**5. Myocardial damage**

Myocardial damage following aortic valve surgery can be permanent and is caused by several mechanisms. Even if the left ventricular function is transiently depressed by these mechanisms, it considerably prolongs the pump time and leads to sustained heart failure in the postoperative period. Prevention is important in avoiding these complications and can be done so through efficient and timely use of intraoperative imaging.

#### **5.1 Visualization of the coronary arteries**

6 Aortic Valve Surgery

midesophageal ascending aorta long-axis view with the probe tip anteflexed, the orthogonal scanning plane is tilted upward. Not only is the distal portion of ascending aorta seen, but the aortic arch is often visualized through the left atrium and left pulmonary artery as an acoustic window. From the upper esophageal arch long- and short-axis views, the ascending

aorta can be visualized by tilting the orthogonal scanning plane downward.

Fig. 3. Tips for visualizing the distal portion of ascending aorta (AAO). In the look-up method, the probe is rather advanced from the midesophageal ascending aorta long-axis view (a), and anteflexed. b: The arch is visualized via the left atrium (LA) and pulmonary artery (PA). In xPlane mode, the scanning plane is tilted upward (c). d: The arch is

following declamping to minimize a delay in recognition and treatment.

be done so through efficient and timely use of intraoperative imaging.

The ascending aorta is assessed for calcification and atheromatous plaque. The former is depicted as a strong echo accompanied by an acoustic shadow. When the aorta is severely calcified, it may be necessary to change the perfusion routes to the axillary artery or femoral artery. In the former, pathologies in the arch branches are checked (Orihashi, 2000). When femoral arterial perfusion is chosen, the atheromatous lesion in the descending aorta should be assessed. If the calcified aorta is clamped, it is checked for a new dissection immediately

Myocardial damage following aortic valve surgery can be permanent and is caused by several mechanisms. Even if the left ventricular function is transiently depressed by these mechanisms, it considerably prolongs the pump time and leads to sustained heart failure in the postoperative period. Prevention is important in avoiding these complications and can

visualized through the LA and left PA

**5. Myocardial damage**

Unfavorable events related to aortic valve surgeries mainly take place in the ostium and/or the proximal portion of the coronary arteries, which can be visualized with TEE.

The ostium of the right coronary artery is found in the right coronary sinus (Fig. 4a,b). Although only a few centimeters of right coronary artery can be visualized due to the large distance from the transducer, the posterior descending artery can be visualized in the posterior interventricular groove in the transgastric mid-short-axis view.

The left coronary ostium is visualized in the left sinus of Valsalva by rotating the TEE probe counterclockwise from the midesophageal aortic valve short- or long-axis view (Fig. 4c,d).

Fig. 4. Visualization of coronary arteries. Left top: diagram showing visualization of coronary arteries. The right coronary artery (RCA) is depicted in midesophageal ascending aorta (AAO) short- and long-axis view (a,b). c,d: The left main truncus (LMT) to the division to left anterior descending (LAD) and left circumflex arteries (LCX) is shown. Left bottom: method of visualizing the distal portion of LCX. e: LAD flow, f: LCX in the atrioventricular groove. AV: aortic valve, CS: coronary sinus, PA: pulmonary artery, RA: right atrium, RV: right ventricle

Further rotation visualizes the division of the left main truncus to left anterior descending artery and left circumflex artery. A few centimeters of left anterior descending artery is often visualized. The distal portion of the left circumflex artery is visualized in the left posterior atrioventricular groove in the 90° to 120° scanning plane (Fig. 4e,f) (Ender et al., 2010; Karthik et al., 2007).

3D TEE provides unique information of the coronary ostium (Fig. 5). This perspective view is helpful for recognizing the distance of the coronary orifice from the annulus.

Intraoperative Imaging in Aortic Valve Surgery as a Safety Net 9

myocardium in the left coronary artery regions can be protected by retrograde cardioplegia, that in the right coronary artery region cannot be protected unless the right atrium is opened and coronary perfusion cannula is inserted with coronary sinus ostium tourniqueted. Otherwise, antegrade cardioplegia is essential in this region. Having TEE information on hand during these situations can help guide the surgeon in the choice of cannulas and

In the case of a short left main truncus, the tip of the infusion cannula can be inserted into either the left anterior descending or left circumflex artery and cause inadequate myocardial protection (Fig. 6d). Therefore, a larger cannula is recommended. Adequate perfusion into both arteries is confirmed by either color flow imaging or checking blood flow in the myocardium (anterior wall for the left anterior descending artery, posterior wall for the left circumflex artery) by pulsed-wave Doppler mode with the sample volume placed on the

Retrograde cardioplegia is used as an adjunct method of cardioplegia in aortic valve or aortic surgery, especially in cases of coronary artery stenosis or difficult cannulation of the left coronary artery. While a coronary sinus cannula is placed with digital guidance in many institutions, it is difficult in minimally invasive cardiac surgery or in cases with an aneurysmal or angulated ascending aorta or in redo cardiac cases with marked adhesions

The coronary sinus is visualized in the 0° and 90° scanning plane (Fig. 7 left). Since this image orientation is rather difficult for guidance, the view is rotated by 180° (flipped upsidedown then right-left: Fig. 7 center). The upper image is oriented as viewed from the atrial side. The cannula enters the right atrium from the 1 o'clock position and is directed to the coronary sinus which is depicted in the 6 o'clock position. The cannula is often found to press the posterior wall of the right atrium near the orifice of the coronary sinus. As the

Fig. 7. TEE guided placement of coronary sinus cannula. The 0° and 90° images of coronary sinus (CS) are rotated by 180°. These images are oriented as shown in the right column, which is surgeon-friendly. LA: left atrium, LV: left ventricle, RA: right atrium, RV: right ventricle

around the heart. The author routinely uses TEE guidance in such instances.

prevent delays in the case.

**5.3 Difficult cannulation of the coronary sinus**

myocardium.

Fig. 5. 3D images of coronary ostia. a: Right and left coronary arteries (RCA, LCA) in midesophageal aortic valve short-axis view, b: 3D image of left coronary ostium, c: 3D image of right coronary ostium

Fig. 6. Pitfalls in antegrade cardioplegia. a: incomplete aortic cross-clamp, b: Aortic regurgitation (AR) shown in B mode, c: calcification at the right coronary ostium, d: short left main truncus (LMT). AAO: ascending aorta, AV: aortic valve, LAD: left anterior descending artery, LCX: left circumflex artery, LV: left ventricle

#### **5.2 Troubles in antegrade cardioplegia**

There are two pitfalls in antegrade cardioplegia via a root cannula. In cases with a calcified aorta, the aorta may be incompletely clamped (Fig. 6a). As a result, cardioplegic solution can be washed out by leaking blood. When a patient goes into ventricular fibrillation soon after cardiac arrest, this pitfall needs to be checked. Furthermore, mild aortic reguritation may be responsible for regurgitation of cardioplegic solution, leading to distension of the left ventricle. Regurgitation is noted in the B mode as echo contrast below the aortic valve (Fig. 6b) as well as in color flow imaging.

Calcification at the coronary ostium is not uncommon in cases of aortic stenosis. This is seen as a highly echogenic area accompanied by an acoustic shadow (Fig. 6c). In such cases, the selective cannula occasionally fails to fit the ostium. Thus, infusion of cardioplegic solution is unintendedly delayed and myocardial protection becomes inadequate. Although the

Fig. 5. 3D images of coronary ostia. a: Right and left coronary arteries (RCA, LCA) in midesophageal aortic valve short-axis view, b: 3D image of left coronary ostium, c: 3D

Fig. 6. Pitfalls in antegrade cardioplegia. a: incomplete aortic cross-clamp, b: Aortic regurgitation (AR) shown in B mode, c: calcification at the right coronary ostium, d: short left main truncus (LMT). AAO: ascending aorta, AV: aortic valve, LAD: left anterior

There are two pitfalls in antegrade cardioplegia via a root cannula. In cases with a calcified aorta, the aorta may be incompletely clamped (Fig. 6a). As a result, cardioplegic solution can be washed out by leaking blood. When a patient goes into ventricular fibrillation soon after cardiac arrest, this pitfall needs to be checked. Furthermore, mild aortic reguritation may be responsible for regurgitation of cardioplegic solution, leading to distension of the left ventricle. Regurgitation is noted in the B mode as echo contrast below the aortic valve

Calcification at the coronary ostium is not uncommon in cases of aortic stenosis. This is seen as a highly echogenic area accompanied by an acoustic shadow (Fig. 6c). In such cases, the selective cannula occasionally fails to fit the ostium. Thus, infusion of cardioplegic solution is unintendedly delayed and myocardial protection becomes inadequate. Although the

descending artery, LCX: left circumflex artery, LV: left ventricle

**5.2 Troubles in antegrade cardioplegia**

(Fig. 6b) as well as in color flow imaging.

image of right coronary ostium

myocardium in the left coronary artery regions can be protected by retrograde cardioplegia, that in the right coronary artery region cannot be protected unless the right atrium is opened and coronary perfusion cannula is inserted with coronary sinus ostium tourniqueted. Otherwise, antegrade cardioplegia is essential in this region. Having TEE information on hand during these situations can help guide the surgeon in the choice of cannulas and prevent delays in the case.

