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Femtosecond Laser Optics Combat Pulse Dispersion, Color Errors, and Reflections

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Femtosecond Laser Optics Combat Pulse Dispersion, Color Errors, and Reflections ULTRAFAST LASER OPTICS Femtosecond laser optics combat pulse dispersion, color errors, and reflections GÜNTER TOESKO and CHRISTIAN DEHNERT Along with the rapid development for improved outcomes Dispersion pace of ultrafast lasers, ultrafast in ophthalmic (Lasik sur- Material dispersion in ultrafast laser op- laser optics must overcome the gery) and biological ap- tics leads to temporal broadening of the plications, the nonlinear laser pulse by introducing a frequency-de- unusually amplified obstacles of attributes of ultrafast la- pendent delay of the different spectral dispersion, color aberrations, and ghost sers are also used to mod- components of the pulse. The higher the reflections through careful design and ify the index of refraction refractive index of a material, the higher manufacture. and distribute the laser the dispersion. In addition, the dispersion energy along the beam effect is greater for shorter wavelengths. The pace of the development of ultra- axis to maintain a near-constant beam For example, a 400-fs-long pulse with a fast lasers—also called ultrashort pulse radius over many Rayleigh lengths, en- central wavelength of 355 nm suffers a (USP) lasers—has been extremely rapid. abling a very large depth of field. temporal broadening of approximately Picosecond and femtosecond laser sys- As a result, USP lasers are well suited to 0.3 fs while traveling through a 20-mm- tems are efficient tools in many indus- contour cutting (filament cutting) of un- thick fused-silica window. trial and scientific applications, offer- cured, chemically hardened glass (cover In long-pulsewidth laser beams, the ing useful nonlinear effects and “cold glass of smartphones) and sapphire, re- wavelength bandwidth is very narrow ablation” for a reduced heat-affected sulting in very high-quality edges and very and typically no compensation is re- zone (HAZ) that reduces or even elim- little material removal. This plasma dis- quired in the lens. But as the pulse width inates post-processing cleanup in mate- sociation process leads to cutting kerfs shortens, the wavelength spread around rials processing applications. smaller than 1 µm—much smaller than the center wavelength increases—it is a Besides multiphoton absorption and the diffraction-limited laser spot diameter. function of the laser, not the lens. self-focusing in transparent materials So, what are the optical challeng- es with ultrafast lasers? Color aberrations Intensity (a.u.) Spectral width Avoiding dispersion, color In femtosecond lasers, the pulse length 1.0 shifts, and ghost reflections is linked to the spectral width of a la- in ultrafast laser optics are ser pulse. As the pulse width of a laser 0.8 of primary importance in decreases into the range of femtosec- 50 fs maintaining optimum sys- onds, the pulse spreads out in frequen- 0.6 tem performance. cy. For example, a 10 ps pulse at 1064 nm has a spectral width of 0.4 400 fs about 0.3 nm, resulting in FIGURE 1. For ultrafast lasers, essentially no pulse spread- 0.2 a formula defines the spectral 10 ps width of a transform-limited pulse ing. At the other extreme, a 50 fs pulse at 1064 nm has 0.0 to be a function of the pulse 1024 1034 1044 1054 1064 1074 1084 1094 1104 duration. (Courtesy of Sill Optics) a spectral width of about 60 Wavelength (nm) nm, yielding much broader Reprinted with revisions to format, from the March 2016 edition of LASER FOCUS WORLD Copyright 2016 by PennWell Corporation ULTRAFAST LASER OPTICS Spectral width l/e2 (nm) Spectral width l/e2 (nm) Spectral width l/e2 (nm) 8 60 3.0 7 50 2.5 6 2.0 5 1064 nm 40 4 30 1.5 1064 nm 1064 nm 3 800 nm 20 1.0 800 nm 2 532 nm 800 nm 1 10 532 nm 0.5 532 nm 355 nm 0 0 355 nm 0.0 355 nm 400 500 600 700 800 900 1000 50 100 150 200 250 300 350 400 1 2 3 4 5 6 7 8 9 10 Pulse length (fs) Pulse length (fs) Pulse length (ps) FIGURE 2. Spectral width increases with decreasing pulse length for a variety of pulse-length ranges; below 400 fs, the spectral broadening increases rapidly. Note the steeper slope of the longer wavelengths. (Courtesy of Sill Optics) spectral content such that the pulse con- proportional to the field angle (field height 1064 nm, this F-Theta lens shows that tains wavelengths from 1034 to 1094 nm, = focal length × field angle) and the field spot performance in the corner of the scan resulting in a “color error” unless the lens height is