Patent Publication Number: US-10329147-B2

Title: Surface plasmon-based nanosensors and systems and methods for sensing photons and chemical or biological agents

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application is a division of and claims priority under 35 U.S.C. 120 to co-pending commonly owned U.S. application Ser. No. 14/168,051, filed 30 Jan. 2014, which in turn is related to and claims priority under 35 U.S.C. § 119 to European Application No. 13159918.5, filed 19 Mar. 2013, the entirety of which is hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to surface plasmon-based nanosensors, a system for sensing photons, a system for sensing chemical or biological agents, a method for sensing photons and a method for sensing chemical or biological agents. 
     BACKGROUND 
     Nano-scale systems have demonstrated many novel and interesting optical properties. These systems are extremely important for future photon-based devices among many other applications. One of the most important nano-devices are nanosensors. 
     SUMMARY 
     It is the object of the present invention to provide a nanosensor that is small, but yet sensitive to weak electromagnetic signals/fields or changes thereof. 
     This aim is achieved by a surface plasmon-based nanosensor, comprising: at least one first element of metal, preferably silver or gold, or of semiconductor, the first element being excitable to surface plasmon resonance, in particular localized surface Plasmon resonance, in the presence of electromagnetic radiation from a source, and at least one second element preferably near the first element that in the presence of the electromagnetic radiation is exiton-plasmon coupled to the first element and emits electromagnetic radiation representative of the exiton-plasmon coupling. Said nanosensor might be called “a plasmonic sensor” as well and can be categorized as an optical sensor. The at least one first element and the at least one second element are usually different. 
     According to further a further aspect, this aim is also achieved by a system for sensing photons of electromagnetic radiation from an external source, comprising: a surface plasmon-based nanosensor and a detector for detecting electromagnetic radiation emitted by the second element in response to electromagnetic radiation from an external source. 
     Further, according to further aspect the invention provides a system for sensing chemical or biological agents, comprising: a surface plasmon-based nanosensor, and a detector for detecting electromagnetic radiation emitted by the second element in response to the electromagnetic radiation from an external source or the internal source with a chemical or biological agent in direct or indirect contact with the at least one first element, in particular further comprising an evaluation unit for evaluating the identity of the chemical or biological agent based on the detected electromagnetic radiation. 
     This aim also achieved by a surface plasmon-based nanosensor, comprising: at least one first element of metal, preferably silver or gold, or of semiconductor, the first element being excitable to surface plasmon resonance, in particular localized surface plasmon resonance, in the presence of electromagnetic radiation from a source and at least one second element preferably near the first element for exciting surface plasmon resonance of the at least one first element. 
     The invention also provides a system for sensing photons of electromagnetic radiation from an external source, comprising: a surface plasmon-based nanosensor, a pumping unit for pumping the at least one second element and a detector for detecting the total electromagnetic radiation emitted by the at least first element and the at least one second element in response to electromagnetic radiation emitted by an external source or the internal source and incident on the at least one first element and the at least one second element, in particular further comprising an evaluation unit for evaluating the statistics, in particular the frequency and/or the intensity and/or photon number, of the electromagnetic radiation from the external source based on the detected electromagnetic radiation. 
     Further, this aim is achieved by a system for sensing chemical or biological agents, comprising: a surface plasmon-based nanosensor, a pumping unit for pumping the at least one second element and a detector for detecting the total electromagnetic radiation emitted by the at least one first element and the at least one second element in response to the electromagnetic radiation emitted by an external source or the internal source and incident on the at least one first element and the at least one second element with a chemical or biological agent in direct or indirect contact with the at least one first element. 
     The present invention is also directed to the use of a nanosensor or of a system for sensing photons and the use of a nanosensor or of a system for sensing chemical or biological agents. 
     The present invention also provides a method for sensing photons of electromagnetic radiation from a source, comprising: irradiating at least one first element of metal, preferably silver or gold, or of semiconductor, excitable to surface plasmon resonance, in particular localized surface plasmon resonance, with electromagnetic radiation from a source for exciting surface plasmon resonance on said at least one first element, providing for exciton-plasmon coupling between the at least one first element and at least one second element and for emission of electromagnetic radiation by the at least one second element, and detecting the electromagnetic radiation emitted by the at least one second element. 
