1. Introduction

The measurement of optical power at the best level of uncertainty is facilitated by either thermal electrical substitution radiometers (ESR) or predictable quantum efficient detectors (PQED). The thermal detector outputs a temperature signal, whereas the quantum detector outputs a current signal. Both types of detector are traceable to SI electrical units, either through a measure of the equivalent electrical power applied or of the current produced by the absorption of photons. In either case, a linearly polarised pseudo-collimated laser beam is typically transmitted through a Brewster window to irradiate the detector, which sits inside a vacuum cryostat. The PQED is a recent development, and through characterisation and simulation the internal losses of the device can be modelled and thus the photo-response of the detector accurately predicted. The responsivity of a PQED has been demonstrated to be extremely stable over many years. The interested reader is directed to references [1–3] for further reading on these topics.

Another recent development is the dual-mode silicon detector that combines both quantum and thermal detection modes of operation in a single device [4]. This led to the demonstration of a self-calibrating dual-mode silicon device at room temperature [5]. Establishing the PQED as a dual-mode detector, where two absolute radiometric principles are combined in the same device with the same absorber, leads to the device being inherently self-assuring. A measure of the responsivity (A/W) at a given wavelength, corrected for internal losses, provides a value for the fundamental constant ratio e/hc, where e is the electronic charge, h is Planck’s constant, and c is the vacuum speed of light. This represents an important development in radiometry as device performance can be readily assured outside the laboratory. Vacuum compatibility, room temperature operation and portability support its use with space borne instrumentation. A European Metrology Programme for Innovation and Research (EMPIR) project called chipS·CALe has been funded to support further development and integration of the device [6].

The electrical substitution radiometer operates at cryogenic temperatures to take advantage of favourable material properties such as high thermal conductivity (W/m-K), low volumetric heat capacity (J/cm³-K), and high thermal diffusivity (m²/s), affording greater detector sensitivity and speed of response [7–12]. Cryogenic operation also ensures that the blackbody radiant loss from the high emissivity detector absorber is negligible compared to a nominal operating level of 0.5 mW, while operation in vacuum minimises convective losses [13].

The measure of radiant power by an absolute radiometer gives rise to a measurement uncertainty, principally limited by the determination of the spectral and spatial transmission of the Brewster window and the optical scatter within the system. The transfer of the absolute optical power measurement (W) to a secondary detector, results in an increased uncertainty of measurement in the power responsivity measurand (A/W) to about 0.02% at a coverage factor k = 2, which for a normal distribution defines an interval with a confidence level of approximately 95% [9–12]. This level of uncertainty is representative of current open-beam cryogenic technology.

Recent work reported a new cryogenic primary standard facility for the measurement of the power responsivity of optical fiber power meters (OFPM) at an expanded measurement uncertainty of 0.4% [14]. The facility was unique in that it featured single-mode fiber-coupled components throughout the system, that included laser diode sources, commercial grade variable optical attenuators and beam-splitters, cryogenic ESR’s and device under test (DUT). The reported uncertainty is at least a factor of ten greater than the performance achieved with open-beam radiometers. Nevertheless, it is regarded as state-of-the-art for the use of fiber-coupling, at least as a primary standard facility within National metrology institutes (NMIs).

This development opened new horizons in fiber-coupled measurements adding an easy-to-use primary standard alongside existing standards [1–12]. However, the performance of the system from an uncertainty perspective, was limited by environmental perturbations of the single-mode fiber beam-splitters and of the fiber within the cryostat.

The all-fiber approach affords flexibility and circumvents two of the largest uncertainty contributors in a conventional open-beam system; determining the spectral and spatial transmission of the Brewster window, and measuring the loss from scattered radiation. Further, temperature stabilised laser diode sources, especially at the telecom wavelengths 1310 nm and 1550 nm, are as stable in power output as externally intensity stabilised gas lasers at approximately 50 ppm power change per hour. The modal stability is also excellent, and thus the fiber approach is not compromised by laser source power or modal instability. However, the approach does introduce other factors, which together result in a higher level of uncertainty of measurement. We investigate and discuss these factors in detail in section 3 of this paper.

