Design Principles

The realization of the previously described pulse-to-cw-converter requires consideration of several design rules or parameters that will be discussed subsequently.

Numerical Aperture

Firstly, the NA of a preceding fiber should not be larger than the NA of the next fiber components attached to this, thus,

NA1≤NA2≤NA3. (5.27)

If Eq. (5.27) is not fulfilled, optical power might be lost as some rays emitted by a large NA fiber exceed the total internal reflection angle of the next fiber with a smaller NA.

Besides that, the fiber NA is also an important design parameter re-garding the temporal shaping abilities of the pulse-to-cw-converter, as a higher NA enhances temporal broadening [70, pp. 351-352]. Therefore, a high NA3 should be chosen to increase the rate of temporal broadening and extend the range of possible NA’s for NA1 and NA2.

Geometrical Properties

In addition to the impact of the fiber’s NA, temporal broadening is also affected by the geometrical properties, thus, core and cladding diameters, of the fibers being used. This relation results from the dependence of small irregularities in a fiber, causing mode coupling (microbends), on the core and cladding diameter of the optical fiber. As e.g. shown by Fermann [99] smaller core diameters result in smaller coupling coefficients.

Regarding the impact of the mode coupling coefficient on a fiber’s impulse response, it can be generally stated, that a low mode coupling coefficient yields increased temporal pulse broadening [100]. Phenomeno-logically this can be explained by considering two rays launched into a multimode fiber at different angles. In an ideal fiber without any mode coupling each ray maintains the same propagation angle, thus, their prop-agation time through an optical fiber will be different (and will scale with

fiber length L[74, p. 53]). For mode coupling rates approaching infinity both rays will instead have identical propagation times as both have been partially propagating in all available fiber modes.²¹ Thus, for enhanced pulse broadening in multimode optical fibers reduced mode coupling is ad-vantageous. This, not necessarily intuitive, feature can be demonstrated by simple numerical simulations based on the approach presented in Sec-tion 5.2.4. The results shown in Fig. 5.15a represent the impulse responses of a 500 m long multimode fiber with NA = 0.39 and a modal indepen-dent, thus, constant diffusion or mode coupling rate. For simplicity ab-sorption has been neglected and an initially uniform modal distribution (uniform launch conditions) is assumed. The results clearly demonstrate that a reduced diffusion coefficient yields a significantly broader impulse response.²²

This simulated impact of the mode coupling coefficient is consistent with the experimental results shown in Fig. 5.15b. Here, impulse responses of identical fiber types with varying core diameters and 100 m length have been compared (FTx00EMT/Thorlabs). The experiments have been conducted with a 4f-setup imaging the fiber output onto a high speed photodiode (818-BB-45/Newport, 12.5 GHz bandwidth) connected to a 33 GHz oscilloscope (DSOX93204A/Agilent). As the launch conditions for all three measurements were very similar, the results demonstrate that a smaller core diameter, hence, a lower mode coupling coefficient [99], yields a broader impulse response.

Besides the impact of core diameter on impulse broadening in multi-mode optical fibers, the diameters of the respective pulse-to-cw-converter fiber components need to be adapted to each other. Naturally, the diam-eter 2aof any part of the converter should not be smaller than that of the preceding part, thus,

2a₁≤2a₂≤2a₃. (5.28)

21The rate of pulse broadening scales with√

Lin that case [100].

22It is noteworthy that for non-uniform modal conditions the relation of mode cou-pling coefficient and pulse broadening becomes significantly more complex. In fact, a higher mode coupling coefficient can result in broader impulse responses as the higher order modes, propagating at slower speeds through the fiber, are excited significantly earlier as for low mode coupling coefficients.

(a) (b)

Figure 5.15: (a) Simulated impulse responses of a 500 m long mul-timode fiber with NA = 0.39 and varying diffusion or mode cou-pling properties. Reduced mode coucou-pling leads to broader impulse responses. (b) Measured impulse responses of the FTx00EMT mul-timode fiber from Thorlabs with 200, 400 and 800µm core diameter and 100 m length each. As mode coupling reduces with core diameter, broader impulse reponses are obtained for smaller fibers.