     Also, the present invention provides a method for sensing photons of electromagnetic radiation from a source, comprising: irradiating at least one first element of metal, preferably silver or gold, or of semiconductor, excitable to surface plasmon resonance, in particular localized surface plasmon resonance, and at least one second element with electromagnetic radiation from a source, the at least one second element being pumped by pumping unit for exciting surface plasmon resonance on or in the at least first element and detecting the total electromagnetic radiation emitted by the exiton-plasmon coupled pumped at least one second element and at least one first element. 
     In addition, the present invention provides a method for sensing chemical or biological agents, comprising: directly or indirectly contacting at least one first element of metal, preferably silver or gold, or of semiconductor, excitable to surface plasmon resonance, in particular localized surface plasmon resonance, with a sample comprising a chemical or biological agent to be sensed, irradiating the at least one first element with electromagnetic radiation from an internal or external source for exciting surface plasmon resonance on said at least one first element, providing for exciton-plasmon coupling between the at least one first element and the at least one second element and for emission of electromagnetic radiation by the at least one second element, and detecting the electromagnetic radiation emitted by the at least one second element. 
     Finally, the present invention provides a method for sensing chemical or biological agents, comprising: directly or indirectly contacting at least one first element of metal, preferably silver or gold, or of semiconductor, excitable to surface plasmon resonance, in particular localized surface plasmon resonance, with a sample comprising a chemical or biological agent to be sensed, irradiating the at least one first element and the at least one second element with electromagnetic radiation from a source, the at least one second element being pumped by a pumping unit for exciting surface plasmon resonance on said at least one first element and detecting the total electromagnetic radiation emitted by the exciton-plasmon coupled pumped at least one second element and at least one first element. 
     According to a special embodiment of the nanosensor, the at least one first element is a nanoparticle and/or the at least one second element is quantum dot. More generally, the second element could be a two-level-system (TLS). 
     Preferably the at least one second element is preferably totally embedded in a matrix of Photonic or Polaritonic Band-gap (PGB)-material, preferably silicon carbide (SiC), and/or wherein the at least one first element is at least or only partially or totally embedded in a matrix of Photonic or Polaritonic Band-gap (PGB)-material, preferably silicon carbide (SiC). 
     A further special embodiment is characterized in further comprising an internal source capable of emitting the electromagnetic radiation. Such an embodiment would be well suited for use of the nanosensor as a bio-sensor for sensing biological or chemical agents (analytes). 
     Conveniently, the system comprises a shielding for shielding the at least one second element against external electromagnetic radiation. 
     According to a special embodiment of the nanosensor, the at least one first element is a nanoparticle and/or the at least one second element is a quantum dot. More generally, the at least one second element might be a two-level-system (TLS). 
     Preferably, the at least one second element is preferably totally embedded in a matrix of Photonic or Polaritonic Band-gap (PGB)-material, preferably silicon carbide (SiC), and/or wherein the at least one first element is at least or only partially or totally embedded in a matrix of Photonic or Polaritonic Band-gap (PGB)-material, preferably silicon carbide (SiC). 
     In particular when being used as a biological sensor (bio-sensor) or chemical sensor, it might further comprise an internal source capable of emitting the electromagnetic radiation. 
     Conveniently the method further comprises evaluating the statistics, in particular the frequency and/or intensity and/or photon number, of the electromagnetic radiation from the source based on the detected electromagnetic radiation. 
     Finally, conveniently the method further comprises identifying the identity of the chemical or biological agent based on the detected electromagnetic radiation. 
     The present invention is based on the unexpected conclusion that by way of using the phenomenon of surface plasmon resonance weak electromagnetic radiation/signals or signal changes can be enhanced and can be made (easier) detectable. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Further features and advantages of the invention will become clear from the claims and following description, in which embodiments of the invention are illustrated in detail with reference to the schematic drawings: 
         FIG. 1  shows a scheme of a system for sensing photons of electromagnetic radiation from an external source according to a first special embodiment of the invention; 
         FIG. 2  shows a scheme of a system for sensing photons of electromagnetic radiation from an external source according to a second special embodiment of the invention; 
         FIG. 3  shows a scheme of a system for sensing chemical or biological agents according to a first special embodiment of the invention; and 
         FIG. 4  shows a scheme of a system for sensing chemical or biological agents according to a second special embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     The system  10  of  FIG. 1  for sensing photons of electromagnetic radiation from an external source comprises a surface plasmon-based nanosensor  12 . Said nanosensor  12  comprises a nanoparticle  14  of metal, e.g. silver or gold, or of semiconductor as a first element. The nanoparticle  14  is excitable to surface plasmon resonance, in particular localized as surface plasmon resonance, in the presence of electromagnetic radiation  16  from an external source (not shown). Furthermore, the nanosensor  12  comprises a quantum dot  18 . A quantum dot is normally a nanometer sized semiconductor region within another material of larger Band-gap. In particular, the quantum dot  18  with diameter d 2  is situated in a distance of R to the nanoparticle  14  with the diameter d 1 . The quantum dot  18  will be exciton-plasmon coupled to the nanoparticle  14  in the presence of the electromagnetic radiation  16  and will emit electromagnetic radiation  20  representative of the exciton-plasmon coupling. 