Optical return loss of a fiber encompasses Fresnel reflection from the media boundary interface and Rayleigh backscatter within the fiber [15–19]. The temperature dependent effective refractive index N_eff of the fiber can be determined from a measurement of each of these parameters as the fiber is cooled, (section 3.1). Many references can be found in the literature to application notes [20–25] and standards [26] discussing polarisation dependent loss (PDL) measurement techniques for fiber components [27,28]. We use the Mueller matrix method to assess the temperature dependent PDL, (section 3.2). An evaluation of the fiber beam-splitter ratio between the absolute detector and the device under test is described in section 3.3. Long term monitoring results demonstrating the temporal and modal stability of the PM fiber pig-tailed Fabry-Pérot laser diode sources are presented in section 3.4.

Our motivation is two-fold. First, to investigate and characterise the performance of polarisation maintaining (PM) fiber-coupled beam-splitters and fiber with the aim of understanding the measurement uncertainty; and second, to assess the performance of high index, solid core, PM photonic crystal fiber (PCF) at low temperature with a view to future use. As PM fiber is resilient to movement, it is expected that endlessly single-mode PM PCF fiber will provide similar performance, but over a much broader range of wavelengths.

This work is relevant to the area of low power radiometry, where fiber-coupled detectors are calibrated for detection efficiency [29] or compared directly to a host of many other few-photon detectors, including superconducting nanowire single-photon detectors [30], dual-mode thermal and quantum detectors [4–6], and fiber-coupled trap detectors with charge integrator amplifiers [31].

2. Experiment

 

Fig. 1. Schematic diagram illustrating the components and sections of the measurement facility. (A) temperature stabilised laser source; (B) variable optical attenuator (VOA) with shutter; (C) 1 × 3 PM beam-splitter with 25%, 50%, 25% split ratio; (D) FC/PC fiber-coupled cryogenic ESR detectors; (E) voltage and current measurement of the equivalent electrical power applied to the resistive heater of the ESR detector during a measurement cycle.

Download Full Size | PDF

 

Fig. 2. Pictorial view of the 4 K cryostat showing the 35 K and 4 K radiation shields, dual ESR detectors mounted within the temperature-controlled isothermal shield, and the PM input fiber. The four aluminium cylindrical cans affixed to the baseplate are charcoal getters.

Download Full Size | PDF

The measurement facility comprises three independent optical sections, one for each wavelength 850 nm, 1310 nm and 1550 nm, and a cryogenic section, see Figs. 1 and 2. The optical section consists of the fiber coupled components; the pig-tailed laser diode sources, variable optical attenuators with shutters and fiber beam-splitters including the plane-cut (FC / PC) terminated fiber to the cryogenic detector. For clarity only the setup for one wavelength is shown. The cryogenic section includes the 4 K vacuum cryostat, two ESR detectors with carbon nanotube absorbers, one for 850 nm and the other for 1310 / 1550 nm, and ancillary hardware [14]. The detectors are mounted on HoCu₂ thermal filters for temperature stability. The fiber within the cryostat operates from room temperature at the vacuum feedthrough to 7.5 K at the cryogenic detector. The optical system presents three terminated output channels; device under test (DUT, FC / PC), radiometer (RAD, FC / PC) and monitor (MON, FC / APC) channels. To determine the power responsivity of a DUT, the beam-splitter ratio between the DUT and RAD channels is required (measured at room temperature), as well as the temperature dependent Fresnel reflection from the fiber end face irradiating the cryogenic detector. This requirement necessitates a plane-cut fiber end to enable measurement of the reflectance change as the fiber is cooled. An angled-cut end face would make this measurement very difficult.

The bold annotated headings above their respective components are the four parameters that are characterised for low uncertainty measurements. These are discussed in detail in section 3.

Traceability to the SI is ensured by the electrical power substitution measurement. The FC / PC fiber ferrules are mounted 2 mm in front of the cryogenic detectors.

A complete description of the ESR detectors can be found in [13], but briefly the 5.5 mm diameter silicon planar micro-machined detectors are operated at 7.6 K, to be within the narrow resistive transition region of the niobium superconducting temperature sensor. Vertically aligned carbon nanotubes, grown on the detector substrate, absorb 99.95% of the incident radiation.

