1. Introduction

The use of high-finesse optical cavities to enhance sensitivity of absorption spectroscopy has greatly expanded since the introduction of Cavity Ring-Down Spectroscopy (CRDS) by Deacon and OKeefe [1]. CRDS and related methods, including Cavity Enhanced Absorption Spectroscopy (CEAS) (also known as Integrated Cavity Output Spectroscopy, ICOS) and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS), exploit the sensitivity of the decay rate and transmission of low loss optical cavities to a small loss, due to absorption or scattering, introduced by a sample inserted inside the optical resonator [2–4]. In almost all of this work, dielectric mirrors have been used to create the cavities because of the ability to obtain super mirrors with losses less than ∼100 parts per million. However, multilayer dielectric mirror coatings are specifically selected for a design wavelength, as such, spectral coverage of the highest reflectivity mirrors is limited to only a few percent of the central design wavelength. Broadband measurements, such as those needed for simultaneous species detection with a single cavity, are therefore limited. Also, as one moves to the ultraviolet (UV) spectral region, the loss in even the best dielectric mirrors increases substantially. In the visible and near-infrared (NIR) regions, mirror reflectivities can exceed 99.999%. However, to the best of the Author’s knowledge, the best available reflectivity at 250 nm is 99.9% [5]. Achieving high reflectivity in the UV region is difficult due to increased absorption and scatter loss in the coating materials.

High-finesse optical cavities have been constructed using Brewster-angle prism retroreflectors for use in the visible and infrared regions [6–8]. Prism retroreflectors utilize two 45° total internal reflections (TIR), which can, in principle, provide high reflectivity over all wavelengths as long as the prism material loss is sufficiently low, the surface scatter loss is low, and the critical angle condition can be met. Lehmann et al. describe the operation of the prism ring cavity in detail [8]. Prisms constructed of fused silica demonstrated optical loss below 400 ppm over wavelengths spanning ∼550 to 1064 nm simultaneously using a supercontinuum light source [9]. The company Tiger Optics has developed a wavelength-multiplexed fused silica prism-cavity sensor for simultaneous multiple species detection [10]. The Tiger Optics’ fused silica prisms have demonstrated reflectivities as high as 99.9987% in the telecom NIR region [11]. The loss of fused silica rises further in the IR region, and is limited to wavelengths of ∼<1.8 μm. Barium fluoride is a promising mid-IR material that should allow high performance prism retroreflectors for wavelengths up to ∼5.2 μm.

As one moves farther into the UV spectral range, bulk scattering loss can prohibit achieving high-reflectivity prisms, as it scales as 1/λ⁴. Calcium Fluoride is a widely used material for deep-UV applications due to scatter loss that is approximately two orders of magnitude lower than fused silica and good transmission deep into the UV [12]. In this contribution, we present a high-finesse and broadband optical cavity in the UV region using Brewster-angle prisms constructed from CaF₂. The prisms follow the same design as in Lehmann et al. [8] Prior to construction of the CaF₂ prisms, the transmission of superpolished CaF₂ windows were measured as a feasibility assessment of CaF₂ prisms. Continuous-wave CRDS at 250 nm was used to measure the spatially-resolved transmission of the CaF₂ windows. The optical loss was correlated with spatially-varying stress-induced birefringence. Final prism reflectivity was measured using continuous-wave CRDS at 250 and 500 nm. Prism surface roughness and quality were measured using white-light interferometry. Limitations to the CaF₂ prisms are also discussed.

The layout of the remainder of the paper is as follows. Section 2 gives details on the prism retroreflector cavity operation. Section 3.1 gives the experimental setup for measuring CaF₂ window optical loss. Section 3.2 discusses the optical-loss measurement results. Section 4.1 gives the specifications of the CaF₂ prisms, and Section 4.2 gives the experimental setup and results for testing of the prism cavity. Conclusions are given in Section 5.

