In free-electron laser diagnostics and inertial confinement fusion (ICF) diagnostics, it is a challenging task to record an ultrafast pulse in one shot, as the temporal resolution of detectors is usually limited by the transmission bandwidth. Recently developed technology based on pulsed radiation-induced changes in optical characteristics (PRICOCs) can record an incident pulse in one shot and demonstrate picosecond temporal resolution [1–5].

RadOptic technology was developed based on PRICOCs and was a potential choice for gamma-ray history diagnostics in ICF [2]. By recording the instantaneous change in the refractive index (ICRI) of semiconductors exposed to radiation pulses, the RadOptic detector converts the intensity evolution versus time (IEVT) of radiation pulses to the IEVT of infrared laser light and overcomes the bandwidth restraint of cables used in classical detectors.

A poor response to mega-electron volt (MeV) gamma-ray pulses has restrained the application of the RadOptic detector [2]. To enhance the sensitivity, bulk semiconductors constitute one potential solution [6]. An evaluation showed that the relaxation time of the ICRI in thin bulk semiconductors was on the order of picoseconds [7] and that the spatial expansion of the ICRI area in thick semiconductors was hundreds of micrometers (i.e., several picoseconds) [8]. The key characteristic of the detector was the evolution of the ICRI of a bulk semiconductor exposed to mega-electron volt X/gamma-ray pulses. Because such MeV pulses vary in pulse width and pulse intensity from shot to shot, the ICRI should be continuously and quantitatively recorded with high temporal resolution in one shot.

Many advanced refractive index (RI) measurement sensors have been developed, including RI/ICRI sensors based on the deflection of an optical beam [9,10], modal change in an image [11], and a change in the reflectivity/transmittance spectrum [12,13]. The temporal resolution of an ICRI measurement is usually limited by the detection method. In some systems, the sensing medium is integrated with fiber, making it difficult to alter the sensing materials. An interferometer based on directly coupling a single-mode fiber (SMF) with bulk material was developed to measure the ICRI of the bulk material [7,14]. The measured ICRI of several types of bulk semiconductors, such as ZnO, GaAs, and InP, has been demonstrated and interpreted [15].

This Letter focuses on the design considerations and flexibility of the abovementioned interferometer. A simple optical model is established to qualitatively describe the formation of the interference and predict the performance of the interferometer. The temporal resolution is approximately 50 ps and can potentially be enhanced. The interferometer works well with several types of bulk semiconductors with thicknesses of several hundred micrometers.

A schematic of the interferometer is shown in Fig. 1. The source of the probe beam was a continuous-wave (CW), tunable, infrared C-band (1528–1566 nm) laser. The laser’s coherent length was several kilometers. Light from the laser was guided by a long SMF to the front face of the bulk semiconductor. The fiber end near the front face was a ferrule connector/angle polished connector (FC/APC)-type connector, with which the reflected light at the interface between the fiber core and the air was eliminated. The probe beam was expanded by a tapered pattern and transmitted over a small air gap before arriving at the front face of the bulk material. Both faces of the bulk material were polished. The band gap of the bulk material is larger than the single photon energy of the probe beam ($\sim 0.8\mathrm{eV}$), so the absorption can be neglected. Reflections occur at the front and rear faces. At the front face, the beams reflected from the faces of the bulk material form an interference pattern like an Airy spot.

 

Fig. 1. Schematic of the interferometer.

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To find a proper angle where the reflected light intensity can be high enough to be recorded by the opticelectric detectors (OEDs), an online adjustment method was used. First, move the bulk semiconductor close to the fiber end. Then, by carefully adjusting the relative angle between the bulk material and fiber and simultaneously monitoring the output of the OEDs by a digital oscilloscope, the angle where the maximum or close to maximum light intensity is reflected can be determined. The light reflected into the SMF was guided through a fiber circulator to the detection system. The detection system consisted of two OEDs (0.2 GHz and 12 GHz) and a 12.5 GHz digital oscilloscope.