3. Evaluation of factors contributing to the measurement uncertainty

In this section we evaluate those sources of uncertainty that contribute most to the measurement uncertainty when comparing fiber-coupled detectors directly with the cryogenic primary standard. These factors include the correction to the beam-splitter ratio (DUT/RAD) due to the Fresnel reflection and Rayleigh backscatter of the fiber within the cryostat altering during the cooling phase; the polarisation dependent loss (PDL) of the beam-splitters; the room temperature fiber beam-splitter ratio between the DUT fiber output and the radiometer (RAD) fiber output (Fig. 1), and the modal and temporal stability of the Fabry-Pérot laser diode sources. For clarity, results are presented within each sub-section and then brought together in section 4 as a complete measurement system with uncertainty budget.

3.1 Return loss measurement of different fiber types

The properties of an optical fiber change as a function of temperature. The cryogenic detector, with its superconducting temperature sensor, is not designed to measure the fiber’s output power until the transition temperature of the sensor is reached. This means that the change in power output of the fiber, caused by the temperature gradient along the fiber, must be determined. A practical solution entails the measurement of the optical return loss (ORL) from the fiber’s plane cut end face to determine the change in optical power incident on the cryogenic detector as compared to room temperature. This is applied as a correction to the room temperature DUT / RAD beam-splitter ratio measurement. We avoided using either a focusing lens or an antireflection coating at the fiber tip to minimise potential problems. The 5.5 mm diameter detector absorber is far larger than the irradiating beam spot size.

An ORL measurement accounts for the Fresnel reflection from the fiber interface as well as the transmission loss from Rayleigh scattering. Therefore, separate measurements of these two properties are necessary to fully understand the temperature dependence of the refractive index. Fresnel reflection occurs at media boundaries with different refractive indices, whereas Rayleigh scatter is an intrinsic property of optical media, resulting from natural impurities and imperfections within the length of the fiber core causing minute fluctuations in refractive index.

Five fibers were investigated to determine their suitability for use within the cryostat of our measurement facility; SMF-28 Ultra*, polarisation maintaining PM15-U25D* and PM13-U25D* (PANDA) and PM photonic crystal fiber; LMA-PM-10* and PM-1550-01*. SMF-28 Ultra is characterised by low attenuation and low bend loss. The PM style PANDA fiber is recognised by the inclusion of two boron-doped rods placed symmetrically in the cladding about the core. This induces stress birefringence in the fiber, which creates an index asymmetry known as the slow and fast axes.

Two examples of PM high index PCF fiber were investigated as the PM ability is realised differently for each fiber. The high index type is defined by a pure solid silica core surrounded by a lower index structure comprising micro-capillaries, which act to induce form-birefringence in the fiber. The large mode area (LMA) series comprises two rods centred about the core, but outside the capillaries, while the PM series uses two holes within the capillary structure to define the fast and slow axes, which in both cases of fiber is confined to the core by modified total internal reflection. The criterion for the waveguide parameter V as described by [32,33] permits large mode area single-mode operation.

Also of interest in this study is the effect the complex structure of PM and PCF fiber has on the stability of the fiber, both mechanical and optical, as it is cooled. As the PCF fiber transmits from 600 nm to 1700 nm, it offers the possibility of using one cryogenic detector to cover the wavelength region of interest, and thus reduce the mechanical complexity. However, the possible retention of air within the micro-structured capillaries requires further investigation, which is beyond the scope of work reported here.

3.1.1 Optical frequency domain measurement of Fresnel reflection at 1550 nm

Equation (1) defines the Fresnel reflection R at a media boundary. For a material of index n₁ = 1.4682 (Corning* SMF-28 normal incidence), propagating to a material of index n₂ = 1.0000 (vacuum) then;

The capability to measure ORL, or more specifically the Fresnel reflection in-situ via a beam-splitter arrangement, improves the measurement uncertainty, and provides assurance to the measurement. To support this approach, both the Fresnel reflection and Rayleigh backscatter were measured with an optical frequency domain reflectometer (OFDR) at 1550 nm, as the fiber was cooled from room temperature to 5 K. The instrument was configured to operate at 1550 nm only.

A Luna OFDR 4600* swept-wavelength reflectometer was set to a centre wavelength of 1550 nm with a scan range of ± 21.44 nm and a detector gain of 12 dB. The strong reflection from the fiber end facet is broadened and can therefore obscure weak peaks from nearby scattering points. Thus, the frequency domain window of the instrument was active during all measurement scans, suppressing the broadened tails. The fiber return loss spectrum was checked in the frequency domain to ensure it was spectrally flat and thus not adversely impacting the measurement.