In the case of a short left main truncus, the tip of the infusion cannula can be inserted into either the left anterior descending or left circumflex artery and cause inadequate myocardial protection (Fig. 6d). Therefore, a larger cannula is recommended. Adequate perfusion into both arteries is confirmed by either color flow imaging or checking blood flow in the myocardium (anterior wall for the left anterior descending artery, posterior wall for the left circumflex artery) by pulsed-wave Doppler mode with the sample volume placed on the myocardium.

#### **5.3 Difficult cannulation of the coronary sinus**

Retrograde cardioplegia is used as an adjunct method of cardioplegia in aortic valve or aortic surgery, especially in cases of coronary artery stenosis or difficult cannulation of the left coronary artery. While a coronary sinus cannula is placed with digital guidance in many institutions, it is difficult in minimally invasive cardiac surgery or in cases with an aneurysmal or angulated ascending aorta or in redo cardiac cases with marked adhesions around the heart. The author routinely uses TEE guidance in such instances.

The coronary sinus is visualized in the 0° and 90° scanning plane (Fig. 7 left). Since this image orientation is rather difficult for guidance, the view is rotated by 180° (flipped upsidedown then right-left: Fig. 7 center). The upper image is oriented as viewed from the atrial side. The cannula enters the right atrium from the 1 o'clock position and is directed to the coronary sinus which is depicted in the 6 o'clock position. The cannula is often found to press the posterior wall of the right atrium near the orifice of the coronary sinus. As the

Fig. 7. TEE guided placement of coronary sinus cannula. The 0° and 90° images of coronary sinus (CS) are rotated by 180°. These images are oriented as shown in the right column, which is surgeon-friendly. LA: left atrium, LV: left ventricle, RA: right atrium, RV: right ventricle

Intraoperative Imaging in Aortic Valve Surgery as a Safety Net 11

occlude the left coronary artery ostium. This intraoperative TEE assessment would be the last chance for confirming the exact spatial relationship between the coronary ostium and

Fig. 8. A case of coronary artery damage. a: preoperative image showing small and calcified left coronary ostium, b: at weaning from bypass without flow in the left main truncus (LMT). c: abnormal space adjacent to the LMT. Direct echo following additional coronary revascularization, flap was noted in the LMT (c) with retrograde flow from the left anterior descending artery (LAD) (e) direct toward left circumflex artery (LCX) (f). AO: aorta, CALC:

Fig. 9. Aortic valve replacement and coronary artery. a: Distance between the annulus and left coronary orifice is measured. b: no obstruction of left coronary orifice. c: accelerated flow

In aortic root repair procedures, the coronary anastomosis is routinely checked for stenosis immediately following declamping of the aorta. When there is significant stenosis, one should not proceed to weaning from bypass because it prolongs the duration of ischemic

in front of the left coronary orifice, suggesting the presence of narrowed space. AAO:

valve prosthesis.

calcification, LA: left atrium

ascending aorta, LMT: left main truncus

insults on the myocardium.

cannula tip is tilted toward the left or the two-stage venous cannula is pulled forward to tighten the right atrial wall, cannulation is facilitated. The bottom view is oriented as viewed from the lateral side: the right atrium is depicted on the left and the right ventricle is on the right.

Once the cannula enters the coronary sinus, the location of the cannula tip is assessed with TEE. When it reaches the vicinity of the left atrial appendage, balloon inflation may interfere with the infusion of cardioplegic solution into the posterior branch of the great coronary vein. TEE assessment is helpful when palpation is not feasible in minimally invasive cardiac surgery or redo surgeries.

When the perfusion pressure of retrograde cardioplegia is low, there are two possible causes: 1) migration of the cannula to the right atrium and 2) an unusually large coronary sinus compared to the balloon. If the flow is undetectable in the coronary sinus and a flow signal is found in the right atrium, the former is probable. The coronary sinus should be checked beforehand to rule out the presence of a persistent left superior vena cava. It is diagnosed by the findings of: 1) a large coronary sinus; 2) a lumen between the left atrial appendage and left upper pulmonary vein; and 3) caudal blood flow in the lumen. However, the coronary sinus can be unusually large without such an anomaly. In this case, a cannula with a larger balloon size is used instead.

#### **5.4 Injury of coronary artery**

The coronary artery may be injured during selective infusion of cardioplegic solution by the cannula tip or the jet stream. Fig. 8 shows the echo views in a case of coronary artery damage during aortic valve replacement.

Before cardiopulmonary bypass, the TEE showed that the left coronary artery was rather small and calcification was present adjacent to the ostium (Fig. 8a). The surgeon needed to press the cannula to the ostium during perfusion. As the patient was weaned from cardiopulmonary bypass, TEE showed akinesis in the anterior and lateral left ventricular wall in the territory of the left coronary artery. Blood flow in the left coronary artery was undetectable (Fig. 8b) and there was another unusual echo-free space adjacent to it (Fig. 8c). Diagnosis of coronary artery occlusion was made and coronary revascularization to the left anterior descending artery was immediately performed. After reperfusion, direct echo was applied to clarify the mechanism of occlusion. A flap was found in the left main truncus which interrupted the flow in the left main truncus (Fig. 8d). Retrograde blood flow from the left anterior descending artery and continuous flow into the left circumflex artery was seen (Fig. 8e,f). The echo-free space adjacent to the coronary artery was the false lumen which developed due to dissection of the coronary artery.

#### **5.5 Occlusion of coronary ostium**

Aortic valve replacement can be complicated by occlusion of the coronary ostium. Although one should be aware of the potential risk of this event in cases with a low take off of the coronary artery, it is rather difficult to predict in preoperative coronary arteriography or transthoracic echocardiography.

In midesophageal aortic valve long-axis view, the ostium is located and placement of prosthetic valve is simulated (Fig. 9a). During weaning from cardiopulmonary bypass, the coronary ostium is checked for obstruction. While there is no obstruction in Fig. 9b, acceleration of flow is noted in Fig. 9c. In the latter case, even a small pannus formation can

cannula tip is tilted toward the left or the two-stage venous cannula is pulled forward to tighten the right atrial wall, cannulation is facilitated. The bottom view is oriented as viewed from the lateral side: the right atrium is depicted on the left and the right ventricle is on the

Once the cannula enters the coronary sinus, the location of the cannula tip is assessed with TEE. When it reaches the vicinity of the left atrial appendage, balloon inflation may interfere with the infusion of cardioplegic solution into the posterior branch of the great coronary vein. TEE assessment is helpful when palpation is not feasible in minimally invasive cardiac

When the perfusion pressure of retrograde cardioplegia is low, there are two possible causes: 1) migration of the cannula to the right atrium and 2) an unusually large coronary sinus compared to the balloon. If the flow is undetectable in the coronary sinus and a flow signal is found in the right atrium, the former is probable. The coronary sinus should be checked beforehand to rule out the presence of a persistent left superior vena cava. It is diagnosed by the findings of: 1) a large coronary sinus; 2) a lumen between the left atrial appendage and left upper pulmonary vein; and 3) caudal blood flow in the lumen. However, the coronary sinus can be unusually large without such an anomaly. In this case, a

The coronary artery may be injured during selective infusion of cardioplegic solution by the cannula tip or the jet stream. Fig. 8 shows the echo views in a case of coronary artery

Before cardiopulmonary bypass, the TEE showed that the left coronary artery was rather small and calcification was present adjacent to the ostium (Fig. 8a). The surgeon needed to press the cannula to the ostium during perfusion. As the patient was weaned from cardiopulmonary bypass, TEE showed akinesis in the anterior and lateral left ventricular wall in the territory of the left coronary artery. Blood flow in the left coronary artery was undetectable (Fig. 8b) and there was another unusual echo-free space adjacent to it (Fig. 8c). Diagnosis of coronary artery occlusion was made and coronary revascularization to the left anterior descending artery was immediately performed. After reperfusion, direct echo was applied to clarify the mechanism of occlusion. A flap was found in the left main truncus which interrupted the flow in the left main truncus (Fig. 8d). Retrograde blood flow from the left anterior descending artery and continuous flow into the left circumflex artery was seen (Fig. 8e,f). The echo-free space adjacent to the coronary artery was the false lumen

Aortic valve replacement can be complicated by occlusion of the coronary ostium. Although one should be aware of the potential risk of this event in cases with a low take off of the coronary artery, it is rather difficult to predict in preoperative coronary arteriography or

In midesophageal aortic valve long-axis view, the ostium is located and placement of prosthetic valve is simulated (Fig. 9a). During weaning from cardiopulmonary bypass, the coronary ostium is checked for obstruction. While there is no obstruction in Fig. 9b, acceleration of flow is noted in Fig. 9c. In the latter case, even a small pannus formation can

right.

surgery or redo surgeries.