different for different wavelengths. field (a location at which the color errors is color-corrected. are at their maximum) results in color er- In USP lasers, the spectral width is de- Correcting color errors rors both in the transverse (scan-length fined by the pulse duration as: Most optical imaging lenses that span the direction) and propagation direction (fo- human visible spectrum such as binocu- cal-length direction). At 400 fs, the spot Spectral width [FWHM] ≥ constant * lars or machine-vision imaging lenses cor- shape is essentially the same as for a 10 ps (central wavelength)2 rect for color errors by combining various or longer pulse, and the lateral color er- pulse duration speed of light * glass types with different indices of re- ror is small in respect to the spot size. The The constant (time-bandwidth prod- fraction and different Abbe numbers. The image size of the Huygens point-spread uct) depends on the actual pulse shape Abbe number is a measure of the materi- function (PSF) plot is 40 µm and the lat- (see Fig. 1). For a Gaussian pulse shape, al’s chromatic dispersion—its variation of eral color error is approximately 8 µm. it is equal to 0.441. If equality is obtained the refractive index vs. wavelength. But at 50 fs, the lateral color error is ap- in the above equation, then it is a trans- Nanosecond and picosecond pulse la- proximately 60 µm and the aberrations form-limited pulse, meaning that for a sers have a very small spectral spread on are quite obvious and extreme. given spectral width, there is a lower lim- the order of a few nanometers or less, re- To combat this color error, Sill Optics it for the pulse duration. sulting in essentially no wavelengths that designed the proprietary, multi-element, A problem most severe at longer wave- are out of focus, both axially in z and lat- multi-material S4LFT7010/450 telecentric lengths is that the shorter the pulse dura- erally in the x and y scan field. In that F-Theta scan lens with a focal length of tion, the larger the spectral width of the case, fused-silica lenses designed for a sin- 100 mm and a maximum field size of 35 pulse (see Fig. 2). For pulse lengths in the gle wavelength and corrected monochro- × 35 mm with color correction from 1.0 to picosecond regime, the spectral width is matically can be used. However, femto- around 1 nm and below, and can usually second USP lasers are more challenging. a) be neglected. In that case, fused silica lens- To illustrate the spectral bandwidth im- es that are color-corrected monochromat- pact on the performance of an F-Theta ically for just one wavelength can be used scan lens, the Sill telecentric F-Theta scan and only one glass material is required. lens S4LFT4010/328 with 100 mm focal Color errors occur from the broad length used with a 10 mm (1/e2, vignett- b) spectrum of the short-pulse input beam. ed at 1/e2) input beam and a maximum Wavelengths are focused to different loca- field size of 35 × 35 mm was analyzed tions along the propagation direction (axial (see Fig. 4). Unlike a normal focusing lens chromatic focal shift) and lateral to it (later- that has field curvature so only the cen- al chromatic color aberration) (see Fig. 3). ter ray would be in focus on a flat field, The amount of the lateral color error is de- an F-Theta scan lens is designed to be in FIGURE 3. In lenses not corrected for pendent on the focal length and the wave- focus over the entire image plane of the color errors, chromatic focal shifts can length, as the image height (“scan length” field scanned by the laser. occur axially (a) or laterally (b). (Courtesy of when referencing F-Theta scan lenses) is Designed for one wavelength only at Sill Optics) ULTRAFAST LASER OPTICS 1.1 μm for a 100-nm-wide color spectrum. For a 10 mm beam, that is color-cor- the lens is diffraction-limited (the maximum theoretical resolu- rected from 1.0 to tion possible) with a lateral color error in the field corner below 1.1 μm and diffrac- tion-limited for a 10 a) mm beam (double 1/ x-y scan eld F-Theta objective No 2 S4LFT4010/328 lateral e diameter). color 10 ps error Ghost 8 µm reflections 400 fs lateral 35 mm color error Ghost (or back) re- flections occur as a 50 fs 60 µm lateral portion of the la- color error ser light is reflected back from various lens elements. Most b) x-y scan eld F-Theta objective F-Theta scan lenses No FIGURE 5. Back reflections on the outer S4LFT7010/450 lateral contain anywhere color surface of lens element four form a focus 10 ps error from 2 to 6 lens ele- in the first lens element. In a pulsed laser, <1 µm ments.
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