Often the refractive index of a fiber is unknown. As we are interested in the relative change it is not a requirement that the index is known. However, it does provide valuable information to the OFDR measurement. The length of a test fiber was physically measured to within ± 1 mm, and the refractive index parameter of the instrument adjusted to yield the same length during a room temperature time of flight optical measurement. This provided a baseline measure of the effective refractive index of the fiber at 1550 nm, which is reported in Table 1 at 293 K. The values at 1310 nm, 293 K, are from the literature.

It is worthwhile to mention fiber cleave angle as this affects the magnitude of the Fresnel reflection signal. From Snell’s law and Fresnel’s equations, the change in reflection for non-normal incidence can be calculated. Given n₁ = 1.47 for a typical fiber, n₂ = 1.00, and θ_i = 0.3° (typical FC/PC fiber cleave angle), θ_t = 0.44° (Snell’s Law) implies a change in reflection, normal and parallel to the plane of incidence (R_s and R_p respectively) of ± 0.008% with respect to normal incidence. We assume the cleave angle remains constant during the cooling phase.

The OFDR records the time of flight along the length of fiber, hence the relationship between refractive index and length could in principle be determined and a small correction applied for contraction according to Eq. (4).

 

Fig. 3. Fresnel reflection at 1550 nm for plane cut end facet PM PCF fibers; PM-1550-01 and LMA-PM-10 with each fiber connectorised (FC / APC) at one end only with modal adaptation of 10 mm fused SMF-28 fiber. Inset: time of flight (ns) for approx. 4 m of PM-1550-01 polarisation maintaining, high index, solid core, photonic crystal fiber at room temperature, 77 K and 5.2 K showing the reflection nodes of the slow and fast axes as the fiber is cooled.

Download Full Size | PDF

A more effective and simpler approach to measure the Fresnel reflection and Rayleigh backscatter with the OFDR, is to integrate the measurement over the relevant length of fiber. The change in Rayleigh backscatter was determined by integrating the signal 10 mm after the source connector to within 10 mm of the plane cut end facet at room temperature, 77 K and 5.2 K. The backscatter for both SMF-28 and PM fiber increased from 0.0002% of input power at room temperature to 0.003% at 5.2 K. This equates to 0.08% of the reflected power. Similarly, an increase of 3 to 4 times was observed for the backscatter of the two PM PCF fibers. The change in backscatter of the fiber depends on the temperature profile, and since we measure over the total length of fiber from room temperature to cryogenic temperature, the backscatter would need to be remeasured if the fiber is replaced or re-configured. However, as our measurements illustrate, this change accounts for about 10% of the change in Fresnel reflection and could therefore be neglected in less rigorous circumstance.

The signal was also integrated over 10 mm about the two reflection peaks (Fig. 3). By comparing the room and low temperature measurement results, the Fresnel reflection loss change could be determined. Note this is an absolute measurement as it excludes the backscatter. If one was not interested in the backscatter, the instrument could be set to measure the absolute reflectance directly [35]. The effective group index of refraction is calculated to change 0.11 ± 0.01% for SMF-28 fiber, 0.15 ± 0.01% for standard PM fiber and 0.30 ± 0.02% for the PM-1550-01 PCF fiber (holey PM rod structure) in going from room temperature to 5 K, Table 1.

Table 1. Temperature dependent effective refractive index for various fiber types and wavelengths.

View Table | View all tables in this article

Assuming ${R_ \bot } + {T_ \bot } = 1,$ i.e. no absorption at the fiber-air interface at normal incidence, the transmission at the fiber end facet at 5 K increases relatively by 0.02% for SMF-28 fiber, 0.03% for standard PM fiber and 0.06% for PM PCF fiber respectively.

3.1.2 Beam-splitter measurement of Fresnel reflection at 1310 nm and 1550 nm

To determine the change in transmission of the fiber upon cooling, a three-way beam-splitter (B, Fig. 4), designed for either 1310 nm or 1550 nm, was inserted before the cryostat. This replicates an in-situ return loss measurement. The crosstalk between the input fiber to the beam-splitter (B) and the two reflected signal level ports was measured to be of the order 3.3 × 10⁻⁵. For this measurement the output port fiber was cleaved at 8^° (APC, not shown) to reduce reflections that would otherwise contribute to the signal level. The crosstalk is subtracted from all measurements. The change in Rayleigh scatter of the fiber is now measured as it is cooled.

