**3.3 Mean-field atomic-scale model (optical Bloch)**

*∂P*~

*<sup>L</sup>* <sup>¼</sup> *<sup>γ</sup>*<sup>↑</sup> 2

*Nanoplasmonics*

*<sup>∂</sup><sup>t</sup>* <sup>¼</sup> *L v*, *<sup>v</sup>* <sup>∗</sup>

þ *γ*↑ 2

þ *γ*↓ <sup>2</sup> *<sup>e</sup>* 2 *∂ <sup>∂</sup><sup>m</sup>* � 1 � �

þ*γ<sup>p</sup>*

þ *g*2 *κ*

> *<sup>d</sup> <sup>σ</sup> ns* � �

> *<sup>d</sup> <sup>n</sup> ns* � �

function [28].

**68**

*g*ð Þ<sup>1</sup> <sup>&</sup>gt; ð Þ¼ *τ e*

*g*ð Þ<sup>2</sup>

*D* ¼ *γ<sup>p</sup>*

<sup>&</sup>gt; ¼ 1 þ 4*DT*1*e*

Γ*T*<sup>1</sup> *N*

Γ*dt* ¼

*<sup>T</sup>*<sup>1</sup> <sup>¼</sup> <sup>1</sup>

*e* �<sup>2</sup> *<sup>∂</sup> <sup>∂</sup><sup>m</sup>* � 1 � �

*∂ ∂v v* þ

2 1 � *e*

2*e* �<sup>2</sup> *<sup>∂</sup> <sup>∂</sup><sup>m</sup>* � 1 þ

, *<sup>m</sup>*, *<sup>∂</sup> ∂v* , *∂ <sup>∂</sup><sup>v</sup>* <sup>∗</sup> , *<sup>∂</sup> ∂m*

� �

*∂ <sup>∂</sup><sup>v</sup>* <sup>∗</sup> *<sup>v</sup>* <sup>∗</sup> <sup>þ</sup>

�<sup>2</sup> *<sup>∂</sup> ∂m* � �

active atoms and the mentioned assumptions [28]:

*n ns* � � *σ*

> � <sup>4</sup><sup>℘</sup> *<sup>σ</sup> ns* � � � �

, *ns* <sup>¼</sup> *<sup>γ</sup>*<sup>↑</sup> � *<sup>γ</sup>*<sup>↓</sup> *γ*<sup>↑</sup> þ *γ*<sup>↓</sup>

*κ*Γ

�ð Þ *<sup>i</sup>ω*þ*<sup>D</sup> <sup>τ</sup>* <sup>1</sup> � *DT*<sup>1</sup> <sup>þ</sup> *DT*1*<sup>e</sup>*

℘0ð Þ ℘<sup>0</sup> þ 1 ℘ � 1

*ns*

� � � �

2

<sup>Γ</sup>*dt* ¼ � <sup>1</sup> � <sup>℘</sup>

*n s* � 1 Γ*T*<sup>1</sup>

*γ*<sup>↑</sup> þ *γ*<sup>↓</sup>

<sup>℘</sup> <sup>¼</sup> <sup>℘</sup>0*ns*, <sup>℘</sup><sup>0</sup> <sup>¼</sup> *Ng*<sup>2</sup>

ð Þþ *N* � *m*

� � *∂*

2*∂*<sup>2</sup> *∂v∂v* <sup>∗</sup>

ð Þþ *N* þ *m*

� �

*vv* <sup>∗</sup> � *<sup>∂</sup>*

� �

*∂*2 *<sup>∂</sup>v∂<sup>v</sup>* <sup>∗</sup> *<sup>e</sup>*

*P*~

*∂*4 *<sup>∂</sup>v*<sup>2</sup>*∂<sup>v</sup>* <sup>∗</sup> <sup>2</sup> *<sup>e</sup>*