**5.4 Injury of coronary artery**

damage during aortic valve replacement.

**5.5 Occlusion of coronary ostium**

transthoracic echocardiography.

cannula with a larger balloon size is used instead.

which developed due to dissection of the coronary artery.

occlude the left coronary artery ostium. This intraoperative TEE assessment would be the last chance for confirming the exact spatial relationship between the coronary ostium and valve prosthesis.

Fig. 8. A case of coronary artery damage. a: preoperative image showing small and calcified left coronary ostium, b: at weaning from bypass without flow in the left main truncus (LMT). c: abnormal space adjacent to the LMT. Direct echo following additional coronary revascularization, flap was noted in the LMT (c) with retrograde flow from the left anterior descending artery (LAD) (e) direct toward left circumflex artery (LCX) (f). AO: aorta, CALC: calcification, LA: left atrium

Fig. 9. Aortic valve replacement and coronary artery. a: Distance between the annulus and left coronary orifice is measured. b: no obstruction of left coronary orifice. c: accelerated flow in front of the left coronary orifice, suggesting the presence of narrowed space. AAO: ascending aorta, LMT: left main truncus

In aortic root repair procedures, the coronary anastomosis is routinely checked for stenosis immediately following declamping of the aorta. When there is significant stenosis, one should not proceed to weaning from bypass because it prolongs the duration of ischemic insults on the myocardium.

Intraoperative Imaging in Aortic Valve Surgery as a Safety Net 13

Visualization of air in the right upper pulmonary vein is often tricky. The pooled air which fills it up to its ostium is hard to see, but a strong echo accompanied by side lobes and acoustic shadowing with a swinging motion indicates the presence of air at the orifice of the right upper pulmonary vein. As venous return resumes, the air pops up as bubbles in the left atrium or scrolls along the left atrial wall. The air in the left atrium often stays in a shallow pocket formed by the superior vena cava and ascending aorta (Fig. 10c). It can be aspirated directly with a needle or led to the vent port by lifting the superior vena cava with a forceps (Fig. 10d,e, c: red arrow). The adequacy of air removal can be immediately

The air in the left ventricle is visualized as a strong echo at the apex to the anteroseptal region. The air masks the image of the apex by acoustic shadowing (Fig. 10g). Aspiration by a needle often produces several milliliters of air. If the amount of air is small, it may be agitated to let the bubble out while the right coronary artery is pressed to avoid new air

When depressed ventricular contraction is associated with echogenic dots, especially in the inferior wall, air embolism is likely to be responsible and circulatory assist at a rather high perfusion pressure is advised. If such findings are not present, other causes are probable.

The function of implanted prosthetic valves is assessed during weaning from cardiopulmonary bypass and is focused on transvalvular and perivalvular leakage. The former originates from inside of the suture ring and the leakage is usually directed inward. This type of leak is allowed to persist unless the regurgitant volume is high. The latter originates from the outside of the sewing ring and is directed outward. This is abnormal and

Unfortunately, the discs of the mechanical valve are hard to visualize by TEE. Instead, the ejected blood just above the valve prosthesis is checked. When the color signal fills the aortic

A case of an everted leaflet of a bioprosthetic valve is demonstrated (Orihashi et al., 2010). This patient underwent aortic valve replacement with a Magna valve [TM] due to severe aortic regurgitation. Following aortic declamping, however, TEE showed an unusual transvalvular regurgitant flow in the left ventricular outflow tract. The noncoronary leaflet was fixed in an open position (Fig. 11). The 3D view from the aorta showed that the left ventricular outflow tract was visible in diastole on the noncoronary side. An attempt at weaning failed due to severe aortic regurgitation. Based on the TEE finding and the

There was no jammed thread or captured leaflet, but the noncoronary leaflet was everted. After it was manually corrected, the leaflet did not spontaneously evert. No needle hole or laceration on the leaflets was noted. Even if the bioprosthetic valve was replaced with another one, a similar event could have occurred. There was no reason for replacement with a mechanical valve. Reimplantation of the same valve would not have been beneficial as it would have prolonged the cardiac arrest time. Eversion of leaflet is unlikely to occur after it starts opening and closing. Thus, the aortotomy was just closed. After weaning from bypass, the leaflet was shown to close normally without significant leakage. Two years after

Thus, TEE is helpful for differentiating the reasons for undesirable hemodynamics.

entry. Again, the outcome can be assessed by TEE (Fig. 10h).

hemodynamic data, we decided to perform a second aortotomy.

discharge, this patient has had no recurrences of an everted leaflet.

**6. Assessment of prosthetic valve**

should be addressed by the surgeon.

lumen, an immobilized disc is unlikely.

assessed by TEE.

#### **5.6 Air embolism of coronary artery**

Air embolism in the coronary artery can occur in aortic valve surgery. Air not only enters the left ventricle during aortotomy, but also reaches the left atrium and even pulmonary veins. It moves to the left ventricular outflow tract during weaning from bypass and enters the coronary artery (predominantly the right coronary artery because of its buoyancy) (Orihashi et al, 1993, 1996).

Fig. 10. Retained air visualized with TEE. a: Air retention in the right upper pulmonary vein (RUPV) and left atrium (LA), which is visualized with TEE (b: RUPV, c: LA). d: removal of air in the RUPV, e: removal of air in the LA. f: air in the left ventricular (LV) apex, which is depicted with TEE (g). h: after aspiration of air. AAO: ascending aorta, RCA: right coronary artery, RV: right ventricle, SVC: superior vena cava

Air embolism causes regional myocardial ischemia manifesting as a conduction disturbance and/or regional wall motion abnormality mainly in the inferior wall. Although the air is washed out within 10 to 30 minutes with gradual improvement of the ischemia, it prolongs the pump time and occasionally results in myocardial infarction. Despite the use of carbon dioxide gas inflation in the pericardial sac during cardiopulmonary bypass, wall suction easily removes the gas.

To prevent air embolism, it is important to detect air retention and remove it before it moves to the coronary artery. Common sites of air retention include the right upper pulmonary vein, left atrium, and left ventricle (Fig. 10a,f). TEE is useful for detecting and guiding aspiration of retained air.

Air embolism in the coronary artery can occur in aortic valve surgery. Air not only enters the left ventricle during aortotomy, but also reaches the left atrium and even pulmonary veins. It moves to the left ventricular outflow tract during weaning from bypass and enters the coronary artery (predominantly the right coronary artery because of its buoyancy)

Fig. 10. Retained air visualized with TEE. a: Air retention in the right upper pulmonary vein (RUPV) and left atrium (LA), which is visualized with TEE (b: RUPV, c: LA). d: removal of air in the RUPV, e: removal of air in the LA. f: air in the left ventricular (LV) apex, which is depicted with TEE (g). h: after aspiration of air. AAO: ascending aorta, RCA: right coronary

Air embolism causes regional myocardial ischemia manifesting as a conduction disturbance and/or regional wall motion abnormality mainly in the inferior wall. Although the air is washed out within 10 to 30 minutes with gradual improvement of the ischemia, it prolongs the pump time and occasionally results in myocardial infarction. Despite the use of carbon dioxide gas inflation in the pericardial sac during cardiopulmonary bypass, wall suction

To prevent air embolism, it is important to detect air retention and remove it before it moves to the coronary artery. Common sites of air retention include the right upper pulmonary vein, left atrium, and left ventricle (Fig. 10a,f). TEE is useful for detecting and guiding

artery, RV: right ventricle, SVC: superior vena cava

easily removes the gas.

aspiration of retained air.

