GPC light shaping a supercontinuum source

: Generalized Phase Contrast (GPC) is a versatile tool for efficiently rerouting and managing photon energy into speckle-free contiguous spatial light distributions. We have previously shown theoretically and numerically that a GPC Light Shaper shows robustness to shift in wavelength and can maintain both projection length scale and high efficiency over a range [0.75 λ 0 ; 1.5 λ 0 ] with λ 0 as the characteristic design wavelength. With this performance across multiple wavelengths and the recent availability of tabletop supercontinuum lasers, GPC light shaping opens the possibility for creatively incorporating various multi-wavelength approaches into spatially shaped excitations that can enable new broadband light applications. We verify this new approach using a supercontinuum light source, interfaced with a compact GPC light shaper. Our experiments give ~70% efficiency, ~3x intensity gain, and ~85% energy savings, limited, however, by the illumination equipment, but still in very good agreement with theoretical and numerical predictions.


Multi-wavelength light shaping
Many important applications of the interaction of light with matter strongly depend on the illumination wavelength. On a fundamental level, the way electrons move between atomic energy levels depend on the interacting photons' energy, which in turn can be controlled by a proper choice of wavelength. Hence, for such studies, a laser source containing multiple wavelengths is much more versatile than normal monochromatic lasers. Tabletop supercontinuum light sources have thus been used in a plurality of applications that include optical coherence tomography, spectroscopy, optical characterization or sensing, imaging and microscopy, neuroscience and neurophotonics, metrology among many others.
Multi-wavelength techniques are invaluable in spectroscopy [1] and provide beneficial enhancements in interferometry [2], well-established fields with significance that cannot be overemphasized. Exploiting the wavelength-dependent material response also allows for controlled photo-excitation, targeted monitoring [3], and even simultaneous excitation and monitoring in pump-probe geometries [4].
Light shaping, on the other hand, increases the diversity of such applications by adding spatial control or selectivity to such light-matter interactions. For example, in two-photon optogenetics research [5], one would like to selectively illuminate intricate patterns of dendrites or axons within neurons [6]. As laser sources typically have limited shapes, many light shaping approaches have been studied to address different demands such as efficiency, speed, beam quality or economy concerns. A typical light source would have a TEM 00 or Gaussian profile. Using an amplitude modulation by placing a shaped aperture on the path of the beam is inefficient. Around 70%, or even more if a more uniform intensity output of the incident power is needed, can be lost while illuminating a rectangle with an expanded Gaussian beam [7]. Besides the obvious disadvantages of inefficiency, the high price tag of state-of-the-art laser sources demands an economical way of managing their available photons. With supercontinuum laser sources, it also becomes important to shape light with consistent output dimensions and efficiency across different wavelengths.

Photon efficient light shaping
Amplitude masks are straightforward, robust to wavelength change, and are dynamically reconfigurable using spatial light modulators (SLM) as commonly found in consumer display projectors [8,9]. However, as mentioned, the energy inefficiency of amplitude masking is low. Hence, a number of solutions based on non-absorbing or phase-only methods exist for the efficient transformation of a Gaussian beams into user specified patterns. Static beam shapers such as engineered diffusers, microlens arrays or homogenizers [10,11] are robust to wavelength shifts but suffer from speckled or grainy output intensities. Refractive mapping [12] does not suffer from grainy or specked output, but its use of specially optimized aspheric lenses, makes it hard to adapt to different shapes. Diffractive approaches such as computer generated holography, diffractive optical elements or phase plates [13,14] form the image at the far field or at a Fourier plane, resulting to output that scales with wavelength. Although SLM based dynamic holograms matched to individual wavelengths may be superimposed into a single element [15], hologram crosstalk generates noise from the mismatched wavelengths. Furthermore, iteratively designed diffractive approaches are more prone to convolution effects that blur the edges of the shaped output and considerably fluctuate due to speckles in the intensity distribution. Diffractive optics encoding complex amplitudes avoid speckles but, nonetheless, yield lower efficiencies (e.g., 49.2% efficiency was reported in [16].