 

Fig. 4. Setup for the measurement of Fresnel reflection change. FC / PC fiber ferrule in cryostat is replaced with FC / APC (8° angled physical contact) to facilitate crosstalk measurements. (A) 1 × 3 beam-splitter with monitoring (MON) channels. (B) 3 × 1 beam-splitter to facilitate reflected signal level measurements (RSL). The two RSL channels are normalised against the average of the MON channels to account for power fluctuations.

Download Full Size | PDF

This is facilitated by attaching 4 m of fiber to the 5 K cold plate with both ends exiting the cryostat. Light from the beam-splitter (B) is launched into one end while the other end is monitored with a photodiode (DET – not shown) as the fiber is cooled. This enables the backscatter to be calculated. The monitored end is then withdrawn into the cryostat, anchored to the cold plate, and the system cooled again. The change in Fresnel reflection is calculated from the measured change in the reflected signal level (RSL) and the Rayleigh backscatter. These measurements were repeated for the five test fibers at 1310 nm and 1550 nm.

We assume the return loss from the FC / PC ferrule connector at room temperature is stable during the cooling phase. This gives a measure of the loss change in each direction. Typically, we observe an average round trip change of input power of 0.06 ± 0.02% (RSL / MON), a return change of 0.035 ± 0.01% (RSL / DET) and a forward change of 0.025 ± 0.01% (DET / MON). A small bias of approximately 0.005% was observed favouring the return trip. However, because no substantive evidence indicates otherwise, we average the fiber transmission loss change to give a directional change of 0.03 ± 0.01% and record a bounded uncertainty of ± 0.005%. In effect this represents a transmitted output signal change of 0.001%. Similar results were observed for both PM and SMF-28 fiber, which align with the result of 0.08% measured with the OFDR of section 3.1.1 above. We were unable to record meaningful beam-splitter measurements of the Rayleigh scatter of the PCF fibers. However, the Rayleigh scatter of the two PCF fibers was measured at 1550 nm with the OFDR.

Subtracting the transmission loss change, we observe a decrease from room temperature to 5 K in the Fresnel reflection for SMF-28 type fiber of 0.52 ± 0.05% and 0.75 ± 0.05% for PM type fiber at 1550 nm. This equates to a ΔN_eff of 0.11 ± 0.01% and 0.15 ± 0.01% respectively. At 1310 nm we observe similar results. For the PCF fiber PM-1550-01 we see a decrease in the reflected signal of 1.45 ± 0.1%, which equates to a change in N_eff of 0.30 ± 0.02%. See Table 1 for a list of results. Measurement of the PCF fiber LMA-PM-10 was inconclusive for both beam-splitter and OFDR techniques. This we attribute to poor evacuation of the microcapillary structure of the fiber.

The change in Fresnel reflection implies a correction to the room temperature splitter ratio of 1.0002 ± 0.0001 SMF-28 fiber, 1.0003 ± 0.0001 PM fiber, and 1.0006 ± 0.0002 PM PCF fiber. We observe monotonic behaviour in the reduction of signal when cooling standard PM fiber and the PCF PM-1550-01 fiber, and oscillatory behaviour for SMF-28 and LMA-PM-10 fiber. The technique provides very similar results to the OFDR measurements at 1550 nm, thereby supporting the approach. We are thus confident in the beam-splitter measurements of Fresnel reflection at 850 nm and 1310 nm. The effective group index of refraction, N_eff, decreases as a function of temperature. The effect manifests as a decrease in the Fresnel reflection from the fiber end facet, leading to a corresponding increase in the transmitted light.

3.2 Beam-splitter PDL temperature dependence at 1310 & 1550 nm, PM & SMF-28

Passive optical components such as fiber beam-splitters and couplers, exhibit polarisation dependent loss, whereby the output signal of the device varies as a function of the input polarisation state S. IEC International Standard 61300-3-2 describes two basic test and measurement procedures for determining PDL in a single mode fiber optic device; the all-states method and the Mueller matrix method [26]. Both methods determine the minimum and maximum optical transmission of the device for variations in polarisation state. The PDL of the component is proportional to the ratio of these two values and is determined in accordance with Eq. (5).

