2.1

Verification of the optical loss of CdMnTe crystals

Optical absorption and scattering processes cause an attenuation of the transmitted light through a crystal. This relative reduction of light intensity can be probed by power meters, as shown in Figure 1 (left). The first power meter (PM1) measures the incident intensity. A second power meter (PM2) is used to measure the light transmitted at the output of the crystal. The power meter PM4 is used to measure the reflection on the input facet of the crystal, and thus, infer the reflection coefficient of the facets of the uncoated crystals. Power meter PM3 measures the output power after round-trip inside the crystal, and this value can be used to independently infer the absorption coefficient, as a cross-check to the main measurement via the transmitted power at PM2.

Figure 1.

Left: Measurement setup for the optical losses in the CdMnTe crystals Right: Overview of the optical losses of two CdMnTe crystals at different wavelengths.

A tilt of the crystal is therefore necessary, firstly, to minimize the effects of a Fabry-Pérot cavity, and secondly, to be able to resolve the reflected light spots. However, tilting increases the geometrical path length inside the crystal and thus needs to be considered in the calculations of the optical losses.

For a crystal of length L and refractive index n, the geometrical path length of a laser beam incident at an angle α is:

Taking the optical power incident on crystal facet to be P_in, the power reflected at the facet to be P_R, and the power exiting the crystal to be P_out, then, the optical absorption coefficient α_i is given by the Lambert-Beer law [2]:

It should be noted that the optical loss comprises the absorption coefficient of the crystals and scattering losses on the facets and within the material, due to, for instance, defects. The crystals measured in this work are not antireflection coated and the optical quality of the facets also shows some imperfections. It is expected that coated crystals will have a lower value of the optical loss.

In Figure 1 (right) the wavelength-dependent optical losses are plotted for two stoichiometric ratios of the CdMnTe crystals. At 780 nm, the absorption coefficients are around 0.05 cm^-1 for both stoichiometric ratios corresponding to a 1% losses due to optical absorption. From the measurement of the optical losses, we can conclude that Cd_0.75Mn_0.25Te as well as Cd_0.86Mn_0.14Te are suitable candidates for the implementation of a magneto-optic material in an optical isolator for visible wavelengths.

2.2

Verification of Verdet constant

The measurement of the Verdet constant has been carried out on crystals with two different stoichiometric compositions (Cd_0.86Mn_0.14Te and Cd_0.75Mn_0.25Te), each at wavelengths of 729 nm, 780 nm, 787 nm, 794 nm, 854 nm, 866 nm, and 1064 nm. The temperature dependence of the Verdet constant has also been measured for operating temperatures of 18.5°C, 22.5°C and 30.0°C at the wavelength of 780 nm.

The angle of rotation of the polarization of light inside a magneto-optical material is given by the following formula [3]

where θ is the angle of rotation of the polarization of the light field, V is the Verdet constant of the material at a given wavelength, B is the magnetic flux density in the direction of propagation of the light, and l is the path length inside the material in which the light’s polarization is rotated. The measurement of the Verdet constant is based on the measurement of the polarization rotation of a laser beam after passing a CdMnTe crystal. For both a known magnetic flux in the direction of the light propagation, and a known optical path length inside the crystal the wavelength-dependent Verdet constant is given by:

The measurement setup for the determination of the Verdet constant of the CdMnTe crystals is depicted in Figure 2 (left). The physical quantity of interest for a measurement of the Verdet constant is the light intensity transmitted through the analyzer. In the described case the analyzer is a Glan-Thompson prism mounted on a rotation stage. The setup only transmits the projection of the polarization relative to the incoming polarization that is set by the polarizing beam splitter (PBS). In case the analyzer and the PBS are oriented in the same direction, the full intensity is transmitted; if PBS and analyzer have a 90° angle, the transmitted intensity is minimized.

Figure 2.

Measurement setup for the determination of the Verdet constant (left) and sketch of the beam path (in red) inside a crystal of length a (right).

By repeating this measurement (maximal and minimal transmitted intensity), once without crystal under test, and once with, the polarization rotation induced by the crystal under test can be recorded. The offset is the Faraday rotation θ(λ) of the specific setup and is used to determine the Verdet constant of the CdMnTe crystal.