> *∂v v* þ

*∂ ∂v v* þ

2 *∂*

*∂v vm* þ

� �

2 *∂*

*∂ <sup>∂</sup><sup>v</sup>* <sup>∗</sup> *<sup>v</sup>* <sup>∗</sup> � �

> *∂ <sup>∂</sup><sup>v</sup>* <sup>∗</sup> *<sup>v</sup>* <sup>∗</sup>

*∂ <sup>∂</sup><sup>v</sup>* <sup>∗</sup> *<sup>v</sup>* <sup>∗</sup> *<sup>m</sup>*

*<sup>∂</sup><sup>m</sup>*ð Þ *N* þ *m*

� �

� �

It should be noticed that Eq. (20) has not an analytical solution in this form and should be linearized or be solved numerically. In order to find a more familiar form of the dynamic rate equations, we should use linearization. By defining plasmon mode using dimensionless polarization "*σ*" and number of carriers by normalized population inversion "*n*," one can write Eq. (21) for a plasmonic nanolaser with N

, *σ* ¼ *tr ρJ*�*e*

, Γ ¼ *γ<sup>p</sup>* þ

where for threshold parameter, "℘>1" stimulated oscillations are dominant and for "℘<1" nanolaser is working in the subthreshold region, and generated plasmons are not coherent. Using this method, quantum fluctuations of plasmon and carrier numbers in the cavity even for a few numbers of plasmons can be estimated. Eventually, you can find first- and second-order correlation functions of the generated plasmons over time for above threshold pumping and the resulting linewidth "D" in Eq. (22). Significant linewidth narrowing with respect to the natural broadening "Γ" for "℘>1" implies proper laser operation, and time damping quantum fluctuations can be seen from the second-order correlation

> *τ* <sup>2</sup>*T*<sup>1</sup> cos

<sup>2</sup>Γ*T*1ð Þ <sup>℘</sup> � <sup>1</sup> <sup>p</sup> *<sup>τ</sup>*

� �

�*<sup>τ</sup>* <sup>2</sup>*T*<sup>1</sup> cos ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

" # !

*T*1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>2</sup>Γ*T*1ð Þ <sup>℘</sup> � <sup>1</sup> <sup>p</sup> *<sup>τ</sup> T*1

*<sup>∂</sup><sup>m</sup>*ð Þþ *<sup>N</sup>* <sup>þ</sup> *<sup>m</sup>* <sup>2</sup>*<sup>N</sup> <sup>∂</sup>*<sup>2</sup>

þ

<sup>þ</sup> *<sup>i</sup><sup>ω</sup> <sup>∂</sup> ∂v v* þ

> þ *∂*2 *<sup>∂</sup>v*<sup>2</sup> *<sup>v</sup>*<sup>2</sup> <sup>þ</sup>

*<sup>i</sup>ω<sup>t</sup>* � �*=N*, *<sup>n</sup>* <sup>¼</sup> *tr <sup>ρ</sup>Jz* ½ �*=<sup>N</sup>*

1 2*T*<sup>1</sup>

þ

*∂v∂v* <sup>∗</sup>

*∂ <sup>∂</sup><sup>v</sup>* <sup>∗</sup> *<sup>v</sup>* <sup>∗</sup> � �

þ

þ

(20)

(21)

(22)

*∂*2 *<sup>∂</sup><sup>v</sup>* <sup>∗</sup> <sup>2</sup> *<sup>v</sup>* <sup>∗</sup> <sup>2</sup>

In this model, the classical wave equation is applied to the electric field, while plasmons are assumed quantized, and using Fermi's golden rule, a kinetic equation describing the behavior of plasmons is derived. This model proved to be consistent with the previous model above the threshold while having the advantage to be used for quantum dot gain mediums. Also, Einstein's spontaneous and stimulated emission coefficients can be calculated from this model. Therefore, it can prove the positive effect of increased spontaneous emission due to the Purcell effect on the stimulated emission of the nanolaser. However, similar to the model described in Section 3.2, it needs some simplifying assumptions and works in atomic scales [12].