The measurement of the response of an optical device to four separately applied input polarisation states (0°, 90°, 45°, 135°), whose power is known, is enough for the first-row coefficients of the 4 × 4 Mueller matrix to be determined. We use states linear horizontal (P₁, P_a), linear vertical (P₂, P_b), linear diagonal (P₃, P_c) and right-hand circular (P₄, P_d) in accordance with ref. [26]. P₁, P₂, P₃, P₄ are the signal levels for the four polarisation states of an output port and P_a, P_b, P_c, P_d are the signal levels, relative to the monitor channel (MON), of the same polarisation states at the input port of the DUT. The first-row matrix components m₁₁, m₁₂, m₁₃, and m₁₄ are written as Eq. (7);

The temperature dependence of the PDL of fused biconical and planar beam-splitters was evaluated. A 1 × 3 SMF-28 wavelength independent splitter and two planar 1 × 4 PM splitters were in turn placed in an environmental chamber, soaked for an hour at each temperature, and measurements recorded. A schematic of the experimental setup is shown in Fig. 5.

 

Fig. 5. Setup for the temperature dependent PDL measurement. The four polarisation states 0°, 45°, 90°, and 135° are applied in turn to the input of the DUT and for each state the power level of each of the four output ports of the DUT is measured. (A) General Photonics PSY-101* polarisation synthesiser for selecting input polarisation states. (B) 1 × 3 beam-splitter with monitoring channel.

Download Full Size | PDF

The four coloured fiber outputs of the DUT illustrated above relate to the colours on charts in Figs. 6(a) and 6(b) below. Figures 6(a)–6(c) highlight the decrease in PDL when changing from SMF-28 type splitters to PM type splitters. The cause of the reduction seen in the PDL for 2 channels of the 1310 nm splitter is unknown. The PDL of the PM beam-splitters is of the order 1% at 20 °C, exhibiting a temperature coefficient ΔPDL / °C of approximately −0.03. This represents the maximum excursion in fiber output signal given all states of input polarization.

 

Fig. 6. (a) Plot of the temperature dependence of the PDL (%) of 1310 nm 4 channel PM fiber beam-splitter. The four colours; blue, green, red, brown represent the four output channels of the splitter. (b): Plot of the temperature dependence of the PDL (%) of 1550 nm 4 channel PM fiber beam-splitter. The two outputs with the lowest measured PDL are used for the DUT and RAD channels, the other two for monitoring as required. (c): Plot of the temperature dependence of the PDL (%) of 1550 nm SMF-28 3 port fiber beam-splitter – only 2 channels shown.

Download Full Size | PDF

We include a rectangular bounded uncertainty of 0.05% to account for PDL of the splitters and fiber connector to the vacuum feedthrough.

3.3 Beam-splitter ratio of PM splitters

As mentioned in the introduction to section 2, the beam-splitter ratio between DUT and RAD channels is required to relate the power incident on the DUT to the power incident on the standard detector. For high accuracy measurements it is important to understand the behaviour of the beam-splitter and the consequence of selecting specific output channels. For instance, an increase in the power of one output channel of a multiport beam-splitter can be observed as a decrease of power in a corresponding channel. Measurements of the splitter output powers encapsulate this phenomenon, which is caused by polarisation and temperature dependent effects as described in section 3.2. A two-detector technique is used to determine the ratio between any two output ports of the splitter, given by Eq. (9). The power at each port is first measured with the detectors m₁(DUT)_, m₂(RAD) and the detectors then switched between ports to measure m₂(DUT), m₁(RAD).

Figure 7 illustrates the setup to measure beam-splitter port ratios showing the fiber-coupled detectors m₁ and m₂. We use either 3 or 4 output port PM splitters at 850, 1310 and 1550 nm.

 

Fig. 7. Room temperature setup for beam-splitter ratio measurement between DUT channel and radiometer (RAD) channel. (A) stabilized laser source; (B) variable optical attenuator with shutter; (C) 1 × 3 PM beam-splitter with 25%, 50%, 25% split ratio; fiber-coupled DUT, radiometer (RAD) and monitoring (MON) channels.

Download Full Size | PDF

They are present to split light between the cryogenic standard (RAD) and the DUT to enable simultaneous measurement of each. The variability of the fiber beam-splitter ratio dominates the DUT responsivity measurement uncertainty.