**5.6 Air embolism of coronary artery**

(Orihashi et al, 1993, 1996).

Visualization of air in the right upper pulmonary vein is often tricky. The pooled air which fills it up to its ostium is hard to see, but a strong echo accompanied by side lobes and acoustic shadowing with a swinging motion indicates the presence of air at the orifice of the right upper pulmonary vein. As venous return resumes, the air pops up as bubbles in the left atrium or scrolls along the left atrial wall. The air in the left atrium often stays in a shallow pocket formed by the superior vena cava and ascending aorta (Fig. 10c). It can be aspirated directly with a needle or led to the vent port by lifting the superior vena cava with a forceps (Fig. 10d,e, c: red arrow). The adequacy of air removal can be immediately assessed by TEE.

The air in the left ventricle is visualized as a strong echo at the apex to the anteroseptal region. The air masks the image of the apex by acoustic shadowing (Fig. 10g). Aspiration by a needle often produces several milliliters of air. If the amount of air is small, it may be agitated to let the bubble out while the right coronary artery is pressed to avoid new air entry. Again, the outcome can be assessed by TEE (Fig. 10h).

When depressed ventricular contraction is associated with echogenic dots, especially in the inferior wall, air embolism is likely to be responsible and circulatory assist at a rather high perfusion pressure is advised. If such findings are not present, other causes are probable. Thus, TEE is helpful for differentiating the reasons for undesirable hemodynamics.

#### **6. Assessment of prosthetic valve**

The function of implanted prosthetic valves is assessed during weaning from cardiopulmonary bypass and is focused on transvalvular and perivalvular leakage. The former originates from inside of the suture ring and the leakage is usually directed inward. This type of leak is allowed to persist unless the regurgitant volume is high. The latter originates from the outside of the sewing ring and is directed outward. This is abnormal and should be addressed by the surgeon.

Unfortunately, the discs of the mechanical valve are hard to visualize by TEE. Instead, the ejected blood just above the valve prosthesis is checked. When the color signal fills the aortic lumen, an immobilized disc is unlikely.

A case of an everted leaflet of a bioprosthetic valve is demonstrated (Orihashi et al., 2010). This patient underwent aortic valve replacement with a Magna valve [TM] due to severe aortic regurgitation. Following aortic declamping, however, TEE showed an unusual transvalvular regurgitant flow in the left ventricular outflow tract. The noncoronary leaflet was fixed in an open position (Fig. 11). The 3D view from the aorta showed that the left ventricular outflow tract was visible in diastole on the noncoronary side. An attempt at weaning failed due to severe aortic regurgitation. Based on the TEE finding and the hemodynamic data, we decided to perform a second aortotomy.

There was no jammed thread or captured leaflet, but the noncoronary leaflet was everted. After it was manually corrected, the leaflet did not spontaneously evert. No needle hole or laceration on the leaflets was noted. Even if the bioprosthetic valve was replaced with another one, a similar event could have occurred. There was no reason for replacement with a mechanical valve. Reimplantation of the same valve would not have been beneficial as it would have prolonged the cardiac arrest time. Eversion of leaflet is unlikely to occur after it starts opening and closing. Thus, the aortotomy was just closed. After weaning from bypass, the leaflet was shown to close normally without significant leakage. Two years after discharge, this patient has had no recurrences of an everted leaflet.

Intraoperative Imaging in Aortic Valve Surgery as a Safety Net 15

Fig. 12. Echo-oriented aortic valve repair. a: preoperative TEE image of aortic regurgitation (AR) by annuloaortic ectasia, b: residual regurgitation following initial repair with a

Valsalva graft, which is directed to the anterior mitral leaflet (AML). c: no regurgitation after plication of right coronary cusp. AAO: ascending aorta, AV: aortic valve, LV: left ventricle

Fig. 13. Three mechanisms of aortic regurgitation in aortic dissection. a: prolapse of a leaflet due to a detached commisure, b: tethering of a leaflet due to an enlarged sinotubular junction (STJ), c: an invaginated flap with tear. d: repair of the sinus of Valsalva sinus based on these mechanisms. e: TEE view after repair. Note that the size of the aortic graft is nearly

equal to the aortic valve (AV) annulus. AAO: ascending aorta

Fig. 11. A case of everted leaflet of Magna valve. a: severe aortic regurgitation in the noncoronary leaflet, b: immobilized leaflet visualized by lateral bending of the probe tip, c: 3D image of valve prosthesis. On the noncoronary side, the left ventricular outflow tract (LVOT) is seen from the aorta side


Nonreciprocal Photovoltaics: The Path to Conversion of Entire Power-Beam Exergy

*Andrei Sergeev and Kimberly Sablon*

#### **Abstract**

Nonreciprocal photonic management can shift the absorption-emission balance in favor of absorption and enhance the conversion efficiency beyond the detailed balance Shockley - Queisser limit. Nonreciprocal photovoltaic (PV) cells can provide the conversion of the entire exergy (Helmholtz free energy) of quasi-monochromatic radiation into electric power. Recent discoveries in electromagnetics have demonstrated the ability to break Kirchhoff's reciprocity in a variety of ways. The absorption-emission nonreciprocity may be realized via dissipationless one-way optical components as well as via the greenhouse-type electron-photon kinetics that traps the low-energy near-bandgap photons in the cell. We calculate the limiting performance of the nonreciprocal dissipationless monochromatic converter and discuss the limiting efficiency of the nonreciprocal converter based on the greenhouse effect. We also perform detailed modeling of the greenhouse effect in the GaAs PV converter and determined its PV performance for conversion of 809 nm laser radiation. In perovskite PV cells the greenhouse filter establishes a sharp absorption edge and reduces conversion losses related to the distributed PV bandgap and laser-cell matching losses.

**Keywords:** photovoltaic conversion, photon exergy, absorption-emission no reciprocity, power beaming, greenhouse effect

#### **1. Introduction**

Power delivery by a laser beam is an emerging technology with numerous potential applications. The capabilities of unmanned aerial vehicles, various robotic platforms, and sensor networks will be strongly enhanced due to remote charging. Currently all technological components for power beam delivery and conversion are commercially available. Integration of lasers with photovoltaic converters requires matching laser quanta to semiconductor material characteristics. In traditional design, the optimal bandgap value is determined by a tradeoff between the low near-bandgap absorption and thermalization losses [1, 2]. The optimal bandgap depends on laser power, optoelectronic properties of semiconductor material, and cell design [1]. Usually, the optimal bandgap wavelength exceeds the semiconductor bandgap by 20–80 nm. Even in optimized converters, the photoelectron thermalization and weak near-bandgap

absorption produce notable losses [2]. Greenhouse-type filter that traps photons with wavelengths above the laser wavelength is a tool of choice to eliminate the laser-cell matching losses [3, 4]. Moreover, as it is shown in this work, the greenhouse filter can generate the greenhouse effect in the cell, which strongly reduces the emission from the cell and, in this way, increases the conversion efficiency beyond the detailedbalance Shockley - Queisser limit. The greenhouse PV effect is a special case of nonreciprocal photonic management, which violates Kirchhoff's reciprocity between absorption and emission [5, 6].

The atmospheric greenhouse effect was discovered by Joseph Fourier, who calculated the balance between the incoming solar power and the outgoing power of emitted radiation and found the Earth's average temperature near of 0°F To shift the absorption-emission balance in a favor of absorption and get the average temperature of 60°F, Fourier proposed that the emitted radiation is trapped by the atmosphere similar to the way a greenhouse glass traps the heat [7]. The greenhouse glass transmits high frequency (high energy) radiation, which is absorbed by the greenhouse media and plants. The media convert the radiation into heat and emit thermal low frequency (low energy) radiation, which is reflected back to the greenhouse by the greenhouse glass. Plants use all high and low energy radiation and convert the radiation into biochemical energy. Photovoltaic conversion directly transfers radiation into electric power via the generation of electrons and holes, which lose part of their energy to crystalline lattice and are accumulated near the bandgap edge. Photocarriers can recombine via nonradiative processes, which convert solar energy into heat. Photocarriers can also recombine via the radiative process and emit bandgap photons. In the absence of nonradiative processes, the photocarrier density and PV performance are determined by the detailed balance between the absorbed and emitted radiation fluxes. As was shown by Shockley and Queisser (SQ), this absorptionemission balance defines a fundamental limit of the photovoltaic conversion efficiency, which in traditional cell design depends on a single material parameter, the semiconductor bandgap [8].