In this model, the nanoscale system consists of a metal layer with permittivity "*ε*(*ω*)" over a dielectric with permittivity "*εh*." The classic eigenvalue wave equation can be written for the plasmonic eigenmodes according to Eq. (23) [12].

$$\nabla.\left[\theta\left(\overrightarrow{r}\right) - s\_n\right] \nabla \rho\left(\overrightarrow{r}\right) = \mathbf{0} \tag{23}$$

where "*θ*(*r*)" is equal to "1" inside the dielectric and "0" inside the metal. Corresponding eigenvalues to the nth mode can be derived by Eq. (24) where "*Ωn*" is the complex frequency of the nth eigenmode in which the real part is equal to the resonant frequency of nth mode "*ωn*" and the imaginary part corresponds to the plasmon decay rate "*γn*" [12].

$$s(\mathfrak{Q}\_n) = s\_n, \qquad s(\boldsymbol{\alpha}) \equiv \left[\mathbf{1} - \frac{\boldsymbol{\varepsilon}(\boldsymbol{\alpha})}{\varepsilon\_h}\right]^{-1} \tag{24}$$

Assuming "*γ<sup>n</sup>* << *ωn*" we can write Eq. (25).

$$\gamma\_n = \frac{\operatorname{Im} [s(o\_n)]}{s\_n'}, \qquad s\_n' \equiv \frac{d \operatorname{Re} \left[s(o\_n)\right]}{d o} \bigg|\_{o = o\_n} \tag{25}$$

For the times shorter than the plasmon lifetime "τ<sup>n</sup> = 1/*γn*," corresponding Hamiltonian to the electric field of the quantized surface plasmons can be expressed by Eq. (26) in which "*T*" is the integration time and should satisfy "*τn*>> *T*>> 1/*ωn*."

$$H = \frac{1}{4\pi T} \int\_{-\infty}^{-\infty} \frac{d\left[\alpha \varepsilon \left(\overrightarrow{r}, \alpha\right)\right]}{d\alpha} \overrightarrow{E}\left(\overrightarrow{r}, \alpha\right) \overrightarrow{E}\left(\overrightarrow{r}, -\alpha\right) \frac{d\alpha}{2\pi} d^3 r \tag{26}$$

Using the extension of the electric field based on the quantized eigenmodes of the system, one can write Eq. (27), and Hamiltonian of Eq. (26) can be written as Eq. (28) which has the standard form of a quantum mechanical harmonic oscillator.

$$\vec{E}\left(\vec{r},t\right) \equiv -\nabla\phi\left(\vec{r},t\right), \qquad \phi\left(\vec{r},t\right) = \sum\_{n} \sqrt{\frac{2\pi\hbar s\_{n}}{\varepsilon\_{h}\epsilon\_{n}'}} \rho\_{n}\left(\vec{r}\right) e^{-\gamma\_{n}t} \left[a\_{n}e^{-i\alpha\_{n}t} + a\_{n}^{\dagger}e^{i\alpha\_{n}t}\right]. \tag{27}$$

$$H = \sum\_{n} \hbar o\_{n} \left(a\_{n}^{\dagger} a\_{n} + \frac{1}{2}\right) \tag{28}$$

#### *Nanoplasmonics*

where "*a*" and "*a*†" are annihilation and creation operators of plasmons, respectively. Consider dipolar emitters (quantum dots) with carrier population densities of the ground state and excited state equal to "*ρ*1(*ra*)" and "*ρ*2(*ra*)," respectively, where "*ra*" corresponds to the location of the a'th emitter with transition dipole moment equal to "*da* ." Transition matrix element [12] for this transition "*d*10" can be estimated by the Kane theory according to Eq. (29) [12] in which "*e*" is the electron charge, "*f*" is the power of the transition oscillator, "*K*" is the Kane constant, "*m*" is the electron mass, and "*ωn*" is the plasmon frequency of the nth mode. "*d*10" is proportional to the rate of spontaneous emission and Purcell effect.

$$d\_{10} = e\sqrt{\frac{f\mathcal{K}}{2m\_0 o\_n^2}}\tag{29}$$

so, a modified version of an initially proposed rate equation for the microcavity lasers in the 1990s can be used [29, 30]. This model as shown in Eq. (37) according to many recent pieces of research [15, 16, 29] can adequately explain the plasmon/ exciton carrier dynamics of a plasmon nanolaser. Furthermore, the macroscopic parameters like output power and pumping current can be easily derived.

