate for relatively lower energy writing. In some instances, the slope of a fitting line in a plot of phase shift versus power on log-log scales may indicate whether a two photon or four photon model is more appropriate. For example the slopes of the lines in FIG. 5(a) are approximately 4, indicating use of a four photon model, and the slopes of the lines in FIG. 7 are approximately 2, indicating use of a two photon model.

[0082] FIG. 6 show a plot of phase shifts written into a Contamac 58 sample at 405 nm at different average powers (in Watts), with the line labeled F showing the two photon photochemical model in eq. (6) fitted to the experimental data. In this example, the fitting constant β is 5*10.sup.−24 and the maximum phase shift written (measured at 543 nm) below the damage threshold is −0.90.

[0083] For some systems and materials, a three or other photon model may be most appropriate, and for a general condition a sum of two-photon, three photon and four photon effects may be most appropriate. For a three photon regime, the following phase change equation may be utilized:

[00013]$\begin{array}{cc}\Delta \Phi :=\frac{\gamma .Math.P^3.Math.{\mathrm{NA}}^3}{{\upsilon }^2.Math.{\tau }^2.Math.{\lambda }^5.Math.S}& \left(7\right)\end{array}$

where P is the average power, NA is the numerical aperture, and π is the pulse duration. Parameter γ is a constant which contains the third photon absorption coefficient and associates the absorbed energy with the phase change.

[0084] For an N.sup.th photon regime, the following phase change equation may be utilized:

[00014]$\begin{array}{cc}\Delta \Phi :=\frac{\gamma .Math.P^N.Math.{\mathrm{NA}}^{2.Math.N-3}}{{\upsilon }^{N-1}.Math.{\tau }^{N-1}.Math.{\lambda }^{2.Math.N-1}.Math.S}& \left(8\right)\end{array}$

where P is the average power, NA is the numerical aperture, and π is the pulse duration. Parameter γ is a constant which contains the N.sup.th photon absorption coefficient and associates the absorbed energy with the phase change.

[0085] For a general condition including a sum of two-photon, three-photon, and four-photon effects, the following phase change equation may be utilized:

[00015]$\begin{array}{cc}\Delta \Phi :=\beta .Math.\frac{P^2.Math.\mathrm{NA}}{\upsilon .Math.\tau .Math.{\lambda }^3.Math.S}+\gamma .Math.\frac{P^3.Math.{\mathrm{NA}}^3}{{\upsilon }^2.Math.{\tau }^2.Math.{\lambda }^5.Math.S}+\delta .Math.\frac{P^4.Math.{\mathrm{NA}}^5}{{\upsilon }^3.Math.{\tau }^3.Math.{\lambda }^7.Math.S}& \left(9\right)\end{array}$

where P is the average power, NA is the numerical aperture, and π is the pulse duration. In this instance, parameters β, γ, and δ are constants which contain the second, third, and fourth photon absorption coefficients respectively.

[0086] Scalable Manufacturing with LIRIC

[0087] Using the information derived from the photochemical models and experiments discussed above, including information about the maximum phase shift obtainable in a given material at applicable scanning speeds, numerical apertures, and repetition rates, commercial scale LIRIC systems and methods with optimal throughput and other efficiencies can be designed and implemented.

[0088] FIG. 8 shows one example of a LIRIC multi-head writing system that may be used for ophthalmic materials such as contract lenses or intra-ocular lenses. The system of FIG. 8 includes a laser 12 and a splitter 14, splitting the laser's beam into N equal outputs 16. Each output may be associated with conditioning, scanning, and delivery subsystems, although, in FIG. 8, only one beam conditioning subsystem 18 and one scanning & delivery subsystem 20 are specifically shown. As also schematically shown in FIG. 8, a handling subsystem 22 may be included to facilitate loading, positioning & aligning the ophthalmic devices relative to the writing heads, and unloading in an efficient manner to further help with overall throughput of the laser writing system.

[0089] Various lasers may be used for the writing system. Non-limiting examples include short pulsed lasers (such as femtosecond lasers with a pulsewidth less than 350 fs and a repetition rate (tunable or fixed repetition rate) in the range of 1 to 60 MHz), operating in the range of 340 nm to 1100 nm (e.g. near 405 nm, 517 nm, 800 nm, or 1035 nm).

[0090] FIG. 9 shows one example of a beam power splitter that that may be used in the LIRIC multi-head writing system of FIG. 1. In FIG. 9, 50% beam-splitters (illustrated by dashed diagonal lines) and 100% reflectors (illustrated by solid diagonal lines) split the relatively high-power beam of laser 12 into eight equal lower power beams 16. In other examples, the splitter may split the laser beam into unequal lower power beams.

[0091] Returning to FIG. 8, at the beam conditioning subsystem 18, the lower power laser beam may undergo, for example, dispersion compensation, beam sizing, power control (e.g. using acousto-optic or electro-optic components), ellipticity control, and/or power monitoring.