Recently proposed greenhouse design [3] mimics the greenhouse effect and nonequilibrium greenhouse processes, such as trapping of near bandgap radiation and reusing it for conversion into electricity.  It establishes a photonic bandgap above the semiconductor bandgap and traps the photons with energies below the photonic bandgap (see **Figure 1**). The mirror may be a wideband Bragg reflector, or photonic crystal reflector, or metallic reflector with small absorption. In the greenhouse design, the photon emission from the converter is limited by recombination processes of hot photo carriers that emit photons with energy above the photonic bandgap. Bandgap photons emitted by the near-bandgap photocarriers are recycled by the filter and reused in the cell for PV conversion. In the PV greenhouse effect, the nonradiative recombination plays a role of a greenhouse media, which heats the greenhouse. The radiative processes play a role in photosynthesis, which convert solar energy into biochemical energy used by plants. Therefore, the greenhouse PV design requires high-quality PV materials with weak nonradiative recombination, i.e. materials with high internal quantum (radiative) efficiency. Fast progress in traditional semiconductor materials and the development of novel optoelectronic materials raises principle questions about photonic management for PV conversion.

Can the greenhouse filter increase the solar light conversion efficiency beyond the SQ limit? The answer substantially depends on a form of the nonequilibrium distribution function of photo-generated carriers. In the greenhouse converter, we have

*Nonreciprocal Photovoltaics: The Path to Conversion of Entire Power-Beam Exergy DOI: http://dx.doi.org/10.5772/intechopen.109923*

#### **Figure 1.**

*PV converter with the greenhouse filter, which establishes the photonic bandgap above the semiconductor bandgap and traps photons with energy below the photonic bandgap inside the converter.*

two characteristic bandgaps. The accumulation and collection of photocarriers occur near the semiconductor bandgap. The photonic bandgap controls the absorptionemission balance in the cell. In this design, only photons emitted by hot electrons can leave the converter. The population of hot electrons and emission from the cell are controlled by the cooling of the hot electrons. If photocarriers near the semiconductor bandgap and hot energy photocarriers above the photonic bandgap have the same photo-induced chemical potential, the greenhouse filter just shifts the PV bandgap from the semiconductor bandgap to the photonic bandgap. In other words, in this quasi-equilibrium case (actually, in a chemical equilibrium between low energy and high energy photocarriers), the limiting conversion efficiency is the SQ efficiency with the PV bandgap equaled to the photonic bandgap. However, hot photocarriers usually rapidly lose their energy and, as a result, the density of hot photocarriers decreases, and their chemical potential is significantly reduced in comparison with the chemical potential of carriers near the semiconductor bandgap. In this nonequilibrium regime with fast photocarrier cooling, the conversion efficiency may exceed the SQ limit. To realize the nonequilibrium regime, the difference between photonic and semiconductor bandgaps should substantially exceed the thermal energy. Therefore, the photonic bandgap should at least be 2 � 3 *kBT* ¼ 50‐75 meV higher than the semiconductor bandgap.

Let us highlight that in the traditional cell design all conversion processes occur in the narrow energy interval above the semiconductor bandgap. Therefore, the conversion efficiency turns out to be insensitive to details of electron, photon, and phonon processes. In particular, the detailed modeling of PV conversion as a function of characteristic photoelectron relaxation and extraction times has shown that optimization of traditional design and operating regimes does not allow for surpassing the SQ limit [9]. The greenhouse design provides a splitting of key conversion processes. The photocarrier accumulation and collection take place near the semiconductor bandgap, while photocarrier recombination with photon escape occurs above the photonic bandgap. The filter provides an effective tool to reduce cell emission and shift the absorption-emission balance in favor of absorption.

To avoid cell heating, the greenhouse design requires photovoltaic materials with low nonradiative losses, i.e. high quantum efficiencies. Among traditional

photovoltaic materials, GaAs has the highest radiative efficiency. In particular, highquality GaAs with internal quantum efficiency (also termed internal radiative efficiency) of 99.7% provides solar cells with external radiative efficiency (ERE) above 30% [10–12]. In silicon, the Auger recombination is stronger than radiative recombination and the corresponding ERE of 1% substantially limits the conversion efficiency. Recent progress in emerging photovoltaic materials, � organic materials, dyesensitized, CuInGaSe (CIGS), and lead-halide perovskites, � has demonstrated strong improvements in ERE. In particular, the ERE of CIGS currently exceeds 24%. ERE is the integral characteristic, which may be calculated via the special averaging of external quantum efficiency (EQE) in the relatively narrow spectral range around the absorption threshold, which in traditional semiconductors coincides with the bandgap [13]. The perovskite materials demonstrate EQE values very close to unity in wide spectral ranges and gradual reduction of EQE near threshold energy [14, 15], which substantially limits the conversion efficiency of traditional PV cells.

In this work, we investigate and optimize greenhouse photonic management for photovoltaic conversion of monochromatic radiation. Recent progress in electromagnetics has demonstrated the ability to break the absorption-emission reciprocity in a variety of ways. To understand the advantages and limitations of greenhouse photonic management, in Section 2 we derive the monochromatic detailed-balance efficiency and in Section 3 we consider the limiting nonreciprocal monochromatic efficiency realized via dissipationless nonreciprocal optical components. In Section 4, we investigate the greenhouse photonic management and present results of simulations of conversion of 10 W*=*cm2 laser radiation with a wavelength around 809 nm by GaAs PV cell with the greenhouse filter. In p-doped A3B5 semiconductors the electron cooling is realized due to energy transfer from hot electrons to holes [16]. We determine the corresponding non-equilibrium distribution with reduced chemical potential of hot photocarriers and calculate the cell performance. Finally, we briefly discuss enhanced PV conversion in perovskite cells due to greenhouse filtering, which establishes a sharp absorption edge.

#### **2. Detailed-balance limiting efficiency for monochromatic radiation**

Let us start with the SQ detailed balance approach, which is based on two assumptions. The first assumption is the reciprocity of photonic (radiative) processes. In the equilibrium, the emitted radiation is exactly given by the absorbed radiation reversed in time. In other words, following Kirchhoff's law, emissivity, *e*ð Þ *λ*, **n** , and absorptivity, *α λ*ð Þ , �**n** , are equal for any photon wavelength and any propagation direction, **n**. Second, in PV conversion, photocarriers and emitted photons reach chemical equilibrium. Thus, photocarriers and photons have the same light-induced chemical potential. The photocarriers are collected in the narrow energy range above the semiconductor bandgap and photons are also emitted in the same range. Therefore, assumption about the chemical equilibrium between photocarriers and photons is only essential for this narrow range, which is of the order of thermal energy *kBT*0*:*.

The generalized SQ model is described by three parameters. The detailed balance is taken into account by the ratio of the absorbed flux to the equilibrium emitted flux, *Nab=Nem*, where *Nab* is the absorbed flux, *Nem* is emitted photonic flux in the equilibrium at the device operating temperature *T*0*:* The incoming flux and its absorption by the cell are characterized by the average photon energy in the absorbed flux, *ϵ* ∗ *:* Nonradiative recombination losses and losses in the photocarrier collection are

*Nonreciprocal Photovoltaics: The Path to Conversion of Entire Power-Beam Exergy DOI: http://dx.doi.org/10.5772/intechopen.109923*

described by the external radiative efficiency of the cell, *kERE:* The generalized SQ model allows for a rather simple analytical solution [17]. The SQ open-circuit voltage and conversion efficiency are given by

$$V\_{\rm OC} = \frac{k\_B T\_0}{q} \cdot \ln A\_k, \qquad A\_k = k\_{ERE} \cdot \frac{N\_{ab}}{N\_{em}} \tag{1}$$

$$\eta\_{\rm SQ} = \frac{k\_{\rm B}T\_0}{\varepsilon^\*} \cdot \left[ \text{LW}(A\_k \cdot e) - 2 + \frac{1}{\text{LW}(A\_k \cdot e)} \right] \approx \frac{k\_{\rm B}T\_0}{\varepsilon^\*} \cdot [\text{LW}(A\_k) - 1],\tag{2}$$

where e = 2.71828, and LW(*x*) is the Lambert W function, which asymptotic form is well described by three terms,

$$\text{LW}(z) = \ln(z) - \ln\ln(z) + \frac{\ln\ln(z)}{\ln(z)} + \dots, \qquad z \gg 1. \tag{3}$$

The SQ efficiency (Eq. 2) is the efficiency for conversion of the radiation power. The thermodynamic efficiency of energy conversion at zero output power is reached in the open circuit regime (negligible current). In the quasi-monochromatic limit, the cell is eliminated by photons within a narrow bandwidth, Δ*ν*<*kBT*0*=h*, around the central frequency *ν*. For thermodynamic analysis, it is convenient to describe the power of the monochromatic radiation by the temperature *Tm:* Assuming that the semiconductor bandgap matches the photon energy, we obtained the thermodynamic conversion efficiency at zero output power,

$$\eta\_{th} \equiv \frac{qV\_{OC}}{\epsilon^\*} = \left(\mathbf{1} - \frac{T\_0}{T\_m}\right) - \ln \frac{\mathbf{1}}{k\_{ERE}}.\tag{4}$$

**Figure 2.**

*The limiting detailed-balance SQ monochromatic efficiency normalized by the Carnot efficiency as a function of the photon energy for the monochromatic radiation with the temperature of 1000 K (red) and 10,000 K (blue).*

As expected, for the ideal cell ð Þ *kERE* ¼ 1 the thermodynamic efficiency is the Carnot efficiency, 1 � *T*0*=Tm* [18].