     The nanosensor  12  and the quantum dot  18  are embedded in PGB-material  22 . 
     The system  10  further comprises a detector (not shown) for detecting the electromagnetic radiation  20  emitted by the quantum dot  18  in response to the electromagnetic radiation  16  from the external source (not shown). Also, said system  10  comprises an evaluation unit (not shown) for evaluating the statistics, in particular the frequency and/or the intensity and/or the photon number, of the electromagnetic radiation  16  from the external source (not shown). Preferably, the system  10  comprises a shielding (not shown) for shielding the quantum dot  18  against external electromagnetic radiation, in particular the external electromagnetic radiation  16 . 
     By way of the nanosensor  12  and the system  10  photons—perhaps even single photons—can be detected within very narrow spectral width and provide statistical information about them, e.g. photon numbers. The PBG-material  22 , e.g. silicon carbide, improves the preciseness of the detection of photons with certain frequency ranges. But the PBG-material is not a must. PBG-materials are characterized as having a gap in their dispersion relation characterized by an upper and lower energy band, corresponding to frequencies of light that are forbidden to propagate within the PBG-medium. 
     The system  10  can be described as made of a receiver or signal transformer, the quantum dot  18 , situated near or close to the nanoparticle  14  that works as a photon collector. When photons of the electromagnetic radiation  16  from the external source (not shown) hit the nanoparticle  14 , they excite certain plasmon modes that depend on the frequency of the photons and on the shape and material of the nanoparticle  14 . These plasmons, in turn, generate a certain dipole moment, which, and through the near-field, will couple to the transformer (quantum dot  18 ), which will also generate a dipole moment that is proportional in magnitude to that of the nanoparticle  14  which in turn is proportional to the frequency and intensity of the incident electromagnetic radiation  16 . The transformer (quantum dot  18 ) will transform the signal coming from the nanoparticle  14  into a more readable signal, e.g. electrical signal, through the population inversion that will occur within the transformer&#39;s (quantum dot) electronic states. This population difference carries within it the statistical properties of the incoming photons. 
     The usage of the PBG-material  22  has the effect of increasing the sensitivity of the nanoparticle  14  to the frequency of the incident electromagnetic radiation  16 . 
     The system  10  can be used to detect specific signals, especially those close to the plasmon frequency of the nanoparticle  14  as these plasmons resonate, almost spontaneously, at their natural frequency leading to a large induced dipole moment in the nanoparticle  14  and consequently a stronger signal will be transmitted. In fact, the whole “system” can be tuned such that to resonate with very narrow frequency range. This can be done by designing the nanoparticle  14  and the quantum dot  18  such that they only resonate at a specific frequency, e.g. by choosing an elongated of spheroid nanoparticle for example instead of spherical. 
     Moreover, by changing the material and/or shape of the nanoparticle  14  it is possible to change its natural plasmonic frequency and consequently fine tune the “system” to be responsive to certain light frequencies, even if the intensity of the light is weak, as in electromagnetic signals emitted from for example some biological entities. The nanoparticle  14  can come in any shape, configuration and material. 
     The above configuration can be put in any other medium or configuration to produce the results desirable by the experimenter or manufacturer. 
     Even though in  FIG. 1  spherical elements (nanoparticle  14  and quantum dot  18 ) are shown, this is not necessary. The elements can take any shape for getting the desired results. The nanoparticle  14  can have non-isomorphic shape that can support multiple plasmon resonances. Thus, by tuning the exciting element (nanoparticle) to these resonances, photons with different frequencies can be detected. It is also to be noted that ensembles of nanoparticles and/or quantum dots can be used. 
     A more readable signal is the usual electric signal that most electronics are using in their operations. 