For Faraday rotation to take place, the magneto-optical crystal must be placed within a magnetic field. In this experiment, a NdFeB magnet with a rectangular aperture is used. Its magnetic field flux is homogeneous along the direction of propagation of the laser beam inside the crystal and has been calculated to be 0.93 T, with an uncertainty of -10% (the magnetic field could be 10% lower than calculated). For this reason, in Figure 3, two values for the Verdet constant are given, one as measured, and a second corrected one with the assumption of a 10% lower magnetic field.

Figure 3.

Verdet constant of Cd_0.75Mn_0.25Te and Cd_0.86Mn_0.14Te as a function of photon energy. The corrected data (mainly magnetic field) takes into account that the magnetic field could be 10% lower than the calculated values. For a comparison we also show data from [1]

It is noteworthy that a tilting of the magneto-optical crystal is necessary. The tilting angle is chosen in a way that the beam overlap with internal reflections is minimized. These reflections modulate the transmitted intensity and, due to the longer optical paths inside the magneto-optical material, they also exhibit other Faraday rotations when they leave the crystal. Both mentioned points would disturb an analysis of the experimental results. However, a tilting changes the optical path length in direction of the magnetic field. It is therefore necessary to consider only the projection of the propagation direction onto the magnetic field lines. This projection is given via:

where α is the angle of incidence, β is the propagation angle inside the crystal relative to the facet normal, and a is the length of the magneto-optical crystal (please refer to Figure 2, right).

An example of the experimental outcome is shown in Figure 4. The intensity measured via a CCD after the analyzer is plotted as a function of the angle of rotation of the laser. Colored in black, is the intensity transmitted by the analyzer without the magneto-optical crystal. It is the reference for the measurements of the Faraday rotation caused by the CdMnTe crystals in a magnetic field. Then, the CdMnTe crystal under test is inserted into the setup and the offset in the polarization rotation it induces is recorded. The exact offset to the reference measurement is determined via a fitting of the curves with a sin²(θ) function.

Figure 4.

Polarization rotation recorded for a 720° rotation of the analyzer, once without CdMnTe crystal (black), and then with a CdMnTe crystal for the laser beam at different wavelengths.

Cd_0.75Mn_0.25Te exhibits a negative Verdet constant that causes together with the parallel magnetic field a “negative” Faraday rotation. Higher photon energies (lower wavelengths) are closer to the bandgap of the crystal resulting in larger Faraday rotations. We have performed likewise measurements for Cd_0.86Mn_0.14Te crystals and calculated the Verdet constants as shown in Figure 3.

The obtained Verdet constants are summarized in Table 2 and are given in rad/Tm. According to the results the Verdet constants of the Cd_0.86Mn_0.14Te crystal are larger than those from Cd_0.75Mn_0.25Te.

Table 2.

Measured values of the Verdet constant [rad/Tm] at different wavelengths for two stoichiometric compositions.

Next, the temperature dependence of the Verdet constant was analyzed. For this measurement, a Cd_0.86Mn_0.14Te crystal was tested at 780 nm. Within the tested temperature range and angle resolution of the measurement, no change of the value of the Verdet constant with temperature could be observed, as shown in Figure 5. This result implies that a micro-integrated isolator with a CdMnTe magneto-optic crystal operating at 780 nm should be insensitive to temperature changes, at least in the range 18.5°C to 30.0°C.

Figure 5.

Measurement of the Faraday rotation induced by a CdMnTe crystal (in a given magnetic field) as a function of temperature

2.3

Optical measurements on critical properties at powers > 1 W

To investigate the limits of the used CdMnTe crystal material the transmission and depolarization were measured for a wavelength of 1064 nm and 780 nm up to the damage threshold.

The optical characterization of the CdMnTe crystal is performed using the setup depicted in Figure 6. Two different laser sources are used: A fiber laser with a center wavelength of 1064 nm and a Ti:Sa laser with 780 nm. In case of 1064 nm, the input power is adjusted by a combination of a half-wave plate and a polarizing beam splitter. Using a telescope, the beam is adapted to a collimated diameter of approximately 0.5 mm to fit to the free aperture of the CdMnTe crystal. Behind the CdMnTe crystal, a set of half-wave plate and polarizing beam splitter is used for transmission and polarization measurement.

Figure 6.

Setup for high-power testing of CdMnTe crystals.

During both measurements, at 1064 nm and 780 nm wavelength, a power drop was detected behind the crystal. This power drop came along with a change of the transmitted beam profile from the original Gaussian shape to a ring-shaped beam and is most probably caused by a small surface damage of the crystal. Therefore, the measurement was aborted at > 1400 mW for 1064 nm respectively > 860 mW for 780 nm.