Generalized phase contrast
The Generalized Phase Contrast method (GPC) [17] is a versatile technique for generating patterned illumination. By projecting intensity images that visualize phase inputs, the GPC is a fairly straightforward technique with a high light utilization [18]. It can generate a wide variety of patterns [7,[19][20][21] and accommodates various illumination profiles [7,22,23]. With reconfigurable phase inputs from phase-only SLMs, it is an effective laser projection system for dynamic multiple beam optical trapping [19]. Furthermore, unlike other phase-only beam shaping techniques mentioned, GPC works on a 4f imaging geometry, hence avoiding wavelength dependent scaling of the output which makes it a good candidate for shaping composite multi-wavelength or supercontinuum lasers [24]. The 4f geometry can accommodate different filters in the Fourier plane and different 4f beam shaping systems have also been proposed by others [25][26][27]. Among these, GPC is unique in shaping light using a direct phase to intensity mapping.
In GPC, a phase-only aperture directly representing the desired output intensity is imaged through its interference with a synthetic reference wave (SRW). This common path mapping configuration renders steep well-defined edges in the shaped intensity output. The SRW is formed by phase shifting the lower spatial frequencies through a phase contrast filter (PCF) at the Fourier plane (Fig. 1). GPC could thus be implemented with binary phase plates that are easier to mass-produce with standard cleanroom or foundry processes common for silicon devices or micro-electronics. Phase masks and PCFs can also be implemented in a number of alternative ways such as a hole in a piece of glass with a controlled thickness or as a bump or depression on a reflective surface. Techniques used for single mode fibers can also be adopted if dealing with high power lasers. Furthermore, the target output shapes could easily be replaced without increasing the fabrication cost or complexity. Light patterns formed with GPC can reach efficiencies of up to 84% in contrast to simple techniques such as rectangular irises [20]. Moreover, the average light intensity in the patterned region is ~3 times larger than the average intensity within the corresponding region of the incident Gaussian. In addition to a standard imaging or telescopic setup formed by the two Fourier lenses, GPC uses a simple binary phase mask at the input and a phase contrast filter at the Fourier plane. In this illustration a Gaussian beam is efficiently transformed into a tophat without speckles.
In this work, we experimentally demonstrate that a GPC-based light shaper works with multi-wavelength Gaussian illumination as predicted in [24]. We briefly review the optimization of a GPC Light Shaper (LS) system in section 2 and also consider the physical effects of changing the illumination wavelength. Sections 3 and 4 present experiments that illustrate GPC LS across multiple wavelengths and discuss the results. Finally, section 5 presents the conclusions and outlook.

Reshaping Gaussian beams with GPC
To have a successfully working GPC system, one has to first determine parameters of a phase mask and PCF given the expected wavelength, beam diameter and other constraints. We therefore summarize how to choose optimal phase masks and PCF sizes based on the formulations in [20] -all currently based on π-shifting phase values at the design wavelength. Given a Gaussian beam with a 1/e 2 radius, w 0 , illuminating a phase mask with phase , we define its normalized Fourier zero order, α , as In the absence of an input phase mask, the input Gaussian would be focused into another Gaussian at the Fourier plane. Assuming a wavelength, λ 0 , and focal length, f, the Gaussian waist radius at the Fourier plane, w f , is given by Δr f is the phase contrast filter's π-shifting region's radius and is measured relative to this Fourier transformed Gaussian. It is characterized by the dimensionless η given by By imposing amplitude matching with a synthetic reference wave [7], and that Δr f coincides with the Fourier distribution's first zero crossing (first dark ring) [20], the conditions for optimal contrast and efficiency of the GPC output lead to the following equations Equations (4) and (5) summarize the conditions for an optimally performing GPC system under Gaussian illumination. The fixed value for η in Eq. (4) means that a reconfigurable GPC system with a fixed PCF will consistently perform optimally with different phase masks satisfying Eq. (5). The phase mask's geometry, ( ) , x y φ , should thus be tweaked such that Eq.