     Every nanoparticle will have a specific plasmonic resonance frequency based on its shape and material and the surrounding material. The more the incoming/incident electromagnetic radiation, for example light, is in resonance with the plasmonic frequency, the more responsive the nanoparticle&#39;s electrons will be and the larger the dipole moment generated by the oscillations of the electrons will be. Consequently, the exciton plasmon coupling between the nanoparticle and the receiver, e.g. quantum dot  18 , will be stronger. The outcome signal (electromagnetic radiation  20 ) from the quantum dot  18  depends on this coupling, labelled omega. 
     Thus, the coupling between the nanoparticle  14  and the quantum dot  18  depends on the dipole moments of the nanoparticle  14  and the quantum dot  18 , which in turn depends on the frequency of the incident electromagnetic radiation  16 . In addition, and as the below equation indicates, the signal lambda(p) coming out of the quantum dot  18  depends on the intensity of the electromagnetic radiation  16 , which is proportional to the number of photons carried in the electromagnetic radiation  16 . Thus, from the below equation, if lambda(p) is known, the other statistics of the electromagnetic radiation  16  (external field) can also be deduced. 
     
       
         
           
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     Here, γ 2 ,γ are the decay constant of the quantum dot  18  and nanoparticle  14 , respectively, γ c =γ 2 Z 2   2 (2n c +1) and n c  is the average number of quanta in the C-reservoir. Z 0  and Z 2  are the form constants of the nanoparticle  14  and the quantum dot  18 , respectively, which are related to the PBG-material  22 . 
             G   =       2   ⁢   Ω       γ   c             
with Omega being the coupling constant of the quantum dot  18  and the nanoparticle  14  which depends on the relative values of their dipole moments μ 2  and μ 0 , Σ Z  is the population inversion between the electronic states of the quantum dot  18 .
 
             K   =       4   ⁢     μ   0   2         γ   ⁢           ⁢     Z   0   2     ⁢     ℏ   2               
and I is the intensity of the field and is proportional to the number of photons.
 
     The signal provided by the quantum dot  18  is an optical signal, because the electronic/electrons of the quantum dot  18  is/are excited to a higher state, when it de-excites, it will emit a photon/photons. It is up to the experimentalist or the manufacturer to decide what to do with this photon/these photons, for example keep it/them this way, amplifying it/them or turning it/them into an electronic signal, etc. It is the electromagnetic radiation  16  that pumps the nanoparticle  14  which in turn will excite a population inversion in the electronic states of the quantum dot  18  and consequently produces the final signal. 
       FIG. 2  shows a further special embodiment of a system  24  for sensing photons of electromagnetic radiation from an external source (not shown). Said system  24  comprises a surface plasmon-based nanosensor  26 . Said nanosensor  26  comprises a nanoparticle  28  of metal, preferably silver or gold, or of semiconductor, as a first element. Said nanoparticle  28  is excitable to surface plasmon resonance, in particular localized surface plasmon resonance, in the presence of electromagnetic radiation from a source. Furthermore, said nanosensor  26  comprises a quantum dot  30  as a second element for exciting surface plasmon resonance of the nanoparticle  28 . In the present example, the diameter d 1  of the nanoparticle  28  is the same as the diameter d 1  of the nanoparticle  14 , the diameter d 2  of the quantum dot  30  is the same as the diameter d 2  of the quantum dot  18  and the distance between the nanoparticle  28  and the quantum dot  30  is R and the same as the distance R between the nanoparticle  14  and the quantum dot  18 . The nanoparticle  28  and the quantum dot  30  are totally embedded in PGB-material  22 . 
     The system  24  further comprises a pump  33  (also referred to as a pumping unit) for pumping the quantum dot  30  by way of electromagnetic radiation  32  and a detector (not shown) for detecting the total electromagnetic radiation  34  emitted by the nanoparticle  28  and the quantum dot  30  in response to electromagnetic radiation  36  emitted by an external source  35  and incident on the nanoparticle  28  and the quantum dot  30 . 
     In addition, said system  24  further comprises an evaluation unit (not shown) for evaluating the statistics, in particular the frequency and/or the intensity and/or photon number, of the electromagnetic radiation  36  from the external source (not shown) based on the detected total electromagnetic radiation  34 . 
