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We report on the performance of a system employing a multi-layer coated mirror creating circularly polarized light in a fully reflective setup. With one specially designed mirror we are able to create laser pulses with an ellipticity of more than ε = 98% over the entire spectral bandwidth from initially linearly polarized Titanium:Sapphire femtosecond laser pulses. We tested the homogeneity of the polarization with beam sizes of the order of approximately 10 cm. The damage threshold was determined to be nearly 400 times higher than for a transmissive quartz-wave plate which suggests applications in high intensity laser experiments. Another advantage of the reflective scheme is the absence of nonlinear effects changing the spectrum or the pulse-form and the scalability of coating fabrication to large aperture mirrors.
©2011 Optical Society of America
1. Introduction
In most experiments, circularly polarized light is created using a quarter-wave plate made of mica, quartz glass or other crystalline material. However, this method is not generally applicable to ultra-high intensity short-pulse lasers due to nonlinear effects, the damage threshold of the material, and the fact that ultra-thin wave-plates have a chromaticity that prevents their usage for broadband laser sources. In addition, variations in the thickness of the wave plates caused by the polishing process lead to imperfections of the beam profile and deteriorate the homogeneity of the phase retardation across the beam diameter. Current polishing technology limits the maximum size of zero-order wave plates to about a diameter of 15 cm due to the high risk of damage on the thin substrate.
We designed, manufactured, and characterized a phase-shifting mirror (PSM) based on a dielectric coating, creating high-quality circularly polarized light for a broad-bandwidth laser system. The advantages of this approach are based on those of fully reflective multi-layer optics and include almost no group-delay-dispersion (GDD), a high damage-threshold and the possibility to produce large aperture optics. To our knowledge, this is the first time that the applicability of such a circularly polarizing mirror is demonstrated for a broad bandwidth high-power femtosecond laser system.
In the mid-infrared region of the spectrum, changing the polarization by influencing the phase upon a reflection of a mirror is a common technique [1]. We extend this technique towards applications with broad-bandwidth ultra-short laser pulses in the visible and near infrared. The idea to create an arbitrary phase-shift with a multi-layer mirror was patented in the 1980s [2].
Linear polarization is called p- polarized when the electric field vector is parallel to the plane of incidence and s- polarized for the field vector perpendicular to the plane of incidence. Reflecting an electromagnetic wave at a surface in general induces a phase-shift between the s- and the p- polarized field component. Typically the geometry is chosen such that the polarization is purely parallel or perpendicular. Therefore, the polarization does not change upon reflection. When, on the other hand, the reflecting surface is tilted such that s- and p- polarization is present, the polarization state changes due to the phase shift.
2. Setup
2.1. Principle of a phase-shifting mirror PSM
Dielectric coatings are a well-known technique to produce, e.g., mirrors with a high reflectivity. The standard design is the so-called quarter-wave stack, i.e. a stack of alternating layers with high and low refractive index (e.g. SiO2 and Ta2O5) and an optical thickness of a quarter of the wavelength. More advanced functionalities can be realized by deviating from this design. In general, numerical methods are used for determining the respective sequences of dielectric layers of varying thickness. In most cases, the matrix method [1], which offers an efficient approach to compute the complex reflectivity of any dielectric coating, is used together with an iterative optimization loop. Well-known recent examples realized with this approach are chirped mirrors, i.e. high-reflection mirrors with a spectrally dependent phase which induce group delay dispersion (GDD) [3–5].
For the problem at hand here, the dependence of the (complex) reflectivity on the direction of the polarization relative to the surface layer has to be considered in addition. Accordingly, each layer of the coating is represented by a 2x2 matrix that differs for s- and p-polarization, see Fig. 1 . For any given wavelength, the complex reflectivity for the different polarizations can be computed by multiplying theses matrices. In this way, the reflectivity of arbitrary layer systems can also be calculated for broad-band femtosecond laser pulses.
Fig. 1 Principle of a dielectric multilayer coating: a) p-polarized (green) and s-polarized (blue) field components are reflected at each surface of an alternating multi-layer stack with a refractive index n 1 and n 2. b) The amplitude and the phase of the reflected wave are given by the superposition of the partial waves. In a simplified picture a certain boundary layer has a major reflection of the p-polarized component and vice versa. The final complex reflectivity of a multilayer coating can be tailored by tuning the optical path n i d i of each layer. The thicknesses d i of the multilayer coating determine the phase shift between the p- and s-polarized field component thus making, e.g., a 90°-phase shift possible. With this coating property circularly polarized light can be created when linearly polarized light is reflected upon a PSM with an equal amount of the p- and s-polarized field component.