2. Prism retroreflector cavity design and operation

Figure 1 shows a schematic of the ring cavity formed by two prism retroreflectors [8]. The beam circulates around the cavity, going through points, R_1,2...8. Total internal reflection occurs at points R_2,3,6,7. The beam enters and exits each prism at Brewster angle at points R_1,4,5,8, requiring p-polarized light for low loss. If both prisms were perfectly aligned to Brewster angle, no light would be coupled into, or out of, the cavity. As such, the first prism is intentionally deviated from Brewster angle, typically by ∼ 1°. Once deviated from Brewster angle, there will be a finite reflection at R₄ where the beam enters the cavity, and at R₁, where the beam exits the cavity for detection. However, the reflection coefficient at R₄ will be small, and the majority of light will transmit through the surface and exit through face $\overline{CD}$. Measurements are performed by exciting the cavity with P-polarized light and detecting the amount of light coupled out of the cavity at R₁. The operation of a prism cavity, including a suggested alignment procedure and sensitivity analysis for design and alignment errors is described in detail by Lehmann et al. [8]

 

Fig. 1 Ray-tracing schematic of prism retroreflector cavity.

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The open-air path length between the prisms allows for an analyte, often gaseous, to be interrogated as in any other cavity-enhanced technique. Additionally, an evanescent wave will be created at the TIR surfaces. Provided the critical angle condition could still be met, evanescence wave spectroscopy could be performed on these surfaces [13].

In order to satisfy the critical angle condition for TIR, the material index must be higher than $\sqrt{2}$, which limits the use of CaF₂ to wavelengths below 3.3 μm. In practice, however, small angular errors in the prism construction, and the need to deviate the first prism from Brewster angle, limit the use to below wavelengths of ∼1 μm. CaF₂ is often quoted as being optically transparent at wavelengths as low as ∼150 nm. However, for use in prism retroreflectors, bulk loss becomes too high for wavelengths below ∼220 nm [12].

Additionally, birefringence in the prism material will cause p-polarized light to be converted to s-polarized light and quickly lost at the Brewster surface. Despite its high symmetry, Burnett showed CaF₂ exhibits anisotropic intrinsic birefringence [14]. However, for light propagation along <111> (i.e. the beam wave vector k⃗ normal to the Miller plane (111)), the intrinsic birefringence is absent. In total, there are 7 directions of propagation for which there is no intrinsic birefringence: three in the <100> directions and four in the <111> directions. Stress-induced birefringence also exists due to residual stresses remaining from crystal growth. Burnett also measured the stress-optic tensor, which relates mechanical crystal stress to birefringence [15]. The measured tensor shows the amount of stress-induced birefringence to be near 0 for light propagating along the <111> crystal axis at 632 nm and still relatively small at 250 nm. Therefore, the optical axis is aligned to the <111> crystal axis in both the CaF₂ test windows and in the prism retroreflectors. Note that the <111> axes are not orthogonal. Since the three beams within the prism are orthogonal to each other, they cannot all be aligned to <111> crystal axes. Figure 2 shows the orientation of the crystal axes within the prism. Minimum loss due to stress-birefringence should occur when the two parallel beams are aligned with the <111> axis, and the third beam 19° off of a <111> axis. It is difficult to predict the contribution of stress-birefringence to the total optical loss, as the internal crystal stress varies throughout the crystal. However, even a low average birefringence of ∼ 0.4 nm/cm (i.e. δn = 0.4 × 10⁻⁷) can result in 1000 ppm loss per prism.

 

Fig. 2 Top view of prism retroreflector showing orientation of the <111> crystal axes (dashed blue) to the optical axis (solid red). Note that all vectors shown are in the plane of the image.

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Light will be lost to scatter at the Brewster surface $\overline{AD}$ and at the two TIR surfaces. Equations for surface scatter loss, given in Lehmann et al. [8], show that the loss scales as 1/λ². For UV applications, it is therefore necessary to obtain very low roughness surfaces. An RMS surface roughness of 1 Å is calculated to result in ∼50 ppm loss per prism at 250 nm.

3. CaF₂ sample testing

Given the high cost of prism construction, total optical loss of two superpolished high purity CaF₂ windows obtained from different vendors were measured to assess the feasibility of achieving high CaF₂ prism reflectivity. The windows were 10 mm thick and 25 mm in diameter. They were cut from a single CaF₂ crystal which was grown along the <111> axis. The <111> axis was oriented at internal Brewster angle (34.3° at 250 nm) relative to the circular input/output surface normal. The two circular surfaces were superpolished to < 1 Å surface roughness, which was confirmed both by the polisher and independently using white light interferometry. The absolute stress birefringence was specified by the manufacturer as <0.5 nm/cm at 633 nm. The total optical loss of the windows was measured using cw-CRDS, the experimental setup for which is discussed in Sec. 3.1. Optical loss measurement results are discussed in Sec. 3.2.