     The configuration of the system  24  is similar to that of the system  10 , with the exception, that in the system  24  the quantum dot  30  is pumped/excited by the electromagnetic radiation  32  and will pump the plasmons of the nanoparticle  28  which in turn will emit electromagnetic radiation, e.g. light, with certain statistics, frequency and spectral width. Applying the electromagnetic radiation  36  to the nanoparticle  28  and the quantum dot  30  will induce changes in the properties of the emitted total electromagnetic radiation, e.g. its intensity and spectral width. These changes are directly related to the properties of the electromagnetic radiation  36 , e.g. intensity. Thus, from theses changes one can gain information on the applied electromagnetic radiation/external field. 
     Both the system  10  and the system  24  can be used to detect specific signals, especially those close to the plasmon frequency of the nanoparticle as these plasmons resonate, almost spontaneously, at their natural frequency leading to a large induced dipole moment in the nanoparticle and consequently a stronger signal will be transmitted. 
     For sensing photons with the system  24 , the final total emitted signal/electromagnetic radiation  34  is read and information about the applied external field/electromagnetic radiation  36  is gathered from it. 
       FIGS. 3 and 4  show special embodiments of nanosensors and systems for sensing chemical or biological agents (analytes). Said systems are similar to the systems  10  and  24 , respectively. 
     In particular, the system  38  comprises a surface plasmon-based nanosensor  40 . Said nanosensor  40  comprises a nanoparticle  42  of metal, preferably silver or gold, or of semiconductor, as a first element. The nanoparticle  42  is excitable to surface plasmon resonance, in particular localized surface plasmon resonance, in the presence of electromagnetic radiation  44  from a source (not shown). In this example, said source might be external from the nanosensor  40  or inside the nanosensor  40 . For example, the source may comprise a nanolaser  31  integrated with the first element  42  and the second element  46 . 
     Furthermore, the nanosensor  40  comprises a quantum dot  46  near the nanoparticle  42  as a second element. Said quantum dot  46  will be exciton-plasmon coupled to the nanoparticle  42  in the presence of the electromagnetic radiation  44  and will emit electromagnetic radiation  48  representative of the exciton-plasmon coupling. In this example, the nanoparticle  42  and the quantum dot  46  have the same diameter d 1  and d 2 , respectively, as the nanoparticle  14  and the quantum dot  18  of  FIG. 1 . The quantum dot  46  is also totally embedded in PGB-material  50 . 
     However, the nanoparticle  42  is only partially embedded in the PGB-material  50 . The nanoparticle  42  protrudes a little bit from the PGB-material  50  into an external medium  52 , e.g. buffer solution, thin film etc., where the chemical or biological agent (analyte) will be supplied. This is for enabling the nanoparticle  42  to sense the presence of the external agent  54 . This protrusion could effect the plasmonic resonance frequency of the nanoparticle  42  a bit or it may not. It depends on how much the nanoparticle  42  is protruding into the external medium  52 . However, this can be easily accounted for by measuring the plasmon resonance prior to the inclusion of the external agent  54 , and once the agent  54  is supplied, the actual shifting of the plasmon resonance can be measured. 
     The system  38  further comprises a detector  49  for detecting the electromagnetic radiation  48  emitted by the quantum dot  46  in response to the electromagnetic radiation  44  with said medium  52  or agent  54  in direct contact with the nanoparticle  42 . In addition, said system  38  further comprises an evaluation unit (not shown) for evaluating the identity of the chemical or biological agent  54  based on the detected electromagnetic radiation  56 . 
     One idea behind the plasmonic bio nanosensor  40  and the system  38  is that the resonance of the plasmons is greatly sensitive to the surrounding environment. In fact, the surface plasmon resonance frequency depends specifically on the dielectric function of the plasmonic material, e.g. gold and silver, and the surrounding material, e.g. silicon, buffer solution, thin film, etc. 
     Now when working as a bio-detector, what happens is that when the biological or chemical agents get into close proximity to the surface of the nanoparticle  42 , either they will change the permittivity of the surrounding material (external medium  52 ), e.g. a buffer solution, or stick to the surface of the nanoparticle  42 . In either case they will change the surrounding conditions of the nanoparticle  42 , which in turn will change the resonance frequency of the surface plasmons, shifting them toward for example the red or blue end of the spectrum depending on the changes induced by the biological or chemical external agent  54 . This shifting can be detected and based upon it can determine the identity of the external agent  54 . In the system  38  the external agent  54  will change the surface plasmon resonance frequency of the nanoparticle  42  and consequently will change how the nanoparticle  42  will interact with the electromagnetic radiation  48 , which will translate into a change in the signal output of the quantum dot  46 . From this change, one can deduce information about the external agent  54 . It should be noted that the quantum dot  46  should be shielded from the external agent  54  to ensure that they will not interfere with the signal coming out of the quantum dot  46 . Otherwise, this interference should be included in the final calculations. 
