The use of laser optical feedback Imaging (LOFI) for scattering-type scanning near-field optical microscopy (sSNOM) is proposed and investigated. We implement this sensitive imaging method by combining a sSNOM with optical heterodyne interferometry and the dynamic properties of a B class laser source which is here used both as source and detector. Compared with previous near field optical heterodyne experiments, this detection scheme provides an optical amplification that is several orders of magnitude higher, while keeping a low noise phase-sensitive detection. Successful demonstration of this complex field imaging technique is done on Silicon on Insulator (SOI) optical waveguides revealing phase singularities and directional leakage.
© 2008 Optical Society of America
Scattering-type scanning near-field optical microscopy (sSNOM) stimulates an increasing interest in the community of Near-Field Optics, mainly for its high spatial resolution (resolution of Atomic Force Microscopy) down to the level of the nanometer scale. Since the introduction of sSNOM, various experimental configurations have been developed and revisited (see for example  and references therein). Despite the diversity of these approaches, they share a main principle: at each position of the scanning probe on the sample surface, one detects, far from the sample, the optical field scattered by the interaction between three elements, namely the incident electromagnetic field, the probe extremity, and the sample surface. Thanks to this controlled near-field interaction, this principle allows for the optical investigation of samples with a lateral resolution, which does not depend on the light wavelength anymore but rather on both the probe size and its distance to the sample, opening the route to the local investigation of optical properties of photonic nano-materials and structures. Despite the fact that sSNOM is now deep-rooted the external far-field detection entails several difficulties.
Firstly, the collected signal is typically weak because of the low scattering efficiencies of the probe with apex radii usually lower than 30nm. Several methods have been proposed to extract the weak signal issued from the local interaction between the tip end and the sample. Among them are tip-to-sample distance modulation with lock-in detection, demodulation at high harmonics of the modulation frequency , classical heterodyne detection [3-4] and excitation of a local field singularity at the tip apex . In many experiments, these methods have allowed the extraction of near-field components in the presence of a strong background field.
Secondly, the field scattered by the probe competes with strong background radiation coming from light scattering from regions other than the probe, for example radiation modes propagating directly towards the detector in the case of optical waveguide probing [6-8]. Numerous authors have stated that the background radiation cannot be fully suppressed because of the coherent adding of the different collected fields . The intrinsic interferometric nature of the sSNOM signal has been investigated in detail in a previous paper . In particular we have theoretically and experimentally shown that the sSNOM signal can describe either the field intensity or the complex field amplitude depending on the sample structures surrounding the tip. The resulting image is the mix of intensity, amplitude and phase signals.
Two crucial issues for sSNOM experiments are thus related to the control of the coherent background field and to the enhancement of the detected signal.
It has been already shown that these two technical hitches can be efficiently counteracted by means of tip to sample distance modulation (intermittent contact mode of the AFM probe) combined with interferometric detection [11-12]. This combination allows for recovering both amplitude and phase of the near field signal, filtering the background and amplifying the scattered light [13-14]
As proposed for the first time by I. Stefanon  and recently in , we investigate in this paper an alternative method of amplitude and phase mapping for sSNOM, based on the technique of Laser Optical Feedback Imaging (LOFI) which has been used for last decade in optical coherent backscattering imaging , laser doppler velocimetry and vibrometry [18-19] and laser optical feedback tomography .
This technique is a very sensitive imaging method combining optical heterodyne interferometry with dynamic properties of B class laser . In this method, the interference takes place into the laser cavity between the intracavity light and the backscattered light by the studied target. The backscattered light is frequency shifted to create an intracavity optical beating. Consequently, the laser output is thus modulated at the shift frequency and detection of this modulation with a lock-in amplifier makes it possible to obtain amplitude and phase images of a non-cooperative target (a diffusing surface or volume, for example). To get the maximum sensitivity, the optical beating frequency must be resonant with the natural oscillation of the laser. Then with a fine tuning of the shift, a great amplification factor of the optical beating can be obtained. For example a Nd:YAG microchip laser gives a LOFI amplification gain 106 times higher than the standard heterodyne gain. Consequently the LOFI method leads to extreme sensitivity to the laser reinjected light. We show in this paper that, combined with tip-sample distance modulation, the LOFI method can be successfully applied to sSNOM applications.