The standard deviation of the ratio of the power output from any two fiber ports of the 3 and 4 port beam-splitters is 0.03% maximum over a measurement period of 5 hours. This change is dominated by the effect of the temperature dependent PDL of the beam-splitters and butt connection of the hermetic vacuum fiber feedthrough. It results from temperature fluctuations of ± 0.3 °C / day in the laboratory environment and small changes in the polarisation state of the propagating light, caused by coupling between the slow and fast axes. The polarisation extinction ratio (PER) is a measure of the relative strength of the slow and fast axis signals. An additional uncertainty of 0.02% is assigned to each fiber as a result of swapping them between detectors during a ratio measurement. Summing these contributions in quadrature yields an expanded uncertainty of 0.06% listed in Table 3, section 4.

The polarisation dependence of the photodiode detectors M₁ and M₂ measuring the beam-splitter ratio, was estimated by rotating the detector about the fiber ferrule within the detectors’ fiber input connector. A variation of less than 0.02% was observed. The fiber ferrule was placed in the receptacle at the same rotational position during a measurement, minimising the effect of this small polarisation dependence.

3.4 Spectral power distribution of Fabry-Pérot laser diode sources

The responsivity of spectrally dependent detectors such as Si and InGaAs photodiodes is affected by the spectral power distribution of the Fabry-Pérot laser diode sources. We used an ANDO AQ6317* optical spectrum analyser (OSA) to measure the spectral power distribution of each source. The spectral power response of the OSA was internally corrected, and the wavelength was calibrated according to ref. [36]. The instrument reports the power weighted centre wavelength λ_c and the spectral width Δλ, calculated in accordance with Eqs. (10) and (11).

The three laser diode sources were characterised according to the equations above and the results are listed in Table 2, while Fig. 8 illustrates a scan at 1550 nm, 210 µW measured power.

 

Fig. 8. Spectral power distribution of the 1550 nm Fabry-Pérot laser diode source. Δλ = 2.82 nm, maximum peak height of 28 µW (0 dB relative), weighted centroid wavelength λ_c = 1549.43 nm, and total measured output power of the 27 modes is 210 µW. These values are calculated only from modes which are within 20 dB of the peak mode height.

Download Full Size | PDF

Table 2. Results of the Fabry-Pérot laser diode sources repeatedly measured over several months.

View Table | View all tables in this article

As noted from Table 2 a shift in the centroid wavelength at 1550 nm of ± 0.01 nm (standard deviation) corresponds to a power responsivity change of ± 0.001%. Thus, a value for δ_i of 0.002% is included in the uncertainty budget with a normal distribution.

The spectral width Δλ is determined from the root-mean-square of the modes whose relative peak height is within 20 dB of the maximum peak height as defined by Eq. (11). The uncertainty associated with the spectral width is not included in the uncertainty budget as the physical basis of this is encompassed in the uncertainty of the weighted centroid wavelength. It is regarded as a figure of merit.

4. Measurement facility and uncertainty budget

The measurement configuration is illustrated in Fig. 9 and draws from the work described in section 3. Fabry-Pérot laser diode sources are connected to custom LIGHTech Fiberoptics* variable optical attenuator / shutter combinations; one for each channel. Separate beam-splitters are utilised for each wavelength. The fibers are connected to hermetic vacuum fiber feedthroughs for ease of use. We use 2 m of fiber within the cryostat which is thermally anchored at 35 K and 5 K to reduce heat flow. To facilitate backscatter measurements the facet at the low temperature end of the fiber is plane cut. PM fiber is used throughout. The source and source housing (ILX Lightwave* module) are temperature stabilised.

 

Fig. 9. Setup for the calibration of an optical fiber power meter (DUT) at three wavelengths using PM fiber throughout. Beam-splitter (A) is optional for in-situ Fresnel reflection signal level measurements (RSL). A dual hermetic fiber feedthrough is used on the cryostat; one for 1310 nm / 1550 nm, the other for 850 nm. There are two identical nanotube absorber detectors within the cryostat, and both are mounted to the same isothermal temperature controlled heatsink.

Download Full Size | PDF

The power output of the laser diode sources, measured over a five-hour period after the final beam-splitter, is stable to better than 0.02% for the 1310 nm and 1550 nm sources and 0.03% for the 850 nm laser diode. The correlation between sets of measurement (MON–DUT, RAD–DUT and RAD–MON) is indicative of the quality of the measurement and thus provides a useful metric during calibration. The correlation is a measure of the effect of the PDL of the splitter and vacuum feedthrough connection.