3.1. Optical loss experimental setup

Cavity ring-down spectroscopy (CRDS) is an ultra sensitive laser measurement technique which uses the enhanced path length of a high-finesse cavity to measure very small optical losses. In CRDS, a high-finesse cavity is excited with a laser, in this case a continuous-wave laser. The cavity is formed by two high reflectivity dielectric mirrors. An acousto-optic modulator (AOM) is used to extinguish the laser beam once significant power is built up between the cavity mirrors. The remaining light within the cavity will leak out through the small transmission of high reflectivity (HR) mirror, yielding an exponential decay with time. The 1/e point of the decay is termed the ring-down time, which can be used to calculate the total loss within the cavity (including loss of the mirrors themselves). The wavelength of interrogation was 250 nm generated by a frequency-quadrupled external-cavity diode laser (Toptica, TA-FHG110).

The CaF₂ window was placed within the cavity at Brewster angle allowing p-polarized light to enter and exit the window with low loss. Also, as mentioned previously, the <111> crystal axis is at Brewster angle relative to the window surface normal and can therefore be aligned to the optical axis. In order to decouple the loss contribution of the CaF₂ window and that from the cavity mirrors themselves, the ring-down time was measured with and without the window in place. The resulting difference is the loss from only the window. Figure 3 shows the loss measurement setup with the window inside the cavity. To also allow measurements without the windows, the back HR mirror was placed on a translation stage such that it could be moved transverse to the optical axis to compensate for the 4.4 mm lateral shift when the beam passed through the window at Brewster angle. Two translation stages moved the window in the plane of its circular face, allowing optical loss to be measured at different points on the window.

 

Fig. 3 Schematic of CRDS optical-loss measurement apparatus. AOM: acousto-optic modulator, MM: mode-match telescope, M: steering mirror, P: linear polarizer, HR: high reflectivity mirror, PMT: photomultiplier tube, CaF₂: test window.

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As mentioned earlier, birefringence in the CaF₂ crystal will convert p-polarized light to s-polarized light, which has a much higher Fresnel reflection coefficient at the Brewster surface. Since the polarizer (100,000:1 extinction ratio) prior to the optical cavity only transmits p-polarized light, any light reflecting off the window Brewster surface is a direct consequence of polarization rotation caused by crystal birefringence. The ratio of the amplitudes of the ring-down signals measured on PMT 1 to PMT 2 is a measure of the relative amount of crystal birefringence integrated along the optical beam path at that location. As the window was translated, the aforementioned ratio was found to change significantly. The spatial variation in crystal birefringence was also measured using crossed polarizers, as depicted in Fig. 4, and showed near perfect correlation with the CRDS birefringence measurement. Note that the AOM and mode-match telescope are not necessary for the crossed-polarizer measurement, but were left in place to ensure the beam interrogated the same point on the window.

 

Fig. 4 Schematic of crossed polarizer measurement apparatus. AOM: acousto-optic modulator, MM: mode-match telescope, M: steering mirror, P: linear polarizer, HR: high reflectivity mirror, PMT: photomultiplier tube, Pol-P: P-oriented polarizer, Pol-S: S-oriented polarizer.

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3.2. Optical loss measurements results and discussion

Figure 5 shows the total optical loss and relative birefringence of the CaF₂ window which exhibited the lowest loss at 250 nm. The same CaF₂ supplier was used for the CaF₂ window discussed here and the prisms. The window supplied by the other manufacturer showed loss approximately 3 times higher and is not discussed in this section. Optical loss was measured over a ∼1 cm region with a 0.64 mm measurement spacing. The 1/e² beam diameter at the window was 0.4 mm. The minimum, maximum and mean window loss were observed to be 340±60, 2420±60, and 1130±60 ppm respectively. The relative birefringence showed very high spatial correlation with the total loss, though not perfect correlation. Such correlation suggests that stress birefringence is a large contributor to the overall optical loss. However, other mechanisms such as crystal impurities may also contribute and explain the imperfect correlation. As discussed in Sec. 2, CaF₂ does possess intrinsic birefringence, however not along the <111> axis to which the beam is aligned [14]. Additionally, the relative orientation between the interrogating laser and the crystal axes did not change throughout the test. Therefore, the spatially varying contributions of the birefringence must be from stress-induced birefringence, which can vary throughout the crystal.