2. Experimental setup
The experimental setup developed in this study is illustrated on Fig. 1. It is obtained by combining a standard sSNOM setup based on a commercial AFM and a LOFI detection system. The laser source is an Erbium-doped fiber DFB laser pumped with a laser diode (customized Adjustik laser from Koheras with no output isolator). It emits infrared light in a single longitudinal mode at 1.55 μm and its typical intensity noise spectrum with no output isolator and for different output powers is shown on Fig. 2. The intensity noise spectrum exhibits a strong resonance centred on the laser relaxation oscillation frequency which varies as a function of the normalized laser pumping factor r, the cavity decay rate γc and the population inversion decay rate γn according to the relation  .
After splitting of the laser beam (frequency f = ω/2π) by a fibre coupler which collect 10% of the laser output, the optical wave is frequency shifted at f + Δf by a pair of crossed acousto-optic modulators (AOM1 and AOM2) working at central frequency of 40MHz. The optical shift Δf = Δω/2π can be set from 10 kHz to a few MHz. The frequency shifted beam is then launched into a SOI channel waveguide that produces a well controlled evanescent wave at the air/waveguide interface.
The local guided field (evanescent tails of the guided modes and eventually radiated fields) is converted into radiating modes by a commercial bulk AFM silicon tip. The tip to surface distance is controlled by the AFM in intermittent-contact mode (also called “tapping mode”). In this mode the probe oscillates along the z direction, perpendicularly to the sample usually at a frequency closed to ftip = ωtip/2π ≈ 300 kHz and with amplitude around 100 nm.
The waveguide is mounted on an x-y piezoelectric stage and is scanned beneath the AFM probe. The atomic force feedback ensures constant vibration amplitude during the scan acquisition and leads to a precise topography image. Simultaneously, the light scattered by the nano-probe is collected by a confocal-type microscope. More details on the optical collection system can be found elsewhere [13, 15].
Finally, the scattering waves are re-injected into the laser cavity by means of an optical circulator which also avoids multiple reflections in the fibre loop. A rapid InGaAs preamplified photodetector (TTI TIA-950) is used to detect 10% of the direct output power from the laser that carries the induced perturbation of the laser cavity resulting from the frequency shifted feedback. In order to extract both the amplitude and phase of the LOFI signal, the photocurrent is demodulated by a lock-in amplifier (Perkin Elmer 7280).
3.1 Frequency-shifted LOFI signal
The main advantage of the frequency shifted LOFI detection compared to classical heterodyne interferometric detection is that its transfer function gives a strong resonance when the frequency shift FE = ΩE/2π of the re-injected wave is set closed to the relaxation oscillation frequency FR = ΩR/2π of the laser. According to Lacot et al.  the laser output power modulation at frequency Fe for weak feedback is given by:
where Pout is the laser output power and γext√Re is the re-injected optical field, Re is the effective power reflectivity of the target, γext is an external coupling ratio related to the total insertion losses in the optical path (losses in the splitter, in the circulator, overlap with the laser mode, etc.), φe is the phase of the effective reflectivity. The amplification gain G(Fe) is defined by the laser parameters :
where γc is the laser cavity decay rate and ΓR is defined as the damping rate of the relaxation oscillation.
As we can see, the LOFI signal [Eq. (1)] exhibits a resonance at the laser relaxation frequency Fe=FR, which also corresponds to a resonance of the laser quantum noise. The gain factor G(Fe) can be up to 106 for a B class laser source. Furthermore, Lacot et al. have shown that the signal to noise ratio remains frequency independent and also shot noise limited .
A typical experimental LOFI/sSNOM power spectrum recorded with a spectrum analyser is shown on Fig. 3 in the case of a direct illumination of the scattering probe (far field illumination) by means of a lensed fibre. The optical frequency shift Δf = Δω/2π was set to 940 kHz. As we can see, for weak optical feedback from the sSNOM collection path, the laser fluctuations are principally composed of the laser quantum noise at the relaxation frequency FR and of sharp oscillation harmonics contained in the LOFI signal. For comparison, the power spectrum of the photodiode detector is also shown on this figure. As we can see, around FR the laser quantum noise is one order of magnitude higher than the detector noise. This means that the detection can be shot noise limited around FR .
The noise fluctuations are mainly due to the resonant amplification of the Langevin quantum noise at the laser relaxation frequency, while the LOFI oscillations are induced by the optical feedback. Because of the vertical oscillation of the probe, the amplitude of the frequency shifted feedback is modulated at frequency ftip which in our case is ftip = 312.9 kHz. It produces in the LOFI power spectrum frequencies which are the sum and the difference of the carrier and modulation frequency, respectively at Δf + ftip and at Δf − ftip. With a good choice of the frequency shift Δf, it becomes then possible to set one of the frequency sidebands Δf ± ftip closed to FR to obtain the desired LOFI amplification gain (at Δf + ftip) and obtain a better SNR than the other one at (Δf + ftip) see Fig.3. Rewriting equ.(1) in the case of our experiment, we obtain for the laser output power modulation at frequency Fe = Δf − ftip under weak feedback:
where Etip and φtip are respectively the amplitude and the phase of the re-injected scattered field.