The transmission is calculated as the ratio between the input and the output power of the crystals and shown in Figure 7 for 1064 nm (left) and 780 nm (right). Since the facets of the crystals have no anti-reflective coating and the refractive index of the CdMnTe crystal is large, the facet reflections have to be considered and the measured transmission is corrected.

Figure 7.

Transmission and PER of the CdMnTe crystal at 1064 nm (left) and 780 nm (right).

The polarization extinction ratio (PER) is calculated from the maximum and minimum transmitted power behind the polarization analysis, P_out,max and P_out,min, respectively:

For 1064 nm, the corrected transmission is in the range of 85-90% until the damage occurs at 1600 mW of input power, while at 780 nm the corrected transmission is only at approximately 80%.

For 1064 nm and low powers, the PER is quite high with >35 dB with an exception of the lowest powers, where the laser operation was not stable enough. For input powers exceeding 700 mW, the PER drops significantly, indicating thermal stresses inside the crystal caused by a temperature gradient. For 780 nm the PER is generally low at <13 dB, which is due to the properties of the used Ti:Sa laser source. Here, no significant change in PER is detected over the full input power range.

While performing the optical measurements, a thermal camera is pointed at the crystal in order to determine its surface temperature. The measured temperatures (Figure 8) are approximately 2-3°C higher for a wavelength of 780 nm than for 1064 nm which corresponds to the slightly higher absorption measured for 780 nm.

Figure 8.

Temperature of the CdMnTe crystal for 1064 nm and 780 nm

3.1

Magnetic Field Assembly

The Magnetic Field Assembly (MFA) consists of only one magnet. This is different to typical multi-magnet assemblies used with TGG crystals (e.g. the 9 magnet assembly used for the optical Isolator of MERLIN [x]). The use of only one magnet is enabled by the much higher Verdet constant for CdMnTe compared to TGG (up to 1 order of magnitude).

While the magnet field inside the free aperture of one magnet is only about a 3rd of a nine magnet assembly, the benefits lie in a significantly simplified assembly, not needing a magnet housing, magnet mounting and complex assembly process. Moreover, it allows smaller isolator assemblies, specifically given the typical magnet tolerances in the range of ±0.05 to ±0.1 mm.

A range of magnet and isolator designs have been investigated through the development phase. Starting from the aimed goal of an outer magnet dimensions of 5.5 mm length and width & height of 6.5x6.5 mm², the MFA has been optimized. For this purpose, several approaches have been considered, e.g. the way the crystal is mounted (directly glued into magnet vs. mounted in Al-Inlay), integrated exit ports, type of adhesive, as well as the size of the mechanical aperture. For all the different designs, the magnetic field has been analyzed and for most a structural and thermal analysis has been performed.

4.1

Crystal stress

Stress in the crystal is an important criterion to achieve good optical isolation. Stresses lead to birefringence, which reduces the achievably isolation. Due to the limited knowledge (compared to TGG), at this point only qualitative results with respect to the designs can be stated.

Table 5 shows a comparison of the stress level in the crystal to an artificially applied force of 5 N (a level at which STI has knowledge that TGG isolators show performance losses). The stress level of the proposed isolator design is with 0.1 MPa peak more than one order of magnitude lower. In addition, the stress level of a crystal glued directly and asymmetric into the magnet has been analyzed. Under the same situation, the crystal is showing about 8 MPa peak stress, a stress level four times higher than admissible.

Table 5.

Qualitative stress level assessment

4.2

Thermal lensing

With the given relatively high absorption in the CdMnTe crystals (about 1 orders of magnitude higher than TGG [6]) thermal lensing need to be taken into account of the isolator design. Asymmetric and non-spherical temperature profiles lead to a power dependent beam deflection and phasefront distortions. Table 6 displays an exemplary analysis of two variants of holding the crystal regarding the thermal profiles in the crystals, assuming a 2 mm long crystal and a 0.5 mm laser beam (top hat) for an absorbed power of 0.1 W (corresponding to approx. 1 W of laser power), relying solely on thermal conduction for heat removal. The thermal gradient perpendicular to the beam reaches 2.9 °C for variant B and 1.9 °C for variants A. In propagation direction the temperature gradient calculates to 2.6 °C and 2.7 °C respectively.

Table 6.

Qualitative thermal distribution comparison of two variants of holding the crystal. Variant A is the baseline design, where the crystal is glued into an insert, and variant B is an alternative design, where the crystal is directly glued into to magnet.