Analytical solution for the monochromatic energy conversion may be found, when the photons in the incoming flux may be described by the Boltzmann statistics, i.e. *hν*>*kBTm* (for example, for photons with energy of 1.4 eV it means that the photon temperature is limited by 18,000 K). Using Eqs. 1–3 we find the monochromatic SQ conversion efficiency for the ideal cell,

$$\eta\_{SQ} = \left(\mathbf{1} - \frac{T\_0}{T\_m}\right) \cdot \left(\mathbf{1} - \frac{\ln(B)}{B} + \frac{\ln(B)}{B^2}\right)$$

$$B = \frac{hv}{k\_B T\_0} \cdot \left(\mathbf{1} - \frac{T\_0}{T\_m}\right). \tag{5}$$

This analytical solution is illustrated in **Figure 2**. According to Eq. 5, the detailedbalance SQ conversion efficiency of the monochromatic radiation increases with an increase of the photon energy and approaches the Carnot efficiency at high frequencies.

#### **3. Nonreciprocal monochromatic conversion limit**

In this section, we consider the thermodynamic limit and material-determined limit of PV converters with negligible emission realized via nonreciprocal dissipationless photonic management. Let us start with the endoreversible thermodynamics of an engine that receives power from an emitter with temperature *Tem* and operates between temperatures *Thot* and *Tcold* with the Carnot efficiency, *ηCarnot* ¼ 1 � *Tcold=Thot* (**Figure 3a**). It is well understood that for this converter the conversion efficiency of the heat power from the emitter into useful mechanical or electrical power is below the Carnot efficiency due to the emission from the hot sink to the emitter. These emission losses are not directly related to the engine operation. The emission is associated with Kirchhoff's absorption-emission symmetry, which leads to losses in the delivery of heat power from the emitter to the engine. Let us highlight

#### **Figure 3.**

*Conversion of the heat power by the engine that receives heat power from an emitter with temperature Tem and operates between heat sinks with temperatures Thot and Tcold* : *(a) a traditional converter with the losses due to emission from the hot sink to the emitter and (b) the nonreciprocal converter with suppressed emission [19, 20].*

#### *Nonreciprocal Photovoltaics: The Path to Conversion of Entire Power-Beam Exergy DOI: http://dx.doi.org/10.5772/intechopen.109923*

that Kirchhoff's law is not a thermodynamic law. According to the Onsager - Casimir reciprocity relations, the time-reversal asymmetry in the system may be generated by a magnetic field, magnetization, electric currents, and time-modulation of optical properties [5, 6]. Nonreciprocal optical components can provide absorption channels with near-zero emissivity and emission channels with near-zero absorptivity. As it is shown in **Figure 3b**, we can split absorption channels into two parts. The first part is used for the absorption of incoming light. The second part of the absorption channels is connected with the emission channels and provides 100% reuse of the emitted photons [19]. Also, the emission can be completely suppressed due to quantum effects [20]. Both effects, � the suppressed emission [20] or recycling the emitted radiation to the engine [19], � eliminate the emission losses and increase the conversion efficiency up to the thermodynamic limit given by the Carnot formula.

The above consideration in the frame of endoreversible thermodynamics assumes that the hot end of an engine may be described by the light-increased temperature. Therefore, it does not apply to the nonequilibrium states of semiconductors, which are described by the light-induced chemical potential. Let us also note, that the detailedbalance approach also cannot be employed for the nonreciprocal conversion with zero emission from the cell. Formally, Eq. 2 in this limit gives a divergent result. To determine the nonreciprocal conversion limit we will directly employ the second thermodynamic law. In the general form applicable to non-temperature distributions, the distribution function of photons emitted by electrons in the cell cannot exceed the distribution function of incoming photons. In the quasi-monochromatic limit, we are interested in values of these functions in the narrow bandwidth near the energy *hv* and, therefore, the limiting value of the light-induced chemical potential may be found from the following equation,

$$\left(\exp\left(\frac{hv}{k\_BT\_m}\right) - \mathbf{1}\right)^{-1} = \left(\exp\left(\frac{hv-\mu}{k\_BT\_0}\right) - \mathbf{1}\right)^{-1},\tag{6}$$

where *Tm* is the temperature of the quasi-monochromatic radiation and *T*0 is the cell operating temperature. Thus, the thermodynamic limit of the light-induced chemical potential in the nonreciprocal quasi-monochromatic converter is

$$
\mu = h\nu \cdot \left( \mathbf{1} - \frac{T\_0}{T\_m} \right). \tag{7}
$$

Taking into account that emission from the nonreciprocal converter is absent and every absorbed photon generates an electron in the output circuit, we see that an ideal nonreciprocal converter provides entire conversion of the photon exergy, *hν* � ð Þ 1 � *T*0*=Tm :* Thus, the conversion efficiency of the nonreciprocal monochromatic converter is the Carnot efficiency,

$$v\_{nr} = \left(\mathbf{1} - \frac{T\_0}{T\_m}\right). \tag{8}$$

As the nonreciprocal photonic management provides 100% reuse of the emitted photons, it is interesting to compare the nonreciprocal limiting efficiency (Eq. 8) with the efficiency of the thermophotovoltaic conversion, where the emitted photons are reabsorbed by the emitter and the corresponding energy is reused in conversion. For the monochromatic emitter, the output electric power may be presented as [21],

$$P = \frac{2Hv^3}{c^2} \cdot \left[ N(T\_m, \mu = 0) - N(T\_0, \mu) \right] \cdot h \Delta v \cdot \left( 1 - \frac{T\_0}{T\_m} \right),\tag{9}$$

where *H* is the etendue of incoming and emitted photon bundle (we assume that absorption and emission angles are the same), *N T*ð Þ *m*, *μ* ¼ 0 is the Bose distribution function of incoming photons with the emitter temperature and zero chemical potential, and *N T*ð Þ 0, *μ* is the Bose distribution function of emitted photons with the cell temperature and light-induced chemical potential. Eq. 9 is the direct consequence of the endoreversible thermodynamics, according to which the limiting output power is given by a product of the Carnot efficiency of the conversion engine and the photon power flux delivered to the engine. The delivered flux is the difference between the absorption and emission fluxes. Assuming that the emitted flux returns to the emitter for later use, the PV conversion efficiency is given by the thermodynamic Carnot efficiency (see Eq. 4.27 in [21]). Thus, the photon reuse via the nonreciprocal photonic management (**Figure 3**) provides the same maximal Carnot efficiency as the photon reuse in the thermophotovoltaic system [21]. Let us highlight, that the Carnot efficiency may be also reached in the PV cell, where the radiative emission processes in the cell are suppressed by quantum effects [20].

Finally, we discuss the material limit of the nonreciprocal (time asymmetric) PV converter. If all emitted photons are reabsorbed by the cell, the radiative recombination lifetime of photocarriers approaches infinity, and photocarrier recombination is realized solely via nonradiative processes. In this case, we can employ the detailed balance SQ approach and corresponding analytical solution given by Eqs. 1 and 2, where the parameter *Ak* should be changed by

$$A\_{nr} = \frac{N\_{ab}}{R\_{nr}} = A\_k \frac{1}{1 - k\_{ERE}} \tag{10}$$

where *Rnr* is the equilibrium nonradiative recombination rate, *Rnr* ¼ *n*0*d=τnr*, where *n*0 is the equilibrium concentration of carriers, *d* is the cell thickness, and *τnr* is the nonradiative recombination time. In the cell design with the nonreciprocal photonic management, effective photon trapping and high photon absorption may be realized via the same external nonreciprocal recycling, which returns radiation to the cell (**Figure 3**). Therefore, the cell thickness may be significantly reduced, which leads to reduction of nonradiative recombination. Also, in high-quality optoelectronic materials the nonradiative recombination time significantly exceeds the radiative time, e.g. in GaAs the ratio *τnr=τr* � 300 [11]. Thus, the nonreciprocal management with strong suppression of the emission from the GaAs converter can increase the detailed balance coefficient *Ak* by three orders in magnitude or more, which increases the open circuit voltage at least by 180 mV.

