# Absorption Measurements of Periodically Poled Potassium Titanyl Phosphate (PPKTP) at 775 nm and 1550 nm

^{*}

## Abstract

**:**

## 1. Introduction

_{3}) [10] and periodically poled potassium titanyl phosphate (PPKTP) [7,11]. The squeezing factor increases with the second harmonic pump intensity; however, it is ultimately limited by optical losses, which include the quantum efficiency of the photo-electric detector, propagation loss, as well as the escape efficiency of the squeezing resonator [12]. To give an example, a total optical loss of 10 % limits the nonclassical noise suppression to a maximum of 10 dB below the shot noise variance. The highest squeezing level demonstrated so far is 12.7 dB at a wavelength of 1,064 nm [11]. The squeezing resonator's escape efficiency is given by [12]

_{RT}is the resonator's round-trip loss with contributions from non-perfect intra-cavity anti-reflection (AR) coatings, from general coating absorption and scattering, and from the bulk absorption of the non-linear crystal. Since a reduction of L

_{RT}allows a reduction of T and thus a reduction of the external pump intensity, the availability of non-linear materials with low absorption is of high interest for the efficient generation of strongly squeezed light. The efficient generation of second-harmonic light sets the same requirement to non-linear materials. The highest efficiency for frequency doubling achieved so far is 95% for continuous-wave light at 1,550 nm [13]. In this work we report on the measurements of the absorption coefficient of PPKTP at 775 nm and at 1,550 nm exploiting the photo-thermal self-phase modulation technique [14].

## 2. Experimental Setups

_{1}and R̃

_{2}, which are also determined from these measurements. As a consistency check R

_{1}and R̃

_{2}additionally were determined in independent measurements, which show no thermal effect. R̃

_{2}is the effective reflectivity of the end-mirror. It includes all cavity round-trip losses apart from the transmission of the in-coupling mirror. The values for the material parameters were taken from literature [16–19]. The time axis of the measurements is calibrated using frequency markers in terms of phase-modulation sidebands generated by an electro-optical modulator. These sidebands are slightly outside the window shown here. Using frequency markers for each measurement also minimizes errors caused by the hysteresis of the PZT. A set of fitting parameters is then found by minimizing the standard deviation between the measurement data and the simulation employing a Nelder–Mead algorithm. To minimize errors due to transient disturbances, multiple measurements of resonance peaks were performed. Also, the scanning speed as well as the light power was varied, providing a self-consistency check of our evaluation.

#### 2.1. Experimental Setup and Results at 775 nm

_{1}. The PPKTP crystal was manufactured by

`Raicol`[21] and had a curved end surface with a high reflection (HR) coating applied to it. The other end surface was plane and AR coated. The cavity was formed by the in-coupling mirror M

_{1}, which was placed 24 mm in front of the AR coating of the crystal and the crystal's HR coating. A photo diode (PD) detected the light power P

_{refl}(t), which was reflected from the in-coupling mirror M

_{1}and partly transmitted by the BS. The input light carried phase modulation sidebands imprinted by an EOM. The modulation frequency was chosen to be 101.25 MHz, which is outside the cavity line width of ≈11 MHz, so the crystal could cool down before the sidebands became resonant. The PD's photo current was demodulated at the EOM modulation frequency by means of a double-balanced mixer to generate frequency markers in terms of a Pound Drever Hall (PDH) error signal [22]. This way, we were able to precisely calibrate the motion of the piezo-driven mirror M

_{1}around the cavity resonance.

_{1}and R̃

_{2}. From the remaining 7 measurements only R

_{1}and R̃

_{2}were independently determined and were found to be in agreement with the first 6 measurements. Figure 2 shows the results of the individual measurements of the absorption coefficient α (purple dots, right graph) as well as their mean value (thick yellow line) and their standard deviation (dashed yellow lines) of α

_{775nm}= (127 ± 24) ppm/cm. The result for the power reflectivity of M

_{1}was R

_{1}= (98.33 ± 0.08)%, which agreed with the specified design value of R

_{1}= (98.5 ± 0.4)%. The result for the effective reflectivity was R̃

_{2}= (99.76 ± 0.01)%. The designed reflectivity for the HR coating was about R

_{2}= 99.95%. The residual loss of about 1,900 ppm per round-trip due to absorption, scattering and reflection at the AR-coating is compatible with the specification of the AR coating of R < 0.1 %.

