>High Angle Resolution Beamsplitters Based on Total Internal Reflection
This article describes a high-angle-resolution beam splitter based on total internal reflection for separating superimposed beams that differ only in angle.
In general, the angular resolution can be improved by adjusting the beam waist or its wavelength and the extended propagation distance. However, if the waist and wavelength are fixed and system compactness and simplicity are design goals, then alternative methods need to be considered. Acousto-optic modulator (AOM) is a good choice. Therefore, this article demonstrates the separation of superimposed beams of different diffraction orders directly behind the acousto-optic modulator. Its working wavelength is 800 nm, and its functional principle depends entirely on the angle of total internal reflection. Because the wavelength dependence of the device is only derived from the wavelength dependence of the anti-reflection (AR) coating, and the optical element only depends on the standard optical element, the wavelength and element size can be easily adjusted to meet the requirements of various applications.
Figure 1. Two right-angle prisms with a refractive index n1 form a cube with an air gap (refractive index n2 <n1), where total internal reflection can occur. When trimmed to a critical angle, one diffracted beam is reflected and the other is transmitted through a beam splitter. (A) Top view of a beam splitter, (b) Beam splitter on a glass-ceramic base.
The schematic diagram of the beam splitter is shown in Figure 1. Two right-angle prisms with opposite hypotenuses form a cube with an air gap of about 125 μm. Total internal reflection may occur at an interface between a first prism having a refractive index n1 and an air gap having a refractive index n2 <n1 having an incident angle greater than a critical angle. The critical angle can be easily derived from Snell's law:
θ c = arcsin (n 2 / n 1 )
在晶体中传播的声波处衍射。 In AOM, light is diffracted at the sound waves that propagate in the crystal. For light incident at the Bragg angle, the first-order intensity becomes maximum, given by
θ B = λf / 2ν
ν 是声速， f 是射频，无衍射光束与一级衍射光束之间的夹角是布拉格角的两倍。 λ = λ 0 / n is the wavelength of light in the crystal, ν is the speed of sound, f is the radio frequency, and the angle between the undiffracted beam and the first-order diffracted beam is twice the Bragg angle.
In order to separate beams of different diffraction orders, the beam splitter must be tuned to the critical angle of total internal reflection in order to reflect a beam of one diffraction order and refract another beam of diffraction order according to Snell's law. 上再次折射，透过光学元件。 When entering the second prism, the beam is refracted again in the original propagation direction and passes through the optical element.
To construct the beam splitter, two prisms made of N-BK7 and 5 mm long edges (Thorlabs PS909) were glued on a glass-ceramic base to ensure a fixed width of the air gap. Use a light-curing adhesive (NOA63) to precisely align the prism before curing. An uncoated fiber is placed between the two prisms as a spacer to ensure that the surfaces are parallel. All prism interfaces have an internally manufactured AR coating, which operates at 800nm. This wavelength has been selected by example and can be easily adjusted. At this wavelength, N-BK7 has a refractive index of 1.5108, and has a critical angle of θc = 41.45 °.
Figure 2 Beam displacement and unwanted reflections R1 and R2 of the transmitted beam, which are suppressed by the AR coating.
Figure 3 According to Fresnel equation ("no AR coating" orange) and AR coating (blue), the reflectance of s-polarized light from the glass (n = 1.5108) to the air interface is a function of the angle of incidence.
When a diffracted beam is completely reflected (independent of polarization), the transmitted beam is not only refracted, but also reflected according to Fresnel's equation when leaving the first prism and entering the second prism (see Figure 1). We used an AR coating with five layers of alternating magnesium fluoride (MgF2, n = 1.4) and zinc sulfide (ZnS, n = 2.4) to reduce these unwanted reflections near the critical angle from 60% The above reduced to less than 1%. The calculated reflectance of s-polarized light as a function of the angle of incidence of the glass-air interface (R1 in Figure 2) with and without AR coating is shown in Figure 3. Since the refraction angle of the prism is equal to the incident angle of the prism, when the refractive index is inverted, the reflectance at the air-glass interface (R2) is also high. Therefore, the same coating applies to both prisms.
The air gap width between the two prisms is a compromise between beam profile distortion and potential etalon effects. Due to the large refraction angle, the beam profile is squeezed on one axis, which results in an oval profile. For small distances between prisms only, this aberration need not be compensated. On the other hand, the distance must be large enough to prevent the reflection itself and thus prevent the etalon effect from occurring. With a selected air gap width of 125 μm, the beam displacement is approximately 1 mm (see Figure 2) and the refraction angle is 41.1 °. In this configuration, we do not see a reduction in fiber coupling efficiency and power stability compared to a beam resolved through a sufficiently long beam path.
Figure 4 Schematic diagram of beam splitter characteristic measurement. FC, fiber collimator; HWP, half-wave plate; PBS, polarization beam splitter; AOM, acousto-optic modulator.
A schematic of our characteristic measurement device is shown in Figure 4. The light from a tunable diode laser (TOPTICA Photonics DL pro) is guided into the device through an optical fiber. The collimated beam (beam waist ≈ 400 μm; divergence angle is within the allowable range of the beam splitter). The intensity adjustment and polarization cleaning are performed by a half-wave plate and a polarization beam splitter. The wavelength meter (HighFinesse WS6-200) is used to monitor the wavelength in the part of the beam transmitted at the polarization beam splitter. The s-polarized reflection part passes the AOM (AA MT80-A1.5-IR), in which the material-acoustic mode speed of the tellurium dioxide crystal is v = 4200m / s, and the refractive index is n = 2.26. θ B = 0.19° ，根据斯涅尔定律，在AOM外无衍射光束和一阶衍射光束之间的角度是0.86°。 The AOM works at f = 80 MHz, and the Bragg angle at 800 nm is θ B = 0.19 ° . According to Snell's law, the angle between the non-diffractive beam and the first-order diffracted beam outside the AOM is 0.86 °.
The beam splitter is placed on the tip, tilted and rotated stage (Thorlabs TTR001 / M) and adjusted to the critical angle of total internal reflection. The reference power measured between the AOM and the beam splitter is recorded in the transmission spectrum as shown in Figure 5. Although birefringence is theoretically related to high loss, we actually achieved a transmission of more than 90% due to our AR coating (illustration in Figure 5).
Figure 5 Calculates the transmission spectrum (blue), which is given by the square transmittance and measurement spectrum (orange) of the s-polarized light of the AR coating for an incident angle of 41.1 °. Coating spectrum calculated using OpenFilters.
Beam splitters allow the development of compact laser system modules, ideally suited for the implementation of highly stable Zerodur-based optical systems for space or other field applications. We have implemented three elements in the successor system of the successful sounding rocket mission MAIUS-1, which is the creation of the first Bose-intein condensate in space. In addition, before constructing the flight hardware, a test bench including a beam splitter has been assembled, and a thermal test and a vibrator test have been performed, and a vibration of a load of 8.8 gRMS is applied. During and after these tests, no damage or failure of the beam splitter occurred. Therefore, the beam splitter is ideal for compact and rugged laser systems.
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