When radiation pulses are incident on the bulk, excess carriers are generated through ionization processes. Based on theoretical computation [16], the RI of the bulk also changes instantaneously. Moreover, the interference pattern changes as the beams refract out of the front face. The intensity of the light back reflected into the SMF also changes and is transformed by the OEDs to a change in voltage, which was recorded by the digital oscilloscope.

The interferometer sensitivity was determined by the slope of the $dn\text{-}V$ curve ($d\lambda \text{-}dV$ curve), and the detection range was determined by the range of the linear interval of the $dn\text{-}V$ curve ($d\lambda \text{-}dV$ curve).

An optical model was established to predict the performance of the interferometer in different settings. A schematic of the model is shown in Fig. 2. The model was based on the following simplifications.

 

Fig. 2. Simple model of interference formation.

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The interference pattern ${|E(r)|}^2$ is computed with the following formula:

To verify the model, several GaAs bulk samples were tested in the interferometer. The parameters of these bulk materials are shown in Table 1.

Table 1. Bulk GaAs with Different Parameters

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The predicted $d\lambda \text{-}dV$ curve of the interferometer was compared to the measured results, as shown in Fig. 3.

 

Fig. 3. (a) Model predicted $d\lambda \text{-}dV$ curve for 0.3 mm GaAs. (b) Model predicted $d\lambda \text{-}dV$ curve for 5.0 mm GaAs. (c) Measured $d\lambda \text{-}dV$ curve for 0.3 mm GaAs. (d) Measured $d\lambda \text{-}dV$ curve for 5.0 mm GaAs. (e), (f) Model predicted and measured $d\lambda \text{-}dV$ curve for 0.3 mm GaAs with 90% coated faces, respectively.

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The predicted $d\lambda \text{-}dV$ curves for GaAs1 and GaAs3 are shown in Figs. 3(a) and 3(b), respectively. The measured $d\lambda \text{-}dV$ curves for GaAs1 and GaAs3 are shown in Figs. 3(c) and 3(d), respectively. Both the prediction and measurement show that as the thickness of the bulk increased, the period of the $d\lambda \text{-}dV$ curve decreased and the slope of the $d\lambda \text{-}dV$ curve at linear intervals increased, suggesting that the measurement with a thicker bulk material had higher sensitivity. However, the modulation ratio (MR) also decreased as the thickness increased, meaning that the interferometer with a thicker bulk material exhibited a lower contrast.

The predicted $d\lambda \text{-}dV$ curves for different reflectivities are shown in Fig. 3(e). The measured $d\lambda \text{-}dV$ curve for GaAs2 is shown in Fig. 3(f). Both the prediction and measurement show that as the reflectivity increased, the sensitivity also increased. However, as in the case of a thick bulk material, the contrast was also lower.

The actual performance of the interferometer can be characterized by a tradeoff between the sensitivity and the contrast. Both the measurement with a thicker bulk material and the measurement with coated faces exhibited a higher sensitivity but had a low contrast. In practice, bulk materials with thicknesses of several hundred micrometers and polished faces are used.

The sensitivity was determined from the relationship between $d\lambda$ and $dn$. First, the $d\lambda \text{-}dV$ curve was measured by tuning the probe wavelength ($d\lambda$) and recording the outputs of the OEDs in units of V. Then, the $d\lambda \text{-}dV$ curve was converted to a $dn\text{-}V$ curve based on $\partial \mathrm{\varphi }(\lambda ,n)/\partial \lambda ·d\lambda =\partial \mathrm{\varphi }(\lambda ,n)/\partial n·dn$, where $\mathrm{\varphi }(\lambda ,n)$ is the phase difference of the interferometer. Based on the structure of the interferometer, the phase difference formula for two beams is $\mathrm{\varphi }=4\pi nl/\lambda$; therefore, $\mathrm{\Delta }n=-n\mathrm{\Delta }\lambda /\lambda (1+\mathrm{\Delta }\lambda /\lambda )$. The dependence of the RI on the wavelength was neglected based on the small range (∼nanometers) of the wavelength variation.