The effects of changing the illumination wavelength
The output of a GPC LS is typically represented as: ) is the image of the phase modulated Gaussian input.
Equation (6) shows the output as the superposition of the input's image, a(x,y), with a synthetic reference wave (SRW) whose spatial variation, transforms back to real space the filtered frequencies resulting from the multiplication of the Fourier transform of the input, A(f x ,f y ), with the truncating circular aperture, circ(…), which has the size of the PCF's phase-shifting region. The SRW is further multiplied by a complex scaling factor that depends on the PCF phase shift, θ. When the optimal GPC parameters for a particular wavelength of Gaussian illumination are found, it would be straightforward to numerically evaluate its performance across different wavelengths. However, an understanding of the underlying physics can give useful insights, as we briefly outline below. For a given wavelength, the output in Eq. (6) yields optimal efficiency when using πphase-shifts for the input and filter masks [20]. Therefore, at first glance, the range of wavelengths from a supercontinuum light sources would seem problematic for the GPC LS. Phase masks that have been etched to a depth, d 0 , to produce π-phase shift at a given design wavelength, λ 0 , will produce a different phase shift when illuminated by another wavelength λ. Etching the input and filter phase masks simultaneously on the same glass wafer results in a common phase shift given by where we also included material dispersion (primarily due to glass). Similarly, from Eq. (2) and (3) above, the dimensionless η will depend on wavelength as: where η 0 is the value of the parameter at the design wavelength, λ 0 (assuming the incident beam waist is independent of wavelength). For simplicity, let us consider the case of Gaussian-to-tophat shaping. This requires an input phase mask having a circular phase shifting region of radius Δr. We may gain some insights about how shifting the wavelength would affect performance by looking at the onaxis value of the superposition: where 0 / r w ζ = Δ is a dimensionless parameter describing the size of the input phase mask radius relative to the input Gaussian waist, and therefore, the size of the output tophat relative to the Gaussian waist that can be imaged at the output by the 2 lenses. The field around the phase-shifting region of the PCF is very well approximated by a displaced Gaussian [20], and so we used this to find the on-axis value of the low-pass filtered input. Using the known wavelength dependence of the phase shifts ( , ) θ φ and the parameter η, we can determine how the intensity will change with wavelength. Figure 2(a) shows how the on-axis intensity is affected when sweeping the wavelength from 350 to 750nm when using GPC parameters optimized for λ 0 = 532nm (the simulations used η = 1.1081and ζ = 0.3979 according to the optimization procedure described in [20] and applied the dispersion properties of fused silica). For comparison, the graph also plots the wavelength dependence for a suboptimal case that uses a smaller input filter, ζ = 0.3 that corresponds to a smaller tophat output. The resulting upper trace in Fig. 2(a) shows that this smaller tophat exhibits a higher peak intensity but a more pronounced wavelength dependence relative to the optimized case (the lower trace in Fig. 2(a) is flatter). Moreover, when comparing conversion efficiencies using the power within the shaped area (Intensity × Area), it is the bigger tophat, ζ = 0.3979, obtained by the optimization procedure obtained in [20] that yields a higher efficiency (see efficiency comparisons in [20]). This means that the higher intensity within the smaller tophat, ζ = 0.3, is unable to compensate for its smaller area resulting in lower efficiency To visualize how GPC's robustness to wavelength changes arises, we plotted how the onaxis image, exp(iφ), and the SRWs corresponding to the two tophats, ζ = 0.3 and ζ = 0.3979, drift in the complex plane as the input wavelength changes from 380nm (A,D) to 700nm (C,F) for phase masks designed for 532nm (B,E). Illustrative phasor diagrams of the superposition are shown for selected wavelengths (A-F). The phasor diagrams show optimal superposition at the design wavelength and, as expected, the input phase deviates a lot from π over the chosen wavelength range. However, unlike the input phase, the SRW phase remains close to π over the range of wavelengths. When using non-π-phase modulated input, optimizing GPC requires finding an appropriate non-π-phase-shifting PCF that will create an SRW that is π-out-of-phase with the designated dark regions to minimize losses by ensuring optimum destructive interference [28]. In this case, we can see that the SRW is able to be close to π-out-of-phase with the 0-phase encoded background. This indicates that the corresponding non-π-phase shift of the PCF due to the change in wavelength ends close to the optimal phase shift. In effect, the input phase changes are compensated by the corresponding PCF phase change when shifting the wavelength away from the design wavelength. This compensation is explained in more detail in [24].

Construction of a pen sized GPC LS
The GPC LS used for our static experiments was designed to interface directly with the output of laser sources in free space. Commercial lasers typically have beam diameters of around 1mm to 5mm. Using two f = 50mm Fourier lenses allowed us to keep the setup compact. This also allows cheap yet controlled mask fabrications with wet etching and offthe-shelf optics assembly. The GPC LS assembled with half-inch optics and 16mm cage system from Thorlabs is shown in Fig. 3. Its overall length is a little over 3f = 150mm, which is around the size of a usual pen. For more compact implementations, such as for OEM use, integrated micro-optics platforms [29] or alternative fabrication and assembly techniques can also be adopted. When compactness is not a requirement, longer focal lengths can be used to minimize the focused light-intensity at the PCF.

PCF and phase mask preparation
We designed the GPC LS for use with the following parameters: laser beam waist diameter 2w 0 = 1mm, laser wavelength λ 0 = 532nm and focal length of lenses as f = 50mm. The material used for the phase mask and PCF is fused silica (n = 1.46 at λ = 532nm). The PCF radius is calculated using Eqs.
The phase masks were based on simple shapes (circle, square, and rectangle) and arbitrary bitmap images (e.g. globe, logos) that were scaled with respect to the preferred beam diameter such that Eq. (5) is satisfied. Conventional UV-lithography technique followed by wet etching in the buffered HF (BHF) was used to form the patterns. The etch depth was determined such that it gives a half wavelength optical path difference relative to the unetched surroundings: where n is the refractive index of fused silica. Hence, the etch depth used is ~577nm. This wavelength was chosen as a central wavelength for the visible part of the spectrum of the supercontinuum laser we used and to work with widely used green (532nm) lasers. From a four-inch wafer, the phase masks and PCFs were diced such that they can be fitted into half-inch optics mounts.