Let us note that emission suppression due to nonreciprocal photonic management strongly enhances photon recycling in the system. The limiting Carnot efficiency of the nonreciprocal converter (Eq. 8) corresponds to the zero-emission and infinite intrinsic photon recycling. Any negligible losses (photon leakage or nonradiative recombination) regularize the solution of the SQ model (Eq. 2). This is a general resolution of thermodynamic paradox related to nonreciprocal power converters and nonreciprocal transfer of electromagnetic energy. In this way, the optical diode paradox was resolved by Ishimaru for the nonreciprocal ferrite-loaded waveguide in 1962 [22]. It was shown that any negligible material loss in ferrites leads to the convergent solution, which does not contradict the second law of thermodynamics [23] (see also a review [5]).

The Ishimarus results and our analysis show that such paradoxes appear, when the Maxwell equations or photon balance equations are applied to a completely lossless medium and systems. Any negligible dissipation eliminates divergent solutions.

#### **4. Photovoltaic greenhouse effect**

The Kirchhoff's law is valid for opaque bodies in thermodynamic equilibrium with the environment. As it is highlighted in Ref. [24], these two assumptions are often not satisfied. In particular, any photovoltaic converter operates in strongly nonlinear regime far from equilibrium. In this section, we investigate the nonreciprocal photonic management realized due to greenhouse type filter, which mimics the greenhouse operation, where the greenhouse glass/plastic reduces thermal emission and preserves more thermal energy in the greenhouse. The greenhouse filter is placed at the front surface of the cell. It reflects low energy photons in some narrower energy interval (� 50–150 meV) above the semiconductor bandgap (see **Figure 1**). In other words, the filter and back surface mirror establishes the photonic bandgap, *σph*, above the semiconductor bandgap, *σg:* The greenhouse filter prevents escape of photons with energies in the range between semiconductor and photonics bandgaps. The filter separates main electronic and photonic processes in the PV converter. Absorptionemission balance and conversion efficiency of this converter drastically depend on the light-induced concentration of hot photocarriers above the photonic bandgap established by the greenhouse filter. For the monochromatic conversion, the photonic bandgap, should correspond to the energy of radiation quanta, *σph* ¼ *hv:* As the photonic bandgap exceeds the semiconductor bandgap by �100–150 meV, the absorption at the photonic bandgap strongly exceeds the absorption near the semiconductor bandgap. To achieve negligible nonreciprocal emission above the photonic bandgap, the population of hot electrons with energy above the photonic bandgap should be strongly reduced by fast cooling processes that dominate over thermo-excitation processes of photocarriers accumulated above the semiconductor bandgap, *σg :* In the limit of strong greenhouse effect, i.e. negligible emission above the photonic bandgap, we can repeat consideration of the previous section and obtain the limiting conversion efficiency of the greenhouse PV converter,

$$\eta\_{gh} = \frac{\sigma\_{\rm g}}{h\nu} \left( \mathbf{1} - \frac{T\_0}{T\_m} \right) = \frac{\sigma\_{\rm g}}{\sigma\_{ph}} \left( \mathbf{1} - \frac{T\_0}{T\_m} \right). \tag{11}$$

The limiting efficiency of the greenhouse PV converter is smaller than the Carnot efficiency by the factor of *σg=σph*, because the nonreciprocity is realized via nonreversible dissipative processes. As all kinetic processes are essentially reversible in equilibrium, the nonreversible relaxation of photocarriers between photonic bandgap and semiconductor bandgap levels requires that the level separation substantially exceeds the thermal energy, i.e. *σph* � *σg* ≥2 � 3*kBT*0*:* In other words, the dissipated energy should exceed � 2 � 3*kBT*0 per photocarrier to reach electromagnetic nonreciprocity via relaxation processes. Without such separation, we will return to the results of Ref. [9], which show that the PV conversion is insensitive to photocarrier kinetics within the thermal energy scale.

As we discussed above, the efficiency of the greenhouse PV converter strongly depends on cooling mechanisms of hot photocarriers. Let us consider kinetics of the GaAs cell. The photon with energy above the semiconductor band gap creates electron and hole with energies

$$E\_{\epsilon} = \left(hv - \sigma\_{\xi}\right) \cdot \frac{m\_h}{m\_h + m\_{\epsilon}}\tag{12}$$

$$E\_h = \left(h\nu - \sigma\_{\mathfrak{g}}\right) \cdot \frac{m\_{\mathfrak{e}}}{m\_h + m\_{\mathfrak{e}}}.\tag{13}$$

Usually in semiconductor materials, the whole mass strongly exceeds the electron mass and practically whole photon energy is transferred to photoelectron. In GaAs these effective masses are *me* ¼ 0*:*067 *m*0 and *mh* ¼ 0*:*45*m*0, where *m*0 is the free electron mass. Therefore, to manage kinetics of hot photocarriers we should choose the p-doped GaAs.

Photoelectrons accumulated above semiconductor bandgap may be described by the Boltzmann distribution function with the light-induced chemical potential *μsc*,

$$f\left(\epsilon \approx \sigma\_{\mathfrak{g}}\right) = \exp\left(\frac{\mu\_{\mathfrak{g}} - \epsilon}{k\_B T\_0}\right) \tag{14}$$

These photoelectrons are collected and produce the output voltage *V* ¼ *μg=q:* In the narrow range of the order of thermal energy above the photonic bandgap, *σph*, the distribution function may be approximated by the chemical potential *μph*,

$$f\left(\epsilon \approx \sigma\_{ph}\right) = \exp\left(\frac{\mu\_{ph} - \epsilon}{k\_B T\_0}\right) \tag{15}$$

If inter-electron interaction dominates over other processes in photoelectron kinetics, the whole system is described by the same chemical potential. The conversion efficiency is given by Eq. 2 with the absorption-emission balance established above the photonic bandgap. In this case, the greenhouse filter only suppresses the matching losses. If cooling of photoelectrons above the photonic bandgap dominates over phonon-induced thermo-excitation of photoelectrons (see **Figure 4**), the

#### **Figure 4.**

*Fast energy relaxation of the beam-generated photoelectrons depopulates energy levels above the photonic bandgap. As a result, the chemical potential of hot electrons and emitted photons that leave converter is much less than the chemical potential of photoelectrons accumulated near the semiconductor bandgap.*

*Nonreciprocal Photovoltaics: The Path to Conversion of Entire Power-Beam Exergy DOI: http://dx.doi.org/10.5772/intechopen.109923*

chemical potential of hot photoelectrons, *μph*, is much smaller than *μg :* A reduced population of hot photoelectrons directly reduces the generation of photons with energy above the photonic bandgap. Because only these photons can leave the converter, emission from the converter is suppressed by the factor of exp *μg=μph* � �*:*.

Typically, cooling processes of hot photoelectrons are rather fast and, therefore, the chemical potential *μph* is much smaller than *μg :* Cooling processes are exceptionally strong in A3B5 semiconductors [16, 25–28], where the valence band consists of light and heavy holes, and photo-induced hot electrons transfer their energy to heavy holes created by p-doping. The electron cooling may be realized via inelastic scattering of electrons on heavy holes that is accompanied by the transition of a heavy hole to the light-hole band [25] as well as via inelastic electron scattering on oscillations of multicomponent hole plasma with heavy and light holes [28]. Evaluations show that the many body processes dominate in hot carrier cooling. Using the results of Ref. 28, in our modeling, we employ the following equation for the energy relaxation rate of hot electrons due to energy transfer to hole plasmons,

$$\frac{1}{\pi\_{e-h}} = \frac{\pi \hbar^2 \cdot p\_0}{m\_{lh}^{3/2} \sqrt{c\_e}} \tag{16}$$

where *p*0 is the hole concentration due to doping, *mlh* is the mass of the light hole, and *ϵe* is the electron energy. Eq. 16 applies to electrons with *ϵe* ≥15 meV above the semiconductor bandgap for the doping levels below 31018 cm�3*:* The energy transfer from hot electrons to holes is not limited by thermal energy. The characteristic transferred energy changes from 5ℏ2 *p* 3*=*2 0 *=mhh* (*mhh* is the mass of the heavy hole) to 5ℏ2 *p* 3*=*2 0 *=mlh* and substantially exceeds thermal energy. As a result, the electron energy relaxation due to interaction with hole plasma oscillations is very fast. Femtosecond electron cooling in GaAs and other A3B5 materials was observed in numerous experimental investigations [16, 29–31]. The femtosecond electron–hole relaxation strongly dominates over electron–phonon processes with a characteristic time of 1–2 ps.