[0092] FIG. 10 shows one example of a scanning and delivery subsystem that may be used in the LIRIC multi-head writing system of FIG. 8. In FIG. 10, a laser beam 30 (in this example, from a Ti:Sapphire laser) is sent through an objective 32 to form a diffraction-limited spot inside an ophthalmic material (in this example, a hydrogel 34 held between two glass slides 35 and 36 in a water based environment 37), thereby forming 3D structures 38. Although not shown, the sample may be mounted on a translation stage for axial scanning along X and Y axes, and the objective may be translated along a Z-axis for vertical translation, allowing precise writing in the material in three dimensions, Any suitable scanning system may be utilized, including, without limitation, high speed XYZ translation stages, high speed galvanometer scanning systems, and shaker scanners (such as described in U.S. Patent Application Publication No. 2016/0144580 published May 26, 2016 to Wayne H, Knox et al.). In some instances, the scanning speed may be in the range of 1 mm/sec to 10 meters/sec.

[0093] The scanning and delivery subsystem may deliver short laser pulses of sufficient energy (e.g. above a minimal threshold but below a damage threshold, as shown in FIG. 11) and at sufficient scan speeds (e.g. above a damage threshold but below an upper speed threshold, as shown in FIG. 12) to cause a nonlinear absorption of photons (typically multi-photon absorption), leading to a change in the refractive index of the material at the focus point. In FIGS. 11 and 12, the damage threshold may reflect a threshold in which a degradation in optical quality of the device is detectable. Moreover, the region of the material just outside the focal region is minimally affected by the laser light. Accordingly, select regions of an optical, polymeric material can be modified with a laser resulting in a change in the refractive index in these regions. The irradiated regions may exhibit no significant differences in the Raman spectrum with respect to the non-irradiated regions. Also, the irradiated regions may exhibit little or no scattering loss, which means that the structures formed in the irradiated regions are not clearly visible under appropriate magnification without contrast enhancement.

[0094] The writing system may be utilized to create lenses or other optical constructs in the interior of the material. For example, FIG. 13 shows LIRIC lenses written into the interior of hydrogels, and FIG. 14 shows a Fresnel-type phase wrapped optical lens written into the interior of a plano hydrogel. Similar lenses or other optical constructs may also be written into contact lenses to change their optical properties. Depending on the maximum phase shift required, the lens or other optical construct can be written into the material in a single layer or in multiple layers. U.S. Pat. No. 8,932,352, issued Jan. 13, 2015 to Wayne H. Knox et al. for an “Optical Material and Method for Modifying the Refractive Index” and U.S. Pat. No. 9,144,491, issued Sep. 29, 2015 to Wayne H. Knox et al. for a “Method for Modifying the Refractive Index of an Optical Material,” describe additional examples of gratings and other optical constructs that may be written into materials.

[0095] Using the information derived from the photochemical models discussed above, manufacturing systems like the one of FIGS. 8-10 can be designed and configured for optimal scale and throughput. There are numerous inputs that potentially impact on the throughput of a LIRIC system, and that could be accounted for as inputs into an optimization model, including, without limitation, laser specifications, scanner specifications, material characteristics, and desired design for the LIRIC devices. Of course, some of these inputs, such as certain desired design characteristics for the device, may not be subject to variation for purposes of manufacturing optimization, while other variables, including certain laser specifications, are more readily subject to variation in order to optimize the LIRIC manufacturing process.

[0096] 1. Laser Specifications

[0097] Laser specification inputs may include, without limitation, average laser power, pulsewidth, wavelength, repetition rate, lens NA numerical aperture, system power throughput, and number of device writing heads. Example pulsewidths include femtosecond scale pulsewidths, and, in some examples, pulsewidths less than 350 fs. Example repetition rates include repetition rates in the range of 1-60 MHz. Example wavelengths include wavelengths in the range of 340 nm to 1100 nm, including wavelengths near 405 nm, 517 nm, 800 nm, and 1035 nm. Example lens NA include NA's between 0.19 and 1.0.

[0098] 2. Scanner Specifications

[0099] Scanner specifications inputs may include, without limitation, maximum scanning speed, slow axis resolution (line spacing), turnaround (blanking) time, full field size, and scan pattern (e.g. raster, box, spiral, etc.). Example scanning speeds include speeds in the range from 1 mm/sec to 10 meters/sec.

[0100] 3. Material Characteristics

[0101] Material characteristic inputs may include, without limitation, non-linear absorption coefficient of the material (such as one or more of the 2.sup.nd order limit, 4.sup.th order limit, and mixed 2.sup.nd through 4.sup.th order terms), as well as the maximum phase shift obtainable (determined at applicable scanning speeds, numerical apertures, repetition rates, or other factors).

[0102] In one example, a first step to determining material characteristics is to measure written phase shifts in the material of interest as a function of, for example, average power and scan speed. Phase vs. power can be plotted on log-log scales to determine slope of nonlinear processes in small signal regime (below saturation). The determined slope may be indicative of the applicable photochemical model for the material of interest (e.g. a slope close to 2 may be indicative of a two photon model, a slope close to 4 may be indicative of a four photon model, etc.). The applicable photochemical models (e.g. the two and/or four photon regime models identified above) may be fit to the data, and a maximum phase shift just below the damage threshold may be identified. This information may be subsequently used to establish a range of writing powers at desired scan speeds. It is noted that, while the best results for at least some systems and methods are obtained when the one-photon absorption is minimized, a small amount of one-photon absorption is tolerable even in those instances.