A listing of the uncertainty components of the optical fiber radiometer is given below in Table 3. The radiant power measurement uncertainty (0.013%) comprises the optical–electrical heating inequivalence, the detector nanotube absorber reflectance correction, and the power measurement repeatability. An expanded uncertainty of 0.1% at a coverage factor k = 2, which for a normal distribution defines an interval with a confidence level of approximately 95%, is reported.

Table 3. DUT responsivity measurement uncertainty components using optical fiber radiometer.

View Table | View all tables in this article

5. Discussion of results and outlook

We have evaluated those factors that most influence the measurement of the power responsivity (A/W) of solid state and thermal fiber coupled detectors. An expanded measurement uncertainty of 0.1% has been demonstrated by direct comparison with a cryogenic primary standard. The temperature dependent Fresnel reflection and Rayleigh backscatter of several fibers, cooled to cryogenic temperatures, were assessed. The observed change in Fresnel reflection led to an increase in the output power of the fiber at 5 K of 0.02%, 0.03% and 0.06% for SMF-28 Ultra, PM single-mode and PM PCF fiber respectively. The Rayleigh backscatter increased 15x for SMF-28 and PM fiber and 4× for the PM PCF fiber from room temperature to 5 K.

The temperature dependence of the polarisation dependent loss of SMF-28 and PM fiber beam-splitters was also evaluated. The PDL of the PM beam-splitters is of the order 1% at 20 °C, exhibiting a negative temperature coefficient of approximately −0.03 ΔPDL / °C. The PDL of the splitters, is overcome by operating in a stable lab environment of 21.5 ± 0.3 °C, humidity 20 ± 10% RH, and using PM fiber-coupled components from the laser diode source to the cryogenic detector.

The expanded uncertainty in determining the room temperature fiber beam-splitter ratio between any two output ports of the multiport splitters was assessed at 0.08%. This included drift due to the nature of the temperature dependent PDL of the splitter and fiber connectors and an additional factor due to the ratio measurement technique of swapping fibers. The temporal and modal stability of the Fabry-Pérot laser diode sources was evaluated over many months and was found to be a relatively insignificant contributor to the overall measurement uncertainty.

We chose Fabry-Pérot laser diode sources as it is our experience that such sources, equipped with optical isolators, are characteristically stable in their power output and power weighted centre wavelength over many hours use, especially at the longer wavelengths. This is beneficial as it avoids using external laser intensity stabilisers while maintaining good measurement repeatability. The results given in Table 2 demonstrate that the uncertainty contribution from this approach, that is the temporal shift in the centroid wavelength, is minimal, less than 0.01% even at 850 nm. If the beam-splitter is illuminated with unpolarised (decoherent) light the PDL value will remain the same as all polarisation states were considered in the PDL evaluation.

The three fiber types, SMF-28, PM single mode and PM PCF, were found to behave similarly. However, PM fiber was selected for its resilience to physical movement and overall stability. Further work is required to fully understand the utility of the PM PCF fiber. It benefits from being single mode over a large wavelength range; however, the possible retention of air within the micro-structured capillaries requires further investigation, especially at temperatures below 273 K. We saw a rise and fall in reflected signal at about 55 K suggesting a change in strain, as evidence of a potential oxygen phase change. Ultimately the goal is to develop a robust beam-splitter ratio measurement technique that utilises the cryogenic detector when cold.

6. Conclusion

We have investigated the principal factors limiting the measurement uncertainty of the NIST cryogenic fiber-coupled primary standard. The facility uses PM fiber-coupled components throughout the system. Rigorous measurement of the change in Fresnel reflection and Rayleigh back-scatter of the cryogenic fiber as it is cooled, the polarisation temperature dependent loss contribution of the beam-splitters, characterisation of the fiber beam-splitters, and the modal and temporal stability of the Fabry-Pérot laser diode sources has enabled a reduction in the expanded measurement uncertainty to 0.1%.

The PM PCF fiber is single mode over a large wavelength range and therefore the performance of the fiber was assessed at low temperature at 1550 nm, with a view to future use. The results are promising which encourages further work to understand the dynamics of the fiber within the low temperature vacuum environment.

A further development encompasses the use of a 2 × 2 switch to facilitate beam-splitter ratio measurements when the cryogenic detector is cold. This ability would further the assurance of the fiber power measurement and enable autonomous operation of the facility. The Fresnel reflection measurement would thus become redundant. The stability of the optical fiber beam-splitters limits the overall performance of the measurement system.