To illustrate the operation of the greenhouse converter we perform simulations of conversion efficiency of 10W*=*cm2 laser radiation with a wavelength around 809 nm by GaAs cell with the greenhouse filter that establishes the photonic bandgap equaled to the laser energy quanta. The integration of GaAs cell with this laser is widely studied for power beaming [32]. To enhance absorption we add the Lambertian scattering layer placed between the filter and the cell (the same effect may be reached by the curved or textured mirror). Lambertian scattering significantly enhances light absorption by the cell. The corresponding absorption coefficient is given by.

$$A = \frac{1 - \exp(-4ad)}{1 - (1 - b)\left(1 - 1/n^2\right) \cdot \exp\left(-4ad\right)},\tag{17}$$

where *d* is the cell thickness, *α* is the GaAs absorption at the laser wavelength, *n* is the refractive index, and *b* is the absorption of the back surface mirror.

The modeling of PV performance is based on analytical SQ solution (Eqs. 1 and 2), which was described in details for GaAs cell in Ref. cite4 and for various thermophotovoltaic cells in Ref. [33]. In Ref. [3] we investigated the same power beaming conversion in quasi-equilibrium approximation *μph* ¼ *μg:* In this modeling, we take

into account the greenhouse PV effect due to fast electron cooling and, using the Boltzmann equation we calculate the reduced emission flux.

The main results of our modeling are presented in **Figure 5**, which shows the increase in the conversion efficiency due to the greenhouse filter as a function of internal quantum efficiency (IQE), *kint* and normalized cell thickness, *dα:* As seen, the increase in efficiency can reach 12–14%, but significant improvements require highquality PV materials with high internal quantum efficiency.

To distinguish the nonequilibrium greenhouse effect in PV conversion, in **Figure 6** we present the conversion efficiency calculated in the nonequilibrium model with fast photoelectron cooling, quasi-equilibrium approximation, and for traditional cell design without the greenhouse filter. The efficiency as a function of the dimensionless cell thickness, *dα*, is shown for several values of the internal quantum efficiency, *kint:* For available GaAs materials, the IQE may reach 0.997 [11] and the greenhouse filter adds 7% to the conversion efficiency, where 1% is added due to nonequilibrium effects (red, blue, and green solid lines). At *kint* ¼ 0*:*998 (yellow line) the efficiency exceeds the SQ power beaming efficiency (blue dashed line). The limiting efficiency (green dashed line) exceeds the SQ efficiency by 7%.

**Figure 7** demonstrates the conversion efficiency of 809 nm laser radiation as a function of the internal quantum efficiency (**Figure 7a**) and the laser power (**Figure 7b**) for the greenhouse GaAs PV converter (green lines), the quasiequilibrium approximation for the same converter (blue lines), and traditional converter without the greenhouse filter. As it is shown in **Figure 7b**, all converters have the same, weak (logarithmic) dependence of the efficiency on the laser power. Dependencies of efficiency on the material IQE are substantially different. While the efficiency of the traditional converter has a rather weak, linear dependence on IQE, the performance of the greenhouse converter in the quasi-equilibrium approximation and especially in the model with photoelectron cooling strongly depends on the IQE.

#### **Figure 5.**

*Increase in the conversion efficiency of the laser light with 809 nm wavelength and power of 10 W=cm2 due to the PV greenhouse effect as a function of internal quantum efficiency (IQE) and normalized cell thickness, dα.*

*Nonreciprocal Photovoltaics: The Path to Conversion of Entire Power-Beam Exergy DOI: http://dx.doi.org/10.5772/intechopen.109923*

#### **Figure 6.**

*PV efficiency of GaAs device, which converts laser light with 809 nm wavelength and power of 10 W=cm*2 *vs. cell thickness. Cell without greenhouse filter: Red lines dashed k* ð Þ *int* ¼ *1*, *solid kint* ¼ *0:997* ; *cell with the filter in quasi-equilibrium approximation: Blue lines dashed k* ð Þ *int* ¼ *1*, *solid kint* ¼ *0:997* ; *cell with the filter and the greenhouse kinetics: Green lines dashed k* ð Þ *int* ¼ *1*, *solid kint* ¼ *0:997 and yellow line k*ð Þ *int* ¼ *0:998 :.*

#### **Figure 7.**

*Increase in the conversion efficiency of the laser light with 809 nm wavelength and power of 10 W=cm*2 *due to the greenhouse PV effect as a function of internal quantum efficiency (IQE) and normalized cell thickness, dα.*

Our modeling shows that for suppression of the laser-cell matching losses (the quasiequilibrium model) we need good PV materials with IQE better than 0.8. The efficiency improvement due to suppression of emission losses via cooling of photoelectrons requires high-quality PV materials with IQE better than 0.99. Otherwise, the nonradiative recombination dominates over the radiative component and determines the converter performance.

Perovskites are low-cost and rather nonhomogeneous materials. These materials show a very smooth absorption edge with the width � 100 nm [14]. While above this range perovskites demonstrate excellent, very close to unity EQE, the smooth absorption drastically reduces the photovoltaic performance [14, 15]. Rau et al. [34] proposed that perovskites may be considered as a semiconductor with the distributed PV bandgap [35]. This model is widely applied to perovskite cells and successfully explains a significant reduction of conversion efficiency with respect to SQ limit [34–36]. In particular, according to the distributed bandgap model, the 100 meV standard deviation from the mean bandgap reduces the conversion efficiency by 6%. The greenhouse filter is a valuable tool to establish the sharp absorption edge above the smooth material absorption edge. Thus, for the power beaming with perovskite cells, the greenhouse design is expected to increase the conversion efficiency due to the suppression of both the laser-cell matching losses and the distributed bandgap losses.

#### **5. Conclusions**

Photonic management of radiative processes is an effective tool to enhance the performance of photovoltaic converters. An ideal nonreciprocal converter provides the entire conversion of the photon exergy, *hν* � ð Þ 1 � *T*0*=Tm :* Nonreciprocal management is the most radical way to change the absorptionemission balance in favor of the absorption. Suppression of spontaneous emission via quantum interference effects was proposed in seminal works of Scully to increase the PV efficiency of quantum photocell [20]. Here we have proposed and investigated a more practical way to suppress emission due to a narrow bandwidth filter, which generates the greenhouse effect in a cell. As an ordinary greenhouse effect, the greenhouse photovoltaic effect requires fast cooling of photocarriers and strong trapping of low-energy photons, which are emitted by photoelectrons near the semiconductor bandgap. In A3B5 semiconductors, effective electron cooling is realized by energy transfer from hot photoelectrons to the plasma oscillations of holes. Let us note, that the greenhouse effect may be also realized in PV design with a 3D photonic crystal, which has a photonic bandgap that overlaps the electronic band edge. In this design, the emission inside the photonic bandgap is rigorously forbidden [37]. Greenhouse photonic management has a strong potential to substantially increase the conversion efficiency due to the reduction of the laser-cell matching losses, the radiative losses, and the distributed bandgap losses in low-cost perovskites and organic materials. Nonreciprocal photovoltaics requires materials with high internal quantum efficiency and high-quality optical components, which provide enhanced photon recycling.

#### **Acknowledgements**

The work is supported by the Army Research Laboratory. Research of AS was accomplished under Cooperative Agreement No. W911NF-18-2-0222. The work of KS is supported by Texas A&M University. The views and conclusions contained in this paper are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the US Government.

*Nonreciprocal Photovoltaics: The Path to Conversion of Entire Power-Beam Exergy DOI: http://dx.doi.org/10.5772/intechopen.109923*

#### **Author details**

Andrei Sergeev1 \*† and Kimberly Sablon2,3†

1 U.S. Army Research Laboratory, Adelphi, Maryland, USA

2 Office of Undersecretary of Defense for Research and Engineering, Washington, DC, USA

3 Bush Combat Development Complex, Texas A&M University, Bryan, Texas, USA

\*Address all correspondence to<EMAIL_ADDRESS>
† These authors contributed equally.

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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#### **Chapter 4**