We started our coating design procedure with an alternating stack of a high and low refractive index material, Ta5O2 and SiO2, on top of a thin silver layer. Since the reflectivity is altered when any of the layer thicknesses di is changed, the optimization of the reflectivity requires appropriate algorithms. As a first step, a function of merit must be assigned. Here we demand a reflectivity as close as possible to 100% over a bandwidth of 800 ± 40 nm, a spectrally flat GDD, for maintaining the short pulses, and a phase shift of 90° between s- and p- polarized light. Particular emphasis was put on achieving the latter homogeneously over the entire bandwidth.
Our optimization routine resulted in a coating design that has the reflectivity shown in Fig. 2 . While usually less than 15 layers are sufficient to achieve 99.9% reflectivity for a simple quarter-wave stack, the additional constraints of low dispersion and a homogeneous 90°-phase shift between s- and p-polarized wave required 24 layers for 98% reflectivity. A reflectivity of R> 99.5% would be possible by increasing the number of dielectric layers.
Fig. 2 Calculated reflectivity (a)) and phase-shift (b)) for the design of the PSM for an angle of incidence of 45°. The reflectivity exceeds 98% for both polarization components while maintaining an almost linear spectral phase. Particular emphasis has been put on a homogeneous phase shift ΔΦ of 90° over a large bandwidth.
A simple tolerance analysis showed that the phase-shift is extremely sensitive to thickness uncertainties of the multilayer design. For example, the thickness deviation must be less than 2% in order to maintain a deviation of less than 5° for the phase shift ΔΦ. Such tight tolerances call for reliable coating technology. The PSM coating was manufactured with a magnetron sputtering technique onto a large aperture fused silica substrate (160 mm x 120 mm x 20 mm). Particular attention was paid to create homogeneous layers by rotating the mirrors during the coating process.
2.2 Ellipticity measurements
For the measurements, the beam of a short-pulse TiSa-laser-system delivering 0.7mJ in 23fs at a repetition rate of 4 kHz was used (Femtopower Compact Pro with a bandwidth of λ = (790 ± 50) nm). The beam was given a circular shape by an iris to create a spot size of 5 mm diameter. In order to rotate the plane of polarization of the incident laser pulse, we used a wave plate in combination with a polarizing beam splitter (PBS) with an extinction-ratio of 1000:1.
For measuring the change of the polarization state induced by the PSM, it was mounted as shown in Fig. 3 . In order to adjust the same amplitude for the s- and the p- component of the polarization the polarization of the incident beam was rotated to 45° with respect to the plane of incidence. Note that rotating the polarization of the incoming beam with a wave-plate is equivalent to rotating the reflecting mirror around the axis of the incoming laser while leaving its plane of polarization unchanged. The polarization state of the reflected beam was analyzed by a PBS on a rotation mount. Then after suitable attenuation, the beam was imaged onto an 8-bit CCD camera for measuring the beam profile and the intensity. The analyzer was rotated in steps of 10° and the intensity was measured by taking a picture for each position. The surface of the PSM was scanned by the 5-mm diameter beam on a matrix of 3x3 positions separated by 3 cm.
Fig. 3 Setup for measuring the phase-shift. a) Planar view of the beam before and after the PSM. b) General setup for the experiment: The amount of the s- or p-polarization component projected in the incidence plane of the PSM can be changed by rotating the wave-plate and the PBS in front of the PSM. The polarization state can be measured with a PBS after the PSM used as an analyzer.
We determined the intensity by taking the mean of the 20% brightest pixels of the pictures after background subtraction. The ellipticity then can be calculated by [1]
Here I Min and I Max denote the minimal and maximal intensity that can be measured while rotating the PBS by 360°. The reflected field strength as a function of the angle of the analyzer is shown in Figs. 4(a) and 4(b) (The field strength data was normalized to the maximum value measured). The blue line shows a fit to the functionFig. 4 Plot of the field distribution measured for the [a)] phase-rotating mirror and the [b)] λ/4 plate for the full spectrum of the laser at one position of both devices. The blue line is a fit, the grey line shows the 0.9 confidence interval. The calculated ellipticities related to these fits are (98.3 ± 0.6) % (PSM) and (83.6 ± 0.3) % (λ/4 plate).
Due to the periodicity following 2φ, B describes the deviation from the circular polarization. An additional variation of the intensity with a periodicity of 1φ can be observed for nearly perfect circular polarization. This is an artifact due to a slight beam deflection induced by the analyzer.