 

Fig. 5 Optical loss from CRDS (left) and the birefringence measured from crossed polarizers (right) at 250 nm.

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Note that the physical beam path length through the window is 12.1 mm (not multiplied by n), while the path length through our prisms is 29.7 mm. Also, the beam must transmit through two Brewster surfaces in the window, but no TIR surfaces, while each prism has two Brewster surfaces and two TIR surfaces. In order to scale the loss of the window to an estimated prism loss, the window loss is multiplied by the ratio of beam path length in the prism to that of the window or 2.45. Not only does this factor include the extra path length within the prism, but it also approximately accounts for the two additional surface interactions the loss of which is additive with bulk loss. From the equations in Elson et al., scatter loss at a TIR surface contributes ∼5 times as much scatter loss than at a Brewster surface for the same roughness [16]. Therefore the scaling factor may somewhat underestimate the total surface scatter loss but should still provide a close estimate.

Using the scaling mentioned above, the window losses translate to a maximum, minimum and mean estimated prism reflectivity of 99.92%, 99.41%, and 99.72% respectively. Such reflectivities were deemed sufficiently high to warrant constructing CaF₂ prisms. The best available dielectric mirrors have reflectivites approaching 99.9% [5]. Based on the loss estimates presented here, CaF₂ prisms have the potential to exceed the performance of dielectric mirrors for single-wavelength operation, as well as provide UV-broadband operation.

4. CaF₂ prism cavity

A pair of Brewster angle CaF₂ prism retroreflectors have been constructed and tested. This section discusses their specifications and performance. Section 4.1 gives the prism geometry and specifications. Section 4.2 gives the experimental setup for the prism testing and their measured performance.

4.1. CaF₂ prism specifications

Figure 6 shows a top-view drawing of the prism with relevant dimensions. The prism height (i.e. the dimension out of the page) is 12.5±0.2 mm. The first prism has all planar surfaces, while surface $\overline{EF}$ (see Fig. 1) on the second prism is spherical with a radius of curvature of 6.7±0.1 m with the tangent point centered on the square face. The spherical surface focuses the beam, creating a stable cavity for cavity lengths (i.e. distance between the prisms) of <1.49 m. Since the beam strikes face $\overline{EF}$ at 45°, the effective focal length of the spherical surface is not the same in the vertical and horizontal directions. The beam within the cavity is therefore astigmatic. Ideally, the prisms would include an aspherical surface or two cylindrical surfaces, giving a non-astigmatic cavity beam. However, such surfaces are much more difficult to manufacture.

 

Fig. 6 Dimensions of the CaF₂ prism.

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As observed with the CaF₂ windows, CaF₂ can be readily polished to surface roughness below 1 Å. However, superpolishing the prisms proved more difficult for manufacturers due to the more complicated prism geometry. White light interferometry was used to measure R.M.S. surface roughness between 2 and 2.4 Å. Since surface scatter loss scales as the square of roughness, this corresponds to a factor of ∼5 increase in scatter loss.