_{1}of the in-coupling mirror of this setup at 1,550 nm was 90%, while the end-surface of the crystal was HR coated. Due to this strong impedance mismatch of the mirror reflectivities, only ≈ 7% of the laser power are transmitted into the cavity at 1,550 nm at resonance instead of ≈ 30% at 775 nm. The resolution of the peaks at 1,550 nm becomes inferior compared with 775 nm and therefore the measured peaks become noisier. Hence, a setup with more suitable parameters was used for the measurement at 1,550 nm.

#### 2.2. Experimental Setup and Results at 1,550 nm

_{1}, which had a design power reflection of 99%, couples the light into the cavity. The remaining three mirrors were HR coated. While M

_{1}and M

_{4}were convex, M

_{2}and M

_{3}were concave forming a waist of 30.5 μm that was located in the centre of the PPKTP crystal. The latter was again produced by

`Raicol`[21]. Both crystal surfaces were AR-coated. The optical round-trip length of the cavity was 832 mm.

_{1}and R̃

_{2}.

_{1,550nm}= (84 ± 40) ppm/cm. This non-monolithic setup with a very large round-trip length in combination with the small waist is very susceptible to acoustic and thermal fluctuations, which most likely caused the large error bar. The result for the reflection of M

_{1}was R

_{1}= (99.03 ± 0.10)%, which agrees with the design value of 99%. The result for the effective reflection was R̃

_{2}= (99.76 ± 0.04)%. R̃

_{2}again included all cavity round-trip losses, which are the absorption of the PPKTP crystal, the reflection of the two AR coatings, the transmission of the three HR mirror coatings as well as the absorption and scattering of all four mirrors. A loss of 1 − R̃

_{2}≈ 4,000 ppm per round trip is a reasonable result for p-polarized light.

_{2}= (99.935 ± 0.008)%, which corresponds to a round-trip loss of (650 ± 80) ppm. Thus, for our cavity operated in s-pol, the absorption of the crystal of 84 ppm/cm (crystal length: 1 cm) is not the dominating loss source.

## 3. Conclusions

_{775nm}= (127 ± 24) ppm/cm and α

_{1550nm}= (84 ± 40) ppm/cm. The error bars correspond to one standard deviation excluding systematic effects due to errors in the material parameters. The latter are, however, estimated to be smaller than our statistical error bars. If such a crystal is used in an otherwise lossless squeezing resonator with an in-coupling reflectivity of R ≈ 90%, the escape efficiency would be as high as η > 99.9%. With this value, a loss of merely 1% is associated, thus allowing the generation and observation of squeezing strengths and second harmonic conversion efficiencies beyond what has been achieved so far. The highest squeezing factor at 1,550 nm observed so far is 12.3 dB [23] with a total optical loss of the setup of 3.5%. The highest efficiency for external continuous-wave second harmonic generation so far is 95% [13]. We conclude that the bulk absorption of PPKTP, by far, does not limit state-of-the-art squeezed light and second-harmonic generation at this wavelength.

## Acknowledgments

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**Figure 1.**Measured and simulated cavity resonance peaks for an external lengthening (dark-blue line and orange dots) and external shortening (light-blue line and red dots) of the cavity (dots: measurements, lines: corresponding simulations).