Finally, the demodulation of the laser oscillations (Eq. (3)) with a lock-in amplifier gives us the amplitude and the phase of the sSNOM signal:
It is worth noting here that a similar result is obtained with a classical two beam heterodyne interferometric sSNOM for which G=1. The benefit of using a lock-in amplifier to demodulate the sSNOM signal at these sideband frequencies (Δf ± ftip rather than Δf) has been already discussed elsewhere (see reference ). The key point is that the optical background inherent in sSNOM experiments can be efficiently suppressed. The main advantage of the possible LOFI amplification gain is that a shot noise limited signal is straightforwardly obtained even using detectors with high dark current level. This gain is very interesting for fast near-field imaging in presence of low signal, which is the case for example when very high spatial resolution is achieved (small scattering cross section) or large scale scanning is performed . Note that the two arms optical architecture combined with detection at the sideband frequencies avoids the effect of parasitic reflections to reach the optimal LOFI performance .
3.2 Waveguide near-field probing
In the following section, to validate the frequency-shifted LOFI detection for sSNOM application, we will focus on the probing of guided waves which produces a well known evanescent near-field outside the waveguide’s core.
A schematic picture of the waveguide’s cross section is shown in Fig. 4. The structure was fabricated using CMOS photonics technology. The silicon on insulator (SOI) substrate (200 mm wafer manufactured by SOITEC) used in this study is composed of a monocrystalline silicon layer with a typical thickness of 200 nm on top of a 1 μm thick buried oxide layer on a silicon substrate. Full details on the fabrication process can be found in .
As it is shown on topographic images A) and E) in Fig. 5, the overclad surface remains very flat after the polishing process, since the waveguide relief is not visible. These topographic images have been taken at two different locations along the waveguide and images B) C) D) and F) G) H) are the corresponding optical images simultaneously taken during the AFM scan with a working wavelength set to 1.55μm and for a TM polarized light injection.
At this wavelength, the waveguide is multimode and a mode beating along the propagation direction is clearly visible on both amplitude and phase images. The circles indicate phase singularities which correspond to isolated points where the amplitude is zero and the phase is not determined. In practice these phase singularities are due to interference between all excited modes in the waveguide, at these peculiar points, the modal field amplitudes are equal and the fields are out of phase leading to destructive interference. Similar observations have been reported with an interferometric PSTM in .
A Fourier analysis of the complex field along the propagation direction leads to the determination of the modes propagation constants. Furthermore it allows for discriminating guided waves contribution from radiated waves. For example, images E) to H) in Fig. 5 show a localized mode leakage into the substrate (measured mean effective index of 1.43) due to the presence of a dust located just above the waveguide core. The radiated waves into the substrate are emphasized on the phase image H) which provides a clear visualization of the weak directional leakage.
To conclude, we have presented in this paper an alternative method of amplitude and phase recovery for sSNOM. The experimental setup is based on the combination of a standard scattering based SNOM working in intermittent AFM contact mode with LOFI detection.
This new type of experimental setup provides near-field amplitude and phase imaging in a similar manner than previously reported interferometry-based sSNOM. Combined with tip to sample distance modulation it also allows for efficient optical background suppression, including back-reflections along optical paths in the setup and background radiation corresponding to light scattering from regions other than the probe. The main advantage of the frequency shifted LOFI detection compared to classical heterodyne detection is that its transfer function gives a strong resonance when the frequency shift of the re-injected wave is set closed to the relaxation oscillation frequency of the laser. At these frequencies amplification factors as high as 106 for B class type laser sources can be achieved. This gain allows reaching the shot noise limit detection in a straightforward way even with low output power sources and low sensitive detectors. In classical interferometers, the optical pathways have to be precisely balanced. Here the interference takes place directly into the laser cavity. No precise alignment is required. The setup is thus easier to implement and could be ideal for backscattering NSOM configuration since it will become self-aligned.
Future works lie in high resolution and large scale near field optical imaging.
This work was partially financially supported by the “région Champagne Ardennes,” and is part of the strategic research program on “Laser optical feedback imaging for s-SNOM applications” of the “Université de Technologie de Troyes (UTT)”. The authors want to thank J.M. Fedeli from LETI/CEA for providing the SOI waveguide structures
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