[0103] A specific example in the two photon regime is provided at FIGS. 6-7. A specific example in the four photon regime of measuring written phase shifts in the material of interest as a function of both average power and scan speed is provided at FIGS. 15-16, which could be analyzed in a similar manner as the data in FIGS. 6-7. FIG. 15 illustrates data plotting phase change as a function of power and speed obtained from LIRIC experiments performed in Johnson & Johnson Acuvue2 contacts in response to 100 fs laser pulses at a repetition rate of 80 MHz and 800 nm, for speeds of (a) 3 mm/s, (b) 5 mm/s, (c) 10 mm/s, (d) 15 mm/s, (e) 20 mm/s, (f) 30 mm/s, and (g) 40 mm/s, while FIG. 16 is a three-dimensional visualization of the data in FIG. 15. Another example in the four photon regime, but measuring phase shifts as a function of average power and repetition rate is provided at FIGS. 4-5.

[0104] 4. Device Design Details

[0105] Device design inputs may include, without limitation, diameter of the optical device to be written, the line spacing required (e.g. to ensure smooth phase shifts that produce no diffraction spots), and details impacting on the maximum phase shift required for the device (e.g. the phase wrapping profile, intended optical power, etc.).

[0106] 5. Scan Layers Required

[0107] The number of scan layers required for the LIRIC process will impact on the time required to write the device. The number of scan layers required is a function of both the maximum phase shift required by the device's specification and the maximum phase shift produced in the device material at the relevant laser and scanner parameters. The number of layers required is the max phase shift required for the device divided by the max phase shift produced in the device material at the relevant laser and scanner parameters.

[0108] 6. Estimated Writing Time

[0109] Estimated writing time for a device is a function of how many layers need to be written, as well as several other variables, including device width or diameter, line spacing, number of lines (device width divided by line spacing), scan speed, and scanner efficiency (to account for dead time). Time to write a device can be estimated by,

[00016]$\begin{array}{cc}T:=\frac{W^2.Math.N_{\mathrm{layers}}}{S.Math.\Delta .Math.\eta }& \left(10\right)\end{array}$

in which W is device width in mm, Nines is the number of lines, S is the scan speed in mm/s, and η is scanner efficiency.

[0110] 7. Number of Writing Heads

[0111] The number of writing heads that can be incorporated into the multi-head writing system is a function of the laser's maximum power, the maximum power required to write a one layer phase shift in the device, and a system loss factor (typically about 50%). Number of writing heads that could be supported by the system can be estimated by,

N.sub.heads=(P.sub.max*F)/P.sub.max-phaseshift  (11)

in which P.sub.max is the laser's maximum power, P.sub.max-phaseshift is the maximum power required to write a one layer phase shift in the device, and F is the system loss factor. As one example, for a 517 nm laser with a maximum power of 10 W, a 50% system loss factor, and a 0.5 W per device requirement to achieve a single layer max phase-shift, it is estimated that the system could support 10 heads with one single laser source.

[0112] 8. LIRIC Optimization for Multi-Head Writing Systems

[0113] We have discovered that laser repetition rate can have a surprisingly significant impact on several aspects of the LIRIC writing process. Surprisingly, relatively low repetition rates can be used to achieve significant phase changes at relatively low power requirements. This can be visualized, for example, using FIG. 4(a), in which the 5-15 MHz processes achieved significant phase change values at much lower powers than the corresponding 60 MHz process. One potential trade off to this is that, in at least some instances, lower repetition rate processes can reach a damage threshold of the subject material at lower phase change and power values, potentially requiring that the device be written in more layers than would necessarily be required with higher repetition rate processes. This can also be visualized using FIG. 4(a), in which it can be seen that the 5-15 MHz processes reach a maximum phase change before material damage (the upper end of the fitting lines for those processes) before the corresponding 60 MHz process does.

[0114] Taking into account these factors, as well as other factors in the LIRIC writing process discussed above, can allow for optimization of manufacturing throughput. One example is presented below in table 1, which assumes a LIRIC process utilizing a 30 W, 1035 nm laser having the same average power at all repetition rates, with the system having a 50% system loss and being used to manufacture a device requiring a max phase shift of 1 wave.

TABLE-US-00001 TABLE 1 60 MHz 5 MHz P.sub.max (W) 3.75 0.45 ΔΦ.sub.max 1.0 0.35 N.sub.heads 4 33 N.sub.layers 1 3

[0115] As can be seen from table 1, the 5 MHz process could power over 30 writing heads, 8.25 times as many as the 60 MHz process can power. However, the trade off is that the 5 MHz process would require three times the number of layers to be written as the 60 MHz process, roughly tripling the writing time required for each device. In this simple example, although it would require three times the number of layers to be written, the much larger number of writing heads supportable by the 5 MHz process would result in that system having a throughput of 2.75× greater than the 60 MHz process.