Absorption Characteristics

Furthermore, the fibers should be chosen to minimize material absorption.

This prevents damage to the fiber device and ensures a maximum output signal for the later measurements. Therefore, glass optical fibers seem to be a better choice than plastic optical fibers that typically exhibit significantly higher absorption.²³ A further reduction of absorption is achieved when fibers designed for distinct spectral ranges (UV, VIS or NIR) are used. In this work, two monolithic pulse-to-cw-converters are realized, one for the UV-to-VIS-region (270-520 nm) the other for the VIS-to-NIR-region (520-1800 nm). Details on their implementation in the Laser-SR-setup can be found in Section 6.2.4.

23Liquid-core and photonic bandgap fibers are not considered here as their proces-sibility is rather limited as compared to glass optical fibers.

DSR-Setup Based on Ultrashort Laser Pulses

In this chapter the Laser-DSR measurement setup will be pre-sented that has been developed in the course of this work. Start-ing from a short introduction motivatStart-ing the application of lasers for measuring spectral responsivities (SRs) or external quantum efficiencies (EQEs), the ultrashort pulse laser sys-tem used within this work is presented. Afterwards, the strate-gies and concepts for spectral, temporal and spatial shaping of the radiation, making it applicable for solar cell measuments, will be outlined giving experimental and simulated re-sults on the performance of the developed system. The opti-cal losses going along with the shaping of the laser radiation will be analyzed subsequently, pointing out remaining potential for an enhancement in optical efficiency. Then, the measure-ment uncertainties of the DSR-setup will be discussed in detail demonstrating the capabilities of the new setup and revealing remaining potential for further reduction of uncertainties. Fi-nally, the chapter is concluded by recapitulating its most rele-vant results and comparing the new facility to state-of-the-art DSR-measurement setups.

107

6.1 Introduction to DSR-Measurements

The SR of a solar cell, or equivalently used the EQE, is an important measurand for solar cell characterization and calibration. The absolute SR allows for a highly accurate determination of the solar cell’s short circuit current (I_SC), which is the major photovoltaic parameter for solar cell calibration (see Section 2.2). Furthermore, the (relative) SR enables a spectrally resolved analysis of solar cell features and a spectral mismatch correction (see Section 2.2.2.1).

The most widely spread and accepted method for measuring the SR or EQE of a solar cell is the differential spectral responsivity (DSR) method [14] (see Section 2.2.2.2). In this method, the test device is illu-minated with a bias light source of variable irradiation level and chopped monochromatic radiation. Using transimpedance and lock-in amplifiers the test cell is kept at short circuit conditions and its differential current response to the chopped monochromatic light can be extracted. Not only that the DSR-approach provides the lowest reported measurement uncer-tainties, it also allows for detecting comparably low signals owing to the lock-in measurement technique. Moreover, the test cell’s linearity can be determined simultaneously by applying different levels of bias irradiation, thus, exciting a different excess carrier density within the test cell.

Due to the importance of precise SR-measurements in calibration of solar cells and driven by economic aspects and technological advances, there is a steady development of new DSR-measurement facilities featur-ing reduced measurement uncertainties. In most state-of-the-art setups, broadband white light sources, like xenon or tungsten halogen lamps, are applied that are spectrally filtered by a (double-)grating-monochromator [101–105] or a combination of various filters [106, 107]. However, the intrinsic limitation in spectral power of the available white light sources often impedes a further reduction of measurement uncertainties in such se-tups. A promising approach to overcome this limitation is provided by ap-plication of spectrally narrow, ideally monochromatic, radiation sources.

Although being spectrally still quite broad, the advent of light-emitting diodes (LEDs) and their nowadays availability over wide spectral ranges

pushed the development of several LED-DSR-setups recently [108–110].

A spectrally more narrow alternative to LEDs is represented by lasers that are not only superior because of their spectral bandwidths, but also because of their availability in a spectrally tunable manner allowing for a free choice of center wavelength. Therefore, lasers were suggested [15, 16]

and, very recently, been successfully applied for a further reduction of measurement uncertainties [17].

In the subsequent sections the development of a laser-based DSR-measurement facility at Fraunhofer ISE CalLab is presented, that has been conducted in the course of this work.