Optical setup
The setup used for the testing a GPC LS across different wavelengths is shown in Fig. 4. The interchangeable phase masks were used to form a variety of speckle-free contiguous patterns at selected wavelengths. For our light source, we used a supercontinuum laser from NKT Photonics (SuperK Koheras) that has a 1mm beam diameter. The beam is guided through the wavelength selector (SuperK Select from NKT Photonics). Light collimation and guidance after the wavelength selector was performed using fiber delivery system (SuperK Connect from NKT Photonics). It should be mentioned that the fiber output beam diameter was slightly wavelength dependent. The beam diameter was close to 1mm at 532nm and increases with wavelength. The spectral FWHM of the filtered beam was 1.5-4 nm depending on the wavelength. The light was then directed to the GPC LS using relay mirrors that also provided beam alignment. Output from the GPC LS was magnified (2x) then guided either to a beam profiler (Gentec-EO) or to a color CCD. The beam profiler's linear intensity response allows post-analysis while the color CCD better visualizes the multi-wavelength results.

Results using laser-line bandpass filters
For initial testing, we first assessed the light shaper's performance on its design wavelength -532nm -by placing a 532nm laser-line band-pass filter along the SuperK path. Figure 5 presents different GPC output shapes tested by interchanging the phase masks on the same GPC LS. To rule out reflection losses, the Gaussian reference is obtained when the PCF is misaligned and the beam goes through the same components. However, to prevent edge effects from the etched pattern, the phase mask was completely removed from the GPC LS. Hence, the reference Gaussian is marginally more intense and the reported efficiencies are marginally lower.

Results using the wavelength selector
Having confirmed results for the 532nm design wavelength, the GPC LS was then tested with multiple wavelengths from the wavelength selector. As noted, the output beam size was wavelength-dependent and slightly differs from 1mm -output beam diameter of the SuperK without the wavelength selector -which was used in the GPC LS design. This influences measurements making efficiencies lower than expected. However, the overall performance is still within acceptable experimental variations, indicating the tolerance of the GPC LS. Figure 6(a)-6(f) presents a globe pattern obtained at different wavelengths. The SuperK power was adjusted for different wavelengths to maintain fairly uniform image brightness on the CCD captures. Even though wavelength was being changed over a wide range, the final patterns shows high contrast and brightness uniformity. Fig. 6. Color CCD images of GPC projections from the same setup, as the wavelength selector is varied from 500nm to 650nm (a)-(f) (see Media 1).The power at different wavelengths is adjusted individually for visibility.
To confirm previous theoretical and numerical predictions [24], we measured the dependence of the GPC LS's efficiency against different wavelengths. The measurements were performed at 25nm steps, changing the tested wavelength and maintaining a small FWHM. Figure 7 shows the experimental data. The error bars for the experimental data were obtained from the difference between several measurements performed at the same wavelength (five in average).These error bars allow room for slight fluctuations caused by the laser beam's intensity and beam size.
The acquired efficiencies and energy savings are, as expected, marginally lower than the simulated ones [24]. The main reason was the deviations from the beam diameter that the GPC LS was designed for. Experiments with the beam obtained directly from the greenfiltered SuperK (Fig. 5) has shown better results closer to theoretical predictions. Despite being lower than theoretical predictions, the GPC LS exhibited good beam shaping performance across the whole visible range with slightly lower results in the very red spectrum range, also as simulations predicted [24]. It should also be noted that as the phase mask was removed to obtain a clean Gaussian signal, partial reflections that the phase mask introduces were also withdrawn. Therefore, the real efficiency is somewhat higher than what we have measured.
The gain was maintained at the level of ~3x throughout the wavelength range. The relative incrase in gain level, seen at the red range (i.e. from 650nm to 675nm), can be explained by the slightly larger beam diameter that causes a mismatch of the SRW. This is also consistent with the lowered efficiencies as the SRW mismatch lessens the effect of destructive interferene that supposedly defines the dark background. The counteracting effects of gain and efficiency, however, effectively maintains a fairly high energy savings value.

Summary and outlook
We have experimentally shown that light shaping based on the Generalized Phase Contrast method shows robustness to wavelength change. The GPC-based projections maintain high quality and efficiency over a doubling of wavelength in Gaussian beam shaping. With some wavelength dependent deviations, experiments showed around ~70% efficiency, ~3x intensity gain and ~85% energy savings compared to the commonly implemented hard-truncated expanded Gaussian. The energy saved by using a GPC LS makes it attractive for many applications wherein light is best utilized in a particular shape, e.g. rectangles for spatial light modulator illumination or digital display projection, circles for laser materials processing or even intricate biological patterns found in neurophotonics research if coupled with a dynamic broadband spatial light modulator. Furthermore, the added benefit of broadband light shaping, makes it an attractive enabling tool for advanced biological research. For even better performance of the GPC LS, i.e. higher efficiency, broadband anti-reflection coating on top of both the phase mask and the PCF can be considered.