*dt* <sup>¼</sup> *Rp* � *An* � *<sup>β</sup>*Γ*As n*ð Þ� � *<sup>n</sup>*<sup>0</sup>

The first equation of Eq. (6) is expressing the rate of carrier changes, and the second one is describing the temporal behavior of the plasmon generation. Plasmon generation is determined by the spontaneous plasmons coupled in the lasing mode (the first term), stimulated emission (the second term), and plasmon loss rate (the

In these equations "*n*" is the excited state population of the carriers, "*s*" is the number of plasmons in the lasing mode, and "*Rp*" is the carrier generation rate. The coupling factor (*β*) is defined by the ratio of the spontaneous emission rate into the lasing mode and the spontaneous emission rate into all other modes. A possible calculation method for this parameter can be seen in

> *<sup>β</sup>* <sup>¼</sup> *<sup>F</sup>*ð Þ<sup>1</sup> <sup>P</sup> *cav kF*ð Þ*<sup>k</sup> cav*

mode, and the summation is over all of the possible propagation modes in the

**4. Different structures of metallic nanoscale plasmon sources**

A plasmonic nanolaser needs a metallic nanocavity, gain medium, and a feedback mechanism. In the past two decades, several structures and materials have been introduced for this purpose. Some of these devices are presented in **Figure 4** [13]. These structures can be subwavelength in one dimension like plane nanolaser (see **Figure 5(a)**) [13], in two dimensions like nanowire-based plasmonic nanolaser

where "*Fcav*(*k*)" is the Purcell factor of k'th mode. k = 1 corresponds to the lasing

Mode overlap with the gain medium which is also known as Γ-factor is defined by the overlap between the spatial distributions of the gain medium and the lasing mode. In a homogenous medium, spontaneous emission rate "A" is equal to "1/*τsp0*" and "*τsp0*" is the spontaneous emission lifetime of the material. However, in a nanocavity, Purcell effect [24] modifies the spontaneous emission rate via "*A=FpA0*," where "*Fp*" is the Purcell factor and "*A0*" is the natural spontaneous emission rate in a homogenous medium. "*n0*" is the excited state population of carriers in transparency, "*vs*" is surface recombination velocity at the sidewalls of the resonator, and "*Sa*" and "*Va*" are the area of sidewalls of the resonator and volume of the gain medium, respectively. Finally, "*γ*" is the total loss rate of plasmons in the cavity. In order to calculate it, the loss coefficient per unit length should be multiplied by the modal speed. Loss coefficient is calculated by "*γ<sup>m</sup> + γg*" where "*γm*" and "*γi*" are resonator mirror loss and intrinsic cavity loss per unit

*dt* <sup>¼</sup> *<sup>β</sup>An* <sup>þ</sup> *<sup>β</sup>*Γ*As n*ð Þ� � *<sup>n</sup>*<sup>0</sup> *<sup>γ</sup><sup>s</sup>*

*nvsSa Va*

(37)

(38)

*dn*

*DOI: http://dx.doi.org/10.5772/intechopen.90842*

*Nanoscale Plasmon Sources: Physical Principles and Novel Structures*

*ds*

last term) [29].

Eq. (38) [15].

cavity.

length, respectively.

**71**

Interaction between the gain medium and the plasmon modes can be described by Hamiltonian of Eq. (30) which is exerted to the system. Accordingly, using the Fermi's golden rule, the kinetic equation of the system can be written for the number of plasmons in the nth mode by Eq. (31) in which "*An*" and "*Bn*" are the stimulated and spontaneous emission coefficients, respectively [12].

$$H' = \sum\_{a} \overrightarrow{d}^{(a)} \nabla \phi \left(\overrightarrow{r}\_a\right) \tag{30}$$

$$
\dot{N}\_n = A\_n N\_n - \gamma\_n N\_n + B\_n \tag{31}
$$

According to the mentioned model, Einstein emission coefficients can be derived by Eqs. (32) and (33).