The resulting thermal lens is estimated at about 250 mm focal length (assuming isotropic situation). While we have not performed a detailed raytracing analysis, this result indicates that a symmetric heat removal is strongly preferred.

4.3

Magnet field properties and performance

The results of the magnet field simulation for the baseline magnetic field design for an isolator operating at an exemplary wavelength of 780 nm are summarized in Figure 10. The magnetic field has an excellent homogeneity of the integrated magnetic field. Over the evaluated optical aperture of 1 mm, the magnetic field has a homogeneity of less than 1% for the foreseen crystal of Cd_0.86Mn_0.14Te for 780 nm and a crystal length of 1.22 mm. This magnetic field enables at least 40 dB isolation over the full optical aperture, likely limited by polarizers and crystals. The design can accept 4 mm long crystals, with reduced isolation of up to 30 dB.

Figure 10.

Magnetic field properties for the baseline design operating at 780 nm.

Figure 11 shows the optical performance of the design, such as the expected transmissions in forward (transmission) and backward (isolation) direction, as well as the optical losses and isolation. Since the optical performance is also depending on the performance of the applied polarizers, the optical losses occurring at the optics have been included in the assessment. For each coating optical losses of 0.2% and for the reflection of p-polarization 3 % have been assumed. The transmission of s-polarization in isolation direction has been adopted with 0.030 % corresponding to 35 dB.

Figure 11.

Optical performance of nominal magnetic field design including optical losses (crystal length = 1.22 mm).

The resulting isolation at a central operating temperature of e.g. 25°C is greater than the required 30 dB. Over the full operating temperature range (15 - 45) °C within the full optical aperture of 1 mm the isolation is still ≥ 25 dB. The performance is strictly limited by the polarizers, as can be seen in Figure 12, which shows the individual contributors to the performance for a beam size fulfilling the full optical aperture of 1 mm.

Figure 12.

Optical performance of nominal isolator for a 1mm beam size: magnetic field design with polarizers, crystal (l = 1.22mm) and wave plate, individual contributions of temperature, magnetic field homogeneity and polarizers.

5.1

Structural analysis

The modal analysis shows the very high eigenmodes of the system with 7642 Hz as the lowest mode. A dedicated sine and random analysis up to 2000 Hz could therefore be skipped. Therefore, the requirements of 23.1 grms for the random test is used as a 3-sigma requirement for a static analysis. For this static analysis 70g in each spatial direction has been used.

The system is hard-mounted in the –y plane. The thermal environment of the non-op temperature range (-40 to +85°C) has been used as boundary condition to check the structural integrity. The operational range (-20 to +70°C) is used to check the stress inside the crystal against optical distortions.

The resulting stresses for the four load cases show enough margin on all parts, as listed in Table 7.

Table 7:

Stress results for the four structural load cases

5.2

Thermal analysis

TMG is part of the FEMAP suite, and is especially suited for thermal mapping in thermo-elastic analyses. The main advantage is that TMG utilizes the same Nastran FE model than used for the structural analysis. No separate and additional ESATAN model has to be established. For this project the solid model is suitable for conductive thermal analysis, the radiation between the components is omitted. This approach is regarded conservative with respect to the temperature gradients. Additional radiation would lead to more homogenous temperatures inside the model, so the results reported here are the worst case for the gradients.

The thermal analysis uses 70°C temperature at the boundary (assuming a thermal interface to the ground) and 0.1 W dissipation inside the Gaussian beam. The beam is assumed with 0.5mm diameter. The heat dissipates inside the crystal through absorption and the heat flow is directed along the aluminum inlay to the ground. The results of the thermal analysis are shown in Figure 13. The maximum temperature is reached inside the crystal with 81.3°C. This maximum temperature is still lower than the non-op temperature of 85°C. The stress analysis using 85°C homogenous temperature is therefore valid. No temperature mapping on the structural thermo-elastic analysis has been conducted.

Figure 13.

Temperature distribution (split model view) A more detailed view of the crystal is illustrated in Figure 14.

Figure 14.

Temperature distribution in crystal, xy-plane, view from –z (left) and view from –z (right)

Using the thermal operational environment the stress inside the crystal was analyzed, the results are illustrated in Figure 15.

Figure 15.

Thermally induced stress inside the crystal: xy-plane (left) and yz-plane (right)

The thermal analysis shows a very homogenous distribution, especially in the xy-plane, which is important for the beam properties.