Nanometric sensing with laser feedback interferometry

International audienceWe demonstrate a nanometric sensor based on feedback interferometry in a DFB laser by using a measurement of either the optical frequency or laser voltage. We find that in an optimal range of optical feedback, the sensor operates reliably down to an extrapolated 12 nm; for the sensor demonstrated here at ∼1550 nm, this provides a minimum detectible displacement of λ/130. Nanodisplacement sensors have been demonstrated based on a variety of physical effects and for a range of applications [1, 2]. The laser feedback interferometry (LFI) or self-mixing interferometry sensor [3, 4] we demonstrate is a noncontact sensor, and therefore we set aside discussion of most MEMS-based approaches. As for noncontact nanodisplacement sensors, there are a number of approaches, including those based on capacitance, eddy currents, and atomic-force microscopy [5, 6]. These approaches, while in some cases sensitive to atomic-scale displacements can be complex, costly, and sensitive to quite small displacement ranges (small dynamic range). LFI is based on light, reflected back into the active region, which in turn affects the laser diode (LD) operation in a fashion dependent on the phase of the reflected light [7, 8]. LFI itself provides sensitivity at least on the scale of the emission wavelength λ, though below we show that the minimum detectible displacement (MDD) can be λ. A LD with optical feedback is generally known as an external-cavity semiconductor laser (ECL). Heuristically, when the target distance L is varied by ∆L, the properties of an ECL (frequency ν, linewidth, and threshold gain) undergo periodic variation, which is broadly understood on the basis of the Lang and Kobayashi (LK) equations [9]. The feedback-phase sensitivity of the LFI sensor depends on the change of frequency ν with L, which in turn is also manifested in the optical output power P PD measured by a photodiode (PD) and change of carrier concentration measured by the LD terminal voltage V LD (under constant injection current J). We demonstrate LFI sensors enabling unprecedentedly high sensitivity providing a linear sawtooth dependence on L of the sensing parameter, here focusing on V LD. LFI has been exploited for imaging [10, 11], biomedical sensing [12] and measuring absolute distance [13, 14], displacement [15-17], reflective index [18], velocity [19, 20], and flow [21]. Recently, Keeley et al. [22] investigated the emission spectrum of a THz QCL by measuring ν and V LD as functions of the displacement ∆L and showed that LFI can achieve a similar spectral resolution as Fourier-transform infrared spectroscopy. LFI displacement sensors have been demonstrated usually using a moving target, e.g. a harmonic piezo-actuator or loudspeaker that sweeps several µm , combined with high sampling rates to measure fringes of the LFI signals. Their MDDs are from a few to hundreds of nm but require post-processing of the LFI signals and/or substantial modifications of the basic LFI setup [23-28], laser feedback grating (< 10 nm) [26], Fourier transform (λ/50) [27], phase shifting (λ/12) [28-30]. In contrast, our approach requires neither modification of the basic LFI setup nor any signal processing, but relies on the direct physical measurement of the LFI signals in parameter ranges leading to high linearity and signal-to-noise ratio (SNR). Specifically, we demonstrate a LFI sensor with a MDD of λ/130, assuming the feedback level can be adjusted in an optimal range. Since the LFI sensing mechanism is based on the feedback phase, such a sensor can also be used as a gas or liquid sensor using refractive index change. For the MDD and geometry we focus upon, this translates into the ability to sense refractive-index changes in the optical feedback loop of ∆n min ∼ 10 −8. In this Letter, because of the key rôle played by ν in LFI, we start with its dependence on L before proceeding to focus on V LD. We first review important theoretical points that describe the variation in ν and consequently in V LD with L.The theory of LFI is discussed in Refs. [7, 31]. Briefly, the excess-phase equation derived from the LK model relates ∆L to ∆ν = ν − ν 0 as a periodic function where ν is the output frequency of the ECL and ν 0 is the frequency of the free-running LD (i.e., in the absence of optical feedback). When ∆L changes, ∆ν obeys ∆ν(∆L) = mF(∆L) with m the optical-feedback modulation index that defines the signal slope with respect to ∆L, F(∆L) a periodic function with period λ 0 where λ 0 = c/ν 0 with c the speed of light in vacuo. Qualitatively, the dependence of ν on ∆L tends to be sinusoidal for weak feedback. The shape can become close to a piecewise linear function