$$A\_n = \frac{4\pi s\_n' s\_n |d\_{10}|^2 p\_n q\_n}{3\hbar} \gamma\_n \tag{32}$$

$$B\_n = \frac{4\pi}{3\hbar} \frac{s\_n' s\_n \left| d\_{10} \right|^2 r\_n q\_n}{\varepsilon\_\hbar \left[ \text{Im} s(o\_n) \right]^2} \gamma\_n \tag{33}$$

where "*pn*" and "*rn*" are spatial overlap factors of the nth mode with the gain medium and "*qn*" is the spectral overlap factor [12]. These parameters can be derived by Eqs. (34–35), respectively.

$$p\_n = \int \left[\nabla \rho\_n(\overrightarrow{r})\right]^2 \times \left[\rho\_1(\overrightarrow{r}) - \rho\_0(\overrightarrow{r})\right] d^3r\tag{34}$$

$$r\_n = \int \left[\nabla \rho\_n \left(\overrightarrow{r}\right)\right]^2 \times \rho\_1 \left(\overrightarrow{r}\right) d^3r\tag{35}$$

$$q\_n = \int F(\alpha) \left[ \mathbf{1} + \frac{\left(\alpha - \alpha\_n\right)^2}{\mathbf{y}\_n^2} \right]^{-1} d\alpha \tag{36}$$

where "*F*(*ω*)" is the spectral characteristic of the transition dipole moments.

#### **3.4 Semiclassical rate equations**

The aforementioned methods will give us much useful information about the operating principles of the plasmonic nanolasers. However, a consistent model with macroscopic measurable parameters is also needed for larger-scale systems. To do

*Nanoscale Plasmon Sources: Physical Principles and Novel Structures DOI: http://dx.doi.org/10.5772/intechopen.90842*

where "*a*" and "*a*†" are annihilation and creation operators of plasmons, respectively. Consider dipolar emitters (quantum dots) with carrier population densities of the ground state and excited state equal to "*ρ*1(*ra*)" and "*ρ*2(*ra*)," respectively, where "*ra*" corresponds to the location of the a'th emitter with transition dipole

be estimated by the Kane theory according to Eq. (29) [12] in which "*e*" is the electron charge, "*f*" is the power of the transition oscillator, "*K*" is the Kane constant, "*m*" is the electron mass, and "*ωn*" is the plasmon frequency of the nth mode.

"*d*10" is proportional to the rate of spontaneous emission and Purcell effect.

*d*<sup>10</sup> ¼ *e*

stimulated and spontaneous emission coefficients, respectively [12].

*An* <sup>¼</sup> <sup>4</sup>*<sup>π</sup>* 3ℏ *s* 0 *nsn*j j *d*<sup>10</sup> 2 *pnqn*

*Bn* <sup>¼</sup> <sup>4</sup>*<sup>π</sup>* 3ℏ *s* 0 *nsn*j j *d*<sup>10</sup> 2 *rnqn*

∇*φ<sup>n</sup> r* ! h i � � <sup>2</sup>

> ∇*φ<sup>n</sup> r* ! h i � � <sup>2</sup>

*rn* ¼ ð

*qn* ¼ ð

*<sup>H</sup>*<sup>0</sup> <sup>¼</sup> <sup>X</sup> *a d* !ð Þ *<sup>a</sup>*

According to the mentioned model, Einstein emission coefficients can be

where "*pn*" and "*rn*" are spatial overlap factors of the nth mode with the gain medium and "*qn*" is the spectral overlap factor [12]. These parameters can be

> � *ρ*<sup>1</sup> *r* !� �

*<sup>F</sup>*ð Þ *<sup>ω</sup>* <sup>1</sup> <sup>þ</sup> ð Þ *<sup>ω</sup>* � *<sup>ω</sup><sup>n</sup>* <sup>2</sup>

where "*F*(*ω*)" is the spectral characteristic of the transition dipole moments.