4.2. Prism cavity testing

Continuous-wave cavity ring-down spectroscopy was used to test the prism reflectivity at both 250 and 500 nm. Figure 7 shows the optical layout for the prism testing. The laser (Toptica, TAFHG110) provided frequency doubled and quadrupled light at 500 and 250 nm respectively. An AOM was used to extinguish the light to the cavity once a resonance was detected. Mode matching the laser to the optical cavity is more complicated than for a typical dielectric mirror cavity due to astigmatic prism focusing. Mode matching was achieved with a series of four lenses. A 35 mm focal length lens focused the beam into a 10 μm pinhole for spatial filtering. A 40 mm focal length lens collimated the beam after the pinhole. Two 500 mm focal length cylindrical lenses, one oriented to focus vertically and one oriented to focus horizontally, matched the laser beam to the astigmatic cavity mode. Q-parameter theory and ABCD matrices from Siegman’s book (including those given in the errata) were used was used to determine the needed distances between optics to match the TEM_0,0 laser mode to the TEM_0,0 mode of the cavity [17,18]. The polarizer only allowed p-polarized light to reach the cavity. While s-polarized light would be quickly lost once the AOM turns off, it will also couple into the cavity much more strongly than p-polarized and mask the p-polarized signal. Therefore, it was helpful to have a high extinction ratio polarizer that is well aligned to p prior to the cavity. Each prism was placed on a Newport 9411 prism mount, which has tip, tilt and rotation adjustments. To avoid inducing additional mechanical stress, and therefore additional birefringence, the prisms were not clamped in any way and simply rested on the mount. The cavity length was 75 cm. The beam exiting the prism cavity was sent to a PMT for detection. Aligning the prism cavity is not trivial and is outlined in detail by Lehmann et al. [8]

 

Fig. 7 Optical schematic for cw-CRDS test of CaF₂ prisms. AOM:acousto-optic modulator MM:mode-match telescope CL1:cylindrical lens 1, oriented to focus vertically CL2:cylindrical lens 2, oriented to focus horizontally POL:linear polarizer M:steering mirror PMT:photomultiplier tube

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Cavity losses of 2500±100 and 400±100 ppm per pass were found at 250 nm and 500 nm respectively. The first prism (left prism in Fig. 1) has all planar surfaces and can therefore be translated vertically a few mm without losing cavity finesse. The cavity loss reported here was the minimum found after translating the first prism ±3 mm. These losses include the loss of one prism and the loss incurred by the beam passing through 75 cm (single-pass cavity length) of air. The loss contribution from ambient air was calculated using the results from Naus et al. and found to be 220 and 10 ppm at 250 nm and 500 nm respectively [19]. Subtracting the estimated loss in air from the cavity loss, one finds prism losses of 2300±100 and 390±100 ppm at 250 nm and 500 nm respectively, which correspond to prism reflectivities of 99.77±0.01% and 99.96±0.01% at 250 and 500 nm respectively. These findings are consistent with the estimated prism loss discussed in Sec. 3.2.

5. Conclusion

We have demonstrated, to the best of our knowledge, the first use of CaF₂ for Brewster angle prism retroreflectors. Optical-loss measurements of <111> oriented CaF₂ windows showed prism reflectivities of ∼99.72% at 250 nm would be achievable with available manufacturing techniques. However, portions of the CaF₂ showed much higher loss, which was attributed to stress-induced birefringence. CaF₂ prisms were constructed with the <111> crystal axes closely aligned with the beam path. Prism reflectivities of 99.77±0.01% and 99.96±0.01% were found at 250 and 500 nm respectively. Not only do these prisms rival the best dielectric mirrors available for 250 nm, they also allow for high-finesse cavity operation simultaneously over hundreds of nm of optical bandwidth.

Several limitations in the prism performance were due to manufacturing difficulties, rather than physical limitations. For example, white light interferometry on CaF₂ showed surface roughness below 1 Å is readily achievable with superpolishing techniques. However, due to the more complicated prism geometry, polishing the prisms proved more difficult, resulting in a surface roughness of ∼2 Å. Therefore, the estimated surface scatter loss is ∼200 ppm at 250 nm, while improved polishing could yield scatter loss below ∼50 ppm. The remaining loss mechanisms contribute ∼1800 ppm of loss and are likely dominated by stress birefringence, which could be improved with lower birefringence CaF₂. Additionally, loss due to bulk absorption, bulk scatter, and birefringence are path-integrated effects and could be reduced with smaller prisms. Given that the spot size within the cavity is ∼400 μm, diffraction loss is negligible. The prism size, and therefore path-integrated loss, could be scaled down by a factor of ∼5 or more without diffraction loss becoming significant. While such scaling would significantly reduce the prism loss, manufacturing becomes much more difficult and costly. Nevertheless, CaF₂ prisms with reflectivities above 99.95% at 250 nm should be physically achievable.