The minimum detectable CRI (MiDCRI) is related to the slope of the $dn\text{-}V$ curve and the noise of the interferometer. The noise sources include the turbulence of the environment (atmospheric turbulence, mechanical vibrations, temperature gradients), fluctuations in the probe light, and the noise of OEDs. For an interferometer with the settings mentioned above, the MiDCRI is approximately ${10}^{-5}$ RI units (RIUs).

The intrinsic temporal resolution is approximately the time required for the probe to travel twice the distance between the faces. For bulk GaAs 300 μm in thickness, the temporal resolution was computed by the optical model to be approximately 6.8 ps, as shown in Fig. 4(a). The intrinsic temporal resolution can be enhanced by using thinner bulk materials. In practice, the temporal resolution is limited by the detection system. The temporal resolution was tested by using a laser pulse with a pulse width of 200 fs. The result showed that the temporal resolution was approximately 50 ps [Fig. 4(b)].

 

Fig. 4. (a) Predicted intrinsic temporal resolution for 0.3 mm GaAs from the model. (b) Measured temporal response of the detection system.

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Several bulk materials were used in the interferometric measurements. The parameters of these bulk materials are shown in Table 2. The measurements show a practical MR (Figs. 5 and 6), suggesting that the setup can be widely used to research the evolution of the ICRI in bulk materials.

Table 2. Characteristics of the Bulk Materials Used in This Research

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Fig. 5. Measured $d\lambda \text{-}dV$ curve for (a) bulk p-type GaAs, (b) bulk n-type GaAs, (c) bulk ZnO, and (d) bulk InP.

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Fig. 6. (a) and (b) $d\lambda \text{-}dV$ curve for bulk diamond and GaP, respectively. (c) and (d) Measured ICRI patterns for bulk diamond and GaP in response to a mega-electron volt pulse, respectively. The monitored intensities of the x-ray pulses are shown in the small insets in (c) and (d), respectively. (e) and (f) Normalized ICRI of diamond and GaP for 200 fs pulses from a 400 nm laser.

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To investigate the actual performance of the interferometer, the interferometer was tested under mega-electron volt pulsed radiation. Mega-electron volt x-ray pulses were generated by a pulsed power facility named “QG-I” of the Northwest Institute of Nuclear Technology. The maximum energy of the x-ray photons was 0.8 MeV, and the average pulse width was approximately 60 ns.

The detection area of the bulk face was no larger than the area of the SMF core, because the light outside this area was not collected. The radiation area was approximately $100{\mathrm{cm}}^2$, which is much larger than the detection area. The diffusion of the excess carriers can be ignored. The density of the excess carriers in the detection area was dominated by the generation and recombination of the excess carriers.

The ICRI signal can be transmitted over a long distance in the SMF, and a high bandwidth can be maintained. The detection system can be positioned far from the x-ray pulse source, and disturbances from the source can be reduced to a neglectable level.

Diamond and GaP are semiconductors with indirect band gaps. ICRI evolution patterns for bulk diamond and GaP in response to pulsed radiation are shown in Fig. 6. The ICRI curves for mega-electron volt gamma-ray pulses [Figs. 6(c) and 6(d)] are obviously different from the curves for ultrashort laser pulses [Figs. 6(e) and 6(f)].

A similar phenomenon has been interpreted for p-type GaAs and ZnO, direct band gap semiconductors, by considering generation and recombination processes [7]. Studies based on this interferometer also compared the lifetimes of excess carriers in nitrogen-doped and boron-doped single-crystal high-pressure and high-temperature (HPHT) diamonds [17] and verified an ICRI sensitivity enhancement with InP [15].

The evolution of the ICRI of bulk semiconductors under pulsed radiation has become increasingly important in developing new optical ultrafast recording technologies. An interferometer that can record an ICRI in one shot continuously and quantitatively was developed in this work. A practical MR can be achieved with different bulk materials with thicknesses of several hundred micrometers. The temporal resolution can be improved by using thinner materials and high-bandwidth detection. This interferometer can also be used to study the excess carrier dynamics of bulk materials under other forms of ionizing radiation, such as heavy ions or neutrons. Moreover, the instantaneous recombination dynamics of excess carriers in some insulators under pulsed radiation can also be studied based on the scheme developed in this work.