The aforementioned methods will give us much useful information about the operating principles of the plasmonic nanolasers. However, a consistent model with macroscopic measurable parameters is also needed for larger-scale systems. To do

� *ρ*<sup>0</sup> *r* ! h i � �

> � *ρ*<sup>1</sup> *r* !� � *d*3

*γ*2 *n*

" #�<sup>1</sup>

." Transition matrix element [12] for this transition "*d*10" can

(29)

(30)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi *fK* 2*m*0*ω*<sup>2</sup> *n*

> ∇*ϕ r* ! *a* � �

*<sup>N</sup>*\_ *<sup>n</sup>* <sup>¼</sup> *AnNn* � *<sup>γ</sup>nNn* <sup>þ</sup> *Bn* (31)

*<sup>ε</sup>h*½ � Im *<sup>s</sup>*ð Þ *<sup>ω</sup><sup>n</sup>* <sup>2</sup> *<sup>γ</sup><sup>n</sup>* (32)

*<sup>ε</sup>h*½ � Im*s*ð Þ *<sup>ω</sup><sup>n</sup>* <sup>2</sup> *<sup>γ</sup><sup>n</sup>* (33)

*d*3

*r* (34)

*r* (35)

*dω* (36)

s

Interaction between the gain medium and the plasmon modes can be described by Hamiltonian of Eq. (30) which is exerted to the system. Accordingly, using the Fermi's golden rule, the kinetic equation of the system can be written for the number of plasmons in the nth mode by Eq. (31) in which "*An*" and "*Bn*" are the

moment equal to "*da*

*Nanoplasmonics*

derived by Eqs. (32) and (33).

derived by Eqs. (34–35), respectively.

**3.4 Semiclassical rate equations**

**70**

*pn* ¼ ð so, a modified version of an initially proposed rate equation for the microcavity lasers in the 1990s can be used [29, 30]. This model as shown in Eq. (37) according to many recent pieces of research [15, 16, 29] can adequately explain the plasmon/ exciton carrier dynamics of a plasmon nanolaser. Furthermore, the macroscopic parameters like output power and pumping current can be easily derived.

$$\begin{aligned} \frac{dn}{dt} &= R\_p - An - \beta \Gamma As(n - n\_0) - \frac{nv\_s S\_d}{V\_a} \\ \frac{ds}{dt} &= \beta An + \beta \Gamma As(n - n\_0) - \gamma s \end{aligned} \tag{37}$$

The first equation of Eq. (6) is expressing the rate of carrier changes, and the second one is describing the temporal behavior of the plasmon generation. Plasmon generation is determined by the spontaneous plasmons coupled in the lasing mode (the first term), stimulated emission (the second term), and plasmon loss rate (the last term) [29].

In these equations "*n*" is the excited state population of the carriers, "*s*" is the number of plasmons in the lasing mode, and "*Rp*" is the carrier generation rate. The coupling factor (*β*) is defined by the ratio of the spontaneous emission rate into the lasing mode and the spontaneous emission rate into all other modes. A possible calculation method for this parameter can be seen in Eq. (38) [15].

$$\beta = \frac{F\_{cav}^{(1)}}{\sum\_{k} F\_{cav}^{(k)}} \tag{38}$$

where "*Fcav*(*k*)" is the Purcell factor of k'th mode. k = 1 corresponds to the lasing mode, and the summation is over all of the possible propagation modes in the cavity.

Mode overlap with the gain medium which is also known as Γ-factor is defined by the overlap between the spatial distributions of the gain medium and the lasing mode. In a homogenous medium, spontaneous emission rate "A" is equal to "1/*τsp0*" and "*τsp0*" is the spontaneous emission lifetime of the material. However, in a nanocavity, Purcell effect [24] modifies the spontaneous emission rate via "*A=FpA0*," where "*Fp*" is the Purcell factor and "*A0*" is the natural spontaneous emission rate in a homogenous medium. "*n0*" is the excited state population of carriers in transparency, "*vs*" is surface recombination velocity at the sidewalls of the resonator, and "*Sa*" and "*Va*" are the area of sidewalls of the resonator and volume of the gain medium, respectively. Finally, "*γ*" is the total loss rate of plasmons in the cavity. In order to calculate it, the loss coefficient per unit length should be multiplied by the modal speed. Loss coefficient is calculated by "*γ<sup>m</sup> + γg*" where "*γm*" and "*γi*" are resonator mirror loss and intrinsic cavity loss per unit length, respectively.