**a**and

**b**were measured with a Fabry–Perot cavity setup at 775 nm (cavity line-width ≈ 10 MHz) using an input power of 9mW at a scan frequency of 550 Hz (

**a**) and 110mW at 15Hz (

**b**).

**c**and

**d**were measured with a bow-tie cavity setup at 1,550 nm (cavity line-width ≈ 750 kHz) at an input power of 760mW at scan frequencies of 149Hz (

**c**) and 11Hz (

**d**). For low power and a high scan frequency, no thermal effect occurs (

**a**). For slower scan frequencies and higher powers, the narrow peaks form for an external lengthening and the broad peaks for an external shortening of the cavity (

**b**–

**d**). From those measurements we derived the absorption coefficients as summarized in Figure 2.

**Figure 2.**The dots show the absorption coefficient obtained from individual measurements at 775 nm (left) and at 1,550 nm (right). The mean value (line) and standard deviation (dashed lines) of the absorption coefficient are α

_{775nm}= 127 ± 24 ppm/cm and α

_{1,550nm}= 84 ± 40 ppm/cm. The absorption results corresponding to the peaks shown in Figure 1 are labeled.

**Figure 3.**(

**a**) half-monolithic cavity setup for the absorption measurement at 775 nm: Mirror M

_{1}and the HR coating on the PPKTP crystal's curved end surface formed the cavity. The length of the cavity was scanned with the PZT onto which M

_{1}was mounted. A photo diode (PD) detected resonance peaks P

_{refl}(t) in reflection of M

_{1}; (

**b**) Bow-tie cavity setup for the absorption measurement at 1,550 nm: The in-coupling mirror M

_{1}and three HR-coated mirrors formed a bow-tie ring-cavity. The PPKTP crystal was placed within the small waist between the concave mirrors M

_{2}and M

_{3}. M

_{2}was moved by a PZT. The PD detected the resonance peak P

_{refl}(t) in reflection of M

_{1}. In both setups the beam passed an EOM for imprinting sidebands before entering the cavity for the calibration of the mirror motion.

**Table 1.**Material and geometric parameters of the bow-tie cavity and the half-monolithic cavity used for the simulations.

Geometric parameters | 775nm | 1,550 nm | References |
---|---|---|---|

Beam waist ω_{0} | 27.6 μm | 30.2 μm | |

Crystal length L | 9.3mm | 10mm | |

Crystal radius R | 1.5mm | 1.5mm | |

Air gap | 24mm | 832mm | |

Material parameters | |||

Index of refraction n | 1.85 | 1.82 | [16] |

Thermal refr. coeff dn/dT | 16.9 × 10^{−6}/K | 10.9 × 10^{−6}/K | [17] |

Specific heat c | 726 J/(kgK) | [18] | |

Density ρ_{KTP} | 2, 945 kg/m^{3} | [19] | |

Thermal expansion a_{th} | 0.6 × 10^{−6}/K | [18] | |

Thermal conductivity k_{th} | 2.23 W/(mK) | [18] | |

Material emissivity ϵ | 1.0^{a} |

^{a}0.0 < ϵ ≤ 1.0 are the boundaries for the thermal emissivity. For our systems the value of this parameter is not relevant since R ≫ ω

_{0}and therefore surface radiation is negligible.

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**MDPI and ACS Style**

Steinlechner, J.; Ast, S.; Krüger, C.; Singh, A.P.; Eberle, T.; Händchen, V.; Schnabel, R.
Absorption Measurements of Periodically Poled Potassium Titanyl Phosphate (PPKTP) at 775 nm and 1550 nm. *Sensors* **2013**, *13*, 565-573.
https://doi.org/10.3390/s130100565

**AMA Style**

Steinlechner J, Ast S, Krüger C, Singh AP, Eberle T, Händchen V, Schnabel R.
Absorption Measurements of Periodically Poled Potassium Titanyl Phosphate (PPKTP) at 775 nm and 1550 nm. *Sensors*. 2013; 13(1):565-573.
https://doi.org/10.3390/s130100565

**Chicago/Turabian Style**

Steinlechner, Jessica, Stefan Ast, Christoph Krüger, Amrit Pal Singh, Tobias Eberle, Vitus Händchen, and Roman Schnabel.
2013. "Absorption Measurements of Periodically Poled Potassium Titanyl Phosphate (PPKTP) at 775 nm and 1550 nm" *Sensors* 13, no. 1: 565-573.
https://doi.org/10.3390/s130100565