**4. Integrated interferometers for ghost imaging in the spectral domain**

The Ghost Imaging, (GI) phenomenon is based on the spatial correlation of light to form images and, since the early pioneering work in 1995, several experiments on the argument have been presented [15–18]. The GI is obtained by correlating the intensities of two spatially separate light beams, one of the two light beams illuminates an object to be imaged. The second beam, which does not see the object, (reference beam), if it is detected with a position-sensitive sensor, gives rise to the spatial image of the object created by the non-interfering photons.

Besides the GI in the space domain, another kind of 'ghost experiments' were performed in the frequency (Spectral), domain [19–21]. It must be pointed out that in Ref. to [20], thes kinds of experiments were performed using a classical thermal light emitted by a broad-band superluminescent diode. These experiments allowed to exploit real spectroscopy measurements detecting spectral lines of chemical molecules like CHCl3 [20] and the spectral lines of Er3+ dopant [21] in LiNbO3 non-linear material placed in one arm of an Asymmetric Non-Linear Interferometer, (ANLI). These preliminary approaches to experimental spectroscopic sensing demonstrate that a new field of sensing can be opened exploiting effects such as 'ghost spectrometry'. These new sensing techniques can allow extending the sensing limits of the traditional detectors and performing spectrometric measurements with non-interacting photons.

Before describing the experimental procedures, of ghost imaging in the frequency domain, let us give a rapid oversimplified description of the basic principles of the 'ghost' phenomena. In Ref. [22], this architecture was studied in detail and it was concluded that it gives rise to a condition that is often referred to as maximally entangled states of a two-mode field. If the two modes are physically separated like in the case of the arms of an MZI, we are in presence of separate path-entangled states that can have important applications to interferometry and interferometric analyses.

In particular, considering the case of a coherent intense light beam injected in an integrated MZI, the photons are spatially confined in geometrically separated singlemode waveguides, where they have a very high spatial and time coherence [22]. Moreover, the photon density inside the waveguides can reach values that are orders of magnitude higher than in the case of free space propagation. In these conditions, an integrated optical device is particularly suitable for both practical applications and basic quantum optics studies.

#### *Integrated Optics and Photonics for Optical Interferometric Sensing DOI: http://dx.doi.org/10.5772/intechopen.103770*

The integrated version of an ANLI, used to obtain ghost imaging in the frequency domain [23], is schematically reported in **Figure 12** as taken from reference [21].

In that case, the ANLI was not built as a monolithic device but was realised in a hybrid set-up in which the 980 nm Laser source was injected in a 50:50 Y coupler single-mode optical fibres. One arm was coupled with an Er3+ doped LiNbO3 monolithic waveguide, whereas the other arm was coupled with a monolithic Pockels phase modulator as the one shown in **Figure 2**. Then the MZI geometry was completed by coupling the two arms with an identical second optical fibre Y coupler. Finally, the injected 980 nm photons arrive in the photodetector passing through a (975 25) nm pass-band filter that eliminates all the photons generated by the interaction of the 980 nm pump with the Er3+ doped nonlinear LiNbO3 arm. In any case, the photons generated by the interaction in the doped arm can only give rise to a continuous background because they cannot contribute to the interference process due to the 'Which Way' criterion.

The principle of the experiment was based on the Quantum properties stating that two Fourier Transform pairs are conjugate variables. So, operating a Fourier Transform in the time-frequency space-domain, it is possible to get information on the wavenumber space-domain of the 930 nm pump photons annihilated, (generating up or down-conversion), as a consequence of the pump photons interaction with the Er3+ doped nonlinear LiNbO3. This intriguing effect takes place when the doped material is placed in one arm of the ANLI and the photodetector do not even see the photons generated by up or down-conversion in the doped arm.

The spectroscopy experiment was performed by injecting the 980 nm laser beam in the input port '*a'* of **Figure 12**. A fraction of the pump 980 nm photons is absorbed by the Er3+ dopant, giving rise to a series of up and down conversions having a widely studied spectral composition as reported in literature. Then, a linear voltage ramp is applied to the undoped arm of the ANLI producing a continuous phase shift variation between the photonic states entangled over the two optical paths of the ANLI. The pass-band filter ensured that only the 980 nm pump photons could reach the detector. The experimental data were collected detecting the intensity of transmitted photons as a function of time (i.e. of the phase shift), giving rise to the raw interferograms

**Figure 12.** *Schematic of the experimental layout. The ANLI is used in [21].*

shown in the inserts of **Figure 13(a)** and **(b)**. Then, the raw interferograms were elaborated by the usual methods used in Fourier Transform Spectroscopy [18, 24]. The same measurement was first performed by using an InGaAs photodetector having a detectability window extending up to wavelengths of 2.5 μm (in the SWIR region). The measurement was then repeated using a Si p-i-n detector that is 'blind' at wavelengths λ ≥ 1.1 μm. The results of the two experiments are reported in **Figure 13(a)** and **(b)**, respectively.

In **Figure 13**, the two spectroscopic measurements of the Er3+ energy levels performed with an In GaAs *p-i-n* photodetector, (**Figure 13(a)**) and with a Si *p-i-n* photodetector, (**Figure 13(b)**) are comparatively reported.

The complete Er3+ Spectrum extending form visible to SWIR wavelengths was obtained reporting most of the spectral lines as listed in the literature.

The difference in the amplitudes can be attributed to the different sensitivities of the two detectors. Moreover, as previously clarified, only the 980 nm monochromatic pump photons that have not interacted with the Er3+ doped crystal can reach the detector. In fact, the 980 nm photons that interacted with Er3+ are annihilated, giving rise to the up or down-conversion photons that are eliminated by the (975 25) nm passband filter.

**Figure 13.** *Spectra obtained by Fourier transform analyses with the setup of Figure 12 (see text).*

In conclusion, with the ANLI integrated architecture reported in **Figure 12**, the Er3+ spectral lines appeared independently of the different sensitivity of the used detectors also over the whole SWIR, where the Si *p-i-n* detector is 'blind'. Considering that, due to the passband filter, only the non-interacting monochromatic photons have reached the detectors, we can say that the Er3+ spectral lines are 'ghost' lines produced by the separate path entangled states correlation [22] generated in the two arms of the interferometer.

The previously described results give a strong indication that, by using 'ghost imaging' in the frequency domain, it is possible to develop a new generation of integrated interferometric instruments, (most likely based on the ANLI architecture of **Figure 12**), having the capability to work with interaction-free photons. This allows extending the spectral measurement remarkably beyond the photodetector sensitivity limits, in particular in spectral regions where the photodetectors are not available or have too low sensitivity. In particular, some preliminary contacts indicate that this effect is of strong interest for several applications, with particular attention to astrophysical applications.