### **4. Different structures of metallic nanoscale plasmon sources**

A plasmonic nanolaser needs a metallic nanocavity, gain medium, and a feedback mechanism. In the past two decades, several structures and materials have been introduced for this purpose. Some of these devices are presented in **Figure 4** [13]. These structures can be subwavelength in one dimension like plane nanolaser (see **Figure 5(a)**) [13], in two dimensions like nanowire-based plasmonic nanolaser (see **Figure 5(b)**) [16], and in three dimensions like nanocavity plasmon laser of [17] (see **Figure 5(c)**).

The gain medium of plasmonic nanolasers can be any material capable of radiative electron decay like any traditional laser. In the proposed structures, a variety of materials like die molecules, bulk semiconductors, semiconductor quantum wells, and quantum dots can be witnessed [13]. Many of the semiconductors were typical optoelectronic materials (III-V and II-IV alloys) like GaAs, AlGaAs, ZnS, InGaAs,

According to our most recent publications [17, 31, 32], we have proposed four nanolaser structures that are discussed in this section. All of these structures are electrically pumped in the room temperature, have subwavelength footprints, and have considerable performance characteristics. The first structure is a GaAs quantum dot-based nanocavity integrated into a plasmonic waveguide [31]. The second is a metal strip nanocavity structure which is based in tensile-strained germanium quantum wells [32]. The next one has a notched nanocavity and germanium quan-

tum wells as the gain medium [17] and the last one is a corrugated metal–

semiconductor–metal nanocavity structure utilizing two sets of germanium quan-

The first structure is a GaAs/AlGaAs QD nanocavity plasmon laser, which can be integrated into plasmonic waveguides for the realization of integrated plasmonic chips. This proposed nanolaser as sketched in **Figure 6** has several advantages over

For instance, it has a high coupling efficiency to the waveguide plasmonic modes because of its thin structure and the monolithic metal layer. In addition, the proposed nanolaser structure benefits from a large beta factor that means lower threshold and also a high Purcell factor, which leads to higher gain and better laser performance. The MSM structure of this device also can provide an efficient heat transfer performance. Therefore, it predicted to efficiently operate without overheating and needs less chip area for fabrication of heatsink. Nevertheless, the threshold pumping current of the proposed device is considerably high, and this structure cannot provide output power in the mW range in the optimal pumping region. Design characteristics related to the first structure can be seen in **Table 1**. The second device is a germanium/silicon-germanium (Ge/Si0.11Ge0.89) multiple quantum well plasmonic nanolaser as shown in **Figure 7**. This device utilizes a thin gold metal strip layer, sandwiched between Ge quantum wells in order to maximize both field confinement and exciton-plasmon interaction possibility, which means higher Purcell factor and better gain medium with mode overlap factor. Using two aluminum electrical contacts, one on top of the resonator and one beside it, an electrical pump current can be applied. Moreover, it can be coupled into

InP, and so on [13].

**5. Proposed nanoresonator structures**

*DOI: http://dx.doi.org/10.5772/intechopen.90842*

*Nanoscale Plasmon Sources: Physical Principles and Novel Structures*

tum dot arrays as the gain medium [32].

the previously introduced ones.

**Figure 6.**

**73**

*3D schematic of the GaAs quantum dot-based nanoresonator.*

#### **Figure 4.**

*Different structures of the plasmonic nanolasers [13].*

#### **Figure 5.**

*Different structures of the plasmon nanolasers: (a) a plane plasmon nanolaser [13] (subwavelength in one dimension), (b) typical nanowire-based plasmon nanolaser [16] (subwavelength in two dimension), and (c) quantum well-based nanocavity plasmon laser of [15] (subwavelength in three dimension).*

materials like die molecules, bulk semiconductors, semiconductor quantum wells, and quantum dots can be witnessed [13]. Many of the semiconductors were typical optoelectronic materials (III-V and II-IV alloys) like GaAs, AlGaAs, ZnS, InGaAs, InP, and so on [13].