Figures 4(c) and 4(d) display the corresponding measurement for a low-order large-aperture quarter-wave plate made of mica. We observe a strikingly better performance of the PSM as compared to the quarter-wave plate.
In fact, the ellipticity generated by the PSM reaches ε PSM = (98.3 ± 0.6)%, while it does not exceed ε λ/4 = (83.6 ± 3.4)% for the mica plate.
It should be noted that the ellipticities cited are the averages across the respective apertures, where the uncertainties include the inhomogeneity as well as measurement errors. The latter are comparable for both cases. Therefore, the much larger uncertainty of the ε λ/4 means that the quarter-wave plate also has a much lower homogeneity.
The same measurement using a spectrometer (Ocean Optics USB2000 + ) instead of the camera shows a homogeneous ellipticity over the full bandwidth range and no spectral changes due to different reflectivity.
2.3 Pulse broadening and spectral changes
When using a PSM for high-intensity femtosecond laser pulses, the temporal properties have to be preserved upon reflection. Conceivable effects are pulse distortions due second-order dispersion and self-phase modulation. We measured the pulse duration for one reflection on the PSM and compared it to the pulse length before and after propagation through the large quarter-wave plate used before. Assuming a Gaussian pulse shape, a dispersion-free pulse with an initial duration τ 0 will be stretched to
after acquiring a second-order dispersion D 2 [6]. The thickness of the coating layer is about 2.5 µm. By numerical simulation of the layer-design we calculated a second-order dispersion of 40 fs2 at 800 nm. This corresponds to about 1 mm of fused silica. With an autocorrelator (FemtoMeterTM) we measured a pulse duration of τ 0 = (24.0 ± 0.9) fs without the PSM and τ F = (23.8 ± 1.1) fs with the PSM. This means the pulse duration remains the same within the error-bars, which is also confirmed by the small GDD predicted theoretically: 40 fs2 causes a broadening by 0.44 fs of 24-fs pulse.Next we checked for effects influencing the spectrum, e.g. like interferences in the dielectric layer. To this end we measured the spectrum behind the PSM and the wave plate (Fig. 5 ). The spectrum was recorded while rotating the analyzer PBM in steps of 10°. Due to the fact that the spectrometer (OceanOptics, USB2000 + ) is based on a grating for which the reflection is strongly depended on the polarization, there are large variations in the measured intensity. Therefore the average value was calculated and normalized. The overall spectrum did not change significantly, however some minor ripples show up in the spectrum of the PSM.
Fig. 5 Measurement of the laser spectrum compared to the spectrum using the PSM and using the wave-plate.
2.4 Damage threshold
For testing the damage threshold, we focused the laser with a f = 500mm spherical mirror at a small incidence angle (< 5°) on a PSM test substrate. The beam size was measured directly on a CCD camera for different beam positions, at which the mirror sample was placed afterwards. For each position, the sample was irradiated for three seconds and then inspected with a reflected-light microscope. In cases where damage occurred, the size of the damaged area was measured. Typical spot sizes used were in the range of 0.1mm2. Within a factor of 2, the measured damage sizes were the same as the spot size. Based on the known pulse duration, pulse energy, and focal spot size, we calculated the damage threshold. This value may need to be corrected due to the fact that we used smaller foci-spots than usually chosen for this kind of characterization. According to some reports in the literature, damage tests with foci smaller than 1mm2 will result in 2 to 3 times higher damage intensities as compared to measurements performed with larger beam diameters [7]. Taking this into account, we estimated the damage threshold at 5 x 1012 W/cm2, which is in good agreement with other damage tests for dielectric coatings [8,9]. It should be noted that the damage threshold is ~400 times higher than the threshold for a wave-plate made of quartz glass (1.2 x 1010 W/cm2) [10]. The damage threshold for a plate made of mica is even lower due to the relatively high absorption in this wavelength range [11].
3. Summary and outlook
We have presented the option to generate circularly polarized femtosecond laser pulses using a reflective system. A homogeneous ellipticity of 98% for a large aperture mirror has been demonstrated. This proves the feasibility of fabricating homogenous phase retarding devices up to the limits of optical coating-machines, which exceed 500 mm to date. The demonstrated damage threshold is almost 400 times higher than for a classical wave-plate. Therefore, this system is an ideal component for experiments with high-intensity laser systems.
Acknowledgments
B. Aurand acknowledges support from the Helmholtz Association (HGS-Hire for Fair) and the Helmholtz Institute Jena. C. Rödel acknowledges support from the Carl-Zeiss Stiftung. This work was supported in part by the Deutsche Forschungsgemeinschaft via project TR 18 and Laserlab Europe.
References and links
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