     The system  58  shown in  FIG. 4  comprises a surface plasmon-based nanosensor  60 . Said nanosensor  60  comprises a nanoparticle  62  of metal, preferably silver or gold, or of semiconductor, as a first element. The nanoparticle  62  is excitable to surface plasmon resonance, in particular localized surface plasmon resonance, in the presence of electromagnetic radiation  64  from an external or internal source (not shown). Further, said nanosensor  60  comprises a quantum dot  66  as a second element near the nanoparticle  62  for exciting surface plasmon resonance of the nanoparticle  62 . The nanoparticle  62  and the quantum dot  66  have the same diameter d 1  and d 2 , respectively, and are spaced apart by a distance R as the nanoparticle  42  and the quantum dot  46  of the system  38 . The quantum dot  66  is totally embedded in a PGB-material  68 , whereas the nanoparticle  62  is only partially embedded in said PGB-material  68  like the nanoparticle  42  of the system  38 . 
     The system  58  further comprises a pumping unit (not shown) for pumping the quantum dot  66  by means of electromagnetic radiation  70  and a detector (not shown) for detecting the total electromagnetic radiation  72  emitted by the nanoparticle  62  and the quantum dot  66 . Also, said system  58  comprises an evaluation unit (not shown) for evaluating the identity of the chemical or biological agent  74  (in an external medium  76 ) based on the detected electromagnetic radiation  72 . 
     In the system  58  of  FIG. 4 , just like in the system  38  of  FIG. 3 , the changes induced by the external agent  74  will translate into changes in the total electromagnetic radiation  72 . In fact, on said system  58 , and when working as a bio-detector, the external agent  74  will shift the plasmon resonance of the nanoparticle  62 . This shift will be detected from the statistics of the total electromagnetic radiation, e.g. light, emitted out of the system  58 , which was generated from the interaction between the pumped quantum dot  66  and the nanoparticle  62 . In addition, as in the case of the system  38 , it might be much better if the quantum dot  66  is shielded from the external agent  74 . 
     The nanosensor  60  as well the system  58  are simple, small and mobile. Like in the system  38  of  FIG. 3 , in the system  58  of  FIG. 4  and integrated source of electromagnetic radiation, e.g. light, like a nanolaser  31  could be incorporated. 
     One important factor that determines the efficiency of the nanosensor is how accurate it is. Plasmonic resonances are fairly narrow. However, the spectrum of the electromagnetic radiation, for example light, emitted from the system is usually not narrow due to broadening processes. This could be overcome by the PGB-material  68 . Incorporating the PGB-material into the system will greatly narrow the spectrum of the electromagnetic radiation, e.g. light, emitted from the system, rendering the sensing operation much more sensitive and accurate. However, an ensemble of anyone of the systems described above may be necessary to ensure better detecting. 
     The features disclosed in the foregoing description, in the claims and/or in the accompanying drawings may, both separately and in any combination thereof, be material for realising the invention in diverse forms thereof. 
     REFERENCE LIST 
     
         
         
           
               10  system 
               12  nanosensor 
               14  nanoparticle 
               16  electromagnetic radiation 
               18  quantum dot 
               20  electromagnetic radiation 
               22  PGB-material 
               24  system 
               30  quantum dot 
               26  nanosensor 
               28  nanoparticle 
               32  electromagnetic radiation 
               34  total electromagnetic radiation 
               36  electromagnetic radiation 
               40  system 
               42  nanosensor 
               44  nanoparticle 
               46  electromagnetic radiation 
               46  quantum dot 
               48  electromagnetic radiation 
               50  PGB-material 
               52  external medium 
               64  agent 
               58  system 
               60  nanosensor 
               62  nanoparticle 
               64  electromagnetic radiation 
               66  quantum dot 
               68  PGB-material 
               70  electromagnetic radiation 
               72  total electromagnetic radiation 
               74  agent 
               76  external medium 
             d 1  diameter of nanoparticle  14 ,  28 ,  62   
             d 2  diameter of quantum dots  18 ,  30 ,  66   
             R distance